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DR. McCOSH'S WORKS.

FIRST AND FUNDAMENTAL TRUTHS. Being a Treatise on Metaphysics.
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THE

Laws of Discursive Thought

& textbook of jformai Eogtc

JAMES McCOSH, LL.D.

EX-PRESEDENT OF PRINCETON COLLEGE

REVISED EDITION

/&rfS n/

NEW YORK
CHARLES SCRIBNER'S SONS

1891

Entered according to Act of Congress, in the year 1870, by

ROBERT CARTER & BROTHERS,

In the Clerk's Office of the District Court of the United States for the
Southern District of New York

THE LIBRARY]

OF CONGREIf j

^ASHlNGTOffj

Presswork by
John Wilson and Son, Cambridge, U.S.A.

PREFACE.

If we look back half a century we find Formal
Logic taught in nearly all the colleges of Great
Britain and America, but exercising an influence infi-
nitely less than nothing (to use a phrase of Plato's) on
the thought of the countries. Some of the professors
and tutors were expounding it in a dry and technical
manner, which wearied young men of spirit, and bred
a distaste for the study ; while others adopted an
apologetic tone for occupying even a brief space with
so antiquated a department, and threw out hints of a
new Logic as about to appear and supersede the old.
The lingering life maintained by that old Aristotelian
and Scholastic Logic, in spite of the ridicule poured
upon it by nearly all the fresh thinkers of Europe for
two or three centuries after the revival of letters, is
an extraordinary fact in the history of philosophy ; I
believe it can be accounted for only by supposing
that the syllogism is substantially the correct analysis
of the process which passes through the mind in rea-
soning. Certain it is that no proffered logical system
has been able to set aside the Aristotelian, whether
devised by Ramus, by the school of Descartes, the
school of Locke, or the school of Condillac ; all have

iv PREFACE.

disappeared after creating a brief expectation fol-
lowed by a final disappointment. It is a remarkable
circumstance that the revived taste for Togical studies
in the last age proceeded from a restoration of the
old Logic by two distinguished men, both reformers
in their way, but both admirers of the Analytic of
Aristotle. I refer to Archbishop Whately and Sir
William Hamilton.

Whately first gave his views to the public in an ar-
ticle in the Encyclopcedia Metropolitana, which was ex-
panded into his Elements of Logic in 1826. The pub-
lication constitutes an era in the history of the study
in Great Britain and America. The admirable defence
of the old Logic against the objections of such men
as Principal Campbell and Dugald Stewart, and still
more, the fresh and apt examples substituted for the
dry stock ones which had been in use for a thousand
or two thousand years, speedily attracted the favor-
able attention of the young thinkers of the times ; and
Aristotle was once more in the ascendant. But while
Whately's Elements is an interesting and healthy
work, it can scarcely be described as specially a
philosophic one. In order to complete the reaction,
another thinker had to appear, and subject the whole
science to a critical examination fitted to satisfy the
deeper philosophic mind of the times. It is a curious
circumstance that Hamilton uttered his first oracular
declarations on Logic in a severe article on Whately,
in the Edinburgh Meviezv, published afterwards in his
Discussions. He embraced the opportunity to bring
forth the result of his profound researches, and spe-
cially to introduce to the English speaking countries,
the Logic which had sprung up in Germany out of

PREFACE. V

Kant's Critick of Pure Reason. Since that date,
Logic has had a greater amount of interest collected
round it in Great Britain than any other mental
science, and has become incorporated with the fresh-
est and brightest thought of the country. The in-
terest in the study has been increased by the Logic of
Mr. John Stuart Mill, who has evidently felt the in-
fluence of Whately in the respect which he pays to
Formal Logic, but adheres, as a whole, to the princi-
ples of his father, Mr. James Mill, introducing some
elements from the cognate Positive Philosophy of M.
Comte. Mr. Mill has given an impulse to the study,
not by the portion of his work which treats of Formal
Logic — which is not of much scientific value — but by
his valuable exposition of the Logic of Induction,
which would have been of much more value had he
left out the constant defences of his empirical meta-
physics.

The New Analytic proceeds directly or indirectly
from the metaphysics of Kant. Not that it is to be
found developed in the works of Kant, but it is largely
grounded on the peculiar principles of the Critioh of
Pure Reason ; it rose out of the searching criticism to
which Kant had subjected the forms of the Old Logic ;
and it ramified directly from the logical treatises of
such men as Krug and Esser who belonged to the
school. It is of a composite structure, resembling the
renovations we see in Britain of mediaeval buildings,
the old and the new adapted to each other with won-
derful skill, but with an occasional incongruity forcing
itself here and there on the notice of the careful ob-
server. I am not convinced that all the parts are
likely to be preserved in the shape they now have, or

vi PREFACE.

that the Analytic always gives the ultimate expres-
sion of the laws of thought ; but I am sure it is a valu-
able accession to the science. Altogether independ-
ent of its positive improvements, it has done great
service, by the careful examination to which it has
subjected the Old Logic — which has come creditably
out of the trial. Forms which had become venerable,
and, I may add, stiff, from age ; and which were
inclined to stand on their dignity and acknowledged
authority, have been obliged to submit to a sifting
scrutiny, which may have shorn them of some of their
ridiculous pretensions, but has, at the same time, de-
livered them from the dry dust which had gathered
around them and threatened to bury them. The time
has now come for subjecting the New Analytic to a
like examination. It has been before us for an age
in a half developed form, and for half an age in a
fully unfolded shape ; and we should now be in a suf-
ficiently impartial position to be able to take from it
what is worthy of being retained, and to lay aside
what is fallacious or mistaken.*

The defects and errors of the new Logic are de-
rived mainly from its German paternity. It is in-
fected throughout with the metaphysics of Kant — just
as the Art of Thinking is with the metaphysics of
Descartes, and Mill's Logic with the empiricism of
Comte. It ever presupposes, or implies, that there
are Forms in the mind which it imposes on objects as
it contemplates them ; and it makes the science alto-
gether a priori, and to be constructed apart from,

* I believe copies may be had of a limited edition of Philosophic Papers pub
lished by me, and in which I examined Hamilton's Logic. 1 have reviewed
Mill's Logic in my Examination of Mr. J. S, Mill's Philosophy.

PREFACE. vii

and altogether independent of experience. Hamilton
quotes (Logic, Led. IV.) Esser with approbation. " It
is evident that in so far as a form of thought is neces-
sary, this form must be determined or necessitated by
the nature of the thinking subject itself. . . . The first
condition of a form of thought is that it is subjec-
tively, not objectively, determined." This fundamen-
tal error (so I reckon it) runs through the whole
system, and injures and corrupts the valuable truth
to be found in the Logic of Hamilton. \ I acknowledge
that there are principles or laws in the mind, original
and native ; but these do not superinduce or impose
forms on objects as we look at them ; they simply
enable us to perceive what is in the objects. \ True,
there are a priori laws in the mind operating prior to
experience ; but we can discover their nature, and give
an accurate expression of them, only by means of care-
ful observation. The science of Logic is to be con-
structed only by a careful inductive investigation of
the operations of the human mind as it is employed
in thinking.

In conducting my independent researches in this
spirit, I have been thrown back on the old Logic
more than even the logicians of the school of Kant
have been. But I have been obliged, in order to
explain certain operations of thought to which Kant
and Hamilton have called attention, to unfold laws
which were not noticed by the older logicians.

The main feature of this Logical Treatise is to be
found in the more thorough investigation of the na-
ture of the Notion, in regard to which the views of
the school of Locke and Whately are very defective,
and the views of the school of Kant and Hamil-

viil PREFACE.

ton altogether erroneous. The Port Royal Logic
complains that the part of Logic which comprehends
the rules of reasoning is regarded as the most impor-
tant ; and maintains that the greater part of the
errors of men arises from their reasoning on wrong-
principles, rather than from their reasoning wrongly
from their principles. It is as true of this age as of
the seventeenth century, that the attention of logicians
has been confined almost entirely to Reasoning. I
believe that it is the Notion which requires at this
time to be specially examined. I believe that errors
spring far more frequently from obscure, inadequate,
indistinct, and confused Notions, and from not pla-
cing the Notions in their proper relation in Judgment,
than from Ratiocination. Even in Reasoning, most
mistakes proceed from confusion lurking in the Ap-
prehensions of the mind. We are in more need, at
present, of a new analysis of the Notion and the
Judgment, than of the Reasoning process. I have
found that in the more thorough evolution of the
nature of the Notion, especially in the thorough-going
separation of the Abstract Notion from the Singular
and Universal, we have the means of settling the
curious questions which have been started in regard
to Judgment and Reasoning in the New Analytic. In
this treatise, the Notion (with the Term, and the
Relation of Thought to Language) will be found to
occupy a larger relative place than in any logical
work written since the time of the famous Art of
Thinking.

Princeton, New Jersey, U. S.,
April, 1S70.

PREFACE TO REVISED EDITION.

Much more attention is now paid to Logic than for
several years prior to the time when I published this
work. It is now seen that Formal Logic is the most
certain science next to Geometry, and is more emi-
nently fitted than any other branch of study to give
accuracy to thinking. It is especially needed in the
present day, when there is so much largeness, but at
the same time so much looseness of thinking, which
is to be restrained and corrected by the science which
treats of the precise nature of thought.

It is well known that our science consists of Simple
Apprehension, Judgment, and Reasoning, or, in other
words, of the Notion, the Proposition, and the Argu-
ment. I am confirmed in the opinion that in the
present day, of the three Parts, that most needing to
be expounded is Apprehension or the Notion. Upon
this the Judgment and the Reasoning largely depend.
Error in thinking proceeds much more frequently and
extensively from inadequate and confused Notions
than from mistaken judgments and reasoning. More
than one half of erroneous propositions and argu-
ments spring from misapprehension and looseness in
our ideas. I have, therefore, taken immense pains to

X PREFACE.

explain the nature of the various kinds of Notions,
and to furnish a correct analysis and division of
them. I have explained the relation of Language to
Thought.

I may mention some other peculiarities of this
treatise : —

Under Judgment I have explained the distinction
between Substitutive (Convertible) and Attributive
(Inconvertible) Judgments, and have given a full ex-
position of Implied Judgments or Immediate Infer-
ences.

Under Reasoning I have enunciated the Regulating
Laws of all ratiocination.

In closing, I have unfolded the Fundamental Prin-
ciples which underlie Discursive Thought. I have
appended exercises to help us to secure accurate
thinking.

I have excluded the process of Induction from
Formal Logic, that it may be placed under the sepa-
rate head of Inductive Logic. But I have shown that
there is Reasoning involved in rising from the scat-
tered observed facts to the law, and how the Reason-
ing may be put in syllogistic form.

The tendency of German thinkers from the days of
Hegel has been to extend the province of Logic, and
to make it embrace the theory of knowledge and much
that is properly metaphysical. I think it of vast mo-
ment to restrict it to its own field, which is that of
Discursive Thought, and thus keep one great science,
established by Aristotle, from endless speculation.

Princeton, N, J., May, 1891.

TABLE OF CONTENTS.

INTRODUCTION,

SUCTION PAGB

t— 5.— Definition of Logic 1

6 — 7.— Division of the Science 2

FOEMAL LOGIC.
8— 11.— The Notion, Judgment, and Eeasoning 4

PART FIRST.
THE NOTION.

1.— Definition of Notion 1

2.— The Term ?

3. — All Notions either Concrete or Abstract 8

CONCRETE AND ABSTRACT NOTIONS.

4 — 6. — Nature of Concrete and Abstract Notions 8

7.— The Phantasy ... 10

8 — 9. — Abstractions from Concretes and other Abstractions 10

10.— Comprehension of Abstract Notions 12

LAWS OF THOUGHT INVOLVED IN ABSTRACTION.

11.— The Abstract implies the Concrete 12

12.— When tlie Concrete is Real the Abstract is Real 13

13.— An Attribute has no Independent Existence 14

14.— The Reality in the Abstract Notion 15

IS — 17.7^Importance of Abstraction 16

SINGULAR AND UNIVERSAL NOTIONS.

18.— All Notions either Singular or Universal 18

19,— Our Primary Knowledge is of Singulars 18

Xll

CONTENTS.

SECTION TAOB

20— 21.— Abstraction and Generalization not the same 19

22.— What is presupposed in Generalization 20

23.— First Step.— Observation of Resemblances 21

24 — 26.— Second Step.— Fixing on Points of Resemblance 21

it.— Third Step.— Formation of a Class 23

28. — A Universal, wherein Indefinite, wherein Definite 2S

LAWS OF THOUGHT INVOLVED IN GENERALIZATION.

29. — The Universal Implies Singulars 24

30.— When Singulars are Real the Universal is Real 25

31.— The Reality of the Universal is in Common Properties of Singulars 25

EXTENSION AND COMPREHENSION OF GENERAL NOTIONS.

32 -33.— A General Notion embraces Objects (Extension), and Attributes

(Comprehension) 26

HIGHER AND LOWER GENERALIZATIONS.

34.— Common Notions with an aggregate of Attributes 27

35.— Genus and Species 28-

36.— It is Implied that the same Objects are Generalized 29

37.— Co-ordinate, Subordinate, and Communicant Species 29

SINGULAR CONCRETE, ABSTRACT AND UNIVERSAL NOTIONS.

38— 39.— Explanation of this Threefold Division 29

40. — The Singular Concrete, or Percept 30

41.— The Abstract Notion or Abstract 31

42. — The Universal Notion or Concept 31

43. — Distinction between Generalized Abstract and Generalized Con-
crete 32

44.— The General Abstract 32

45. — The General Concrete 32

46. — Admits of Higher and Higher Generalizations 33

47.— Relation of General Concrete to Natural Classes 33

MIXED NOTIONS.

48.— Singular Terms Proper. Singulars Classified. Collective. Sin-
gulars Abstracted 34

49. — Terms both Abstracts and Concepts, (Denotation and Connota-
tion) 35

50. — Abstract Notions becoming General 36

51.— Mixed Modes of Locke 37

52. — All Notions are Percepts, Abstracts, or Concepts 37

53.— Privative Notions 38

54. — Contrary and Contradictory Notions 30

55. — Relative and Correlative Notions 39

CONTENTS. xiii

SECTION TAGE

LOGICAL DIVISION.

56.— Its Nature 39

57. — First Rule. — We must proceed according to Marks 40

58. — Second Bule. — The Species must make up the Genus 41

59. — Third Bule. — The Members must exclude one another 42

60—61.- Fourth Bule.— There should be a due Subordination 43

ANALYSIS AND SYNTHESIS.

63.— Analysis 41

63.— Synthesis 45

64. — Purpose served by Analysis and Synthesis 4S

LOGICAL DEFINITION.

65.— Its Nature 46

66. —Distinguished from Description 46

67.— Definition of Abstract Notions 46

68. — Notions which cannot be defined. . . 47

69. — Definition of General Notions 47

70.— Bule First. — Bring out a Distinguishing Attribute 48

71.— Definition of General Concrete Notions 48

72. — Bule Second.— The Definition must be Adequate 49

73.— The Test of a good Definition 49

14i.—Bule Third.— Give the Genus and Differentia 49

75.— Practical Rules 50

AIDS TO ABSTRACTION AND GENERALIZATION.

76. — Need of a Sign of some kind , 50

I.— Mental Image, or Phantasm.

77.— Nature of such 50

78. — Difference between Phantasm and Abstract and General Notion. 51

79. — Criticism of Locke's views hi

II.— Language.

80.— Advantage op Language as an Instrument of Thought 53

81. — (1) A Sign and Register of Abstractions and Generalizations 54

82. — (2) Puts us in possession of Abstractions and Generalizations 55

83—85. — Character of a people shown in their Language 56

86.— Advantage of being acquainted with more than one Language . 58

87. — Benefit got by our tongue from other tongues 59

88— 90.— (3) Gives a form to Thought . 59

91.— How it may restrain Thought 61

92— 94.— (4) Lightens Thought by being used as a Symbol 65

95.— (5) Enables us to carry on Thinking to a greater extent 64

96— 97.— Men can reason without Language 65

98—101 —But are always the better of Language 67

xiv CONTENTS.

SUCTION PA OB

102.— (6) Helps Thought to make Progress 69

103 — 105.— Incidental Disadvantages op Language 70

IOC— (1) The vagueness of so mauy phrases 72

107— 110— (2) Different Meanings of the same Word 73

111. — (3) Misleading Associations 76

112 Words derived from Matter applied to Mind 77

113.— (4) We use Words without inquiring into their Meaning 77

114.— How are the E vils to be avoided 78

(1) Ascertain the Meani ng of the Word 79

115.— (2) When Ambiguous ascertain the Various Meanings 79

116. — (3) Determine the Notion for which it stands 79

117.— (4) Ask whether the Notion is Singular, Abstract, or Universal. . . 80

118.— Especially in Abstruse Thinking 81

119.— (5) Consider the Things from which the Notions are formed 83

LAWS OP THOUGHT INVOLVED EN USE OF SIGNS.

130. — First Law. — A Term stands for a Notion, Singular, Abstract, or

Universal 83

121.— Second Law.— We can Predicate of Sign only what can be Predi-
cated of Notion 84

122.— Third Law.— We may demand that the Notion be substituted for

Sign 84

HI. — Classes in Natube.

123— 125.— There are such Classes 88

106— 127.— Classes called Kinds 88

128. — Are Aids and Guides in Generalizing 89

REALISM, NOMINALISM, AND CONCEPTUALISM.

129 — 132. —Brief History and Criticism of Opinions 90

PART SECOND.
JUDGMENT.

1.— Definition of Judgment <J8

CATEGORICAL PROPOSITIONS.
-Subject, Copula, and Predicate 93

—Nature of the Copula 94

— Modals 98

—In Quality, either Affirmative or Negative........ 95

—In Quantity, either Universal or Particular 95

Meaning of words 'All' and 'Some' 96

Indefinite or Indesignate Propositions . ... 98

CONTENTS. xv

SECTION PAGE

9. -Fourfold Division of Propositions, A, E, I, O 96

10.— Distribution of Terms 96

11.— Distribution of Subject and Predicate 97

18— 13.— Various Eelations between Subject and Predicate 97

14.— Equivalent Propositions 98

15.— Propositions in which the Relation is op Extension and

Comprehension 99

16. — Inconvertible and Convertible — Substitutive and Attributive 100

17— 18.— Difference between these 100

19— 20.— Cases in which Predicate is a General Notion Distributed (U) 101

21. — Predicables of Aristotle and Porphyry 109

22.— Should the Predicate always be Quantified ? 103

23.— Hamilton's Table of Judgments 104

CONJUNCTIONS OF PROPOSITIONS, CONDITIONALS, AND DISJUNC-
TIVES.

24.— Various Conjunctions 105

25. — Conditionals and Disjunctives 10B

26.— Conditionals, their Nature 106

•-J7— 28.— Antecedent. Consequent, and Consequence 106

29. — Conditionals may be Equivalent or Attributive 107

80— 31.— Disjunctives, their Nature 107

IMPLIED JUDGMENTS, OR IMMEDIATE INFERENCES.

82.— Their Nature 108

33.— Conversion 108

34. — Opposition in Equivalent Propositions 109

35.— Opposition in Attributive Propositions 109

SQ.—Subalternation 110

37. — Contrary Opposition Ill

38.— Contradictory Ill

^.—Demonstration 112

40. — In discussion Propositions put as Contradictories 112

41.— Transposed Propositions obtained by Opposition 113

42. — Transposed Judgments obtained by Extension 114

43. — These not applicable to Equivalent Propositions 114

44. — The Interpretation, of Judgments gives Implied Propositions... 114

45.— Implied Judgments are obtained by Comprehension 116

The Interpretation of Marks 115

46.— Added Maries 115

47.— Added Subject and Predicate 115

48. — Summation of Predicates 115

49. — Privative Conceptions , 115

50.— Conditional Propositions 117

Si.— Disjunctive Propositions 117

52.— Rule as to Distribution of Terms in Implied Judgments 117

53. — Implied Judgments obtained from " men are responsible " 117

54.— How Logic aids in Determining the Truth of a Proposition 118

xvi CONTENTS.

PART THIRD.
REASONING.

MOTION VABl

1. — The Process in the mind when we reason 120

2. — The Sameness of the Process 121

3. — Importance of Analyzing the Process 121

4.— Difference between Judgment Proper and Reasoning 122

5.— Involves Three Propositions. The Syllogism 123

6. — Syllogistic Analysis made by Aristotle 123

7.— Cannot reason from One Judgment. Enthymeme 123

8.— Extremes and Middle ; Premisses and Conclusion 124

RULES APPLICABLE TO EVERT KIND OF REASONING.

9.— (1) There should be only Three Terms 125

10— (2) And only one Middle 135

11. — (3) One Premiss must be Affirmative 125

12. — (4) If either Premiss Negative, the Conclusion Negative 125

13.— (5) To prove a Negative, one Premiss must be Negative 125

14. — What are the Regulating Principles of Reasoning ? 125

15.— First Regulating Principle. " Notions Equivalent to one and

the same third Notion equivalent to one another." 126

16.— The TJnfigured Syllogism of Hamilton 127

17.— Second Regulating Principle. " Whatever is predicated of a

Class, may be Predicated of the Members of the Class." 127

18.— Major and Minor Terms. Major and Minor Premisses 128

19.— Rules derived from the Dictum of Aristotle ; being

EULES APPLICABLE TO REASONING IN EXTENSION.

20.— (1) Middle Term distributed once 128

21. — (2) Term distributed in Conclusion only when in Premisses 12h

23.— (3) From two Particular Premisses no Conclusion 129

23.— (4) K one Premias Particular, Conclusion Particular 130

24.— These Rules apply only to cases in which there is a Concept 130

25— 26.— Moods 130

27.— Figure 131

28— 29.— First Figure.— Its Special Rules 131

30— 31.— Second Figure.— Its Special Rules 132

32— 33.— Third Figure.— Its Special Rules 132

34— 35.— Fourth Figure.— Is it allowable? 133

36.— Mnemonic Lines 134

37.— Reduction 134

38.— Made by Implied Judgments 135

39. — Ostensive Reduction 135

40.— Reductio per lmpossibile 136

41 . —Immediate Inferences in Mediate Reasoning 137

12 — 44.— Reasoning in Comprehension 13*

CONTENTS. xvii

SUCTION PAGE

45.— The Two Dicta Combined ; 140

46.— Hamilton"s Table of Forms of Seasoning 141

47. — Mill's Theory of Reasoning Process 143

48 — Reasoning from Plurative Judgments 144

CONDITIONAL REASONING.

49. — Its Nature and Rules 145

60.— Common Forms 146

51— 63.— Relation of Conditional to Categorical Reasoning 146

DISJUNCTIVE REASONING.

54.— Its Nature and Rules 148

55.— Its Principal Forms 149

56.— Can be Reduced to Categorical 149

DILEMMA.

57.— Its Nature 150

58.— Its Principal Forms 151

59.— A Trilemma, etc 151

60. — Reduction to Categorical Form 151

CHAINS OF REASONING, SORITES.

61.— Prosyllogism and Episyllogism 152

62.— Sorites 153

63.— Reduced to Series of Syllogisms 153

GENERAL REMARKS ON REASONING PROCESS.

64.— We get tbe Premisses from Intuition and Observation 155

65.— Individual and Combined Observation 155

66.— Some of the Observational Maxims written out, others not 156

67. — Some of them Certain, others only Probable 157

68.— Demonstration, in which the new steps are Intuitive 157

69.— Experiential or Probable Evidence 158

70.— Is all that can be had in Practical Matters 160

71.— Falls under the Dictum of Aristotle, and needs a Major Premiss. . 161

72 -73. — Reasoning Involved in Induction ; the Canons of Induction ; the

Major Premiss 161

74. — When Premisses only Probably True 16?

75— 76.— Concurrence of Evidence 165

77.— Whence the Rapidity of Reasoning Process ? r. . . 166

78.— In what sense are the Truths reached New ? 168

xviii CONTENTS.

SECTION PAOB

FALLACIES.

79. —Definition of Fallacy 169

80.— What Logic can do in guarding against Fallacies 169

8< -How the Heart sways the Head 171

82.— Division of Fallacies , 172

83.— Formal Fallacies 172

Undistributed Middle 178

84.— Elicit Process of Major or Minor Term 173

85.— Negative Premisses 174

86.— Arguments with more than Three Terms 174

87.— Fallacies of Conditionals. . 175

88.— Material Fallacies 175

88— 90.— Ambiguous Terms, especially Ambiguous Middle 175

91. — Fallacia Accidentis 178

92.— Equivocation 179

93.— Oblique Expression 180

94.— Fallacies of Confusion 180

95.— Fallacy of Division and Composition 181

96. — Imperfect Division 182

97.— Fallacy of Shifting Ground 183

98.— Fallacia Plurium Interrogationum 184

99.— Petitio Principii 184

100.— Syllogistic Seasoning not Petitio Principii 185

101.— Arguing in a Circle 185

102.— Ignoratio Elenchi 186

103.— Proving only part of the Question 187

104.— Fallacy of Objections 187

105.— Argumentum ad Hominem 187

106.— Argumentum ad Populum 188

107.— Argumentum ad Verecundiam 188

108.— Argumentum ad Ignorantiam 188

109.— Fallacy of Pretension 189

110. — Argument from Consequences 189

111.— Mistakes as to Onus Probandi 190

112.— Fallacies of Analogy 191

113.— Imperfect Enumeration 192

14.— Non Causa pro Causa 193

15.— Post Hoc ergo Propter Hoc 193

16.— Mistaking Sign for Cause 194

17.— Causa Essendi and Causa Cognoscendi ; Reason and Cause 194

FUNDAMENTAL LAWS OF DISCURSIVE THOUGHT.

118. — How they are discovered 195

119— The Law of Identity 195

120.— The Law of Contradiction 196

121 .-The Law of Excluded Middle 196

122.— The Principle of Equality 196

CONTENTS. X!X

SECTION PASB

123.— The Dictum of Aristotle 19ti

124.— The Principle of Attribution 197

125.— The Law of Division 197

126. —The Principle of Whole and Parts 198

127.— The Consideration of these belongs to Metaphysics 198

APPENDIX.

I.— Exercises as to Forms

1—7.— The Notion 199

8— 14.— Judgment 201

15— 27.— Reasoning 202

II. — Exercises as to Violations of Laws of Thought

27— 31— In Notions 207

82— 35.— In Judgments . 209

86— 68.— In Reasoning 909

INTRODUCTION.

DEFINITION AND DIVISION OF THE SCIENCE.

1, Logic may be defined as the Science of the Laws ol
Discursive Thought. The matter about -which it is em-
ployed lies in the mind : it is Thought, which is an exer-
cise of the understanding, the intelligence, or the intellec-
tual or cognitive powers, as distinguished from operations
of the motive faculties such as emotion, moral perception
or volition. Thought or intelligence may be of two "kinds.
In some cases we perceive the object or truth at once :
as when we see or touch the table before us, as when we
know that the shortest distance between two points is a
straight line. In other exercises we perceive the thing or
truth by a process : from something given we draw some-
thing else, as when we argue from certain appearances in
the sky that it will be rain, or from the structure of
certain strata of the earth's surface that they have been
formed in water. This second kind of thought is called
Discursive, in which we proceed from something allowed
to something else derived from it by thinking ; as dis-
tinguished from Intuitive Thought, in which we discern
the truth immediately. The science which treats of the
intuitive operations of the mind is called Metaphysics ;
the science which considers the discursive acts is Logic.

2. The discursive operations, like all other agencies in
nature, proceed in a regular manner, that is, according to
laws. By carefully observing the acts of the mind in

2 INTRODUCTION.

thinking, we may discover what these laws are, and ex.
press them in language or in formulae. In doing this, we
are constructing a science, which is co-ordinated know-
ledge, as distinguished from the knowledge of individual
things as they present themselves. As Logic co-ordinates
what it observes, it is a science ; it is the science of the
laws of discursive thought.

3. There is no definition of Logic" in any of the extant writings
of Aristotle the founder of the science. Of later logicians some
have given a narrower and some a wider definition than that
adopted in the text. Some represent it as a pure science ; some as
a mere art. Some, such as Whately, would have it treat of Seasoning
exclusively (omitting the Notion and Judgment), while others
would enlarge it so as to make it embrace all intelligence. The
definition of the text gives it a rigidly exact field, while it comprises
all the mental operations embraced under the laws of discursive
thought.

4. It should be noted that Logic does not profess to
impart to man the power of thinking any more than
Grammar gives him the capacity of speech. Logic finds
men engaged in apprehending, judging, and reasoning,
and it seeks to unfold the laws involved, just as Grammar
presupposes that men can speak, and proceeds to detect
the rules of correct speech. And as Grammar by its
rules enables persons to express themselves accurately,
so Logic by expounding the laws of thought guards
against mistakes in thinking. So far as Logic unfolds
the laws of a department of our nature it is a science; so
far as it supplies rules to guide and guard us in our dis-
cursive operations it is an art.

5. As Logic deals with Thought primarily, and looks at Language
only secondarily and incidentally, it is thus easily distinguished from
Grammar, Ehetoric, and the Science of Language, which all treat of
speech, writing or language generally.

0. Discursive Thought may be viewed in its general
aspects or in its more special applications. It may be
contemplated as directed to objects of any kind, no

DEFINITION OF THE SCIENCE. 3

matter what they be, within or without us ; or it may
be considered as looking to certain classes of objects ;
thus it is evident that thinking is somewhat differently
employed in mathematical demonstration from what it is
when arranging objects in natural history. This gives us
the grand division of the science. So far as it treats
of discursive operations, whatever be the objects about
which it is employed, it is called Universal or more com-
monly Formal Logic. So far as it considers thinking as
lirected to special kinds of objects, it has been called
Particular Logic or might be called Objective Logic ; it
embraces such subjects as Demonstration and Induction.
This work takes up the former of these.

7. Kant says, " Logic maybe considered as two- fold : as Logic of
the general (universal) or the particular use of the understanding.
The first contains the absolutely necessary laws of thought, without
which no use whatever of the understanding is possible, and gives laws
therefore to the understanding, without regard to the difference of ob-
jects on which it may be employed. The Logic of the particular use
of the understanding contains the laws of correct thinking upon a par-
ticular class of objects. The former may be called elemental logic ;
the latter the organon of this or that particular science. The latter is
for the most part employed in the schools as a propaedeutic to the
sciences, although, indeed, according to the course of human reason,
it is the last thing we arrive at, when the science has been already
matured and needs only the finishing touches towards its correction
and completion; for our knowledge of the objects of our attempted
science must be tolerably extensive and complete before we can
indicate the laws by which a science of these objects can be
established. General Logic is again either pure or applied. In the
former, we extract all the empirical conditions under which the
understanding is exercised, for example the influence of the senses,
the laws of the memory, the force of habit, of inclination, conse-
quently also the sources of prejudice, &c." He tells us, General Logic
" makes abstraction of all content of cognition, that is of all relation
of cognition to its object, and regards only the logical form in the
relation of cognitions to each other, that is the form of thought in
general." (Critique of Pure Reason, Part II., Meiklejohn's Trans
lation.) The distinction between Universal and Particular Logic is

4 INTRODUCTION.

adopted in the text, but with an important modification. Kant
makes Universal Logic look at thought apart altogether from content
or objects, and supposes that the mind has laws or forms which it
imposes on objects. In the text it is supposed that the laws of
thought are the laws of the understanding in contemplating objects.
Formal or Universal Logic treats of thought, not apart from content,
out whatever be the content, that is, whatever be the objects.

UNIVERSAL OR FORMAL LOGIC.

8* Let us look at some of the common exercises of
Discursive Thought. We have before us a piece of ice.
So far as we simply look at it, and perceive its form and
color, there is no discursive thought. But we can distin-
guish between its form and color, or we may think of its
qualities, say, its coldness, its brittleness, its transparency ;
we are now exercising thought upon the object perceived.
The mere bodily senses can draw no such distinction.
I can not by the eye separate the shape of the piece of ice
from its transparency. But on the bare inspection of the
object the mind can distinguish between it and any of its
properties, or between one property and another. This
is Abstraction, a simple and elementary exercise of dis-
cursive thought.

0. Again, on looking at two or more objects, we may
notice that they resemble each other. An inhabitant of a
northern country is travelling for the first time in a south-
ern clime, and beholds a plant such as never fell under
his view before, a plant with a leaf like a fan, and on
going a little farther he notices another plant of much
the same general form. Already he is exercising dis-
cursive thought. He was not doing so as long as he was
a mere passive recipient of the impression left on the eye
by the shape and color ; but when he discovers the like-
ness of the plants he is exercising what is called Com-

DIVISION OF THE SCIENCE. 5

parisou. As other like plants fall under his view, he
will probably take a farther step ; he will form a class 01
kind which shall embrace not only the plants which he
has seen, but all others, with the points of agreement,
. which may fall under his notice or that of any other man ;
and he will rejoice if some one gives him the name of
' fan palm ' to designate them.

The product of these two processes is the Abstract and
General Notion. The First Part of Formal Logic con-
siders the Notion, specially the Abstract and General
Notion.

10. Suppose now that we have acquired Notions, we
may proceed to compare them. By a process like that
described above, the traveller may have formed the
notion of fig-tree out of specimens of plants of a different
order growing in the same region, and he may compare
tne two kinds of objects of which he has the notion,
and he declares the fig to be of a different shape from
the palm, and its leaves to be of a different color. "When
he does so, he is said to be exercising Judgment, which
is a discursive operation comparing two or more notions.

The Second Part of Logic treats of Judgment.

11. But Judgment may be of two kinds. In many
cases we pronounce a judgment at once on the bare con-
templation of two notions. It is thus that, considering
the palm tree and the fig-tree, we discern that the leaf
veins of the one are parallel, whereas those of the other
are curvilinear. But in other cases we cannot discover
the agreement or disagreeraent at once by simply
considering the notions we have. Thus we cannot by
merely looking at the palm and fig-tree determine how
they grow, whether from one seed lobe or two seed lobes •
whether from within or by adding rings from without.
But we observe that the veins of the palm leaves are
parallel, and that those of the fig are reticulated : and we

6 INTRODUCTION.

have learned somehow that parallel-veined plants proceed
from one seed lobe or cotyledon (are monocotyledons),
and grow from within ; whereas net-veined plants spring
from two cotyledons (are dicotyledons), and add rings
without ; and now we are in a position to draw an in-
ference ; we argue that the palm, being parallel-veined, is
monocotyledonous, and the fig-tree, having netted veins, is
dicotyledonous. In drawing these conclusions, we called
in a third notion, monocotyledous or dicotyledons, to
combine the other two. The process is one of Judgment ;
but it is to be distinguished from the second operation
mentioned above, the Judgment Proper, or what we shall
commonly call Judgment. In Judgment we compare two
notions directly, and declare their agreement or disagree-
ment ; whereas in the process now before us, we compare
two notions by means of a third. The process is called
Reasoning, Ratiocination or Inference, and its laws are
unfolded in the Third Part of Logic.

PART FIRST.
THE NOTION.

1. The operation of the mind in contemplating an ob-
ject or objects is called Simple Apprehension. The object
or objects apprehended constitute the Notion. Sometimes
the notion is of an object apart from any relation to
others, as ' man ' and ' horse,' and is called Simple or In-
complex ; sometimes it is of objects in a relation to each
other, as ' man on horseback,' and is said to be Complex.
In order, however, to its being a Notion, the mind must
have brought the objects into a unitj of apprehension.
' Man on horseback ' is one notion ; we contemplate it as
one thing.

2. A notion expressed in language is called a Term, as
two terms constitute the termini or boundaries of a pro-
position. A term may consist of one word or of several
and one word may contain two terms and express their
connection. A word is said to be categorematic when it is
capable of being employed by itself as a term, as, for ex-
ample, nominative nouns, such as horse, dog, deer. Other
words, such as adverbs, prepositions, and nouns not in
the nominative case, can only form part of a term, and are
said to be syncategorematic : thus ' bird on the wing '
is one term, though expressed in four words. Again ;
such words as sum (I am existing), amat (he is loving),
contain two terms, I and existing, he and loving, and in-

8 THE NOTION.

tiraate their relation. In all cases we must look to the
thought — to the notion in the mind — and not to the mere
words, to determine what is the notion, and what sort of
notion it is.

3» All notions are either Concrete, as ice, or Abstract,
as coldness. Again, all notions are either Singular, as
Aristotle, or Universal, as logician. Combining these
cross divisions we get a three-fold division of notions, the
Singular, the Abstract, and Universal. It is of great
importance in Logic that we know the exact nature of
each of these kinds of notion and the distinction between
them. Terms are divided as notions are into Singular,
Abstract, and Universal, which last are usually called
General or Common (into three, not four kinds, p. 30).

THE CONCRETE AND ABSTRACT NOTION,

4, All Notions are either Concrete or Abstract. A Con-
crete Notion is of objects as they are with an aggregate of
qualities. An Abstract Notion is of part of an object as a
part, more technically of an attribute of an object. In
order to comprehend this distinction we must look at the
nature of the original cognitions or apprehensions
which we have by the power of intuition which looks
immediately on things. In all such we contemplate ob-
jects with qualities more or fewer, and the notions thus
formed are said to be concrete. The word is derived
from con together, and cresco I grow, and means literally
grown together. Some have derived it from con and
ierno3 when it means seen together. Either derivation
brings out the meaning : in a Concrete Notion the ob-
jects with their qualities as it were grow together, and
are perceived together. We cannot look on that table
without perceiving it at one and the same time as colored

THE CONCRETE AND ABSTRACT. 9

and extended : we never can view the color without the
colored surface, or the surface without seeing it as hav-
ing color of some kind. Nor can we by any mechanical
or chemical process separate the one from the other. But
human intelligence is subtler than any material agent; and
we can in thought consider the one without taking the
other into account. This process is called Abstraction,
from abs from, and traho to draw, and signifies a drawing
off ; and an Abstract Notion is of a part or a quality or
qualities drawn off from the rest of the object.

5. Abstraction may be taken in a wider or a narrower
sense. In the wider sense it is thus defined by Whately:
" When we draw off and contemplate separately any part
of an object presented to the mind disregarding the rest
of it, we are said to abstract that part of it." Thus under-
stood, the part abstracted may exist separately : thus if I
speak of the leg of a table in relation to the table, the
phrase is abstract ; but I may cut off the leg or consider
it as it is in itself and without reference to the table,
in which case our notion is concrete. But abstraction
may be viewed in a more limited way as that operation
of mind in which we contemplate an attribute of objects ;
" by abstract name, I mean the name of an attribute."
(Mill.) In this sense the thing abstracted cannot be said
to have a separate or independent existence. Thus I can
think and reaso.i about the coldness, or transparency, or
brittleness of ice, but there cannot be coldness or trans-
parency or brittleness existing separate or apart from the
ice or an object that is cold, brittle, and transparent.

0, We may now give examples of each of these kinds
of Notions. When I think of a stone, the notion is con-
crete ; but if of heaviness or hardness, the notion is ab-
stract. If I contemplate a fellow-man, the notion is con-
crete ; but if I consider his wisdom, or his learning, or his
wealth, the notion is abstract. If I remember a mother,

10 THE NOTIOJS

the mental operation is concrete ; but if I muse on her
kindness, her care or faithfulness, the process is ab-
stract. If I contemplate God, the notion is concrete — it is
God with all his perfections as known to me ; but if I
meditate on his infinity, his justice, or benevolence, my
idea is abstract.

7. In Abstraction taken in the wider sense, we are
much aided by the phantasy or the imaging power of the
mind. Having seen an object in its totality I can pic-
ture to myself a part, provided that part can be separated.
Thus, having seen a plant, I can have an idea of its roots,
its stem, its leaves, separately. Having seen a lion, I can
picture its head and its jaws distinct from the rest of
its body. But these are exercises of the imaging power
of the mind, and not of abstraction considered as an act
of thought. In forming the Notions of attributes, the pic-
turing power of the mind can be of little service. True,
when they are of properties of objects perceived imme-
diately by the senses, it may help us somewhat, thus in
thinking of transparency, we may have an idea before us
of glass or of ice ; but when the abstractions are high
and refined, we can find no image to represent them, and
any idea we might fashion, would rather have a mislead-
ing influence, at least in rigid thinking. Who can form
an idea, in the sense of image, of such abstractions as gov-
ernment, liberty, peace, prosperity, civilization, religion ?

8* It is evident that the mind can draw a number, in
some cases an indefinite number, of abstractions from one
and the same concrete object. Thus in contemplating a
rose, we can abstract its form, its color, its odor, its mode of
growth, its stage of growth, its vital functions, its beauty,
and I know not how many qualities. From man we ruay
abstract his bodily frame or any part of it, his shape, his
size, his reason, his weight, his age, or any of his mental
attributes, such as his conscience, his feelings, his sinful-

THE CONCRETE AND ABSTRACT. H

ness. It would require hours or clays to run over the
innumerable attributes we might ascribe to such complex
objects as the Hebrew Commonwealth, the Eoman Empire,
Greek Literature, the English Language, the Political Con-
stitutions of Britain and America. The abstractions made
by any one man in the course of a day, or even an hour,
are beyond calculation ; and we cannot form the dimmest
idea of the number fashioned by a man in the course of
his life, and still less of those formed by all mankind
since they appeared on the earth. Some of these have been
embodied in language, but by far the greater number
never have been and never will be expressed in words.

9. We cannot have an adequate idea of the process of
abstraction, unless we take into account that we may form
abstractions from abstractions, and rise to abstractions
more and more refined. Perhaps the fittest illustration is
to be found in the science of numbers. Number of every
kind is an abstract notion : as one, ten, a hundred, or a
thousand ; you cannot find one apart from one thing,
or ten, a hundred, or a thousand apart from ten, a hun-
dred, or a thousand objects. From these notions we may
frame higher abstractions as, a, b, c, standing for known
quantities, and x, y, z, for unknown. A still higher pro-
cess of abstraction is involved in the Fluxionary and Dif-
ferential Calculus and in Quaternions. In thus abstract-
ing it is possible to think of (not to image) an object apart
from its qualities. This is the farthest point which can
be reached by us ; that is, we come to the to ov, the Ens
or Being of which metaphysicians, beginning with the
ancient Eleatics, have made so much, and yet to so little
profit, because they have mistaken its nature. When we
speak of Being, we do not mean that there is any one
existing thing with a separate or independent reality
which can be so designated ; but simply to point to an at-
tribute which all things have, namely, that they exist.

12 THE NOTION.

10. When we come to speak of the General Notion, we shall find
that there is an important distinction between the Extension and
Comprehension of a Notion. By the Comprehension of a Notion is
meant the qualities comprised, in it ; by Extension, the objects em-
braced under it. Abstract Notions may be said, to have Comprehen-
sion, for they embrace qualities ; and some have more Comprehension,
that is, more qualities, than others. Thus ' intelligence ' and ' char
acter,' which include a whole aggregate of properties, is more Com
prehensive than 'reasoning,' which is only one form of intelligence.
or 'tamperance ' which is only one element of character. But Ab
stract Notions can scarcely be said to have Extension, at least as we
have above defined it. They are apprehensions, not of objects, but
of qualities of objects. At the same time a quality always is in an
object, and may be in more or fewer. Thus impenetrability and
gravity, which are in all matter, are in more objects than fluidity or
redness, which are only in certain forms of matter. The distinc-
tion between Extension and Comprehension is one applicable to
general, rather than abstract, notions.

From the account now given, the following laws may
be derived :

11. First Law, TJie Abstract implies the Concrete. — We
have seen that the primary knowledge acquired by us is
of objects with qualities more or fewer. By the eye we
become acquainted with bodies as at one and the same
time extended and colored. By touch, we know things
as at once extended and solid. By self-consciousness,
we know self as perceiving by the senses, as thinking and
feeling. Not only so, but when we recall by the mem-
ory, a scene, a person, an event, it comes before us with
more than one quality. Even in imagination, the figure
or scene comes up in the concrete ; we cannot picture to
ourselves a body with a shape without also giving it
color, or as having color without also conceiving it a-e
extended. Proceeding on these concrete ideas, the mind
can distinguish between a whole and its parts, between an
object and its qualities, and between one quality and an-
other. It can consider specialty any one quality of body,
such as its form, its size, its weight, its density. Tt car

THE CONCRETE AND ABSTRACT. Yd

distinguish between man as a whole and any one quality
of his, such as his bodily strength or stature ; and dis-
tinguish between any one attribute and another, as be-
tween his bodily and intellectual power, between his in-
tellect and his feelings, between any one feeling such as
joy, and any other feeling such as sorrow. But we are
not to think that because we can thus distinguish between
a quality and its object, or between one quality and an-
other, that therefore the quality can exist of itself. The
part abstracted implies the whole of which it is a part ;
in particular the quality or attribute implies an object
from which it is taken. The question has often been put,
Is there a reality in the abstract notion, and if so, what
sort of reality ? The answer is that it has a reality in the
concrete object or objects, and when it is a quality, as a
quality of the object or objects. Hence,

12. Second Law, When the Concrete is Beat the Abstract is
also Beat. — In laying down this rule it is of course pre-
supposed that the abstraction has been properly made •
that is, that we contemplate a real part of a whole, a real
attribute of an object ; that when we speak of the white-
ness of a lily, the lily is really white. Let, then, the ob-
ject be a reality, that is, have a real existence, and the qual-
ity contemplated has also an existence. True, if the
objects be imaginary, say a hundred-handed Briareus in
one body, we cannot declare that these hundred hands
ever had an existence anywhere except in the imagination
of the poet ; but if we see a real human being with hands
before us, we are sure that the hands exist as well as the
possessor of them ; and if these hands be strong, that the
strength also is a reality. I can separate in thought the
beauty of Venus from the person of Venus ; but as the
person is an ideal creation, so also is the beauty. But, on
the other hand, if the beautiful person be a living being
then the form and the color which constitute her loveli-

14 THE NOTION.

ness have also an actuality. This proposition is laid
down in opposition to those who represent all ab-
stractions as unreal, as imaginary. Some speak of such
qualities as existence, beauty, virtue, as mere fictions of
the mind, for which it is vain to seek any corresponding
reality. It is true all abstractions are creatures of the
mind, but when we abstract a real part from a real whole.
a real quality from a real object, the abstract has an
existence quite as much as the concrete thing.

13. Third Law, When the Abstract is the property of an
object, we are not to regard it as having an Independent Exist-
ence.— Sometimes, indeed, it is a separable part, as the
root of a plant ; but in this case, when actually separated
it is no longer an abstract, but concrete. But when it is
a quality such as color, solidity, weight, thinking, desir-
ing, revolving, then it is inseparable from the objects, and
has no independent existence — its existence is simply in
the objects. Much error has in all ages taken its rise
from mistaking abstracts for independent wholes. The
Eleatics very properly formed the abstract notion Being,
but then they mistook its nature and gave it an existence
like the objects, say, earth, or gold, or animals which pos-
sess it. All the Greek philosophers erred, less or more,
in this respect, giving a separate actuality to the abstrac-
tions fashioned by their own acute intellects ; and speak-
ing of ideas, substance, physical elements, as if they were
agents capable of action like God or individual men. We
see a like misapprehension among the scholastic logicians
and theologians of the Medieval Ages ; and their prac-
tical errors came to have a theoretical sanction giver, them
by the sect of the Realists, who gave a confused and mystic
reality to the abstract and general notions formed by the
mind. The ideal metaphysicians of Germany have in
much the same way given to Nothing, Something Be-
coming, a place and a power in themselves. Nor have

THE CONCRETE AND ABSTRACT. 15

our modern physical inquirers escaped the tendency, foi
they speak of nature, force, gravity, motion, as if they
were entities, acting independently of the objects whose
action and mode of action they express.

14:. Corollary. — It is of great importance to trace up
abstractions to the concrete objects from which they are
derived. We should thus be saved from the two opposite
errors into which we are apt to fall : the error of those
who regard abstractions as nonentities, and that of those
who give them a distinct being. By following them up
to the substances, whether mental or material, from which
they are taken, we shall see that they have a reality, and
we shall find what is the nature of that reality. Gravita-
tion has no reality distinct from matter, but it has a
reality in the stars and planets which it holds in their
spheres. Nature is not a separate agency, but is a name
for the combined system of things falling under our view
in the world. Beauty is a reality, as our esthetic senti-
ments testify ; but has no embodiment except in some
beautiful object, though the foolish laudations of some
might lead us to think that she has a personality of her
own, which she may one day or other reveal to some en-
raptured boy-poet, or painter, provided he could rise to
a sufficiently ecstatic state. Virtue has no separate ex-
istence in some ethereal sphere, as we might be tempted
to think by the way in which some speak of it ; but it has
a reality in the voluntary acts of beings possessed of intelli-
gence, conscience and free will. The Alexandrian mystics
recommended us to rise to the contemplation of the One
and the Good : all very useful and important, we say,
provided we seek for it, where alone we can find it, in
the One Living and Good God.

IS. We cannot close the subject of Abstraction with-
out pointing out the value and the importance of the
process. It is involved in all our mental operations which

16 THE NOTION.

deserve the name of thinking, and in all practical opera
tions which require thinking. We cannot speak intelli-
gently without abstracting, for in speaking about an
object we separate it from other things. We cannot per-
form any practical work without such a process, for in
doing it we must distinguish the things falling simulta-
neously under our notice. It is an essential element in
all scientific pursuit ; for in science we have to gather
the law out of the scattered phenomena of nature, and in
order to this there must be the " necessary rejections and
exclusions" (Bacon), that is, the omission of the acciden-
tal and indifferent. In particular it is by this operation
we reach those lofty ideas which philosophy ponders.
We draw off from the objects which present themselves
to the senses that which is peculiar to the individuals, and
we have the idea of matter or material substance. In
contemplating bodies we leave out in our thought al
other properties except those by which it resists impulse
and we have the notion of solidity or impenetrability
From extended body we omit other ideas, and there re-
mains the idea of pure space. In contemplating ourselves
and other intelligent beings, we pass by the peculiar-
ities of the individual, and fixing on the permanent, we
have the idea of spiritual substance. We separate
the producing power from the events occurring, and we
have the idea of potency or causation. We fix on the
good or bad qualities of moral agents, and we have the
notion of good and evil. These ideas, matter and spirit,
substance and quality, space and time, production and
power, good and evil, are all reached by abstraction, and
like the primary rocks of our earth, they go down the
deepest and they mount the highest. Passing beyond
those qualities that are fleeting, Abstraction goes on to
those that are fixed ; brushing aside the contingent, it
reaches the necessary ; and thus discovers the stationary

THE CONCRETE AND ABSTRACT. 17

amidst the flowing, the stable at the basis of the tran-
sient, and the eternal underneath the temporary. The
mind is thus carried to an elevation where it is above all
passing occurrences, which it can survey in the thought
that it is above them, while it feels itself planted on a
rock which is unmoved amid all mutations.

10. On the other side, let us not in our search after
the abstract lose sight of the concrete. Abstract notions
do indeed serve most important purposes. They have
been wittily called "the ghosts of departed quantities;"
they might be more aptly described as the bones, the skele-
ton, of real bodies. But however essential the skeleton
may be to the frame, and however important the study of
it may be for the ends of science, it is not in itself an
attractive object — except indeed to the anatomist ; — one
would not just choose to dwell in a chamber full of rat-
tling bones. For scientific and philosophic purposes it is
necessary to have abstractions, and these high abstrac-
tions ; but abstractions cannot promote every good pur-
pose. In particular they are not calculated to call forth
feeling or to warm affection into life : it can be shown
that emotion is evoked, not by abstract notions and prop-
ositions, but by living objects and concrete apprehensions
and representations. We do not feel gratitude for ab-
stract kindness, but for the kind deeds of a kind person.
Our admiration is excited, not by some grand idea ol
beauty or sublimity, but by a lovely person or a grand
scene. Our love is kindled by the contemplation, not of
goodness (as the pantheist would have it) but by a good
God or a good man or woman.

_/7. In order to brace their frame, students should be
encouraged to mount the heights of philosophy where they
have a wide and glorious prospect opened to them ; but
lest, by the cold to which they are there exposed, they have
the warm current of feeling frozen at the heart, let them

18 THE NOTION.

ever be ready to return to what they feel after all to be
the dearest of spots — the home of the affections. We do
not wish to find the youth parting with his youthful feel-
ings ; we do not like to see the young man with the face
of the old man ; we rather like to see the old man retain-
ing some of his boyish buoyancy. Our noble English
tongue has happily been retaining the old Saxon words
and idioms which furnish " sweet household words and
phrases of the hearth," while it has been adding to them
scientific phrases derived from the Greek and Latin lan-
guages. On a like principle let students, while seeking
to master the deep abstractions, the high generalizations
of science and philosophy, cherish their love of the indi-
vidual, the concrete, the natural : thus only may they be
able to keep the simplicity of childhood amid the growing
wisdom of age.

SINGULAE AND UNIVEESAL NOTIONS.

IS. All Notions are either Singular or Universal. — A
singular notion is of an object considered as a single ob-
ject, as Homer, Virgil, Julius Csesar, Cromwell, Mount
Blanc, this horse, that dog, yonder mountain. A Univer-
sal is of objects possessing a common attribute or common
attributes, the notion being such as to embrace all the
objects, real or potential, possessing the common attri-
bute or attributes, as poet, warrior, animal, mountain.

19. Our primary knowledge is of single objects. The
boy does not commence with a notion of man or human-
ity in general, but with an acquaintance with an individ-
ual person, say his father or his brother ; nor does he
start with an idea of womankind, but with a kindly know-
ledge of his nurse or his mother. It is the same with any

SINGULAR AND UNIVERSAL. 19

other idea he forms, as of sheep, or cow, or dog ; he first
notices a single animal, and then as he sees others he
fashions for himself, or understands as others speak about
it, the general notion ' animal.'

20. Abstraction and Generalization, though frequently
confounded, are not the same. In Abstraction, we sepa-
rate in thought a part, an attribute, from the whole. In
generalization, we put objects together as possessing the
same attributes. In contemplating only one object, we
can abstract : thus if it be Alexander the Great, we can
consider his military genius apart from his other quali-
ities, such as his impulsiveness. But in generalization
we must always have before us a number of objects which
we place together by the supposed possession of some com-
mon attribute : thus in the notion ' conqueror,' we com-
prise all the great military geniuses of present, past, and
future time. At the same time the two processes are
closely connected. Abstraction is always implied in gen-
eralization : we can combine the objects in the general
notion only by one or more common attributes, which we
have therefore abstracted. There may indeed be abstrac-
tion, the abstraction of a quality, when there is no gen-
eralization, no combining of objects by the quality. But
abstraction often leads on to generalization : having ob-
served a number of rocks which bear marks of having
been formed in water, we put them in the one class of
aqueous rocks.

21. Since the days of Locke, who confounded abstract and gen-
eral ideas, the distinctior between these two kinds of idea has been
very much lost sight of. There are metaphysicians, however, who
have noticed it. Thus Dugald Stewart : " The words Abstraction and
Generalization are commonly, but improperly, used as synonymous ;
and the same inaccuracy is frequently committed in speaking- of
abstract or general ideas as if the two expressions were convertible.
A person who had never seen but one. rose might yet have beer
able to consider its color apart from its other qualities ; and, tlier**

20 TEE NOTION.

fore, (to express myself in conformity to common, language) there
may be such a thing as an idea which is at once abstract and par-
ticular. After having perceived this quality as belonging to a
variety of individuals, we may consider it without reference to any
of them, and thus form the notion of redness or whiteness iu general
which may be called a general abstract idea." {Elements, Part I, Chap
IV., § 2, Hamilton's Ed.) Hamilton says : " We can rivet our atten
tion on some particular mode of a thing, as its smell, its color, its
figure, its size, etc., and abstract it from the others. This may be
called Modal Abstraction. The abstraction we have now been con
sidering is performed on individual objects, and is consequently par-
ticular [singular]. There is nothing necessarily connected with
generalization in abstraction ; generalization is indeed dependent on
abstraction, which it supposes ; but abstraction does not involve
generalization. I remark this because you will frequently find the
terms abstract and general applied to notions used as convertible."
{Metaphysics, Lect. XXXV.) But in his Logic he has allotted no
separate place to the Abstract Notion, and like all the logicians of
the school of Kant, he has no other notion than the Concept or the
General Notion. In consequence of this oversight he has not been able
to give accurate account of certain peculiarities of thought which he
has had the shrewdness to notice. As we advance in this treatise we
Bhall find that we have only to give the abstract notion its proper
place, to render a clear and scientific account of certain processes of
thought which the old Logic had overlooked, but which the Kantian
and Hamiltonian Logic had observed ; and that we can thereby
remove the hiatus between the Kantian and Aristotelic Logic ; aDd
rear out of the two a simple and consistent structure.

22. There is no subject around which there has gath-
ered a greater amount of confusion of thought and logom-
achy than the General Notion or Universal. It is oi
vast moment that we should carefully mark the steps in-
volved in its formation.

In order to Generalization two things are pre-supposed.
The first is, that objects resemble each other, that is,
possess like qualities. In every department of nature
there are common properties of form, color, weight, and
number which enable us to group objects. The second
circumstance is, that the mind has a tendency to seek out

SINGULAR AND UNIVERSAL. 2 J

and discover resemblances. It is induced to do so by
a native tendency, and it is compelled to do so by
the circumstances in which it is placed, by the analogies
which everywhere fall under our notice, and by being
obliged to put the innumerable particulars that would
oppress the memory and the understanding into conve-
nient and comprehensible groups. " To shorten its way
to knowledge and make each perception more compre-
hensible, it binds them into bundles." (Locke.) With
these preliminaries the operation of generalization is
ready to commence.

23. First Step. — "We observe a resemblance, more or less
clearly, among the objects which present themselves. This
operation begins in early life. Children soon learn to
distinguish, by their points of agreement, human beings
from other beings, and the man from the woman, and thei
child from the adult, and to appreciate practically what
constitutes a bird, or a cat, or a sheep, or a goat, or a
horse, provided always that they are in the way of com-
ing frequently in contact with such animals. All our
lives we are inclined or compelled to discover agreements
in the objects or incidents falling under our notice.
Sometimes the analogies observed are of a practical kind,
and impart to the man who notices them foresight and
sagacity ; at other times they are of an intellectual or
scientific character, and open enlarged views of the con-
nections of things in the universe ; while others are more
of a literary or poetical nature, and give rise to com-
parisons, images, similes and metaphors.

24. Second Step. — We fix more or less definitely on the
points of resemblance. The process formerly noticed is
Comparison ; that now under consideration is a special ex-
ercise of Abstraction. This abstraction is often of a very
loose description ; that is, we have not accurately defined
what the common properties are. We have observed tha

22 TEE NOTION.

there is some general resemblance among objects in
shape, color, or property, and yet if we were to catechize
ourselves, or if others were to question us, we could not
tell what it consists in. In other cases, more especially
in the classifications of natural science, the points of re-
semblance are precisely fixed and rigidly defined. A
great deal of the confusion of thought and unsatisfactory
controversy to be found in the world, originate in men
never having definitely determined what are the proper-
ties which combine objects in our common notions.
Logic promotes clearness of thought by showing that all
our concepts are formed by common attributes, and by
insisting on our knowing exactly what those attributes
are. The common attributes are called technically JVotce
or Marks by logicians.

2o» No absolute rule can be laid doAvn as to which of
the steps now referred to is the prior. In most cases
there seems to be first a perception of some sort of gen-
eral likeness, and then the fixing with more or less pre-
cision on the point or points of resemblance. But there
are cases in which the abstracting process seems to come
first. We fix on a quality which is evidently significant,
and then put all the objects possessing it into a class. It
is thus that in zoology naturalists fix on the posses-
sion of a vertebrate column as a characteristic, and in
botany the springing from one (or two) seed lobes,
and put together the objects possessing the mark fixed
on.

"4(j, Whjchever of these may come first, both are in-
volved in generalization. But there is more in the process
than either or than both of these. These are after all
only preparations for the all-important step. Were the
operation to stop at this point, there would after all be no
general notion. For observe that in the comparison we
have only got individuals, more or fewer, and in the ab

SINGULAR AND UNIVERSAL. 23

straction a quality or qualities possessed by individuals.
The consummating step has yet to be taken.

27. Third Step. — This is the formation of a class or
head embracing all objects possessing the common at-
tribute or attributes. In the first step, the comparison, we
must have observed or contemplated more or fewer objects
possessing points of likeness ; still the number was limited.
In the second step, the abstraction, we have fixed on some
quality or qualities possessed by them in common. But
in taking the final step the number of objects becomes in-
definite : we must have for convenience sake a head
under which we may place not only the objects we have
seen, but others we may yet see ; in short, all others possess-
ing the quality or aggregate of qualities. It is only when
we take this third step that we have a General Notion or
a Universal. On seeing only half a dozen buffaloes, W9
may have been struck with their points of likeness, an 1
may have been able to determine what these were in our
minds, specially their shape and mode of motion. But
feeling it to be useful, we take the farther step and con-
struct the class ' buffalo,' which must include not only
these few, but all others of the same form and habit ; not
only those now living, but all which have lived and shall
ever live ; not only so, but all conceivable, all possible buf-
faloes, the wild oxen of fiction and of the ever active
imagination.

28. The Universal is thus, in one sense, indefinite ; it
includes an indefinite number of objects, we know not
how many, all that possess the Marks. In another sense
it is definite ; it is defined by the Marks. Sometimes,
however, the Marks, though supposed to be fixed, are
very vaguely apprehended by us : thus the great mass of
mankind know what a buffalo is only by some loose idea
of its form. We fashion a class called the ' beautiful,' but
it has been found extremely difficult to determine what

24 THE NOTION.

are the common qualities possessed by objects entitled to
the epithet, and by no others ; and provisionally we can
only define it as that which raises certain pleasing
emotions within us. Most classes are ormed in the
first instance without scientific precision, for mere conve-
nience sake. Science as it advances seeks to determine
precisely the Marks of classes, and generally to decide
what generalizations are worthy of being kept, and what
are not, and may therefore be allowed to disappear. This
advance in accuracy sometimes breeds confusion from the
felt discrepancy between the scientific and popular ar-
rangements. The class heath was probably formed first
from the common heather (Calluna vulgaris), which now,
from the greater precision of the marks, is excluded from
it. The correct determination of what constitutes ' fish '
lias driven out the whale, which is still placed in it in the
common apprehension. Such general names as value
and money, have a different signification in political
economy from what they have in popular language. It
is one main advantage of the advancement of thinking
and science, that greater precision and fixedness are im-
parted to the loose, though often useful, generalizations
originally fashioned for practical purposes.

As the aim of every science is to discover Laws, and the
aim of the science of Logic is to discover the Laws of
thought, let us enquire what are the

LAWS OF THOUGHT INVOLVED IN GENERALIZATION

29» First Law. — The Universal implies Singulars. It
has been formed out of the singulars. The boy perceives
an individual crow before he forms any conception of the
class crow, and it is from the sight or contemplation of a
number of crows that he forms the general notion. The

ij AW S IN GENERALIZATION. 26

Universal notion crow thus throws ns back on the indi-
viduals entitled to be put under it. It is the same with
every other common notion. The Universal is neither
less nor more than individuals viewed as possessing cer-
tain attributes in common.

SO. Second Law. — When the Singulars are Eeal, the
Universal is also Real. We perceive a number of bushes
before us, and observing that they agree in having tne same
shape and structure and in having spines, we put them
under one head, thorn. What is now affirmed is, that
if the individual bushes exist, so also does the tribe. The
tribe has a reality in the real bushes, and in the common
attributes possessed by them. True, if the singulars are
ideal, so may also be the genus. If there be no such beings
as ghosts and. fairies, then the class cannot be said to have a
reality. The question of the reality of the class is thus to
be determined by inquiring whether the individuals, and
the attributes involved in the classification, have a rea.
existence.

31. Third Laio. — The "Universal has a reality in the
Singulars, and in the Common Properties possessed by
them, but no Independent Existence. We are not to sup-
pose that the species ' rose ' has the same kind of existence
as the individual rose : or that ' the beautiful ' has the
same sort of reality as a lovely star or a lovely woman :
or that ' the good ' exists as the good God does. The
Universal, say rose, beautiful, good, has an existence only
in the single roses, and in the objects which are beautiful
and good, and in the common qualities combining them,
If the Singulars were to cease, the Universal would also
cea.e. Give us individuals possessing a common attri-
bute, and we may form a common notion out of them.
Let the individuals have an actual existence, and the
notion will have the same, always in the objects and the
marks by which they are grouped. In this sense not

26 THE NOTION.

only what are called natural classes such as Ranuncu-
lacese, Rosacea, Mollusca, but even such generalizations
as beautiful, virtuous, clear, high, low, level, united, scat-
tered, have a reality in the common properties of the
things joined under these heads. "When we say that this
rose is beautiful, we mean that it is an object possessing
the attributes which bind in one notion the objects en-
titled to be called beautiful.

EXTENSION AND COMPEEHENSION OP GENERAL
NOTIONS.

32. According to the account now given, every General
Notion embraces two things : it embraces objects, and it
embraces attributes. Thus the notion vertebrata com-
prises objects, viz. : all animals possessing the common
property ; and it also implies an attribute, the possession
by all the animals of a vertebrate column. The former of
these is called by logicians the Extension, and the latter
the Comprehension or Intension of a notion. The no-
tion Rational Being is said to have Extension, inasmuch
as it embraces all objects possessing reason ; and Com-
prehension, inasmuch as all these possess the attribute of
reason. The Extension of a Notion is reached specially
by generalization as above described ; the Compre-
hension specially by abstraction, that is, by fixing on
marks. It is clear that some notions have greater Exten-
sion than others : thus man has greater Extension than
Frenchman ; that is, it embraces a greater number of
beings. Some Notions, again, have greater Comprehension
than others : thus Frenchman has greater Comprehension
than man, for he has all the attributes found in mankind
generally, and some peculiar to those who dwell in France.
It is evident that the greater the Extension of a term.

EXTENSION AND COMPREHENSION. 27

that is, the number of objects denoted by it, it has the
less Comprehension, that is, fewer attributes common to
the objects ; and vice versa, the more the Comprehension
of a term, that is, the number of marks possessed by all
the objects, the less its Extension, that is, the fewer are
the objects possessing the whole of them.

S3. The distinction between the Extension and Comprehension
of a Notion, though stated earlier, was introduced formally into
Logic in La Logique ou VArt de Penser, by Arnauld and Nicole
(1662 A. c). It is found in a number of logical treatises published in
the end of the 17th and beginning of the 18th century. It has been
revived by Sir W. Hamilton. It should be remarked that it applies,
only with a modification of its meaning, to Abstract Notions (§10)

HIGHEK AND LOWEE GENEEALIZATIONS.

34* The objects embraced in a Common Term are
commonly combined, not by the possession of one attri-
bute but of several, sometimes an indefinite number. In
all such cases we can form higher and higher generaliza-
tions. Take the class Dog, it is evident that it includes
an aggregate of attributes, so many indeed that we can-
not specify them all. Now we may fix on any one of
these, and put all the objects possessing it into a group :
thus we may fix on the quality of eating flesh, and form
the general notion Carnivora. Looking again at Carniv-
ora, we may fix on the possession of a backbone and form
the class Vertebrata, and in Vertebrata we may single out
the property of organization and form the notion Organ-
ized Being. The following table may illustrate the pro-
cess :

Being.

Substance.

Matter.

Organized Matt* j

Animal.

28 THE NOTION.

Vertebrata.
Mammal.

Carnivora.
Dog.
Terrier.
Snap.
35 '. It is desirable to have a nomenclature to express
the relation of the classes in this scale, and logicians have
supplied us with such. Thus suppose we fix on any class
possessing a group or aggregate of properties such as
Dog, the logicians would call this Species ; and then the
class above it, Carnivora, would be called Genus. But
as we may often have occasion to speak of the relation of
a greater number of classes we need other phrases, and
logicians use Proximum Genus to express the class next
above the species, and Subaltern Species the class next
below the species. Thus fixing on Dog as the species,
Carnivora might be the Proximum Genus, and Mammal
the Genus ; while Terrier would be the Subaltern Spe-
cies. The highest genus which we can form is the Sum-
mum Genus ; and the lowest species which Ave can form,
the Infima Species — a point which, however, we can never
absolutely fix. If we take all things, the Sum mum Genus
is Being ; if we take merely an order of things, the Sum-
mum Genus is the highest in that order ; thus Plant is
the Suminum Genus in Botany, and Discursive Thought
in Logic. It is evident that the Sumruum Genus can
have no species above it, and that the Infima Sjoecies has
only individuals and no species below it. Looking to
the Table we see that the individual has the greatest
Comprehension, it has an aggregate of attributes which
nobody could specify ; and the least Extension, for it has
only one object. On the other hand, the Summum Genus
has the greatest Extension, for it includes all objects ; and
the least Intension, for it comprises only one attribute.
Between these two extremes, the Extension rises as we

HIGHER AND LOWER GENERALIZATIONS. 29

ascend the scale, while the Comprehension diminishes ;
and as we descend, the Extension is lessened while the
Comprehension is increased. All this follows from the
nature of Generalization and the General Notion.

30. These remarks as to relative Extension and Inten-
sion presuppose that £he same objects are generalized
throughout. But mankind form classes among the in-
numerable objects which present themselves as conve-
aience induces and necessity requires ; and it is only in a
few sciences that we have such a regular subordination
as in the above table. In such general notions as plant,
planet, money, revolution, virtue, we have no relation
implied except that they may be all placed under some
one high genus such as Being. In comparing such no-
tions we can say nothing as to their relative Extension or
Comprehension.

37. A notion is said to be Subordinate to another no-
tion when it is included in the Extension of that other :
thus 'carnivorous' is Subordinate to ' mammal.' Notions
are said to be Co-ordinate when they are species imme-
diately under the same genus : thus mammals, birds,
fishes, reptiles, are co-ordinate notions under the genus
vertebrate. Notions are said (by Leibnitz) to be Commu-
nicant when they overlap each other, as e. g. ' poetical
writers' and 'writers of tales,' there being some writers of
tales who are poetical writers and others who write in prose.

TEE SINGULAR CONCRETE, THE ABSTRACT, AND
UNIVERSAL NOTION.

38. All notions we have seen are either Concrete or
Abstract. All notions wTe have farther seen are either
Singular or Universal. These divisions are made accord-
ing to different principles or marks. The former is a

30 THE NOTION.

division in respect of attributes or notce, that is, marks ;
the mental process involved is abstraction ; and it pro-
ceeds according to the comprehension of the notions
The latter is a division in respect of individuals and
classes ; the mental process involved is generalization ;
and it takes place according to the extension of the no-
tions. These are cross divisions ; let us combine them.
Our first idea might be that we ought to have four kinds
of notions. But it so happens, that all notions which are
Singular are also Concrete, that is, have an aggregate of
attributes ; and abstraction is in the Universal as well as
the Abstract Notion. We have, in consequence, a three-
fold division :

1st. The Singular Concrete, as Bucephalus, This
Animal.

2d. The Abstract, as Swiftness, Life.

3d. The Universal, as Swift, Animal.

30, The things apprehended in the first may be called
Percepts, in the second Abstracts, in the third Concepts.
It will be found that all the notions which the mind of
man can form, are either Percepts, Abstracts, or Concepts.

40. The Singular Concrete Notion, or Percept. — This is
the notion with which the mind starts, and from which
the two other kinds are derived. It is of objects as
they present themselves ; and these are known as sin-
gle, but with a number of qualities. As our observation
increases we come to know a greater number of indi-
vidual objects ; and we know each possessing a greater
number and variety of qualities, as it were more and more
in the concrete. This piece of iron : we may know it
first as a mere lump of matter, with a certain shape and
color ; then we know it as hard ; as capable of being
melted by heat ; as capable of being rusted, that is, com-
bined with oxygen ; as capable of being formed into
certain useful utensils, and as possessing special mag-

PRECEPTS, ABSTRACTS, CONCEPTS. 31

uetic powers. As we thus add one property after an*
other to objects, we are constrained at last to acknow-
ledge that we cannot know all the attributes possessed
by any one thing. Who can tell all the qualities pos-
sessed by any one metal, plant, or animal ?

41. The Abstract Notion, or the Abstract. — This is pro-
bably the second kind of notion formed by the mind in
the order of things. On a concrete object coming before
us, we can contemplate a part of it as a part, or an attri-
bute of it : thus having seen Bucephalus we can think of
his swiftness. Having an idea of an animal, we can con-
template its life. These Abstract Notions, like all other
notions, may be expressed in one word or in several.
Thus ' swiftness ' and ' life ' are abstracts designated by
one word. Quite as frequently the notion is embraced in
a number of words ; and it is of importance that we be
able to fix on the one Abstract in the midst of the multi-
plicity of phrases. When we say, " to repeat a hundred
lines on once hearing them can be done only by a few," the
words in Italics express only one abstract idea. " It is a
true saying, and worthy of all acceptation, that Jesus Christ
came into the world to save sinners ; " here " Jesus
Christ coming into the world to save sinners " is one no-
tion, and that abstract. Logic serves a most important
purpose when it leads us to detect the Abstract No-
tion wherever it is found ; to perceive exactly what sort
of existence it has ; ever to go back from the abstract
quality to the concrete objects ; and to acknowledge in the
abstract no other reality than that which is to be found
in the objects.

42. The Universal Notion or Concept. — To this Notion,
or rather thing conceived, I am inclined to restrict the
phrase 'Concept' (Begriff in German). The derivation
of the word (from con and capio) requires that it should
be applied to those notions, in which we seize on a

yz TEE NOTION.

number of things and bring them into a unity of
thought. The Concept thus understood always em-
braces an indefinite number of objects, all the objects, real
or potential, possessing the attribute or attributes which
we have fixed on as the ground of the generalization.
The Common Term, which is the Concept expressed in
language, can be applied to any one of these objects.

43. A distinction of some importance may be drawn
between two kinds of Universals — between what I venture
to call the Generalized or (simply) General Abstract,
and the Generalized or (simply) General Concrete.

4:4. The General Abstract. — In this we have only some
one quality, or with qualities involved in it, to constitute
the marks of the notion. Thus 'just' is evidently a
common term — it embraces all intelligent beings and acts
possessing the quality of ' justness.' But it denotes only
one attribute, that designated by the term. Of the same
description are such classes, as faithful, true, frank, gen-
erous, hard, soft, tough, elastic, indeed all adjectives. To
such I would apply the scholastic phrase, connotative ;
they denote an attribute and they connote objects.

4o. The General Concrete. — In this, a number of the
aggregate of qualities to be found in the singular objects,
go up into the General Notion. Thus we have in every
individual animal a variety of properties which no one
can number. Not only so, we have in the general term
' animal' a collection of attributes the whole of which no
wise naturalist will venture to specify. Of the same
character are man, mineral, vegetable, metal, horse, dog,
rose, lily ; no one should profess to be able to fix on all the
attributes which are found conjoined in every individual
of the class. It is not difficult to perceive the difference
between these two kinds of notions. Both are Universal,
for they include an indefinite number of objects. But in
the one the attributes are specified ; they are such as faith-

THE GENERAL ABSTRACT AND CONCRETE. 33

fulness, generosity, hardness. In the other they are not
denned ; they consist of an aggregate of qualities found
in all the objects.

4:0. It should be specially observed, that it is classes
of this latter description which admit of higher and ever
higher generalizations. The boy observes that certain of
the animals with which he is familiar resemble each other,
and he groups them into such convenient classes as dogs,
horses, cows. Then, as he is introduced to the elements
of science, he is taught that all these have certain
agreements, and that they may be placed in the class
quadruped, or mammal. Comparing this with other
tribes, such as birds, fishes, reptiles, he finds them all in
possession of a back-bone, and he calls them vertebrata.
In this way we may mount upward till we come to Being,
which denotes existence without qualit}7. Let it be ob-
served that all this proceeds on the circumstance, that as
individuals possess an aggregate of qualities, so also may
classes of objects. When we come to Being we have
risen above the General Concrete to the General Abstract
Notion.

47. The circumstance that there are Concrete General
Notions has cost logicians a great deal of trouble, and
often landed them in inextricable confusion. It was sup-
posed by many of them that a genus or a species was con-
stituted by a certain number of knowable attributes. The
schoolmen were ever seeking after a species which would
constitute the whole essence of its objects. And this leads
me to remark that we believe the schoolmen would not have
applied the phrase Species to any class except one with
an aggregate of properties. But in natural classes we
are not able to point out all the qualities possessed in
common by the objects. No man of science will venture
to say that he knows all the qualities which go to consti-
tute the essence of metal, or plant, or man.

34 THE NOTION

" Men define a man
The ci sature who stands frontward to the stars,
The creature who looks inward to himself,
The tool-wright, laughing creature. 'Tis enough ;
We'll say the inconsequent creature man,
For that's his specialty. What creature else
Conceives the circle and then walks the square ? "

The circumstance that every object, and most classes of
objects, possess a number, apparently an infinite number
of properties, lands the logician in perplexities and
threatens to destroy the symmetry of his system. And
were the various properties of things loose and uncon-
nected, it would be impossible to reduce the Concrete
Generals to anything like order. As an infinitely worse
consequence, it would be found impossible to arrange
natural objects iuto natural classes. For the number of
qualities in all objects material and mental being innu-
merable, we might fix with equal propriety on any one as
the ground of the arrangement, and different persons
would fix on different qualities, and there could be no
agreement among those investigating the kingdoms of
nature, or rather we should not be able to speak of the
kingdoms of nature. But the Grod who made all things
has, happily for our understandings and our practical con-
venience, instituted an order among the separate qualities
of objects, so that it is possible to arrange them into
orders which have such Marks as enable us to fit them
into our natural systems. This will be explained in a
coming section, when we consider the aids to generaliza-
tion in the works of nature.

MIXED NOTIONS.

4S» We hold that all notions can be referred to one or
other of these three heads. At the same time the three

MIXED NOTIONS 35

may be mixed up with each other in a number of ways.
Thus there is the Singular Classified, as ' that statesman,'
' that orator,' ' that general,' c that philanthropist.' These
notions are all singular, but the object is put into a class
Such singular terms are to be distinguished from Singu-
lars Proper, or proper names, such as William Pitt, Ed-
mund Burke, George Washington, William Wilberforce.
A.gain, there is the Singular Collective, or Collective
Term, which is in itself Singular, but embraces objects
put in a class : thus the ' Forty-second Regiment ; is
a Singular Notion, but it applies only to soldiers who are
classified ; ' House of Representatives ' cannot be applied
to each of the members, but each of the members is a
representative of the people. There is also the Singular
xlbstracted : as when we say Wellington was the con-
queror at Waterloo, the term " Conqueror at Waterloo "
is Singular, is one thing, but that thing viewed under an
abstracted aspect.

40. It is to be specially noticed that very many Terms
are used both as Abstracts and Concepts. The tendency
always is, when we have seized on an important quality,
especially when we have coined a word to express it, to
make it the bond of objects, which we join in a class.
Thus, having noticed that certain persons possess a qual-
ity which we call ' learning,' we form a class called
' learned,' to embrace all who possess the attribute. Quite
as frequently we constitute a class by the possession of a
number of attributes, known or unknown, and we join
ah these in one by giving them a name. Thus, without
settling what living beings possess in common, we desig-
nate what they agree in by the abstract phrase ' life.' It
is thus that we have ' generous ' to connote the class, and
' generosity ' to denote the quality. In these cases the
abstracts and concepts are designated by somewhat dif-
ferent though related words. But in raanv cases the

36 THE NOTION.

same term may denote both the abstract and general
notions. Thus ' virtue ' is primarily an abstract term ;
we have formed it by abstracting a certain quality of in-
telligent and moral beings. But then the quality has
various forms as it appears in different individuals, and
at different times, and we classify the diversities and
speak of different virtues, such as justice, and temperance,
and benevolence, thus making the phrase general. Fine
Arts is an abstract term, but it may become a common
term with painting, architecture, and sculpture, as sub-
classes. Pain and pleasure are in themselves Abstracts,
but may embrace under them various kinds of sensations,
as corporeal and mental enjoyment, and suffering of
body, and anguish of spirit. In many cases it is of
great importance to determine as to a phrase which may
be both abstract and general, in which of the senses it is
employed in a given passage or discussion. Such terms
as ' substance,' ' quality,' and ' mode,' may be one or
other ; and in every speculative investigation we should
settle in which of the senses we are employing it. Sub-
stance is primarily an Abstract, standing for that which
abideth in objects material or mental. It stands for a
Concept when we speak of two substances, mind and body.
50. Students of logic should notice that there is one
class of Abstract Notions which always tend to become
general. Verbs are primarily abstracts expressing ob-
jects, not in the concrete, but as being, doing, and suf-
fering. But when they are used in propositions they may
become general. When we say that " man speaks," the
sentence is primarily attributive ; it means that man has
the power of speaking. But the term ' speaks ' may also
be interpreted as universal ; it may mean that man is in
the class of speaking creatures. We shall see, as we ad-
7ance, that when a verb is used as a middle term in
reasoning, it is alwavs to be understood as a universal.

MIXED NOTION'S. 37

Thus, when we argue that since men speak, and gorillas
do not speak, therefore gorillas are not men, we must, in
order to the legitimacy of the reasoning, understand
c speak ' as denoting all speaking creatures.

51. We form notions of various complexity by accre-
tion and agglomeration. These are called Mixed Modes
by Locke. Thus we speak of ' a procession,' implying
persons, and a train, and time, and succession. We talk
of ' a triumph ' implying a battle and a victory, and a
display. We join abstracts to abstracts ; we speak and
write of ' the triumph of excellence,' of ' the defeat of wick-
edness,' of ' the reward of righteousness ' and ' the pun-
ishment of evil,' of ' the beauty of natural scenery,' of ' the
hopefulness of spring,' of ' the gloominess of winter,' of
'the madness of passion,' ' the terrors of despair.' We join
general with abstract notions. Thus we have the abstract
idea ' wickedness,' and we have the general notions
' human,' and ' demoniac,' and we talk of ' human wick-
edness ' and ' demoniac wickedness.' We have expe-
perienced ' joy ' and ' sorrow,' and we know what ' eleva-
tion ' is and what ' depression ' is, and we speak of ' the
elevation of joy ' and 'the depression of sorrow.'

52. But whatever be the genesis of our notions, in the
end they come to be either Percepts, or Abstracts, or
Concepts. To avoid confusion of thought and misappli-
cation of terms, it is of moment that we should be able
to say as to every given notion, under which of these
heads we are to place it. When we say " Shakespeare's
Plays are the best in the English language," the one no-
tion " Shakespeare's Plays " is Singular Concrete (Collec-
tive), and the other "the best in the English language,"
an Abstract. When we say " Logic is the science of the
Laws of Discursive Thought," the two terms "Logic"
and " the science of the Laws of Discursive Thought," are
both Abstracts. When we say "the hearts of sufferers

38 TEE NOTION.

can be won only by love," the two notions " hearts oi
sufferers " and " can be won only by love" are both
Universal.

PEIVATIYE NOTIONS.

53. We have seen that in Universals, objects are bound
into one by the possession of Marks. But we may also
unite objects by the absence of Marks. Thus we say that
all quadrupeds are vertebrates ; and we say of mollusca,
that they are invertebrate. The former of these notions is
called Positive, and the latter Privative. Logicians have
remarked that a Positive and Privative Term divide
among them the universe of being, that is, all objects
must either be vertebrate or invertebrate. But when in-
terpreted properly, this means simply that each object
must either possess or not possess a given attribute. It
does not imply that the non-possession of that attribute
is a proper mark by which to join objects. There would
be no propriety in putting all objects which do not pos-
sess a back-bone, say thought, the soul, probity, dress,
planet, into the class invertebrata — which should be ap-
plied only to those portions of the genus animal which
we wish to distinguish from vertebrates. It should be
remarked that some seemingly privative phrases really
imply a positive Mark : thus the phrase ' immortal ' im-
plies not merely that the object does not die, but that it
lives forever ; and the term ' infinite ' may be held as
meaning more than merely the absence of bounds, it in-
volves the occupation of all space and all time.

LOGICAL DIVISION. 39

CONTKAEY AND CONTRADICTORY NOTIONS.

54. Positive and Privative Terms are said to be Con-
tradictory ; that is, they are such that we cannot concvjive
them as applied to the same object at the same time, such
as existent and non-existent, organic and inorganic.
Contrary Terms, called by some Id compatible, are such
as might be conceivably applied to the same object, but
cannot, in fact, be so applied, such as good and bad, light
and darkness, cold and hot.

KELATIVE NOTIONS.

55. These are derived, not from a quality in one ob-
ject, but from the relation of one thing to another. When
we speak of the objects under this relation, they are said
to be Correlative. Thus we have sovereign and subject,
parents and children, husband and wife, master and ser-
vant. The one of these implies the other. The;y are
connected by the ground of the relation {fundamentum
relationis). The phrases themselves are Universals (Gen-
eral Abstracts) ; the relation, say that of sovereignty and
subjection, is abstract ; for relatio non est per se reale, sed
per suum fundamentum.

LOGICAL DIVISION.

50. In generification, that is, in the formation of
common notions, we rise from singulars to classes, and
from lower classes to higher. But after the classes have
been fashioned by ourselves or others, we may reverse
the process and descend from higher classes to lower

tU THE NOTION.

This operation is called Logical Division, which may be
defined, as the process by which we spread out a genus
into its co-ordinate species. It is to be distinguished
from Partition, which consists in separating an individual
object into its parts ; as when we sunder a plant into stems,
roots, and branches. Logical Division takes up a common
notion, such as plant, and spreads it out into acotyledons,
monocotyledons, and dicotyledons. To every such sub-
class the name of the higher class may be applied ;
thus we speak of plants, monocotyledonous, and dicotyle-
donous, and in the same science of Geum urbanum and
Gfeum rivale. It is evident that Division proceeds speci-
ally according to the Extension of a notion ; and it in-
volves Comprehension only so far as Extension implies
Comprehension. The rules are :

o7. First Rule. — We must proceed according to a
Mark or Marks added, and according to the same Mart
or Marks throughout. We have seen that in the ascend-
ing process of generification, Ave leave out marks ; thus
in ascending from dog to camivora, we leave out every
property of the dog except that of eating flesh. In the
descending process of division we add marks. Thus in
dividing plants, we add the property of growth by seed-
lobes, and put those growing from one seed-lobe under
one head, and those growing from two, under another.
Discursive Thought is divided into the Notion, Judgment,
and Eeasoning, according as we exercise thought in ap-
prehending, in comparing the things apprehended di-
rectly, or comparing them by means of a middle term.
As in our divisions we proceed on a principle, so that
principle should always be clearly understood and very
commonly be enunciated. What should be the Marks
fixed on must be determined by the nature of the objects,
and the scientific or practical end we have in view at the
time. Here Logic can be of little use to us ; but then it

LOGICAL DIVISION. 41

serves an important purpose by insisting that there must
be Marks. It does more : it requires that we proceed
throughout on the same Marks. In dividing mankind,
we may proceed on various principles : as on the princi-
ple of race, into Caucasian, Malay, Mongols, Negro ; on
the principle of enlightenment, into savages, uncivilized
and civilized ; of religion, into Christians, Mahometans,
Pagans. But it would be wrong to flit from one of these
to another, and divide mankind into Christians, Mahom-
etans, and savages ; or into Europeans, Americans, Pa-
gans and Mahometans. The logician would err were he
to divide discursive thought into the term, the proposition,
and argument ; for in the first he would be proceeding on
the principle of language ; in the second, on that of
thought. Arrangements violating this rule are called
' cross-divisions.' " It is a useful practical rule, whenever
you find a discussion of any kind very perplexing and
seemingly confused, to examine whether some cross-
division has not crept in." (Whately).

58. Second Rule. — The specie^ must make up the
genus, or, as it is otherwise expressed, the dividing mem-
bers (membra dividentia) must make up the whole. This
rule would be violated were we to divide vertebrate ani-
mals into quadrupeds, birds, fishes, and reptiles ; for there
are animals — man, for instance — included in vertebrata,
but not in the division. We shall see, in treating of Judg-
ments, that Immediate Inferences can be drawn on the
principle of division ; but this can be done only on the
assurance that the division is complete. There is often a
fallacy lurking in imperfect divisions. Thus the Eleatics
argued that there could not be such a thing as motion,
for that the motion must either be in the place where it
is, or in a place where it is not, neither of which is pos-
sible ; whereas there is a third supposition that it may
have been from the place where it was, to the place wherf

42 THE NOTION.

it now is. Another sophism proceeds on the same mis-
take. It is argued that academical honors are useless,
inasmuch as they are not needed by those who have a
taste for study, and that they have no effect on the idle,
and such as are indifferent to mental improvement. Here
it is tacitly assumed that all students must belong either
to the diligent class or the idle class ; whereas there
may be a large intermediate class, not altogether hope
lessly idle on the one hand, nor with confirmed habits oi
application on the other, and these may be influenced by
academical distinctions.

5i). Third Rule. — The dividing members must exclude
one another. This rule would be violated were we to
divide lines into straight, curved, circular, and elliptical, or
notions into singular, concrete, abstract, and universal —
for concrete notions may be universal. He who neglects
to attend to the rule, will offend every person of correct
judgment, and confuse the minds of those who do not
see the fault of the division. The preacher violated it
when he proposed proving a particular doctrine from
reason, and from revelation, and the testimony of Paul ;
his division should have been from reason and from rev-
elation, and under the latter, he might have said, espe-
cially from the testimony of St. Paul. The barrister trans-
gressed it when he talked of establishing his point by
moral law, by the law of the land, by Act of Parliament
and precedent ; for Acts of Parliament and precedents
are included under the law of the land. The Chinese are
said to furnish a ludicrous example of this error in their
division of the race into first Chinese, then men, and then
women. The error arises commonly from introducing
subordinate species and not adhering to co-ordinate
species. It will often happen that a division contraven-
ing any one of these rules will also violate all the others.
Thus a librarian who would arrange his volumes as books

LOGICAL DIVISION. 43

of prose, poetry, morals and religion, as proceeding on no
principle, would never be able to make up tlie whole, and
would find his divisions running into inextricable con
fusion.

GO,- Fourth Bide. — There should be a due subordina-
tion of classes — Divisio non faciat solium. The contents
of elaborate treatises are commonly distributed into
Boohs, Chapters, and Sections. We should never be able
to arrange the vegetable kingdom if we proceeded to dis-
tribute plants as they cast up into roses, oaks, lilies,
lichens ; nor the animal kingdom if we began to divide
them into horses, dogs, leopards and lions. Naturalists
fix on a regularly ascending or descending series of
divisions and sub-divisions ; thus Agassiz arranges the
animal kingdom into Branches or Types, Classes, Orders,
Families, Genera, Species.

01. These rules are of value in the sciences, especially
those which are concerned with classification, such as
Botany and Zoology. True, they do not tell us how we
are to arrange the organic world, for this must be done
by a careful observation and induction of the facts ; but
they lay down certain stringent laws of thought which
must be attended to in the classifications formed. They
may also be of great service in the construction of essays,
papers, sermons, and discourses of every kind. It is not
necessary in all cases to announce the division. Some
people have argued that such an announcement must
make the composition stiff and formal, and is apt to
damp the curiosity of the reader or hearer who ought to
be kept awake by a desire to know what is coming. On
the other hand, it is argued that when our end is not
merely to please or tickle the fancy, but to impart in-
struction, it is of importance to announce the divisions
an i subdivisions, which will be found greatly to aid the
memory and comprehension. The question of whether

44 THE NOTION.

we should or should not lay down a formal division is tc
be decided by the end we have in view, whether it is sim-
ply to amuse or interest for the time, or to convey impor-
tant truth which we expect to be recalled and pondered.

ANALYSIS AMD SYNTHESIS.

62. Analysis (from dvaXvo), I unloose), is that process
in which we separate in thought, a concrete object or a
complex abstract notion into its parts or qualities. Analy-
sis is always performed by means of Abstraction, but the
two differ. In Abstraction we mentally separate any
quality ; in Analysis we spread out the qualities which
make up the whole. It is seldom we can unfold all the
properties of a concrete object, and not always that we can
fix on all those of a complicated notion. There are times,
however, when we can bring' out to view the attributes
involved in an abstract which we have fashioned. Thus
we analyze discursive thought into thought as directed to
objects whatever they be, and thought as directed to special
classes of objects : and the former we analyze into Simple
Apprehension, Judgment, and Reasoning. We thus see
that Analysis is not the same as Division. In Division
we take a class and distribute it into sub-classes ; in
Analysis we take a concrete object, or more frequently a
comprehensive abstract, and spread out its qualities. It
may happen that where an abstract term is also a com-
mon term, division and analysis coincide. Thus, as
' Discursive Thought,' and as ' Notions,' ' Judgments,'
and ' Reasoning,' are at one and the same time Abstracts
and Concepts, it is of little moment whether we call the
distribution of them a division or an analysis — whether
ive say that we divide or that we analyze the notion into
percepts, abstracts, and concepts.

ANALYSIS AND SYNTHESIS. 45

03. Having found the parts by Analysis, we may join
the parts to show that they niake up the whole by a pro-
cess which is called Synthesis (from ovvrldrjiu, I place
together). When we can prove that the parts by their
junction constitute the whole, the synthesis is a confirma-
ation of the accuracy of the previous analysis. It is clear
that in the study of a new or hitherto unexplored subject,
we must begin with analysis. But after we have made a
successful analysis, we may then advantageously employ
synthesis in corroborating the previous analysis, and the
synthetic method in expounding the science which treats
of the objects. Thus in chemistry, having shown what
the elements of bodies are, we may then take up these
elements one by one, and show how we can explain by
them the composition of all bodies. Thus in Logic, hav-
ing ascertained by analysis that thinking consists in Simple
Apprehension, Judgment, and Reasoning, we then con-
sider each of these, and show how they together consti-
tute the discursive operations of the mind. Whately has
imparted a great interest to his Elements of Logic by in-
troducing us to the subject by an analysis of the reason-
ing process, and then proceeding to develop the science
in the synthetic method.

64. Analysis and Synthesis used to occupy a much more important
place in Logical treatises than they now do. They were represented
as the main instruments in the investigation of nature. It was, in
fact, very much by mental analysis and synthesis that the philoso-
phers of ancient Greece and Rome and the medieval logicians and
theologians proceeded in their physical speculations. The instru-
ment is now seen to be Induction, and Deduction joined with it in
certain walks of inquiry. But it can be shown that analysis is an
important element in Induction Phenomena falling under the
senses or our observing faculties are always concrete or complex
and we must so far separate the things which are joined together
before we caii reduce them to a law, or even observe them. Hence
Bacon says, we must begin Induction by the "necessary rejections
or exclusions ; " and Whewell says by " the Decomposition of Facts '

*6 THE NOTION.

It can be shown also that Synthesis may act an important part in
Deduction. But these questions carry us into Inductive Logic.

LOGICAL DEFINITION.

(to. By definition (opLOfiog) is meant in the most gen-
eral sense " a description which manifests the nature of
the thing defined." Logical Definition is to be distin-
guished from mere verbal explanation : as when a child
does not understand what is meant by perspicuous, and
you say it means clear ; or when you say that salubrious
means tending to produce health. It is the province of a
dictionary to give the explanation of words. But in de-
finition we must manifest the nature of the thing defined.

6'6» We can logically define only those notions in
which there has been a process of discursive thought ;
that is, abstract or general notions. We cannot, pro-
perly speaking, define a singular notion, for we cannot
manifest its nature by bringing to view all its attributes,
the attributes being innumerable. All we can do is to
give some marks of the individual, technically called a
description, sufficient to detect the object and distinguish
it from others. We have such a description in the " Hue
and Cry" sent after a criminal, " five feet eight, light
hair, blue eyes, a scar on the right cheek." We have
such descriptions, sufficient to enable us to recognize them,
of towns, rivers and mountains, in our traveller's guide-
books.

07. It has been remarked by many philosophers tha!
there are some notions which cannot be defined. It wil]
be found that these are abstracts : they are qualities which
cannot be resolved into anything simpler, such as sweet-
ness, sourness, pleasure, pain. We can give no idea of
them to one who does not know already what they are :

JUOGIGAL DEFINITION. 47

all that we can do in explaining our meaning is to appeal
to our experience of them. But while we cannot define
them so as to manifest the nature of the thing, we can
make a great many affirmations and denials regarding
them. Thus we can say that such a sour taste is pro-
duced by vinegar ; that a purple color proceeds from the
union of yellow and blue rays. Much information can
often be given by specifying the objects in which the
quality is to be found : thus we can say that pleasure
and pain are affections of beings endowed with sensation.
We car always make an indefinite number of negative
statements regarding these simple ideas, to face misap
prehensions or misrepresentations, as that pleasure does
not consist in the mere possession of wealth, or the means
of sensual gratification. But there are cases in which we
can give a definition of an Abstract Notion ; being com-
plex we can analyze it into its constituents. Thus we can
define Discursive Thought as an exercise of mindinwmich
we proceed from something given or granted, to some-
thing else founded on it.

68. It is disputed among metaphysicians whether such ideas as
those of Extension, Power, Moral Good, are to be put under the
same head as those of pleasure and pain ; that is, under the head of
original ideas, revealed to us by the senses or primitive perceptions.
When asked to define virtue, or moral good, we can only say virtue
is virtue, good is good. But then we can make an indefinite num-
ber of negative propositions regarding them : thus we say that vir-
tue or good does not consist in mere happiness ; and that the rela-
tion of cause and effect does not consist in invariable antecedence
and consequence.

00> We should always be able to define a General
Notion. We have seen that objects are brought together
mto a common notion by means of the possession of a
common attribute. Now we can bring out this attribute
in definition, and in doing so, we indicate the bounds of
the common notion, and thus what it is as distinguished

48 THE NOTION.

from other things. It is evident that definition proceeds
specially according to the Comprehension of a notion.

70. First Rule. — We must bring out a distinguishing
attribute of the notion defined. When this is done there
is always a true definition. When this is not done there
is no proper definition. When we say man is a rational
being, we have given a sufficient definition ; for rationality
is a characteristic quality not found in inanimate nature,
or in the brute creatures. When we say Logic is the
science of the discursive laws of thought, we have brought
out a distinctive mark, distinguishing the science from all
sciences with which it might be confounded, such as
Ethics and MetajDhysics. As to what is a distinguishing
property of a notion, this must be determined not by
Logic, but the sciences which deal with the objects. But
Logic insists on our fixing on such a property. Herein is
the person trained to logical habits distinguished from
others. How often do we find the uneducated man
struggling to give expression to what he knows in a loose
way, and failing. You ask him what Logic is, and he
answers a branch taught in our colleges ; what Arithme-
tic, and he says a branch taught in our schools ; what
Language, and he says a means of expression — as if there
were not other branches taught in colleges and schools,
and as if there were not other ways of expressing thought.
The person disciplined in Logic knows that in giving a
definition he must fix on a distinguishing attribute, and
he seeks for it and is not satisfied till he finds it.

7 1, And here it is of importance to remark how it is
that what we have called the General Concrete Notion is
defined. It is evident that we may not be able to bring
out all the attributes common to the notion, for we may
not know what they are. It is enough in such cases to
specify one characteristic which may be a sign of the others.
We may not be able to mention all the attributes found

LOGICAL DEFINITION. 49

in mammals ; but it is a good definition when we say
that " they are animals suckling their young," for thi,3
brings out to view a quality common to the whole class,
and a quality which is the sign of others.

72* Second Bide. — The definition must be adequate to
the notion, neither wider nor narrower. If we defined
grammar the art of speaking a language with propriety,
the definition would be too narrow, for grammar treats of
writing a language as well as speaking. If we defined it
as the science of language, it would be too wide, for
grammar does not discuss all the scientific questions con-
nected with language. If we defined Logic as the science
of our intellectual nature, it would be too wide ; if as the
science of reasoning, it would be too narrow.

73. N.B. — The best test of this property of a good
definition is, that the subject can take the place of the
predicate, and the predicate of the subject, without any
change. Thus defining a straight line as the shortest
distance between two points, we can say the shortest dis-
tance between two points is a straight line. We can say
truly ' all poets are men of genius,' but this is no definition,
for we cannot say all men of genius are poets.

74. Third Rule. — It is expedient to give the genus as
well as a characteristic quality. "When we do this we are
said to define by genua and differentia — that is, characteris-
tic quality. This cannot always be done, as there may be
notions which it is difficult to put into a genus in any way
fitted to clear up their nature. But when it is possible Ave
should give both the genus and the differentia, as by the one
we show wherein the notion agrees with others to which
it is most clearly allied, and by the other we show where-
in it differs from the notions with which it might be coil-
founded. In giving a genus it is expedient to give the
proximum genus. Thus we may define Ethics as "the
mental science unfolding the laws of man's moral nature ; "

50 THE NOTION.

in which " mental science " is the proximum genus, put-
ting ethics under the same head, as psychology, logic, and
metaphysics ; and " unfolding the laws of man's moral
nature" is the differentia, separating it from these de-
partments of knowledge.

75. Some important practical rules may be laid down
as to the language in which the definition should be
given. The general rule is, that the definition should
always be clearer than the thing defined. More partic-
ularly (a) the definition must not be expressed in ambig-
uous or figurative language, as Aristotle's definition of
Motion, " the act of being in potency, so far as being in
potency;" as " matter and mind are sides of one thing."
(b) It must not contain covertly the name of the thing
defined, as when we say abstraction is a process in which
we abstract or draw off, or that life is the sum of the
vital functions, (c) When the class has positive attri-
butes, the definition should not be put in a negative form.
Those who say that infinite is a positive quality, should
give a better definition of it than when it is said, it is that
which has no bounds. Naturalists no longer give inver-
tebrata as the name of a scientific class to be placed
alongside of vertebrata.

AIDS TO ABSTRACTION AND GENERALIZATION.

70. In the employment of abstract and general no
tions, the mind must always have some sign before it.
This sign may be

I -A MENTAL IMAGE OR PHANTASM.

77. We have occasion, let us suppose, to speak of the
rose tribe of plants ; as we do so, we may notice that

TEE MENTAL IMAGE OR PHANTASM. 51

are have a loose idea, in the sense of image, of a plant
which may have as many as possible of the characteristics
of the rose without those of other plants, such as the
tulip or the lily. Or we have occasion to think of plant
generally, and we fashion a figure, very possibly with
axis, branches, and leaves (though there are plants with-
out these), which may stand for all plants. The image
may also aid us in our abstractions. When we think of
great size, we picture a huge bulk ; when of tallness, we
picture great length ; when of transparency, ice or glass
with light shining through ; when of wealth, a heap of
money ; when of dignity, a man of imposing form and
address ; when of pomp, a dazzling show ; when of mar-
tyrdom, a person suffering for the truth ; when of mirth,
a man laughing ; when of sorrow, a person crying. It is
by help of such images, that children, savages, rustics, in
fact the great body of ordinary men and women, are able to
form abstracts and concepts. When such, phantasms can
be formed, they always render our thinking more lively, and
therefore more interesting and better fitted to call forth
emotion. Our pictorial, who are always our most popular
writers, help our understandings by furnishing concrete
pictures of abstract notions, and thus enable us to carry
on our thinking more easily and pleasantly — often, it has
to be added, more obscurely and confusedly.

78. These ideas or phantasms are not to be under-
stood as constituting the abstract or general notion. It is
usually said of our common notions that they are inade-
quate. But this is not true of our concepts as exercises ol
thought ; they may be regarded as adequate, for they are
of things joined by common attributes, the concept em-
bracing all objects possessing the common attributes,
But it holds good of the ideas considered as mental pic-
tures : we can form no correct image of gravity, or hard-
ness, or weight, or indeed of any quality. Nor can we

52 THE NOTION.

fashion a full phantasm of a concept, for the objects are
joined by a quality or qualities abstracted, and the ob-
jects are innumerable. We cannot form a correct picture
of man in the general, for if we make him white we do
not include the Negro or Red Indian ; if we make him
black we leave out the Caucasian race ; and if we make
him neither black, nor white, nor red, we leave out the
whole of these three tribes of mankind. In all cases the
phantasm is to be regarded as a mere sign or representa-
tion of the result of elaborative thought. It is not of
the mere phantasm that we make affirmations or denials,
but of the things for which it stands as apprehended by
the mind. In certain cases the mental image when used
as a sign, is quite sufficient to enable us to think accu-
rately, that is, when it stands for ideas not far removed
from the singular and the concrete. But when the no-
tion becomes more and more abstract or general, more
especially when it is the idea of spiritual objects or qual-
ities, or when it is a composite one, the formation of a
mental picture becomes more and more difficult, and at
last is seen to be altogether impossible. Who can form
an image, for instance, of law, of truth, of right, of gov-
ernment, of learning, of civilization ? When we have
occasion to think of such things, we must call to our aid
external Signs, and especially Language.

70. Locke confused himself on this subject by not distinguishing
between the image and the notion, both of which were embraced in
bis favorite phrase ' idea,' which, however, he commonly used in its
literal sense as image. In forming our idea of man or humanity,
persons leave out that which is peculiar to the individuals, they
leave out of the complex they had of Peter and James, Mary and
Jane, " that which is peculiar to each, and retain only what is
common to them all." (Essay, Booh III, iii, 7.). Bishop Berkeley
saw the absurdity o/ this view, and not seeing the way out of it,
lauded himself in nominalism, which thence descended to Hume.
Stewart, and Whately. " The mind having observed that Peter
James, and John resemble each other in certain common agree-

THE MENTAL IMAGE OR PHANTASM. 52

merits of shape and other qualities, leaves out of the complex or
compounded idea of Peter, James, and any other particular man that
which is peculiar to each, retaining only what is common to all,
and so makes an abstract, wherein all the particulars equally
partake, abstracting from and cutting off all those circumstances
and differences which might determine it to any particular ex-
istence. And after this manner, it is said, we come by the ab-
stract idea of man, or, if you will, of humanity or human nature ;
wherein, it is true, there is included color, because there is no
man but has some color ; but then it can be neither white nor
black, nor any other particular color wherein all men partake.
So likewise there is included stature ; but then it is neither
tall stature nor low stature, but something abstracted from all
these." Such considerations show that we cannot form an idea of
man in general in the sense of a mental picture. But they do
not prove that we cannot form an intellectual conception of objects
joined by common properties, the conception including all the ob-
jects possessing the properties. We are thus thrown back on the
distinction drawn by Aristotle between the phantasm (ipavTcla/ia)
and notion (vor/fia). The difference between them and yet their
relation are accurately expressed by him when he says that the
notion is not the same with the phantasm, and yet is never without
the phantasm. Norj/iara tlvI dwioei tov /xt) fyavTuoficiTa elvai, tj ovde
TavTa ipavrda/iara, akV nvn avev Qavrao/iaTup. (He Anim, iii, 7.)

IL— LANGUAGE.

SO, Language may be defined as the expression of our
mental actions and affections by means of words spoken
or written. The primary benefit derived from it arises
from its being a means of communicating with our fellow-
men, and thus enabling us to convey to them our varied
thoughts and feelings, wants and wishes, and to have theirs
imparted to us. This is the first and final end of lan-
guage, subordinating every other, and determining in a
great measure the changes which it has undergone
throughout its whole history. But this is not the aspect
under which we are required to contemplate it in this

54 THE NOTION.

work, where we view it simply as the instrument of dis-
cursive thought.

81. First. — Language is advantageous, inasmuch as it
is a sign and register of the abstractions and generaliza-
tions which mankind are ever forming. We have seen
that all men are led by a native intellectual tendency, and
by the circumstances in which they are placed, to separate
and to combine the objects they meet with ; to distin-
guish between a thing and its qualities ; to observe the
relations of things, and then put the things which are re-
lated into a class. Many of the distinctions thus drawn,
and groupings fashioned, are valuable only for the mo-
ment ; but others are of permanent importance, and
should be carefully preserved ; and this can be done only
by a name, by what is technically called Denomination.
A simple illustration or two will enable us to understand
this. A merchant, say a druggist, has in his warerooms
a large number of miscellaneous articles lying promis-
cuously on the floor ; as long as they are in this state he
feels that he has not absolute command of them ; and
so he fixes on some ground of distribution and arranges
them in shelves or drawers on which he puts some kind
of mark or label. Having done so, he and his assistants
find that they can at once lay their hands on the article
they require. Or, a naturalist enters a country the flora
of which has hitherto been unexplored. As he views
the profusion before him his first act is to observe, and
his second is to classify ; but unless he take a third step,
he is made to feel that all his researches are likely to be
valueless, if not to himself, at least to others ; he has to
give a name to the plants which he has put into a class«
This name finds its way into botanical books, and becomes
the index of the genus or species to students of every
country and of all coming ages. These illustrations show
us the benefit of names in the business of life and in

LANGUAGE. 55

natural science. But they serve a like, and, in most
cases, a vastly more important purpose in regard to all
the multiplied operations of the mind; preserving (hem,
when they might otherwise be lost, for our own use and
that of others ; it may be handing them down to all pos-
terity, or spreading them over all civilized nations. In
contemplating the objects which present themselves in the
world without, and the still more wondrous world withic
under its divers moods and impulses, mankind fashion an
infinite variety of thoughts, which can be preserved and
profitably employed only by the instrumentality of lan-
guage.

82. Second. — Language puts us in possession of the
abstractions and generalizations which have been made
by other men. In saying so we do not refer to the cir-
cumstance that it is not so much by personal observa •
tion as by intercourse with others, that it is by the
instruction imparted by teachers, companions, and our
fellow-men generally, and by books ancient and modern,
that we acquire by far the larger portion of the know-
ledge possessed by us ; for this proceeds from the pri-
mary use of language as a means of communication. A
reference is made under this head, not to the information
thus conveyed, but to results of discursive thought em-
bodied in words and phrases. It should be observed
indeed, that the abstractions and generalizations must
first have been formed before they could be expressed in
language. But the name being given it becomes at once
and forever a sign of the idea. On the word being
brought under the attention of the young, they ask what
is meant by it, and are thus put in possession of the
thought which it may have cost so much pains to ela-
borate. An intelligent youth hears the phrases ' conser-
vation of physical force ' and ' correlation of physical
forces ' employed, and on inquiring into their signification,

56 THE NOTION.

he is taught that the amount of force, potential and actual,
in the universe, is always one and the same, and cannot
be diminished or increased by any human means, and
that all the physical agencies, mechanical, chemical, elec-
tric, and vital, are modifications of that one force. Or he
hears the word ' aesthetics ' used, and is thus introduced
to a science which seeks to investigate the laws, subjec-
tive and objective, of the beautiful and sublime. What is
thus seen so clearly in science is also manifested in moral
and practical matters. Some one saw very keenly that
there is a vast amount of pretension in the world, and
that there are persons who recommend as great and good
what is not really so, and gave expression to his percep-
tion in the word ' humbug ; ' and the phrase goes down
to posterity because of its felt truthfulness. Some terms
spring up by a sort of accident and are retained because
found to be useful ; there is, for example, the word
' cabal,' made up of the names of persons who were sup-
posed to have formed a party combination, and the
phrase has kept its place ever since^ because an ever
recurring feature of human nature. The British sol-
diers who had been in the wars of Gustavus Adolphus,
brought back with them certain terms such as ' plunder,'
'life-guard,' and ' furlough,' which have ever since been
retained in our tongue. Thomas Carlyle, with that vig-
orous grasp of intellect and atrabilious temperament by
which he is distinguished, in order to show his contempt
for those who are ever fawning on the great, gave expres-
sion to what he observed and felt in the word ' flunkey-
ism,' a phrase likely to go down to all future generations
To an American custom we owe the phrase 'stump-
orator,' so descriptive of a style of speaking which cannot
otherwise be so briefly characterized.

83. The occupations, the tastes, the habits, indeed the
whole character of a people, are apt to embody themselves

LANGUAGE. 57

in their language. It is said that in Arabic there are 500
names for a lion, 201) for a serpent, 80 for honey, 400 for
sorrow, and 1000 for a sword ; and it seems certain that
there are 5744 relating to the camel. The French have
given us the words ' finesse,' ' prestige,' ' ennui,' ' foible,'
' chagrin,' and many others descriptive of their character
and experience ; and the English have given them in
return ' jockey,' ' club,' ' sport,' and the phrase ' comfort-
able,' so expressive of genuine English feeling. The
Scotch have designated one feature of their national
character by the word ' canny ; ' and the Irish have ex-
pressed one of their national traits by the phrase ' blar-
ney.' A number of words which have of late come in
upon us with such weight and gravity, such as standpoint
God-consciousness, claim Germany as their fatherland.

84 . In holding intercourse with each other, persons fashion or
modify phrases in accordance with the native tendency of thought,
and in order to promote mutual convenience. This remark holds
good, not only of individual words, but of the structure of language
generally. Hence we have in so many tongues prefixes, suffixes,
and reduplications ; the gender, number, and case of nouns, and the
moods and tenses of verbs. These modifications, say declensions
and conjugations, invented or adopted in the first instance for con-
venience sake, become in the next generation the means of intro-
ducing the young to the distinctions of sex, and quantity, and time ,
to the more important relations of things one to another; and the
contingency, the certainty, and necessity of events. Language thus
becomes an important means of training the youthful mind to an
acquaintance with the habitual and useful modes of human thought
and contemplation.

85. It is not possible to express the higher forms of thought in
the language of a people low in the scale of intelligence. In the
Iroquois there is no word for goodness in the abstract, they have only
a word for good man. In the Mohican there is no verb for ' I love,'
the forms involve the subject as well as the action, ' I love him,' ' I
love you.' In those islands which the Loudon Missionary Society
has done so much to elevate, there was one word for the tail of. a
dog, another for the tail of a bird, and a third for the tail of a sheep,
but no word for tail in general. In Chinese there are terms for

58 THE NOTIOJH

elder and younger brother, but none for brother. Christian mis-
sionaries found great difficulty in fixing on an unexceptionable word
in that tongue for God, and disputed among themselves as to which
of the available phrases was the least objectionable. The fixed
forms of that language and its want of inflections have, I doubt not,
acted with other causes in keeping that people in a stationary con-
dition for thousands of years. Notwithstanding the strong attach-
ment of the people to the Gaelic, the Welsh, and the Irish, it is de
sirable that these tongues should give way as speedily as possible
in favor of the English, with its advanced intelligence, its refined
sentiment, and noble literature. The circumstance that one tongue,
and this enriched by the thoughts of the highest science, philoso-
phy, and theology, is used in all the schools of the United States,
has helped more than any other agency to produce a unity of belief .
character, and aims, which keeps the people together in spite of the
many disturbing causes which might make them fly asunder.

86. The line of thought we are pursuing is fitted to show the
advantage of being acquainted with more than one tongue. Every
educated people has fashioned thoughts for itself and embodied them
in peculiar phrases ; hence the difficulty of translating the words of
one tongue into precisely synonymous phrases in another. By learn-
ing the language of a race, we come into possession of their mode of
thought, which is to us fresh and original. Ennius used to say that
he had three hearts (the heart being reckoned the seat of intel-
ligence) because he knew three languages, the Greek, Latin, and
Oscan. The Emperor Charles V. declared that a person is as many
times a man as he knows a number of languages. Often do we find
in other tongues a phrase embodying an idea which never occurred
to us ; or we are delighted to fall in with the expression of an idea
which had floated in our minds without our being able to give it an
exact shape. It sometimes happens that an inaccuracy or confusion
of thought in one tongue may not occur in another tongue, to which
we have only to look to have our ideas cleared up. Thus the dis
tinction between the phantasm and the general notion, drawn by
Aristotle and known in the middle ages, was lost sight of by the
English-speaking nations for ages after the time of Locke, who con-
founded them and expressed them both by his favorite phrase
'idea.' Of late years the distinction has been revived in our coun
trv greatly to the benefit of philosophy and specially of logic, by
bcfolars who noticed, in perusing works of German speculative phi
lo«ophy, that the two had been distinguished.

LANGUAGE. 59

87. Modem European thought has been greatly benefited by the
Btudy of the ancient classical languages, which commenced in the
fifteenth century and has been continued to the present time in all
the higher seats of learning. We have thereby got good not merely
from the faultless models of brevity, elegance, and taste presented
by the Greek and Koman writers, but from the very words them
selves and the ideas embodied in them. We have derived a like —
in some respects a higher — advantage from the introduction of
Eastern thought, especially from the Divine thought received from
the Scriptures with their elevated views of God and holiness — w<
get the very idea of holiness, or separation from sin, from the Word
of God, there being no such idea in the writings of Greek or Eoman
authors. The English language has been farther enriched by ideas
conveyed by the Italian from the time of Spencer to that of Milton
by the French in the last century, and by the German in this. Our
language, like our race, is a happy mixture of very diverse elements :
while we have as the basis the phrases and inflections of the old
Saxon tongue, we have made free additions from the Greek and
from the Latin (either directly or through the Norman French)
which have introduced us to a more advanced style of thought, and
a more refined mode of life.

88. Third. — Language constrains us to give a form to
thought which would otherwise be loose and vague.

" Language is a perpetual Orphic song,
Which rules with Daedal harmony a throng
Of thoughts and forms, which else senseless and shapeless were."

Let us try to understand how this takes place. We
enter a large factory ; we see the complicated machinery,
the work done, and the persons doing it, and we are filled
with a general astonishment. Our ideas meanwhile
may be very indeterminate. But we meet with one ac-
quainted with the work, and he names the parts one after
another, the machinery, and the raw materials, and the
products at the various stages of advancement ; we now
feel that our notions are becoming clearer. Or, we know
that after we leave the work we shall be obliged to de-
scribe it to a friend, and we try to get names for the varied
apparatus, and to reduce what we have seen to heads. No\?

60 THE NOTION.

there is a like process going on, often without our noticing
it, in the formation of our higher and subtler thought.
In being obliged to express our thoughts, we have to
make them definite in order to bring them within the
forms of settled language. This is specially the case
when we have to write out our thoughts. " Conference,"
says Bacon, " maketk a ready man," that is, ready to ex-
press intelligently the thoughts that occur ; " and writ-
ing an exact man," that is, having leisure to put his
thoughts into shape, and knowing that others will have
time to examine them, he has to make them assume a
more accurate form. How often does a student imagine
that he has an idea of a subject about which he is read-
ing, or on which he has heard his teacher lecture, till
such time as he is examined on it, or has to write de-
finitely upon it, when he discovers how vague his notions
have been. It is the great advantage of systematic ex-
aminations and of essay-writing, that they force the stu-
dent to understand his topic in order to his being able to
unfold it in language spoken or written. The interrog-
ative or maieutic method of Socrates was specially fitted
to accomplish this end, by constraining the person
questioned to give his thoughts a definite shape and
order.

80. The determinate moulds supplied by language,
into which to pour our solvent thoughts, are of various
kinds. Sometimes they are abstractions or analyses,
which enable and constrain us to decompose concrete or
complex objects. More frequently they are common no-
tions, under which we are led or obliged to put single
objects or lower classes.

9 O. It is commonly said that language is first synthetic, and then
analytic. The more correct statement is, that it is first concrete, thai
is, stands for things with an aggregate of qualities, and then be-
comes more and more abstract, that is, designates common qualities,
or objects joined by common qualities. First a word is fixed on to d*

LANGUAGE. 61

note an object ; then it is modified by additions, by affixes or suffixes,
or otherwise, to denote related objects; and then it becomes a root or
norm of other phrases clustering round it with allied meanings. It is
in its growth that language becomes synthetic in the proper sense
of the term, that is, words are joined to express a complexity.

01. As thought and language make progress, more
and more is taken in from the void (rb drreigov, as the old
Greek philosophers called it) ; the waste becomes meas-
ured and fenced in ; and those who come after must
accommodate themselves to what their predecessors have
settled. It thus comes that while language aids thought,
it tends at the same time to limit and restrain it. In
using the tongue provided for us, we must fall in with the
forms which it furnishes. The analyses and generaliza-
tions of words have, as it were, laid down rails on which
our thoughts run easily and rapidly, and we are induced
to travel on these accustomed ways instead of striking
out new paths for ourselves. This may be one reason
why the earliest poets of a country — such as Homer and
.ZEschylus in Greece, Lucretius in Borne, and Dante in
Italy, and Chaucer and Shakespeare in England — are
often the freshest ; they looked at things with then* own
eyes, and not as other men through the eyes of others.
This may be one of the ends served in Providence by the
confounding of old tongues and the necessary formation
of new ones ; as when the northern nations came in upon
the Roman empire, and Norman French became mixed
with the Saxon ; the same purpose is served as by the
mixture of races — the hereditary sameness is disturbed
and we have a new progeny with fresh life and new char-
acteristics. Still, the incidental evils arising from a
language being settled, are as nothing compared with the
advantages proceeding from a cultivated tongue, which
pi'ovides innumerable analogies and analyses to stimulate
and guide thought. Any evils which might arise from a
slavish adherence to fixed inflections and routine phrases.

62 ,< TEE NOTION.

are to be overcome by our forming the resolute determ-
ination to make language our useful servant without
allowing it to become our arbitrary master.

92. Fourth. — Language lightens thought by being
used as a symbol. When we think of objects not present,
we must always have some representation of them before
the mind - This, we have seen, may primarily be a men-
tal image ; thus when we are thinking about mothers
generally, we fix on some one mother, say our own, and
leave out as many of her peculiarities as may make the
idea stand for mothers generally. But we have shown
that this phantasm must always be inadequate to represent
an attribute, or a class comprising an indefinite number
of objects ; and as the generalizations become wider and
the abstractions more refined, and when different abstrac-
tions are mixed with each other, it may be impossible to
form a picture resembling the reality in the remotest
degree. Besides, even though we could fashion an ade-
quate image, it would be sure to distract the mind by
calling it away to adventitious circumstances. These in-
conveniences can be obviated only by the use of external
signs, and particularly of language.

03. Let us notice how external symbols are fitted to
lessen the labor of thinking. They do so inasmuch as
they render it unnecessary to take notice of the unnuin-
bered objects which go to constitute a class ; as they
save us from conceiving the attributes which combine
the objects in the class ; and from thinking of the pecu-
liarities of the individuals. To illustrate by an example.
In the natural arrangement of plants there is a sub-
class, thalamiftorce, from thalamus and flos (flower) ; its
characteristics are said to be " calyx and corolla pres-
ent, petals distinct, inserted into the thalamus or recep-
tacle, stamens hypogynous." Now had this tribe oi
plants not received a name, we should have beei

LANGUAGE. 63

Dbliged, every time we thought or spoke about them, to
represent to ourselves or enumerate to others their
various characteristics, and we should have been forced
to endeavor to conceive of the numberless plants be-
longing to the class ; and as we tried all this, we should
have found ourselves distracted and overwhelmed. This
burdensome work is avoided by using the phrase thalami-
floroe to stand for the whole tribe.

04. As feeling the convenience of it, and as being en-
dowed with the organs of speech, and the mental capa-
city and inclination to employ them, man naturally and
spontaneously betakes himself to words, to stand for
thoughts and things. " It is not necessary, even in the
strictest reasonings, that significant names which stand
for ideas, should every time they are used create in the
understanding the ideas they are made to stand for. In
reading and discoursing, names are for the most part
used as letters are in algebra, in which, though a partic-
ular quantity be marked by each letter, yet to proceed
right it is not requisite that in every step each letter
should suggest to your thoughts that particular quantity
it was appointed to stand for." (Berkeley.) In many
processes of thought, the attention seems to be very much
fixed on the verbal sign ; and conception comes to be what
Leibnitz calls Symbolical. Words come to be used like
algebraic symbols, a, b, c, which stand for quantities
without our thinking of any particular quantity, like
counters which represent money, like bank-notes which
stand for gold. The mind yields willingly to this state
of things, as feeling how much the memory and the power
of imaging and apprehending are thereby eased. We do
not choose every time we use such words as liberty, in-
dependence, order, civilization, virtue, commonwealth,
church, religion, to think of all that is comprised in them.
We pass them on as the banker gives away a hundred

64 THE NOTION.

pound note, or a hundred dollar bill, without thinking ot
the gold it stands for ; or as we receive it without con-
ceiving how many articles of utility or of comfort it would
purchase. Language is thus a species of stenography by
which the mind lightens its labors and makes its higher
efforts less irksome.

95. Fifth. — It follows as a corollary, that by means of
language we can carry on thinking to a greater extent
than we should otherwise be able to do.

We do not allow indeed, that language, or even that
external signs, are necessary to thought. It is forever
rung in our ears by certain writers, that there could be
no reasoning, no thought of any kind, without language
Dugald Stewart goes so far as to maintain, that c: without
the use of signs our knowledge must have been confined
to individuals, and that we should have been perfectly in-
capable both of classification and general reasoning ; " and
" lays it down as a proposition which holds without any
exception, that in every case in which we extend our
speculations beyond individuals, language is not only a
useful auxiliary, but is the sole instrument by which they
are carried on." This is a very extreme position, pro-
ceeding on a doctrine which tends to degrade the human
faculties, and which has been most eagerly maintained by
those who derive all men's ideas from sensation. In op-
position to it I lay down the counterpart statement, that
without thought language could not be fashioned, could
not be understood, could not be intelligently employed.
" Parrots," says Locke, " will be taught to make articulate
sounds enough, which yet are by no means capable of lan-
guage. Besides articulate sounds, therefore, it was farther
necessary that man should be able to use these sounds as
signs of internal conceptions, and to make them stand as
marks of the ideas within his mind." " From whence it
follows," says his critic, M. Cousin, " that language is not

LANGUAGE. 65

the product of sounds, that is to say, of the organs and
the senses, but of the intelligence ; 2. That the intelligence
is not the product of language, but, on the contrary, lan-
guage is the product of intelligence ; 3. That the greater
part of the words having, as Locke well remarks, an ar-
bitrary signification ; not only are languages the product
of the intelligence, but they are even in great part the
product of the will ; while *in the system that has pre-
vailed both in the school of Locke and in a school alto-
gether opposed to his, intelligence is made to come from
language ; in the latter, without much inquiring whence
language comes, in the former, by making it come from
the sensation and the sound, without suspecting that
there is a gulf between the sound considered as a sound
and the sound considered as a sign, and that what makes
it a sign is the power to comprehend it, that is, the
mind, the intelligence."

OS. Two circumstances show that the mind can reason
without language. One is, that we can point out cases in
which there is reasoning without words. An experienced
seaman looking on the sky, which to our eye seems so
calm, utters something about a storm. We ask what he
means, and his explanation only renders the subject more
confused. But we know what he intended when a few
hours after we see an angry sea, and find the waves lash-
ing on the vessel as if bent on sinking it. There has cer-
tainly been a process of reasoning, and the logician could
state it in syllogistic form ; but it is doubtful whether
language has been of any use in enabling him to conduct
it. Another circumstance is, that infants reason. Eefer-
ring to the view of those who deny the possibility of
reasoning of any kind without the aid of general terms,
Dr. Brown says : " As if the infant, long before he can be
supposed to have acquired any knowledge of terms, did
not form his little reasonings on the subjects on which it
5

66 THE NOTION.

is important for him to reason, as accurately probably as
afterwards, but at least, with all the accuracy which is
necessary for preserving his existence and gratifying his
few feeble desires. He has, indeed, even then, gone
through processes which are admitted to involve the
finest reasoning by those very philosophers who deny
him to be capable of reasoning at all. He has already
calculated distances, long before he knew the use of a
single word expressive of distance, and accommodated
his induction to those general laws of matter of which he
knows nothing but the simple facts, and his expectation
that what has afforded him either pain or pleasure, will
continue to afford him pain or pleasure. What language
does the infant require to prevent him from putting his
finger twice in the flame of that candle which has burned
him once? or to persuade him to stretch his hand, in
exact conformity with the laws of optics, to that very
point at which some bright trinket is glittering on his
delighted eye ? To s appose that we cannot reason with-
out language, seems to me, indeed, almost to involve
the same inconsistency as to say that man is incapable of
moving his limbs till he have previously walked a mile "
{Led. : XLYII.)

9t. Such considerations show that,

" Thought leapt out to wed with thought,
Ere thought could wed itself to speech."

And then have we not all had thoughts and sentiments
which, so far from being the product of words, we have
felt it to be impossible to translate into words, and we

have reason to complain,

" Oh dearth
Of human words, roughness of mortal speech.''
Our men of profoundest thought and deepest feeling,
have ever striven to rise above human phrases and gaze
directly upon realities.

LANGUAGE. 67

" Words are but under agents in their souls ;
When they are grasping with their greatest strength
They do not breathe among them."

This does not prove, on the opposite side, that even such
thoughts might not be made more definite, and therefore
more thoroughly significant, by being expressed in words ;
it simply shows that language, with all its refinements,
does not come up to the extent ard variety of thought.

,98. It should be freely allowed that very much of our
thinking is carried on by means of language. We have
already had before us the circumstances which furnish an
explanation. Though, in the order of the formation of
language, the notion comes before the name, yet it is com-
monly by the name, at least in countries richly supplied
with common terms, that the notions are first gained.
The name and the notion are thus indissolubly associated
in our minds, so that there is never the one without the
other. Then, as feeling the notion to be complex and a
burden upon our conceptive power, we prefer thinking by
the simple word rather than be at the trouble of appre-
hending all that is involved in its signification.

09' While we can think and reason without words, we
are all the better of language in every case, and in many
complicated operations we should be lost as in a laby-
rinth without signs of some description. Even in the
apprehending of abstract and general notions, we are the
better of names ; but we especially need them when we
come to compare our notions, either immediately in Log-
ical Judgment, or mediately in Reasoning. The botan-
ist, let us suppose, is comparing two classes of plants, one
whose characteristics have already been given, and the
other thus described : — " Sepals 4, deciduous, the twu
lateral ones gibbous at the base : stamens 6, tetradyna-
mous.'- How troublesome would it be to specify these
marks every time we had occasion to consider or speak of

68 THE NOTION.

the relation of these two tribes of plants. "We are
saved from all this by having a name for each of the
groups ; the one is called thalamiflorce, and the other
cruciferce, and the relation between them is expressed
by saying that the cruciferce are an order under the sub-
class thalamvflorce.

100. And if language be useful in judgments in which
we have only two notions, it is still more advantageous in
reasoning, in which we have three notions. In order to
see the utility of symbols in reasoning, we have only to
consider that all inference, except in a few simple cases,
implies one or more class notions. It proceeds, as we
shall see, on the principle that whatever is predicated of
a class, may be predicated of all the members of the class.
In all cases there is a class notion in the argument, and
in many cases all the three notions compared, minor,
major, and middle, are general. How cumbersome should
we find it, were we obliged in every argument, to consider
the indefinite individuals and the common marks that
combine them in every concept. And when in our ratio-
cinations there is not only one argument but a chain of
arguments, each containing one, two, or it may be three
new concepts, with their numerous individuals and their
combining attributes, I believe the mind would feel itself
utterly bewildered and oppressed without the use of sym-
bols to stand for the classes.

101. In thinking with the assistance of words, we can
pass as far beyond thought conducted by mere mental
signs, as by numbers we go beyond counting with the
fingers, and by algebra beyond arithmetical computations.
The transmission of messages by the electric telegraph
hundreds of miles in a few seconds, is an outward picture
of the rapidity with which the most remote and recondite
thoughts may be brought into communion by the refined
phrases of a cultivated language. " Though we should be

LANGUAGE. 09

capable of reasoning without language of any sort, and of
reasoning sufficiently to protect ourselves from obvious
and familiar causes of injury, our reasonings in such cir-
cumstances must be very limited, and as little compa-
rable to the reasoning of him who enjoys all the new
distinctions of a refined language, as the creeping of a
diminutive insect to the soaring of an eagle. Both ani-
mals, indeed, are capable of advancing, but the one passes
from cloud to cloud, almost with the rapidity of the
lightning which is afterwards to flash from them, and
the other takes half a day to move over the few shrunk
fibres of a withered leaf." (Brown.)

102. Sixth. — It is one of the special advantages of
language that it helps thought to make progress. This is
very happily brought out by Sir W. Hamilton : " A sign
is necessary to give stability to our intellectual progress
— to establish each step in our advance as a new starting-
point for our advance to another beyond. A country may
be overrun by an armed host, but it is only conquered
by the establishment of fortresses. Words are the for-
tresses of thought. They enable us to realize our do-
minion over what we have already overrun in thought — to
make every intellectual conquest the basis of operations
for others still beyond. Or another illustration : You
have all heard of the process of tunnelling, of tunnelling
through a sand-bank. In this operation it is impossible
to succeed unless every foot, nay, almost every inch, in
our progress be secured by an arch of masonry, before
we attempt the excavation of another. Now, language
is to the mind, precisely what the arch is to the tunneL
The power of thinking and the power of excavation are
not dependent on the word in the one case, nor on the
mason -work in the other ; but without these subsidiaries
neither process could be carried on beyond its rudimen-
tary commencement. Though, therefore, we allow thai

70 THE NOTION.

every movement forward in language must be determined
by an antecedent movement forward in thought ; still, un-
less thought be accompanied at each point of its evolution
by a corresponding evolution of language, its further de-
velopment is arrested. Thus it is that the higher exertions
of the higher faculty of Understanding, the classification
of the objects presented and represented by the subsidiary
powers in the formation of a hierarchy of notions ; the
connection of these notions into judgments ; the inference
of one judgment from another ; and, in general, all our
consciousness of the relations of the universal to the par-
ticular, consequently all science strictly so denominated,
and every inductive knowledge of the past and future
from the laws of nature : not only these, but all ascent
from the sphere of sense to the sphere of moral and re-
ligious intelligence, are, as experience proves, if not alto-
gether impossible without a language, at least possible to
a very low degree."

INCIDENTAL DISADVANTAGES OF LANGUAGE,

103. Bacon directed the attention of modern thinkers
to that subject in illustrating the Idola Fori, or those
which arise from the intercourse of mankind one with
another. " Though we think we govern our words, yet
certain it is that words, as a Tartar's bow, do shoot back
upon the understanding and do mightily entangle and
pervert the judgment." The subject thus opened has
been prosecuted by Hobbes, by Locke, by the French
school of Condillac, by Stewart, by Whately, and others,
some of whom trace almost all errors to the influence of
language. Locke has dilated on this subject (JEs^ay, B.
OT.), and has offered many valuable cautions, but often
exaggerates the evils. "He that shall well consider the

LANGUAGE. 71

errors and obscurity, the mistakes and contusion that are
spread in the world by the ill use of words, will find
some reason to doubt whether language, as it has been
employed, has contributed more to the improvement or
hindrance of knowledge among mankind." When men'?
ideas are confused, the language they employ will also be
confused, and thus increase the confusion — just as when a
master does not thoroughly organize his household, the
servants instead of aiding him will throw everything into
disorder. Examples of the evil influence of terms, are
often taken from imperfectly formed sciences, material
or mental ; but there the error has sprung from the state
of the department of knowledge ; and when the science is
properly constructed by its appropriate means, inductive
or deductive, it soon finds an appropriate nomenclature.

104:. M. Cousin, in criticising Locke, lias some fine remarks on
this subject. " The question is, does all error spring from language>
and is science nothing else than a well-constructed tongue ? No :
the causes of our errors are very different, both wider and deeper.
Levity, presumption, indolence, precipitation, pride, and thousands
of causes influence our judgment. The evils of language may join
on to natural causes and aggravate them, but do not constitute them.
If you consider them, you will see that the greater part of disputes
which appear to be about words, are, at the bottom, disputes about
things. Humanity is too earnest to trouble itself and shed its
purest blood for words. Wars do not turn on disputes about words ;
they rise from other quarrels — from quarrels theological and scien-
tific, of which they mistake the depth and importance who resolve
them into pure logomachies. Assuredly all science ought to seek
a language well constructed ; but it is to take the effect for the
cause, to suppose that sciences are well constructed because lan-
guages are well constructed. The contrary is the truth ; the
sciences have well-constructed languages when they themselves are
well constructed." He illustrates this by mathematics, where the
terms are good because the ideas are thoroughly determined ; and
by such departments as medicine, where we must first employ care-
ful observation and rigid reasoning, and then the appropriate no
uaenclature will be furnished.

72 THE NOTION.

105. But it should be frankly allowed that words,
while they are generally a great help to thought, do often
hinder it. It may serve some good purposes to consider
the evils which arise from the abuse of language. In do-
ing so we shall not dwell on the intentional perversion of
words by the sophist, the flatterer, the politician. For
these abuses language is not responsible ; though it is
true that the ambiguous nature of words very much aids
the liar and equivocator, and lends some plausibility to
the saying that language is rather an instrument for con-
cealing thought.

100. (1.) There is the vagueness of so many phrases.
How this should be, the observations we have made on
the formation of notions may enable us to understand. In
forming abstract terms, we join an aggregate of attri-
butes having a merely superficial and no deep or intimate
relation in the nature of things, or more frequently with-
out knowing what are the attributes comprised ; and then
we make unwarranted assertions regarding that term,
saying of one part what is true only of another, or of the
whole what is true only of a part. Again, what has been
represented (§ 24) as the second essential step in general-
ization is often performed very imperfectly. We perceive
a general resemblance, and we form a class, and we give
a name ; but meanwhile we have not fixed, except in a
loose way, on the points of resemblance, and the phrase
goes into circulation carrying its dross with it. Then it
is to be taken into account, that in our first generaliza-
tions we may fix on the superficial rather than the deeper
properties of things. Thus the word money meant orig-
inally articles used in exchange, and then was applied to
coin ; in time it came to have a larger and more scientific
meaning ; but the ambiguity led the popular mind to
identify money with wealth, to conclude that a country
must be enriched by increasing its coin, and by passing

LANGUAGE. 73

laws against the exportation of money. It is one of the ad-
vantages arising from science, from honest discussion, and
the progress of thought generally, that it gives greater
precision to language by compelling us to distinguish the
diverse things wrapt up in one complex phrase, and to
get a separate term for each. It was disputed whether
the syllogism was or was not an invention of Aristotle,
and both parties were right and both wrong according to
the use they made of the term. Such discussions led to
a distinction being drawn between invention and dis-
covery, the former being confined to the devising of some-
thing new, and the latter to the finding out of what
before existed : and we now deny that Aristotle invented
the syllogism, while we claim for him that he discovered
it to be the form to which all reasoning can be reduced.
The ancients, and the moderns down to the middle of last
century, used the word Sensation to denote both the
knowledge and the sensitive feeling got through the-
senses ; Reid drew the distinction between Sensation and
Perception ; and now, to avoid ambiguity, we employ the
phrase Sense-Perception to designate both. It is thus we
are getting new notions and new distinctions to super-
sede or supplement the old ; and a permanence is im-
parted to them by their being stamped with names.

107 • (2.) There are different meanings and shades of
meaning attached to a word. It is not difficult to under-
stand how this should originate. Every word has a his-
tory. If it could speak for itself, instead of being a mere
unconscious instrument in the hands of a higher power,
it might furnish us with a biography. In doing so, it
would have to commence with its genealogy. Many
words might furnish us with an older one than the most
ancient nobility. Some could point to their ancestrv
among the Roman patricians ; some go back to the
Greek gods and demigods ; while others ascend to the

74 THE NOTION

Hebrew patriarchs and prophets ; not a few boast that
they come to us from Paris with the last new fashion ;
while a considerable class bring with them the broad
sense and deep thought of Germany. Our tongue is en-
riched by these constant importations. But it is to be
expected that in such a mixture of emigrants there should
be some whose character is very ambiguous. There is
the word 'idea/ which has had so many meanings : des-
ignating now an image, now an eternal model, now a con-
cept, now an intuitive truth ; and the most satisfactory
judgment we can pronounce upon one which has had so
many aliases is, that it should be banished altogether from
the commonwealth of philosophy — where it has wrought
only mischief — leaving it still a place in common conver-
sation and in poetry. "With some, Keason stands for the
undefined qualities possessed by man and not by brutes ;
with others, it signifies much the same as understanding
or intelligence, and including the process of reasoning ;
with others, and especially with the higher metaphysi-
cians of Germany, denoting the capacity which discovers
necessary truth immediately, as distinguished from the
logical understanding which proceeds discursively, — in
this last sense reason and reasoning are contrasted.

108» The perplexity is increased by the circumstance
that the phrase has one meaning in one age, and another
in another age. Unwilling to offend prejudice, and to
give their writings an affected and repulsive aspect, our
fresh thinkers retain the old phrase, while they alter the
meaning to suit the new aspect of truth to which they
would introduce us. " We have resolved to accompany
antiquity as far as possible, since we are anxious, so far
as it can be done with the pen, to make an alliance be-
tween what is old and new in learning. We therefore
retain old terms, though we often alter their meaning
and definitions, according to that moderate and laud-

LANGUAGE. 75

able mode of innovating in civil affairs whereby the con-
dition of things being changed, the usual names are re-
tained ; as Tacitus remarks regarding the names of the
magistrates which were retained even when the offices
were somewhat changed." (Bacon.) This circumstance
has bred great confusion. Thus the word Form as dis-
tinguished from Matter, has been used in one sense by
Aristotle, in another by Bacon, in a third by Kant
From the time of Aristotle to that of David Hume and
Kant, to argue ' a priori,' meant to proceed from
cause to effect, or from reason to consequent ; and to
argue ' a posteriori,' to proceed from effect to cause, and
from consequent to reason. Since the rise of the Kant
ian philosophy, by the ' a priori ' method is meant pro-
ceeding from principles imbedded in the mind and inde-
pendent of experience.

In the former sense, the famous argument of Samuel Clarke for
the existence of God would be called a 'priori, as it proceeds from
reason to consequent ; but in the latter sense it is partly a 'posteriori,
inasmuch as arguing frcm our idea of space to a being of whom
space is an attribute, it proceeds on the fact that man has an idea of
space.

109. Little evil would arise from this provided we
always distinguished between the meanings. But one
use of names, we have seen, is to save us from imaging or
remembering all the objects and properties denoted by
them. But hi the use of ambiguous phrases, especially
in abstract discussion, we are apt unconsciously to slide
from one meaning to another ; and we make an affirma-
tion or denial of a word, using it, in the rapidity of
thought, in one sense, whereas the predication would be
valid only if we used the phrase in another sense. The
ambiguity of the words 'idea,' 'a priori,' 'reason,' has
helped to prolong the discussion as to whether there are
innate ideas, a priori truth, and an intuitive and inde-
pendent reason in the human mind.

76 THE NOTION.

110. The greater number of the words in our language have come
down to us from a rude and simple state of society, and they bear
the impress of their origin, — resembling in this respect the man who
has risen in the world from the lower ranks, and is now admitted,
because of his talents and success, to the most polite circles, but who
has not been able to shake himself free from the manners of his
youth. This, in some aspects, is a disadvantage, as it allows less
accuracy of language and thought. To avoid the evil, we very
properly bring in terms from the dead classical languages, to express
rigidly exact scientific truth. But seen in another light, it is a bene
fit that our language has sprung from a less artificial condition of
things, — just as the most polished circles are all the better of the
occasional introduction of persons whose manners, if not so refined,
are, at least, more fresh and natural. These old home-born phrases,
if not so fitted to express abstract truth, are more effective in evok-
ing genuine and heart-born feeling. I can conceive that some lan-
guages, like the manners of some men, might become too artificial.
The most perfect tongue is that which has both elements, which
Beeks to retain the freshness of youth in the midst of the maturity
of age.

111. (3.) There are words that mislead us by their
associations. Such are phrases which stir up feeling,
pleasant or tumultuous. "Who can reason calmly when
the appeals made deal in such words as home, native
land, liberty, independence. Any evil thus arising may
be counteracted by the ennobling influence produced by
the ideas thus suggested ; but it is different when the
language raises up passions which agitate the soul as the
wind does the ocean, or lusts which pollute it by sinking
it in the mire. Again, there are phrases used by our old
authors which were not offensive iu their day, but are felt
by us to be coarse and indelicate. As illustrating the
same point, we may refer to the fallacies into which men
fall from " usually taking for granted that paronymous
(or conjugate) words, i. e., those belonging to each other,
as the substantive, adjective, verb, &c, of the same roots,
iiave a precisely correspondent meaning ; which is by no
means universally the case." (Whately.) As examples

LANGUAGE. 77

we may give art and artful, design and designing, theorj
and theorist, scheme and schemer. Thus a man is repre-
sented as having an art, a design, a theory, or a scheme,
and we look upon him as artful, a designer, a theorist, or
a schemer. Home Tooke, the grammarian, argued from
the derivation of the word ' true,' that there could be " no
such thing as eternal, immutable, everlasting truth."
"True," as we now write it, or trew as it was formerly
written, means simply and merely, that which is trowed,
ind instead of being a rare commodity on earth, except
mly in words, there is nothing but truth in the world."
Two persons may contradict each other and yet both
speak the truth, for the truth of one person may be op-
posite to the truth of another. To speak truth may be
a vice as well as a virtue."

112. Under this same head we may place the mislead-
ing influence of words which now denote mental acts, but
which were originally applied to material objects. Thus
' idea ' meant originally an image ; ' apprehension ' and
' conception ' are derived from the act of taking hold of a
thing ; ' understanding ' signifies something placed be-
neath ; ' substance,' that which stands beneath ; and
'spirit,' in a number of tongues, air or breath. Since
mind and body are called substances, some have argued
that in addition to the mind and body which we know,
and know as having being, permanence, and potency,
there must be something standing under them. It is
difficult for those whose thoughts are habitually em-
ployed about sensible things to conceive of spiritual
truths, and the difficulty is increased by the circumstance
that the language in which they are expressed was at
first materialistic, and is still apt to call up sensible
images.

113. (4.) We are led by the advantages which lan-
guage supplies to use words without inquiring into their

78 THE NOTION.

meaning. This is in itself the greatest of all the evils,
and is the source, directly or indirectly, of most of the
others. We have seen that it is one of the main pur-
poses served by symbols, that they render it unnecessary
to conceive all that is in the notion, all its objects, and all
its marks. But then, just because language so eases thought
aud labor, we come to give up rigid inquiry and allow
words to guide us at their will or caprice. This is one
reason why mankind are so apt to follow hereditary or
popular beliefs embodied in cherished phrases. " Men,"
says Locke, " having been accustomed from their cradles
to learn words which are easily got and retained, before
they knew or had framed the complex ideas to which they
were annexed, or which were to be found in the things
they were thought to stand for, they usually continue to
do so all their lives ; and without taking the pains neces-
sary to settle in their minds determined ideas, they use
their words for such unsteady and confused notions as
they have, contenting themselves with the same words
other people use, as if their very sound necessarily carried
with it constantly the same meaning. This, though men
make a shift with in the ordinary occurrences of life,
where they find it necessary to be understood, and, there
fore, they make signs till they are so ; yet this insignifi-
cancy in their words, when they come to reason concern-
ing either their tenets or their interest, manifestly fills
their discourse with abundance of empty unintelligible
noise and jargon, especially in moral matters, where the
words, for the most part, standing for arbitrary and nu-
merous collections of ideas, not regularly and permanently
united in their nature, their bare sounds are often only
thought on, or at least very obscure and uncertain no-
tions annexed to them."

114. The question arises, how are these evils to be
avoided ? It is evident that it is not to be done by dio-

LANGUAGE. 79

carding the use of language — which would be like putting
out one's eyes in order to avoid mistakes in vision. Ad-
vantage may arise from attending to some such rules as
the following :

First. Let us begin with ascertaining the meaning of the
word. We may do this by the help of a dictionary ; or by
looking to the sense in which it is used by those who in-
telligently employ it, more specially by resorting to the
writings of those who treat expressly of subjects in which
it ought to be accurately employed.

115. Second. When a word is ambiguous, we should
make ourselves acquainted with the various senses in
which it is used, not only by the writer whose works we
are reading, but those in which others, or in which we
ourselves, have been accustomed to employ it. If we
have not before us the various senses and the difference
between them, we shall ever be tempted to slide from the
one to the other without knowing it. Thus, in mental
philosophy, we must never lose sight of the various
senses in which the phrases 'idea,' 'a priori,' ca pos-
teriori,' ' experience,' ' form ' and ' matter,' ' subject ' and
' object,' ' conditioned ' and ' unconditioned/ are em-
ployed. If we neglect this, we are certain to be led
astray by the errors which lurk beneath these phrases,
all of which have been used in different senses and been
the vehicles of false doctrines.

116. Third. We must be at pains to settle the precise
notion which the word stands for. This implies much
more than a dictionary understanding of it. It requires
that we go back to the notion in the mind. For every
term stands primarily for an apprehension of the mind ;
that apprehension must, no doubt, be of objects, but it is
of objects apprehended, and so we must look first at the
apprehension, and then compare it with the things. This
is a counsel frequently pressed by Locke. " A man

80 THE NOTION.

should take care to use no word without a signification,
no name without an idea for which he makes it stand.
This rule will not seem altogether needless, to any one
who will take the pains to recollect how often he has met
with such words as instinct, sympathy, antipathy, &c., in
the discourse of others, so made use of as he might easily
conclude that those that used them had no ideas in their
mind to which they applied them ; but spoke them only
as sounds, which usually served instead of reasons, on the
like occasions. Not but that these words, and the like,
have very proper significations in which they may be
used, but there being no natural connexion between any
words and any ideas, these and any others may be
learned by rote and pronounced or writ by men who
have no ideas in their minds to which they have annexed
them, and for which they make them stand ; which is
necessary they should, if men would speak intelligibly
even to themselves." " Justice is a word in every man's
mouth, but most commonly with a very undetermined,
loose signification, which will always be so, unless a man
has in his mind a distinct comprehension of the compo-
nent parts that complex idea consists of : and if it be de-
composed, must be able to resolve still on, till he at last
comes to the simple ideas that make it up ; and unless
this be done a man makes an ill use of the word ; let it be
justice, for example, or any other. I do not say a man
need stand to recollect and make this analysis at large,
every time the word justice comes in his way ; but this
at least is necessary, that he Lave so examined the signi-
fication of that name, and settled the idea in all its parts
in his mind, that he can do it when he pleases."

117> Fourth. — Let us observe whether the notions are
Singulars, or Abstracts, or Universals. We are reading,
let me suppose, of beauty, and we are anxious to have
3lear ideas on the subject. Let us first inquire what sort

LANGUAGE. SI

of notion is denoted by the word. We easily and at once
discover that it is an Abstract notion, and therefore we
do not for one instant supposev that it has, or can have, a
separate existence. We are not, on the other hand,
rashly to conclude that it has no existence. It is a
reality, but a reality in objects ; and we are led to look
to objects and inquire what it is in them that we desig-
nate by this name.

Or the word we have occasion to employ is a General
one. We have now to inquire what is the class of ob-
jects connoted by it, and what the common qualities in
respect of which they are grouped. The word used, I
shall suppose, is ' instinctive ; ' it is said of such an ac-
tion that it is ' instinctive.' We proceed on the idea that
it points to a reality ; but we do not suppose that it is a
reality distinct from the beings possessing it : we look
for it in the living beings endowed with it, and we pro-
ceed to inquire what it is, whether it is a single property
or, as is more probable, a number of properties adapted
to each other and tending to one end.

When the notion is what I have called a Generalized
Concrete one, we are to bear in mind that we cannot
expect to exhaust all the properties of the objects em-
braced in the class. It was foolish and vain to seek, as
Socrates seems to have done, for some one thing as con-
stituting the to ov of a%class notion, say the to aaXbv ; or
as the schoolmen did, to specify the essence of every uni-
versal, as, for instance, of man.

118* It is of great moment to take these cautions with
us in all our higher thinking, in which we are ever tempt-
ed to look upon abstractions as independent wholes. The
ancient Greek philosophers often gave a separate existence
to the abstractions fashioned by them. Thus the Elea-
tics, and Plato after them, were accustomed to discuss the
nature of to ov, or being, as if it were a distinct sub-
6

82 THE NOTION.

stance like mind or body. We have fallen into a like
mistake in modern times. We speak very properly of the
faculties of the mind, such as the memory, the imagina-
tion, and judgment ; but then we are led to think and
write about them as if they were acting entities, whereas
they are merely capacities of the thinking mind. We
find ethical writers speaking of virtue as if it were some-
thing separate from and above the virtuous mind ; where-
as it is a mere attribute of virtuous agents, from which it
cannot be separated except in mental abstraction. Some
write about gravitation as if it had an independent exist-
ence, whereas it is a mere property of matter having no
existence separate from individual, bodies. Again, gen-
eral terms are apt to be regarded as singulars. Men
speak and reason as if general phrases pointed to some
one existence, whereas they merely connote a class of
things having one or more points of resemblance. Some
discourse about the laws of nature, as if they were some-
thing different from the objects in the universe, whereas
they are generalizations of the modes in which the objects
operate. Having begun with this blunder in thought,
there are some who go a step farther and make the laws
of nature a substitute for Deity. They have first given
them an existence separate from God's works, and having
got such a convenient mode of accounting for these
works, they feel as if nature could work without God al-
together. We are reminded of an analogous error. We
employ the word ' nature ' as a convenient one to denote
the whole knowable creation as it comes from God's
hands. But we forget that the phrase is merely a generic
one, and then are led to talk of nature as haying an
existence separate from the combined works of God.
Having given it an independent existence we end by
deifying it — I fear nature is the only God worshipped b\
many of the votaries of physical science in our day.

LANGUAGE. 8H

110. Fifth. — We must carefully consider the things
from which the notions have been formed. I believe, in-
deed, that we ought first to look to the notions, for words
stand primarily for apprehensions of the mind. But ap-
prehensions, so far as they profess to be drawn from
things, must conform to them, and in order to see
whether our notions are accurate and adequate, we must
over compare them with the things from which they are
derived. We have seen that the great English metaphy-
sician has done signal service to philosophy by insisting
that we always rise from terms to the ideas they stand
for. But another English philosopher has, if possible,
conferred a greater benefit by requiring that we should
ever go beyond notions to things. Bacon complains, I be-
lieve justly, of the ancient Greek philosophers and of the
scholastic logicians, that they looked at names which had
no corresponding objects, or at notions abstracted from
things ; that their very definitions consist of words, and
" verba gignunt verba. Verba notionum tesserse sunt, quare
si notiones ipsoe (quae verborum animoe sunt) male et varie
abstrahantur tota fabrica corruit." And so he recom-
mends the observation of things by a careful induction as
the means of attaining truth and certainty ; and in doing
so has given a nobler contribution to the science of Logic,
in the enlarged sense of the term, than any other except
Aristotle.

LAWS OP THOUGHT INVOLVED IN THE USE OF SIGNS.

120. First Law. — Every Term stands for a Notion,
which must be either a Singidar Concrete, an Abstract,
or a Universal. We should accustom ourselves, in think-
ing, to look more to the notion than the phraseology, and
we should ever be ready to translate our words into

84 TEE NOTION.

thoughts. But if the analysis which we have given of
notions be correct, these terms when turned into no-
tions will be found to be one or other of our threefold
division : they will be Percepts or of single things thought
of in the Concrete ; or Abstracts, that is of qualities ; 01
Concepts, that is of a class of objects joined by common
qualities. Now it is often of great moment in discussing
a complicated subject, that we should know precisely to
which of these classes the notion which we are using be-
longs, and that we should understand it, and use it ac-
cordingly. If we neglect this, if we employ, for example,
abstract and general terms as if they were singulars, or
treat abstract and general terms as if they had no sort of
reality, we shall find ourselves involved first in inextri-
cable confusion, and then in positive error.

12 I. Second Law. — We can predicate of the Sign only
what might be predicated of the Notion. "We have seen
that after we have denoted a notion by a sign we can
judge and reason about the sign without thinking of all
that is signified by it. But we must not allow ourselves
for one moment to suppose that the sign has acquired
any new power not found in that which it stands for, or
that we are at liberty to affirm or deny of it what we
would not affirm or deny of the notion itself provided it
stood fairly before us. If A stands for a square number,
we are not allowed to predicate of it what we could not
predicate of the square number itself, say that it is a virtue.
If B stands for a moral quality, say justice, we are not to
be allowed to affirm of it what could not be affirmed of
justice, say that it has four sides. The sign is still a sign,
a sign of what it was made to stand for.

122> Third Law. — We may demand at any time, that
the Notion should be substituted for the Sign. As we
are always at liberty to do so, so we should actually do so
from time to time, in order to determine whether we are

LANGUAGE. 85

or are not making a proper predication. In abstruse
discussion and in perplexing ratiocination, we are apt to
lose sight of the signification, or at least of the precise
signification, of the language we employ. But as we do
so we are ever liable to make affirmations or denials
which we should never make of the ideas denoted by the
words. Principal Campbell inquires : " What is the
cause that nonsense so often escapes being detected both
by the writer and reader ? " The cause, I believe, is to be
found mainly in this, that we are ever making assertions
as to the sign, taking a loose view of what it signifies.
Thus our forefathers reasoned that as money is wealth,
so wealth might be increased by passing restrictive laws
to keep money from leaving the country. The fallacy is
seen at once when we properly define and studiously
comprehend what the phrases money and wealth stand
for. From the causes now referred to, mainly proceed
the endless logomachies to be found in controversy of
every kind. We shall often find that we have only to re'
translate the word into the notion, and then compare the
notion with the thing, to discover that the propositions
which men utter with such gravity, or such confidence,
are altogether meaningless, and that the sophistry which
was deceiving us, is thus stript of its plausibilities.
Every one will be inclined to allow that we should be
careful to follow this rule when we are apt to run into
extreme positions, or are penetrating into profound
depths or vast heights. But in fact, it is equally needful
to do so, when we are using familiar phrases, which we
fancy we understand fully because we have been employ-
ing them daily from our childhood. As Newton is said
to have risen to his great discovery by narrowly inquiring
into so commonplace a fact as the fall of an apple, so
the detection of wide-spread fallacies and the discovery of
important truth are ofttimes made bv instituting a sift-

86 THE NOTION.

ing inquiry into the real signification oi a phrase, which
without being questioned by any one, has passed current
from mouth to mouth for long' ages.

Ill -CLASSES IN NATURE.

123, These become aids and guides to the mind in its
generalizations. I speak of them as aids, for the mind by
its own internal power can form genera without any spe-
cial reference to natural groupings. It must always, in-
deed, have some supposed attribute to bind the objects
together, and act as ground of the arrangement. But
then it can fix on any one attribute and form a class com-
posed of all the objects which possess it. Every thing
may be arranged in as many classes, actual or potential,
as it possesses qualities. The same man may, in respect
of his country, be an Englishman or an American ; of his
religion, a Catholic or a Protestant ; of his race, a Celt or
a Saxon ; of his profession, a lawyer or a physician ; of his
domestic condition a bachelor, or married ; of his politics,
a conservatist or a liberal ; of his knowledge, a scholar or
an ignoramus. Looking to any given company of men,
women, and children, we might arrange them in a great
number of ways : according to their native country or coun-
ty ; according to their sex, age, weight, strength, mental
capacities, education, business in life, character, creed ;
nay, according to such insignificant qualities as the color
of their hair or eyes, or their Christian names. Wherever,
in short there is a property which more than one person
possess or are supposed to possess, we have a ground
for a classification which may be expressed by a generic
term. The classes which man may form cannot be said
to be infinite, but they are indefinite ; no limits can be
pet to them. There is a manifest advantage in all this ;

CLASSES IN NATURE. 87

for we can arrange the objects we meet with, now in this
way and now in that way, according to the end we have
in view at the time.

124:. But so far as natural and especially organic ob-
jects are concerned, there are groupings formed which
men should notice, and which have an existence whether
they notice them or no. In the study of nature we are
constantly made to feel that we have not to form or create
classes ; the classes are already formed for us, and all we
have to do is simply to observe them. And if we would
construct any thing like a complete classification of natu-
ral objects, it is imperative on us to attend to the natural
groupings. An arrangement which overlooks this will
turn out to be incomplete, and incapable of serving any
practical purpose ; and however ingeniously formed will
be characterized as artificial, even when not denounced
as arbitrary and capricious. The Creator has so con-
structed and disposed his works that there are facilities
for forming classes, and it is the business of the natural-
ist to discover and follow the natural order. So far as he
gets hold of it his classifications will be natural, and use-
ful for the accomplishment of an immense number and
variety of purposes, scientific and practical.

125. We have shown {Method of Divine Government, B. II., C.
L, § 4, and Typical Forms and Special Ends in Creation), that there
s an order running through all nature iu respect of such qualities
is Number, Time, and Form. (1.) Ntcmoer. The laws of physics
and of chemistry, etc., are expressed in quantities. The law of
gravitation is, that all matter attracts other matter inversely ac-
cording to the square of the distance ; and all chemical compositions
and decompositions take place according to numerical rule. (2.)
Time. All the leading events in the earth and heavens run in pe-
riods : there are days and months and seasons and years, and magni
anni. (3.) Form. The heavenly bodies have spheroidal shapes ;
minerals crystallize geometrically with fixed angles and proportions
and every animal and plant and every organ of the animal an<*
plant has a typical form which it tends to assume.

88 THE NOTION.

126. We are thus introduced to those classes which
have been called Kinds by some logicians. In these the
possession of one characteristic mark is a sign of a num-
ber of others. The botanist has seized on a classification
of this hind. The grand division of plants is into acoty-
ledons, monocotyledons, and dicotyledons. This is a dis-
tinction of Kinds, and the mark fixed on becomes the sign
of others. Thus monocotyledons grow from within and
their leaves are parallel-veined, whereas dicotyledons
glow from without by adding rings and have netted veins.
In the same way in the approved classifications of zoology,
the possession of one mark becomes a sign of others. Thus
certain animals are called mammals because they suckle
their young ; but all these are found besides to be warm-
blooded, and to have four compartments in the heart.
How different are these from artificial classes, as suppose
we were to divide plants according to their height, or
animals according to their color. Every one sees how
arbitrary, in short how unnatural, such an arrangement
would be. It would separate plants from each other
which are most closely allied, and might put in one group
bird and fish, man and brute, while it separated an ani-
mal from its mate or from its offspring.

127. " There are some classes the things contained in which
differ from other things only in certain particulars which may be
numbered ; while others differ in more than can be numbered, more
even than we need ever expect to know. Some classes have little
or nothing in common to characterize them by, except precisely
what is connoted by the name : white things, for example, are not
distinguished by any common properties except whiteness: or if
they are, it is only by such as are in some way dependent upon, or
connected with whiteness. But a hundred generations have not
exhausted the common properties of animals or of plants, of sul-
phur or of phosphorus ; nor do we suppose them to be exhaustible
but proceed to new observations and experiments, in the full con
fidence of discovering new properties which were by no means im
Dlied in those we previously knew." " There is no impropriety iD

CLASSES IN NATURE. 8tf

Baying that of these two classifications, the one answers to a much
more radical distinction in the things themselves than the other
does, etc." (Mill's Logic, B. I., C. VII.)

128. These groupings of nature, while they are a
help, are at the same time a rule in the formation of
classes. They assist, but they also control mankind in
the construction and use of their general notions. Things
come to be arranged by practical observation and by
science in a certain way ; a corresponding nomenclative
is devised, and all men must accommodate themselves to
it. Such divisions of time as into days and years and
seasons, of material objects into mineral, plant, and ani-
mal, of the heavenly bodies into star, planet, comet, and
meteor, come to be universally adopted, and all persons
must proceed upon them ; while science is every year add-
ing newly-discovered laws, which become known first to
the learned and then descend as a heritage to the people.
The concepts thus formed on distinctions in nature, have
a reality above other concepts. Such a concept as ' white-
colored,' has, no doubt, a sort of reality in the nature of
things — it has a reality in the white color possessed by all
the objects in the class, say lilies and snow. But such
concepts as Eosacese and Cruciferse, as Crustacese and
Foraminiferse, have a deeper signification — the class has
a reahty in the divinely appointed order of things. It is
the same with such generic notions as beautiful, good,
holy — they denote primarily one quality, but they imply
other qualities associated with it and numberless affinities.
This was one of the truths pointed at, but never accu-
rately expressed in, the ideal theory of Plato and the
medieval doctrine of realism. Concepts of this descrip-
tion have a place in the very nature of things and in theii
ramified connections. But while this holds good of cer-
tain concepts, it is not true of all ; and even in regard to
those of which it is true, the reality is, after all, in the

90 TEE NOTION.

individual things and their mutual relations, and not in a
mere idea in the mind of the person contemplating
them.

REALISM, NOMINALISM, AND CONCEPTTJALISM.

•

129. In the Eisagoge of Porphyry there occurs the following
statement : " I omit to speak about genera and species as to whether
they subsist (in the nature of things) or in mere conceptions only ;
whether also, if subsistent, they are bodies or incorporeal, or whether
they are separate from or in sensibles and subsist about these."
Boethius (6th Gent) commented on this passage and declared :
" non est dubium quin vere sint." " Stmt autem in rebus omnibus
conglutinatae et quodam modo conjunctae atque compactae." This
came to be the general and the orthodox opinion of the early scho-
lastic teachers. But as curious youths mused on this cautious pas
sage of Porphyry with the comment of Boethius upon it, we can
conceive that some would be tempted to form an independent,
opinion on so complicated a subject. This seems to have been the
case with Boscellinus, a native of Brittany, who flourished in the
eleventh century. Unfortunately we have no writings of Boscelli-
nus, and we have to gather his opinions from the statements of his
opponents, particularly Anselm. He is represented as maintaining
that genera and species had no true existence — that they were no-
thing but words {flatus vocis), and this doctrine was denounced as
inconsistent with the higher doctrines of religion, particularly the
doctrine of the Trinity. We have now, then, an expounder of
Nominalism as opposed to Realism. At a little later date appeared
the illustrious Abelard, who opposed with great acuteness the sys-
tems both of the Realists and the Nominalists, pointing out the dif-
ficulties in which the former are involved when they maintained
that uuiversals are realities different from individual things, and
showing the insufficiency of the theory of the latter. His own
opinion is regarded by some as Conceptualisin — it is at least an
anticipation of Conceptualisin. The following is M. Cousin's ac-
count of it : " There exists nothing but individuals, but none of
these individuals is, in itself, either genus or species, but the indi
viduals have resemblances which the mind can perceive, and these

iWALISM, NOMINALISM, ETG. 91

resemblances considered alone and abstraction being made of theii
differences, form classes more or less coinprehensive which they call
genus or species. Species and genus are then the real products ol
the mind ; and they are not words, although words express them ;
nor are they things without or within the individuals — they are con-
ceptions. Hence the intermediate system named Conceptualism."
(Fragmens). We have now the three possible systems contending
with each other. Realism was the~prevailing doctrine throughout
the Middle Ages, and was defended with great zeal and ability by
Albert of Cologne (Albertus Magnus), and Thomas Aquinas {Doctor
Angelicus). Opposed to Thomas the Dominican was John Duns
Scotus (Doctor SubtUis) the Franciscan. Like Thomas be was a
Realist, but he maintained that the universal existed in individuals
not really, but formally (formaliter). William Occam (Doctor I/i-
wncibilis) a disciple of Scotus, is usually regarded as a Nominalist,
but Dr. Mansel declares that he is a Conceptualist like Abelard. In
modern times it is difficult to find a genuine Realist, but we have
one in Harris, the author of Hermes. Adhering to the Nominalist
theory we have Hobbes, Berkeley, Hume and Whately ; and among
numerous Conceptualists we may mention Locke, Reid, Kant, Brown,
and Whewell.

l.'iO. The controversy has been characterized throughout by
great confusion of thought. The extensive survey we have taken of
the Notion and of Language should enable us to discover the truth
and the error in each of the systems.

Realism errs by excess. It errs when it ascribes to the universal
an existence independent of singulars or distinct from them. Plato
held that Ideas had an existence in or before the Divine Mind from
all eternity. He was met by Aristotle, who showed that they had
no existence except in the individuals. The medieval doctrine of
the reality in universals was a modification of the Platonic doc-
trine. In both there is a tendency to mysticism, and a disposition
to hypostasize the conceptions of the mind. Yet the system has no-
ticed certain important truths. First the mind has a tendency to
rise beyond the particular to the general, and to reduce multiplicity
to unity. Then all organisms, all plants and animals, tend to as-
sume a typical form. The individuals all die, showing how perishing
they are, but the genus and species survive. The flowers of last
summer are all faded, but in the coming summer flowers of the same
form will spring up. Then all the powers of nature act according
to laws imposed on them, and amidst the flux of things these laws

92 THE NOTION.

are permanent. Still more important, we find, amidst the impel
tectums and sins of humanity, the moral law of God abideth for-
ever.

131. Nominalism errs by defect. It forgets that there must be
grouping of objects by the mind in order to the introduction of a
common term, and an apprehension of the grouping in order to an
intelligent use of the term. It forgets that the mind can form an
image of a class of objects, inadequate, but still sufficient in most
cases to enable it to think about them. It overlooks the important
circumstance that in nature there are laws and types ordained by
the Being who formed the objects themselves. The truth contained
in nominalism is, that words greatly aid the mind in thinking, and
enable it to conduct its cogitations much farther than it otherwise
could.

132. Goneeptualism has often taken a wrong form. It does so
when it regards the conception combining the objects as an idea in
the sense of image. This was the mistake of Locke, when he says
that in forming our idea of man we leave out of the complex idea
that which is peculiar to each of the individuals, and retain only what
is common to all. (See §79.) Again it errs when it overlooks or
denies the utility, in some cases the necessity, of signs to enable us
to conduct our thinking. And Conceptualists have often, in looking
at the idea, forgot that there is an actual order among the things
on which the idea is founded. But if it avoids these mistakes and
oversights, which are not parts of the doctrine properly understood,
conceptualisin is the true theory. For in general notions, the essen-
tial element is the grouping by the mind of objects by common
properties, and putting in the group all objects possessing the
properties.

There are universalia ante rem in the Divine Mind. There are uni-
versalia in re in Natural Classes. There are universalia post rem in
human concepts and terms.

PART SECOND.
JUDGMENT.

1. Judgment is defined by logicians " as the comparing
together in the mind two of the notions or ideas which are
the objects of apprehension, and pronouncing that they
agree or disagree." But this definition can be accepted
only when we understand by notions, not mental states
as such, but objects apprehended. When we say " Alex-
ander the Great was ambitious," we are comparing
" Alexander the Great " and " ambitious," and not mere
ideas of the mind — it being always presupposed that the
objects are previously apprehended by us. A Proposition
is a Judgment expressed in words, and in it we compare
two Terms, so called because they are the termini (boun
daries) of the proposition.

CATEGORICAL PROPOSITIONS.

2. Judgment is psychologically one act of the mind,
but is of a concrete nature, and we analyze it into three
elements, two notions, and the declaration of their agree-
ment or disagreement. That notion which we seek pri-
marily to compare is called the Subject ; that with which
we compare it, the Predicate ; and the determination oi
the agreement or disagreement, the Copula. The Judg-

94 JUDGMENT.

ment may be expressed in three words, or in a number oi
words, or even in one word. When we say " selfishness
is hateful," we bave subject, copula, and predicate, each
in one word. But there are tongues in which the judg
ment can be expressed in one word, as amat ; which, when
we wish to bring out each of the parts we analyze and
say, itte est amans, he is loving. Active verbs in a sen-
tence commonly express both copula and predicate ;
thus, when we say " the horse neighs," the word ' neighs '
contains both predicate and predication, and when ex-
panded takes the form " the horse is neighing." In order
to determine what are the terms, we must look, not to
the mere words, which may differ in different languages
and even in the same language in expressing the same
idea, but to the notions. When it is said that " it is a
true saying and worthy of all acceptation, that Jesus
Christ came into the world to save sinners," the two
terms, as ascertained from the two notions, are " Jesus
Christ coming into the world to save sinners " and " a
true saying and worthy of all acceptation ; " these are the
things compared in the mind, and in respect of which we
predicate their agreement.

3, The copula is usually expressed by logicians by the
present tense of the verb ' to be,' by ' is,' or ' is not,' (or
' are ' and ' are not.') But we are not to understand ' is ' in
such a connection, as being the substantive verb — the sub-
stantive verb in the Latin form, est, contains subject,
copula, and predicate, meaning "he is existing." The
copula is an abstract, expressing neither less nor more than
the agreement or disagreement. Every thing else in a
proposition is to be regarded as part of the subject or of
the predicate. The element of time, when it is involved
in a judgment, is not to be attached to the copula. When
we say " Napoleon Bonaparte was unfortunate in 1815,"
the notions compared are "Napoleon in 1815 " and "un-

CATEGORICAL PROPOSITIONS. 95

fortunate/' and it is on comparing these that we declare
their agreement ; if we were speaking of " Napoleon in
L808," we should have to declare that it disagreed with
" unfortunate."

4:. It is thus that most logicians do now dispose of what are
called Modals, that is, propositions in which we make a predication,
not absolutely, but after a mode. Thus, when it is said that " Bru-
tus killed Caasar justly," we are not to understand the predicate as
being " the killer of Caesar," but " the just killer of Caesar."

Sm The Quality {iroiorriq) of a proposition, that which
makes it to be a proposition or a judgment, is its predica-
tion, its affirming or denying an agreement or disagree-
ment between the terms. In respect of Quality, all prop-
ositions are either Affirmative or Negative — they either
affirm or deny the agreement of the subject and predicate.

0. The predicate may be affirmed or denied either of
the whole or part of the subject. When it is predicated
of the whole, the proposition is said to be Universal ;
when not of the whole, it is said to be Particular (ei> iiepei,).
This division of propositions is said to be made in respect
of their Quantity, that is, the extent of the predica-
tion. "When it is said "all poets are men of genius,"
the proposition is universal, the affirmation is made of all
poets. When it is said " some poets have not common
sense," the assertion is made only of a part of the class.
Such phrases as " every one " and " all " in affirmative
propositions, and " no," " no one," and " none " in nega-
tive propositions, are the signs of universality. The sign
of particularity is " some " in the sense of " some at least,"
— we may not know how much or how many.,

7. The word " all " is ambiguous. It may mean " every one,"
every one of a class, as when we say " all books are meant to be
read." It may also mean all collectively, meaning the whole class,
as " all the books constitute the library." In this latter sense, the
term is singular-abstract. (See §48). In both senses the proposi
tion is reckoned Universal. The word " some " is also ambiguous

96 JUDGMENT.

It may signify " some, not all," "some at most ; " as when we say
" some lawyers are not greedy," implying that there are some
who are. It may mean " some-certain," as when it is said that
" some sciences are classificatory," pointing to mineralogy, botany,
and zoology. In Logic " some," as the sign of particularity, signi
fies " some at least ; " it may be only one, or it may even be all,
provided we do not declare it to be all.

8* In order to determine the quantity of a proposition;
we must look, it is evident, to the subject. In many sen
tences the quantity is not indicated by the language, but
v it must always be understood in thought. When it is
said that " men have the power of speech," we mean " all
men," and not merely " some men." But when it is said
that " books are necessary to a library," we mean not " al]
books," but " some books." Terms in which the quantity
is not indicated by the language are called " indefinite "
or " indesignate " (Hamilton).

0, Combining these cross-divisions, we have a fourfold
division of propositions :

Universal Affirmative denoted by A.
Universal Negative " E.

Particular Affirmative I.

Particular Negative " 0.

Asserit A, negat E, verum generaliter ambo.
Asserit I, negat 0, sed particulariter ambo.

' 1ft. This may be the proper place for explaining what
is meant by the Distribution of Terms in a proposition.
A term is said to be distributed when it is used for all its
significates. When it is said " reptiles are cold-blooded,"
the general term " reptiles " is distributed — it includes all
and every reptile. But when it is said that " food is
necessary to life," the general term "food" is not dis-
tributed, for it does not mean every kind of food, but
food of some kind. Singular Terms and Abstracts are
always to be reckoned as distributed. When it is said

CATEGORICAL PROPOSITIONS. 97

Shakespeare is the greatest poet that ever lived,"
Shakespeare is to be taken for the man, for the man as
a whole — we do not make the affirmation of some Shake-
speare, or Shakespeare in part ; and the proposition is
regarded as universal, A„ by logicians. It is the same
with abstracts proper, as "pride goeth before destruc-
tion," meaning, not " some pride," but the one thing
" pride." It is always to be kept in mind, indeed, that
abstracts may become common terms (see § 49), as when
we talk of various kinds of pride, as pride of intellect,
pride of life ; in such we are to ascertain whether the
term is distributed or not, as we do in the case of any
other general term.

11. From the account now given, it is clear that in all
Universal propositions, A and E, the Subject is distribu-
ted, and that in all particular propositions, I and O, it is
undistributed. As to the Predicate, it is to be regarded
as distributed in all negative propositions. When we
say " no brute is immortal," " some men are not misers,"
we exclude brutes from the whole class of immortals, and
certain men from the whole class of misers. When the
Predicate is a general notion, it is not to be understood
as distributed in affirmative propositions. When it is
said that " men are mortal," the term mortal is not taken
for all its significates ; we cannot say " all mortals are
men." But it is of importance to remark (the signifi-
cance of it will come out as we advance) that as singular
and abstract terms are distributed and regarded as uni-
versals, so the predicates which are formed by such are
always to be regarded as distributed. In the proposi-
tions " Homer was the author of the Iliad " and the
" Uiad was the greatest of Greek poems," the terms
"author of the Iliad," and "the greatest of Greek
poems," are taken in all their extent.

12. The question is much discussed, what are the re-

98 JUDGMENT.

lations between the objects compared in a judgment.
The proper answer is that they may be as many and va-
ried as the relations which can be discovered between
things by the mind of man. What is the number and
what the nature of these relations, is a question to be
settled — if it can be settled — by physics or metaphysics,
and not by logic. The varied relations are all involved
in those acts in which we compare single objects with
each other. Judgments in regard to individual things
must evidently be the first formed by the mind — they
must precede the formation of concepts, for it is by re-
semblance between individuals in respect of some quality
that we are able to gather them into classes. Sfcich judg-
ments have been called Psychological by Dr. Mansel, to
distinguish them from Logical. For logical purposes,
that is in the discursive comparison of notions, judg-
ments may be regarded as of two kinds.

13. N.B. The relations which the mind can discover have heen
variously classified by philosophers. In the Intuitions of the Mind,
(P. II., b. iii.), the human intellect is represented as capable of per-
ceiving the relations of (1) Identity, that is, that the same is the
same observed at different times and in different circumstances ; (2)
Whole and Parts (Comprehension, Abstraction, Analysis, Synthesis) ;
(3) Space (Extension, Figure) ; (4) Time ; (5) Quantity (Less or More) ;
(G) Resemblance ( Classification) ; (7) Active Property ; (8) Cause and
Effect. These may all be noticed in the relation of individual
things. But for logical ends the relations may be considered as
two.

14. First. There are Equivalent Propositions, or
Equipollent Propositions — to use a phrase of the old lo-
gicians somewhat modified. Here the agreement of the
terms is one of identity or equality. In all such the sub-
ject may take the place of the predicate, and the predi
cate the place of the subject without any change. Under
this head should be placed all those cases in which both
the notions compared are Singulars or Abstracts, as

' Milton was the author of Paradise Lost," " Bomulus

CATEGORICAL PROPOSITIONS. 99

was the founder of Rome." These propositions being
given, we can say " The author of Paradise Lost was
Milton," " The founder of Rome was Romulus." To this
class belong arithmetical and geometrical propositions as
3 + 3=6. Here the terms are abstracts, and we can say
6 = 3 + 3. It is of importance to observe that to this
class belong all definitions, as "Logic is the science of
the laws of discursive thought," Natural History is the
science of the classification of animals and plants." In
these propositions the terms are Abstracts, neither Per-
cepts on the one hand, nor Concepts on the other ; and
we can convert simply, and say " the science of the Laws
of discursive thought is Logic " and " the science of the
laws of the classification of animals and plants is Natural
History." (See P. I., § 73.) In all such, neither term has
any claim in itself to be regarded as subject or as predi-
cate. That is the subject which is primarily before the
mind of the speaker to be compared with something else,
and that is the predicate with which it is compared ; and
the speaker or writer may have either term primarily in
his thoughts, or now he may have one and now the
other.

15. Second. There are propositions in which the
agreement is one of joint Comprehension and Extension.
In all such it will be found that one of the notions is a
concept, or that both are so. Take the proposition
" Longfellow is a poet." Here the subject is a Percept,
and the predicate a Concept. The proposition may be
interpreted in one or other of two ways : in Comprehen-
sion, meaning that "Longfellow has the attribute of
writing poetry ; " or in Extension, meaning that "he is in
the class of poets." Or we may take a case in which both
terms are Concepts, as " Crocodiles are reptiles ; " which
may be interpreted " the class crocodiles possess the at-
tributes of reptiles ; " or, " the class crocodiles are in the

100 JUDGMENT.

class reptiles." It has often been disputed whether prop-
ositions are to be understood in Comprehension or Ex-
tension. The proper account is that in those we are now
speaking of they are to be understood in both. I be-
lieve, indeed, that in the greater number of propositions,
in particular in all propositions in which the predicate is
a verb, the uppermost thought is in Comprehension :
when we say " men think," we mean that they are in
the exercise of thinking. But as an attribute possessed
by objects maj always be a bond to unite them into a
class, so we may interpret the proposition in Extension
also, and say "men are among the class of thinking
beings." And in many propositions the uppermost
thought is in Extension. When we say " the crocodile is
a reptile," our primary intention may be to indicate
that it is in the class. But as Extension always implies
Comprehension, that is, a class always implies a quality
to bring the objects into the unity of a concept, so we
may always interpret the proposition in Comprehension
likewise, and say " the crocodile has the attributes of
reptiles."

16, The distinction between these two classes is of
great logical importance. It was noticed by Aristotle
who divided propositions into Convertible and Uncon-
vertible, and appears in the present day in the distinction
drawn by Archbishop Thomson between Substitutive and
Attributive Judgments. We have seen that in the former
class we can at once put the subject in the place of the
predicate, and the predicate in the room of the subject.
In the other we cannot do so without changing the predi-
cate ; thus in the Attributive Judgment " all men think,"
we cannot convert simply, and affirm "all thinking beings
are men." It has not been noticed that in the first class
both notions are Percepts or Abstracts, and that in the
second the predicate is a Concept.

CATEGORICAL PROPOSITIONS. 101

17. In the second class there is a real difference be-
tween the subject and the predicate, whereby the one
comes primarily and the other secondarily in the order of
thought. We may say for poetical effect " sweet is the
breath of morn," but the natural order in thought is
" the breath of morn is sweet." The rationale is, that in
predication we ascribe an attribute to an object, or we
place it in a class ; and in both the predicate must be
more extensive and less comprehensive than the subject.
This is the the rule at least for affirmative propositions,
that the subject is the more comprehensive and less ex-
tensive.

18. Certain negative propositions seem to be exceptions. Thus
when we say " all Greeks were not Athenians," the subject is more
extensive than the predicate. But the proposition is not a univei-'
sal negative, E : we do not say of every one of the Greeks that they
were not Athenians, or that no Greek was an Athenian ; but that
" some Greeks were not Athenians." But then even in this form the
subject is the more extensive. But is not the proposition in thought
" some Greeks were Not-Athenians," in which we constitute a clasB
of all persons Not-Athenians, which is more extensive than Greeks ?

10. It is disputed what we are to make of those prop-
ositions in which the predicate is a general notion dis-
tributed, e. g., "all men are all rational beings." It is
clear that when we say simply " all men are rational," we
mean that every one man, every one in the class man, is
in the class rational. But if we have farther found that
every rational being is in the class man, we are entitled
to say '•' all men are all rational." But what do we mean
when we say so ? The terms, it appears to us, are no
longer general, standing for each and every one of a class ;
we do not mean " every one man = all rational," nor
" every one man = every rational." The word " all "
does not now mean " every one," but the whole collec-
tively (see § 48). The meaning in fact now is, " the
whole class men — the whole class rational." If so, the

102 JUDGMENT.

terms are not General, applicable to each and every one
of an indefinite number, bat Singular, with a process of
Abstraction involved. To take one other example. The
mathematician demonstrates that " equilateral triangles
are equiangular," meaning that every one equilateral tri-
angle is so. He also demonstrates that " equiangular tri-
angles are equilateral." He can now say "the whole
class of equilateral triangles is equal in extent to the
whole class of equiangular," and the terms are Singular
Abstracts, and the propositions Convertible, Substitutive,
Equivalent or Equipollent.

20. We have called attention (§ 9) to the fourfold
division of propositions A, E, I, O. But we have now
seen that there is a class of Universal Affirmative prop-
ositions in which the predicate is distributed. To dis-
tinguish them from A, in which the predicate is not dis-
tributed, it is proposed to designate them by the vowel
U (Hamilton), or A2 (Spalding), which would represent
that class of propositions in which the terms are Sin-
gulars or Abstracts, and Convertible.

21. According to Aristotle, every proposition declares a genus
(vevoc), or a property (L5lov), or a definition (<5pof), or accident (av/nj3e
8?]k6(), of the subject. Genus denotes a part or attribute belonging
to the subject, but also to other subjects, as " mammals are verte-
brates," where the predicate applies to other subjects as well. A
property belongs invariably to the subject, but without being the
mark which explains its nature, as that "mammals are warm-
blooded." Definition is an attribute or set of attributes explaining
the very nature of the subject, as that mammals suckle their young.
Accident is an attribute belonging to the subject, but which might
be conceivably separated from it, as that mammals are found in
America. This makes the predicables four in number. Porphyry
has five Predicables, genus, species, proprium, differentia, and acci
dent, leaving out definition and adding species (tvJof) and differentia
(diafopu). Species is the whole essence of its subject. Differentia
is that attribute or set of attributes by which a species is distin
guished from other species of its genus.

CATEGORICAL PROPOSITIONS. 103

Some of these distinctions are of great importance, as that be-
tween genus and species (P. I., § 35) ; and that between definition
and proprium, or, as Porphyry makes it, between differentia and
proprium. In species and differentia, e. g., " mammals suckle their
young," the subject and predicate are convertible or equivalent or
coextensive. In proprium, e. g., that " mammals are warm-blooded,"
the terms are not convertible, for there are warm-blooded animals
which are not mammals. The distinction between differentia and
proprium is valuable as showing that when we have fixed on the
differentia of a class, we may often find other attributes conjoined
with it which may be called propria. This is the case with those
classes which are called Kinds (Part I., § 126). It is difficult, how-
ever, in some circumstances, to determine what is differentia and
what is property. Under one view, that is, to the sailor, polarity
would be the differentia of the magnet, while under another aspect,
" to those manufacturers who employ magnets for the purpose of more
expeditiously picking up small bits of iron and for shielding their
faces from the noxious steel-dust in the grinding of needles, the at-
tracting power of the magnet is the essential point." (Whately.) It is
extremely difficult to carry out these distinctions thoroughly and con-
sistently. We cannot tell what is the whole essence of any subject ;
all that we can do is to specify one or more of the determining attri-
butes of a species. Nor can we say in all circumstances what is an
accident as distinguished from a property, say, e. g., whether that it
lives on the earth is the property or accident of a mammal. The
distinction adopted in the text between Equivalent propositions in
which the terms are coextensive and interchangeable, and Attribu-
tive propositions in which the relation is one of joint comprehension
and extension and in which the predicate is undistributed, seems to
be the important one for logical ends.

22. Hamilton maintains that the predicate should always b©
quantified, that is, declared to be either particular or universal ; that
we should say logically, " all men = some fallible." He argues this
on the ground that whatever is contained implicitly in spontaneous
thought should be unfolded explicitly in logical forms. We admit
the principle, but we deny that it requires the quantification of the
predicate in affirmative propositions. In the great majority of
affirmative propositions, the predication is made in comprehension
rather than extension. When we say " the bird sings," we are at-
tributing a quality to the bird, and we are not determining in
thought whether there are or are not other creatures that sing

104 JUDGMENT.

When we say " man reasons," we are ascribing a property to him
probably without settling whether there are or are not other beings
who reason ; and so the logician is not required to put the proposi-
tion either in the form "all men = some reasoning beings," or " all
men = all reasoning beings." And this may be the proper place
for stating that there is no appropriateness in using the sign of
equality, =, which has a definite meaning in mathematics, to ex-
press the connection of the notions in attributive propositions in
which the relation is one of comprehension and extension and not
jf mere equality.

23. Carrying out his doctrine of the thorough quantification ol
the predicate in all propositions, Sir W. Hamilton gives the follow-
ing Table of Judgments :

A All plants grow.

E No right action is inexpedient.

I Some muscles are without our volition.

O Some plants do not grow in the tropics.

IT Common salt is chloride of sodium.

T Some stars are all the planets.

j) No Frenchman is some German.

u Some trees (oaks) are not some trees (elms).
The two marked by the Greek letters are criticised by Thomson and
rejected on the ground that while they are conceivable cases of neg-
ative predication they are not actual — we woidd add in spontaneous
thought. Thus rj has the resemblance, not the power of denial ; it
denies nothing, and decides nothing. T should also be discarded on
the ground that it is never uttered by us in spontaneous thought, in
which we say instead " all the planets are stars," which is A. Kejecting
these three forms on these special grounds, we farther decline to give
them a separate place in the Table of Judgments, on the general
ground that in spontaneous thought the predicate is not quantified
in all or even in most judgments. We admit that they are forms
which may be reached by Conversion or other kinds of Immediate
Inference to be explained forthwith ; but then it has never been
deemed necessary or even proper to introduce such among the forms
of spontaneous j udgment ; and if we adopt these we must by parity
of reason introduce others, and make the Table contain many more
judgments. We are inclined, however, to think that it is of im-
portance to separate those propositions which are Equivalent from
others, and to have a letter, U, to designate them. But let it be
observed that in the Judgments thus denoted, the notions compared

CONJUNCTION OF PROPOSITIONS. 106

are Percepts or Abstracts. We are thus enabled to retain the old
Table, A, E, I, 0, for all those judgments in which we have a Con-
cept, while U is added to designate that class of propositions which
have been seen to be Convertible since the days of Aristotle, and
which turn out to be those in which the notions compared are not
general or class notions.

CONJUNCTIONS OF PROPOSITIONS, CONDITIONALS, AND
DISJUNCTIVES.

24:. We have now to consider propositions in their
relations one to another. Most of these relations are of
so loose a nature that they cannot be brought under any
laws of discursive thought. When we say " the road was
long and steep," we have two propositions, " the road was
long " and " the road was steep," but with no special con-
nection except that in both the affirmation is made of
" road." When we say that " the fever was virulent, but
the patient recovered," we have two affirmations so far in
a state of opposition, but not involving any discursive pro-
cess falling under Logic. Such connections of sentences
are indicated by connective particles, such as " and,"
" but," " then," " afterwards," " either," " neither," " so,"
" however," and attempts have been made by gramma-
rians, with only imperfect success, to classify them into
conjunctive, adversative, &c.

25. But propositions may be so connected as to in-
volve a discursive process falling under the laws of
thought. We do not refer now to that formal conjunc-
tion of propositions which forms reasoning, but to the
tin-owing of two or more connected propositions into one.
The propositions hitherto considered are called Categor-
ical, in which one proposition is simply said to agree or not
to agree with another. But there are propositions in which
the predication is made hypothetically, and which are

106 JUDGMENT.

therefore called Hypothetical. They are of two kinds, one
called Conditionals, the other Disjunctives.

26» There are Conditionals or Conjunctives in which
the predication is made under a condition. "If the night
continues clear there will be dew on the grass." Here we
have two categorical propositions, " the night is clear "
and " dew will be on the grass,5' and we put them into one
proposition, which affirms that they are so related that the
one depends on the other. It is certainly desirable in every
way to have the propositions spread out and then- connec-
tion intimated in the conditional form, as it is only thus we
can perceive fully the relations of things and of thoughts.
But it is of equal importance that we should be able to
detect the one proposition in the affirmation that they
agree, and that we should be able to point out its subject,
its predicate, and copula.

27. The proposition on which the other depends, wheth-
er placed first or last, is called the Antecedent, that which
depends on it the Consequent, and the relation between
them the Consequence. Sometimes there are four terms
in the Conditional. " If the sun attracts in the same line
as the moon, the tides are at the highest." Here we have
four terms ; " sun," " attracting in the same line as the
moon," "tides," "at the highest." But in propositions
with such a connection it will often happen that the same
term appears both in the antecedent and consequent,
either as subject or as predicate. " If the man pursues
an honest course he will prosper." " If virtue is volun-
tary, vice is voluntary." In all cases the two propositions
are put into one in the Conditional, and we have to find
the one subject and the one predicate in the affirmation.
" The night continuing clear," subject ; " will have dew
on the grass," predicate. " The sun attracting in the
same line as the moon," subject ; " will have tides at the
highest," predicate. All Conditional Propositions are to

CONJUNCTION OF PROPOSITIONb 10?

be regarded as affirmative. Even when we say that " ii
the night becomes cloudy there will be no dew," the prop-
osition is not to be regarded as negative, for what we
affirm is a relation between the cloudiness of the night
and the absence of dew.

28. The logician does not require to consider what is the nature
of the dependence of the consequent on the antecedent, whether
it is in things or in thought, whether it is or is not the relation ol
;ause and effect, or whether the relation of cause and effect is neces-
sary or contingent. He leaves all these questions to the physical
investigator or the metaphysician. To him the relation of the two
propositions is given, aud he has to consider the discursive thought
involved in the relation of the two propositions.

29. Conditional propositions may be Equivalent or
they may be Attributive, and we are to determine to which
class they belong, in the same way as we do in Categori-
cals. The examples given above are all of Attributives.
But when the terms are singular and abstract, we shall
have Equivalent Conditionals, e. g., " If the relation be as
4 to 16, it is the same as that of 1 to 4," or, in Categorical
form, " the relation of 4 to 16 is the same as the relation
of 1 to 4."

30. Disjunctive Propositions express the relation of
two or more judgments which cannot all be true, but one
or more of which must. It involves two or more judg-
ments brought into one. It jxroceeds on the principle of
Logical Division (Part I., § 58), implying that we have
divided a genus into its co-ordinate species. "Judgment"
is the genus, and we find in respect of quality that " every
judgment is affirmative or negative." Here we have two
members in two propositions, " every judgment affirms,"
" every judgment denies," and we declare that " everv
judgment either affirms or denies." These cannot both
be true, but one or other must, on the supposition that
our division of the species is adequate to the genus. In
the same way we may have three members, as " all notions

108 JUDGMENT.

are Percepts, or Abstracts, or Concepts." Or we may havo
four members, as when we say that in respect both of
quantity and quality, every proposition is A, or E, or I, or
0 ; or we may have live members if we add U, and say
" all propositions are A, E, I, 0, or U."

31* All Disjunctive Propositions are Equivalent or
Substitutive. The predicates in the above examples,
" either affirms or denies," " Percepts, Abstracts, or Con-
cepts," " A, E, I, and 0," are not general notions embrac-
ing an indefinite number of individuals, but abstract no-
tions to be taken in their full extent.

IMPLIED JUDGMENTS, OR IMMEDIATE INFERENCES.

32. From any given proposition certain others can be
drawn discursively by processes which the logician can
analyze and express. These have been called Syllogisms
of the Understanding by Kant, to distinguish them from
Syllogisms of Seasoning. Some British writers call them
Immediate Inferences, as distinguished from Mediate In-
ferences, or reasoning by means of a middle term. We
are inclined to designate them Implied or Transposed
Judgments. They all flow from the nature of the Notion
as above unfolded, from its interpretation, comprehension,
extension and denomination, and from the relation of the
notions in the jn'oposition.

33, CONVERSION. In this process the terms are
transposed so that the subject becomes the predicate, and
the predicate the subject. In order to its validity, the
truth of the converse must be implied in the truth of the
exposita or proposition given. The main rule for secur
ing this is, that no term is to be distributed in the con-
verse which was not distributed in the exposita. It
may be effected in two or three ways. (1) Simple Conver

IMPLIED JUDGMENTS. 109

sion, in which the terms are transposed without any change
of quantity. This can be done in propositions in E,
in which both terms are distributed, and in I, in which
neither is, as E "No man is perfect," converted "No per-
fect being is man ; " I " Some men are generous," con-
verted " Some generous beings are men." (2) Conver-
sion by Limitation or per accidens, by changing the
quantity. It being given that " all deception is mean," we
cannot say " all mean things are deception," but " mean "
being undistributed in the exposita, we give it the sign
of particularity or non-distribution in the converse,
and say, " Some mean thing (or among mean things) is
deception." A can be converted in this way, as may also
E. (3) It is disputed whether O can be legitimately con-
verted. " Some students are not industrious." We can-
not, therefore, say " some industrious are not students,"
for you would have students limited in the original prop-
osition and distributed in the converse. Some logicians
think that conversion may be accomplished by what is
called Contraposition, that is, by attaching the negative
to the predicate and reckoning the proposition affirmative,
thus making the predicate undistributed. "Some stu-
dents are not-industrious," converted " some not-indus-
trious are students." This is certainly a legitimate dis-
cursive process, but seems to imply Privative Conceptions
(see infra, § 49).

34. OPPOSITION. Light is often thrown on the
nature of a proposition by its being put in the various
forms of what is called Opposition. In Equivalent prop-
ositions there is, properly speaking, only one kind of
Opposition, that between an affirmative and negative
proposition with the same terms. " Common salt is
chloride of sodium," its opposite is " common salt is not
chloride of sodium." This Opposition is Contradictory :
that is, both propositions cannot be true ; and yet one o>

110

JUDGMENT.

other must be ; and the truth of the one implies the false-
hood of the other, and the falsehood of the one the truth
of the other.

35. But when we have Concepts in the proposition,
then the forms of Opposition become more varied. They
are exhibited in the following diagram.

Fvery man has a conscience

Home men have a conscience.

No man has a conscience

men have not a conscience

Subalternation, or the relation between two propositions
which with the same terms differ in quantity, the one
being universal and the other particular. It holds be-
tween A and I, between E and 0. It can scarcely be
said to be a form of Opposition. The rule is, that the
truth of the universal implies the truth of the particular.
If it be true that " all men have a conscience," it follows
that " some men have a conscience." If it be that " no
man is free from sin," it is also that " some men are not
free from sin." From the falsehood of I we can argue the
falsehood of A, and from the falsehood of O the falsehood
of E. It is evident that we cannot reversely argue the
truth of the universal from the truth of the particular,
that we cannot argue A from I or E from O.

36. Subalternation depends on the principle that
whatever is true of a class, is true of any and of each of
the members of the class. We are now on the very verge
of Mediate Reasoning. In Subalternation we say "ah

IMPLIED JUDGMENTS. HI

bodies attract each other " (A), and so " some bodies
attract each other." In Mediate Seasoning we introduce
a third term and declare, on the same general principle,
that "the planets, being bodies (some bodies), attract
each other," (see Pakt Third.)

37. Contrary Opposition, in which the propositions,
always having the same terms, differ in Quality. It holds
between A and E. Contraries cannot both be true. If all
men are liars, that is, included in the class liars, it cannot
be true that no men are liars. But they may both be
false, that is, it may not be true either that " all men are
liars," or that " no men are liars." The Opposition be--
tween I and 0 is called Sub-Contrary. They may both
be true but cannot both be false. Thus it is true that
" some men are liars " and that " some men are not liars."
But if it be false, that " some men are sinless," it must be
true that " some men are not sinless," and if it be false
that " some men have not a conscience," it must be true
that " some men have a conscience."

So it is usually said. But it should be observed that in the twc
last instances we use " some," not in the proper logical sense 01
' some at least," " some, we know not how many," but in another
^ense, " some at most," " some, not all." (See § 7.)

38. Contradictory Opposition, in which the propositions
differ both in quantity and quality, as A and 0, E and I.
From the truth of a proposition we can posit the false-
hood of its contradictory. If it be true that " all men
have a conscience " (A), it cannot be that " some men
have not a conscience " (0) ; and if " some men have not
a conscience " (0), it cannot be that all men have a eon-
science (A). If "no man has a conscience" (E), it can-
not be that " some men have a conscience " (I) ; and if
"some men have a conscience" (I), it cannot be that
" no man has a conscience " (E). When two prop-
ositions are in the relation of contradictories, the truth

112 JUDGMENT.

>f the one implies the falsehood of the other, and
the falsehood of the one the truth of the other. This is
the Law of Contradiction, or, as it is called by Hamilton,
of Non-Contradiction. But there is another law involved
called the Law of Excluded Middle, — that of two contra-
dictories one or other must be true, there is no Middle
between. It must either be that " all men have a con-
science " (A), or that " some men have not a conscience "
(O) ; that "no man has a conscience " (E), or that "some
men have a conscience " (I). It follows that if you prove
the truth of a proposition, you thereby prove the false-
hood of its contradictory ; or if you prove the falsehood
of a proposition, you establish the truth of its contradic-
tory. If you prove that some doctrines, such as the con-
nection of mind and body, are to be believed, though they
are not comprehensible, you have thereby shown that a
doctrine is not to be disbelieved because it is incompre-
hensible.

30. Demonstration, that is, the establishment of a
point by a pure discursive process founded on truth al-
lowed, is of two kinds, direct and indirect. When the
proposition is established by proving its truth, it is said
to be direct. We should use this method, as being the
most satisfactory, whenever it is available. But there is
another mode called indirect which is also valid. You
may prove not that a proposition is true, but that its con-
tradictory must be false, which implies the truth of the
proposition of which it is the contradictory opposite.
Euclid often employs this method of demonstration,
showing that you contradict a conceded truth by follow-
ing any other supposition than that which he makes. We
shall see that the same mode is employed in Logic in
establishing the Special Rules of the Figures and in cer-
tain forms of Reduction,

4:0. It is desirable in controversy to have the prop-

IMPLIED JUDGMENTS 113

ositious defended, put in the form not of contrary but ol
contradictory opposition. Without this the combatants
may fight without ever facing each other, and the whole
discussion will be characterized by hopeless confusion.
One asserts that men may be trusted, another that men
may not be trusted, and the contest may go on forever
with abundant evidence on both sides ; but let the posi-
tions assume the form " all men are to be trusted " and
" some men are not to be trusted," and the question may be
settled. One holds that such branches as history and meta-
physics should be studied, another that they should not,
and both are right and both are wrong ; but let the state-
ments be, on the one hand, that " no history is to be stud-
ied," or that "no metaphysics are to be studied," and on
the other that "some history is to be studied," or that
" some metaphysics are to be studied," and the victory
will easily be gained by those who hold the affirmative.
When arguing with an opponent, let it be your business
to prove the contradictory of his position ) and you niay
insist on his proving not the mere sub-contrary of your
statement, but the contrary or contradictory. In all
cases it is desirable that we should know what is the con-
tradictory (s'/ley%oc) of the proposition we are holding
or impugning.

4:1. The following are the transposed propositions we may oh
tain by means of Opposition :

If A be true, E is false, I true, 0 false.

If A be false, E is unknown, I unknown, O true.

If E be true, A is false, I false, 0 true.

If E be false, A is unknown, I true, 0 unknown.

If I be true, A is unknown, E false, 0 unknown.

If I he false, A is false, E true, 0 true.

If 0 be true, A is false, E unknown, I unknown.

If 0 be false, A is true, E false, I true.

From the truth of a universal or falsehood of a particular, we maj
titer the quality of all the opposed propositions ; but from the false
8

114 JUDGMENT

hood of a universal or truth of a particular we can know only tlw
quality of the contradictory.

42. It should be observed that both in Conversion and
Opposition we gain the Implied Judgments simply by the
contemplation of the Extension together with the involved
Comprehension of the Notions. In Subalternation, if A
be true, I must be true, because I is involved in the Ex-
tension of A. If A be true, E is false, for in A we ascribe
an attribute to all A and in E we deny it. In all the
transposed judgments we must see that the judgment
reached has not a greater Extension than the judgment
given, and that we predicate of both the same attribute
or group of attributes.

43. Conversion and Opposition are treated of in all the oldei
logical treatises, in which, however, it is not noticed that the prop-
ositions reached, are drawn by a contemplation of the Extension
and Comprehension of the Notions. Nor has it been explicitly
stated that the above rules of Conversion and Opposition do not
apply to propositions in which there is no concept. Of such all Con-
version is Simple, and all Opposition is Contradictory ; thus it
being stated that " Newton discovered the law of gravitation," it
would be unmeaning to say, by the law of subalternation, that
" some Newton discovered the law of gravitation." Later logi
cians have noticed that there are other Immediate Inferences equally
entitled to a place in the exposition of Logical Judgment. It may
be doubted whether they have seen their exact nature.

44. Tlie Interpretation of Judgments gives certain Im-
plied Propositions. If it be given "the orbit of the
planets is elliptical," we have by Denomination " the epi-
thet elliptical may be applied to the orbits of the planets ; "
by Extension, " the orbits of the planets are among the
things that are elliptical," and by Comprehension " ellip-
tical is an attribute of the planetary orbits." Like Trans-
posed Judgments may be derived from propositions in E,
I, and O : as I, " some metals are lighter than water,"
by Denomination the phrase " lighter than water " may
be applied to " some metals ; " by Extension " some

IMPLIED JUDGMENTS. 115

metals may be included in the things which are lighter
than water ; " by Comprehension " the property of lighter
than water belongs to some metals." Propositions in U
may always be interpreted by Denomination and Com-
prehension. It being given that " Ethics is the science
of man's motive and moral nature," we may say " the
phrase science of man's motive and moral nature may be
applied to Ethics," and " the attributes of the science of
man's motive and moral nature belong to Ethics."

4o* There are Implied Judgments obtained by the
special consideration of the Comprehension of the No-
tions, as by

TJie Interpretation of Marks, as when it is said "John
loved Jesus," it is implied that " John lived " and that
" Jesus lived," and that " there is such a thing as love."

4z6» Added Marks to both subject and predicate. Thus
if it be declared that " a negro is a fellow-creature," we may
say " a negro in suffering is a fellow-creature in suffering."
If " learning be useful " then " injury to learning would
be injury to what is useful."

47. Added Subject and Predicate may give other judg-
ments by being added to a conception. Thus as " hon-
esty is the best policy," " the disregard of honesty would
be the disregard of the best policy."

48. A Summation of Predicates may give us an Im-
plied Judgment. Thus if it is found (1) that virtue is
voluntary, (2) in obedience to a law, which is (3) the law
of God, then we may combine the predicates and get a
definition of virtue : " Virtue is a voluntary act done in
obedience to the law of God."

A9. Privative Conceptions may yield Transposed Judg-
ments. We have seen (Part I., § 53) that from any given
concept we obtain another by leaving out its mark : thus
from the positive concept " wise," we may obtain the
privative concept "unwise." Any judgment pionounceO

116 JUDGMENT.

on the positive concept, implies judgments upon the
privative.

The following is taken from Thomson's Outlines of the Laws of
Thought (see also De Morgan's Formal Logic, p. 61), leaving out the
examples in Y :

I. A All the righteous are happy.

None of the righteous are unhappy.
All who are unhappy are unrighteous.

E No human virtues are perfect.
All human virtues are imperfect.
No perfect virtues are human.

I Some possible cases are probable.

Some possible cases are not improbable.
Some probable cases are not impossible.

U The just are all the holy.
All unholy men are unjust.
No just men are unholy.

[I. A All the insincere are dishonest.
No insincere man is honest.
All honest men are sincere.

E No unjust act is unpunished.
All unjust acts are punished.
All acts not punished are just.

I Some unfair acts are unknown.
Some unfair acts are not known.
Some unknown acts are not fair.

O Some improbable cases are not impossible.
Some improbable cases are possible.
Some possible cases are not probable.

U The unlawful is the only inexpedient.
The lawful is the expedient.
The lawful is not the inexpedient.

We may make a proposition assume any one of these forms as
may seem best fitted to give clearness of thought and to enable us
to affirm or deny it ; and we may express it in the form which may
best accomplish the end we have in view in the expression. It is
by this process that from 0, " some mathematicians have not had

IMPLIED JUDGMENTS. 117

much practical wisdom," we get "some without practical wisdom
have been mathematicians," (§33.) From any one of the abo\e
propositions (except those in Oj we may derive another proposition
by conversion.

50. Conditional Propositions give implied judgments.
" If this man has consumption he will not recover." This
implies that the " case of a man who has a consumption
is the case of a man who will not recover," or bringing
the notions into closer relation, " One who has consump-
tion will not recover."

51. Disjunctive Propositions involve other propositions.
Thus if it be allowed that " every given time must be
spring, or summer, or autumn, or winter," we are entitled
from the rule of Logical Division, that the members must
make up the whole (I., § 58), to say, that " all times not
spring, or summer, or autumn, must be winter," and from
another rule, that the members must exclude one an-
other (I., § 59), to affirm that " winter is neither spring,
nor summer, nor autumn."

52. In all these cases the rule is to be rigidly observed,
that a term must be distributed in the transposed prop-
osition only when it is distributed in the original one.
Because we are entitled to make a predication of some,
we are not therefore entitled to make the same predication
of aU.

53. The above are examples of Implied Judgments
derived according to rules specified. We believe there
may be other kinds drawn by discursive thought, and
that the logician could formulize the law which rules
them. It may be interesting to show how many other
propositions could be got from the single one " men are
responsible," by simply contemplating the Extension and
Comprehension of the Notions.

Extension.
Every man is in the class responsible.
This man is responsible.

118 JUDGMENT.

.Some men are responsible.

Every tribe of mankind are responsible.

Some responsible beings are men.

It is not true tbat no men are responsible.

It is not true that some men are not responsible, &c &c

Comprehension.

Man exists.

Responsibility is a real attribute.

Responsibility is an attribute of every man.

Responsibility is an attribute of this man.

Responsibility is an attribute of every tribe of mi-n.

Responsibility is an attribute of some men.

Irresponsibility may be denied of all men.

No man is irresponsible.

Irresponsible beings are not men.

Men of wealth are responsible with their wealth.

To punish men is to punish responsible men, &c, &c.
In treating of Implied Judgments we have been indebted tc
Thomson's Outlines of the Laics of Thought, where, however, they
are called Immediate Inferences and placed under Reasoning, aud
are not derived from the nature of the Notions.

#4. We may close the part of Logic which treats of
Judgment, by showing what Logic can do in settling for ns
what are and what are not true propositions. It is evi-
dent that it cannot determine for us directly what prop-
ositions imply and what do not imply Objective reality,
e. g., whether there is or is not a sea-serpent. But it can
do much in the way of enabling us to pronounce a right
judgment upon evidence. It requires us to ascertain what
are the Notions, that is, the things compared and in regard
to which we make the affirmation or denial. It makes us
look at the nature of the notions and find whether they
are singulars, abstracts, or general concepts, and to de-
cide about them accordingly. Thus when it is said that
" virtue is that which promotes the greatest happiness,"
we see that both subject and predicate are abstracts, and
that therefore the terms must be convertible (§ 14) ; and
as we see this, we are better able to determine whethei

IMPLIED JUDGMENTS. 119

the proposition is true, for we ask whether " that which
promotes the greatest happiness is (always) virtue ? " If
it be maintained that "sea-serpents exist," we perceive
that serpent is a common term, and we inquire what are
the common qualities (differentia) of serpents, and are
thus in a better position to determine whether serpents
can exist in the sea, and whether the appearances which
sailors have noticed can be of sea-serpents. Logic urges
us farther to inquire into the relation of subject and
predicate, whether it is one of equivalence or attribution.
Every one will admit the truth of the attributive prop-
osition that " virtue promotes happiness," but many deny
the truth of the equivalent one, "that which promotes
happiness is virtue." We believe that more than one
half of the error in the world proceeds not from mere
ignorance, but from inattention and confusion, which find-
ing us ignorant, tends to keep us in ignorance. Logic
helps to cure the evil by requiring of us to determine
what are the notions, and to place these fully and fairly
before the mind ; and when this is done, we will be able
either to see what judgment we should pronounce, or to
wait for further light before we come to any decision.

PART THIRD.

REASONING

1. " In every instance in which we reason, in the strict
sense of the word, i. e., make use of arguments (I mean
real, i. e., valid arguments), whether for the sake of refut-
ing an adversary, or of conveying instruction, or of satis-
fying our own minds on any point, whatever may be the
subject we are engaged on, a certain process takes place
in the mind which is one and the same in all cases, pro-
vided it be rightly conducted. Of course it cannot be
supposed that every one is even conscious of this process
in his own mind ; much less is competent to explain the
principles on which it proceeds. This indeed is, and can-
not but be, the case with every other process respecting
which any system has been formed ; the practice not only
may exist independently of the theory, but must have
preceded the theory. There must have been Language
before a sj'stem of grammar could be devised ; and mu-
sical compositions previous to the science of Music. This,
by the way, will serve to expose the futility of the popular
objection against Logic, that men may reason very well
who know nothing of it. The parallel instances adduced,
show that such an objection might be applied in many
other cases where its absurdity would be obvious ; and
that there is no ground for deciding thence, either that the
system has no tendency to improve practice, or that even

ITS NATURE. 121

if it had not, it might not still be a dignified and interest-
ing pursuit."

2° It will be shown that the principles involved in the
reasoning process are one and the same, whatever be the
things about which we argue, be they material, or mental,
or moral, or mathematical, or political, or theological.
" One of the chief impediments to the attainment of a
just view of the nature and object of Logic, is the not
fully understanding, or not sufficiently keeping in mind,
the sameness of the reasoning process in all cases. This
error may at once be illustrated and removed by consider-
ing the parallel instance of Arithmetic, in which every
one is aware that the process of a calculation is not af-
fected by the nature of the objects whose numbers are
before us ; but that (e. g.) the multiplication of a number
is the very same operation, whether it be a number of
men, of miles, or of pounds." Nor is Logic to be regarded
as a peculiar method of reasoning, " which is in fact as
great a blunder as if any one were to mistake grammar
for a peculiar language, and to suppose it possible to
speak correctly without speaking grammatically."

3. " Supposing it then to have been perceived that the
operation of reasoning is in all cases the same, the analy-
sis of that operation could not fail to strike the mind as
an interesting matter of inquiry. And moreover, since
(apparent) arguments which are unsound and inconclusive,
are so often employed, either from error or design, and
since even those who are not misled by these fallacies are
so often at a loss to detect and expose them in a manner
satisfactory to others, or even to themselves, it could not
but appear desirable to lay down some general rules of
reasoning applicable to all cases, by which a person
might be enabled the more readily and clearly to state
the grounds of his own conviction, or of his objection
to the arguments of an opponent, instead of arguing at

122 REASONING.

random without any fixed and acknowledged principles
to guide his procedure. Such rules would be analogous
to those of Arithmetic, which obviate the tediousness and
uncertainty of calculations in the head ; wherein after
much labor, different persons might arrive at different
results, without any of them being able distinctly to point
out the error of the rest. A system of such rules, it is
obvious, must, instead of deserving to be called ' the arc
of wrangling,' be more justly characterized as ' the art
of cutting short wrangling' by bringing the parties to
issue at once, if not to agreement, and thus saving a
waste of ingenuity." — "Whately's Elements, Analytical Out-
line.

4« In Judgment Proper, we compare immediately the
two notions, that is, the things apprehended, and declare
their agreement. But there are cases in which we do not
perceive the relation of the notions immediately, but in
which we may discover them mediately, by means of a
third or mediating notion. Thus I wish to know whether
John the Baptist was a priest, and I cannot pronounce au
immediate judgment, for it is not expressly said in Scrip-
ture that he was a priest. But we remember that his
father Zacharias was a priest, and using son of a priest aa>
a middle term, and finding from the Old Testament that the
sons of priests were themselves priests, we argue that " the
Baptist, being the son of a priest, was a priest." Here, it
will be observed, we have three terms, the two terms we
wish to compare, " Baptist " and " priest," and the term
by which we compare them, " son of a priest." In the
discursive process, when we analyze it, there will be found
three acts of comparison : one in which we compare one
of the original terms with the middle ; a second in which
we compare the other original term with the middle ; and
the third in which we bring the two terms, which we
have compared separately with the middle, into compar-

ITS NATURE. 123

ison with each other. This is Seasoning which is denned
as " the act of proceeding from certain judgments to
others founded on them."

5. To bring out the acts of comparison involved, we
an fold them in three propositions :

The sons of priests were priests ;
The Baptist was the son of a priest ;
The Baptist was a priest.

When reasoning is thus analyzed and expressed, it is
called a Syllogism.

6. The syllogistic analysis of reasoning, so far as is known, was
first unfolded by Aristotle in the Prior Analytics, and. constitutes
the most certain, and altogether the greatest, discovery ever made
in mental science. It has been discussed, and attempted improve-
ments made on it, by commentators on Aristotle, by the medieval
scholastics, by the logicians of the 17th century, and by modern
writers from Kant to the present time.

7. Some have thought that we can reason from on«
judgment. And it is quite true that from any one judg-
ment we -can draw others immediately in the mode ex-
plained in speaking of Implied Judgments. But the
judgments thus reached are confined within very narrow
limits. When we have two judgments in a certain rela-
tion to each other, a much wider range of judgments can be
drawn, and the process involved constitutes Mediate
Reasoning, or Reasoning Proper. It often happens, in-
deed, that in reasoning thus understood, there is only
one judgment expressed in what is given or allowed. But
if we carefully examine the process it will be found that
there is another judgment, which though suppressed in
statement, is involved in thought. A man has taken ar-
senic and we conclude that he shall die. Here are two
judgments implied in order to the validity of the reasoning.
One is, the matter of fact that he has taken arsenic ; and the
other, the general fact that he who has drunk arsenic shall
die. We may not think it necessary to enunciate both of

124 REASONING.

these. We would not mention the one to a person who
had seen him take the arsenic ; we would not announce
the other to a man who knew that arsenic was poison.
But we would have to state both to one ignorant of both ;
and both if not explicitly announced are implicitly im-
plied in the reasoning.

An argument with one premiss suppressed is vulgarly called an
Entliymeme. Aristotle, however, defines Entbymeme tvdv/i?//u.a /uiv
ovv iarl avXAoyicjuog e? elkotov f/ arj/aeiuv (Anal. Pr. II., 27. See Ham-
ilton's Discussions, Art. Logic, and Trendelenburg Elementa, § 37).

8, In a syllogism as an analysis of the reasoning pro-
cess we must have, as we have in the reasoning process
itself, three, and no more than three terms : the two
whose agreement or disagreement we are seeking to deter-
mine, and a third by which we determine it. The two first
are called the Extremes, and the third the Middle. Again
in a syllogism, in order to unfold the relation of the three
terms, there must be three propositions, two in which we
compare each of the Extremes with the Middle, and a
third in which we compare them with each other. The
two first are the Premisses, and the third the Conclusion.
It is evident that the Middle term will appear in each of
the premisses, but not in the conclusion. The laws of
discursive thought do not require us to follow any order
in the arrangement of the three propositions. What we
have to look at is the relation of the terms ; and if we
bring out this, it is no matter whether we begin with the
premisses, or which of the premisses we place first. Thus
instead of the order followed above, we might say,

The Baptist was a priest ;
for, He was the son of a priest ;
and, The sons of priests were priests.

From these definitions and general statements we may
derive certain Rules, which are applicable to reasoning of
every kind.

ITS RULES. 125

0. (1) In a syllogism there should only be three terms.
This has already been explained.

10. (2) In a syllogism there can only be one middle
term. It is only thus we can bring the extremes into
comparison. When a middle term is ambiguous we may
have two middle terms in sense though not in sound ;
and we are ever liable to compare the one extreme with
the middle used in one sense, and the other extreme with
the middle in another sense. Hence the fallacy of Am-
biguous Middle which will often fall under our notice.

11. (3) One premiss must be affirmative. In other
words two negative premisses prove nothing. For unless
there be an affirmative judgment declaring the agree-
ment of the middle with one of the extremes, there can be
no inference about the terms which we wish to compare.
Two negative judgments simply declare that there is no
relation between the middle term and the extremes, and
authorize no judgment as to the relation of the extremes.

12. (4) If either premiss is negative, the conclu-
sion must be negative. For one of the premisses being
negative, the other is affirmative, and so in one premiss
we assert that the middle disagrees with one extreme,
and in the other that it agrees with the other extreme,
and if so the extremes must disagree with one another.

13. (5) To prove a negative conclusion one of the
premisses must be negative. We cannot argue that
there is no connection between the extremes till we have
shown that there is no connection between one of the ex-
tremes and the middle.

14. The question now rises, can we determine and
3nunciate what is the principle in the mind which
regulates reasoning. The answer is that this can be
done by carefully observing examples of valid reasoning, by
ascertaining what is common to them all, and expressing
this in a general formula. The rule in its most general

126 REASONING.

form is, that "notions which agree with one and the
same notions agree with one another." This for affirm-
atives, and for negative conclusions, "notions, one of
which agrees, while the other disagrees with one and the
same notion, disagree with each other." But in such a
rule the phrases ''agree" and "disagree" are wide and
vague, and it is desirable to become more particular ana
specify the nature of the agreement. The distinction
which we have drawn between percepts and abstracts
on the one hand and concepts on the other (P. I., § 38)
leading to the distinction between propositions in which
the relation is one of equivalence, and those in which it is
one of joint extension and comprehension (P. II., § 14,
i.5), will help us here, and show us two regulating princi-
ples emerging for two kinds of reasoning.

15. FIRST REGULATING PRINCIPLE. "No-
tions equivalent to one and the same third notion are
equivalent to one another ; " and for negative reason-
ing " notions, one of which is equivalent and the other not
equivalent to one and the same notion, are not equivalent
to one another." This dictum rules all reasonings in
which the three notions are Percepts or Abstracts.

Shakespeare wrote Hamlet ;

He wlio wrote Hanilet is tlie greatest English poet ;
.-. Shakespeare was the greatest English poet.

Under this same head I place the following, and in- .
deed most arithmetical and geometrical inferences :

A = B

B = C

•. A = C

In all ratiocination of this description, the subject of
each of the propositions may be made the predicate, and
the predicate the subject, and the reasoning will be valid
and formally correct.

REGULATING PRINCIPLES 127

He who wrote Hamlet was Shakespeare ,
He is the greatest English poet who wrote Hamlet ,
.'. The greatest English poet was Shakespeare.

In these and in like propositions, the terms are per-
cepts or abstracts, and the relations in the propositions
and in the argument is of identity or of equality. It is
of great moment to separate these simple cases of reason-
ing from more complex ones, to be immediately consid-
ered, in which we have concepts, and extension, and
minor and major terms, and mood and figure.

16. We are now in a position to understand what we should
make of the unfigured syllogism of Hamilton.

Copperas and sulphate of iron are identical ;
Sulphate of iron and sulphate of copper are not identical ;
/. Copperas and sulphate of copper are not identical.
Here he has turned " identical," which is neither less nor more
than the copula, into a separate term. The reasoning should stand
t,hus :

Copperas is sulphate of iron ;
Sulphate of iron is not sulphate of copper ;
.•. Copperas is not sulphate of copper.

17. SECOND REGULATING PRINCIPLE. "What-
ever is predicated of a class may be predicated of all the
members of that class." In the affirmative form, the Dic-
tum de omni, it is, " Whatever is affirmed of a class may
be affirmed of all the members of the class." In the nega-
tive form, the Dictum de nullo, it is, " Whatever is denied
of a class may be denied of all the members of the class."
It is otherwise expressed, " Whatever is predicated of a
concept distributed may be predicated of all that is con-
tained in the concept." This is the famous Dictum of
Aristotle, which has been held to be the regulating prin-
ciple of reasoning by most logicians from the time of the
Stagyrite. We hold it to be the true regulating principle
in all reasoning in which there is a General Notion. It
must be so from the very nature, from the very meaning,
of a General Notion, and the employment of it in reason-

128 REASONING.

ing. For it will be found that in the reasoning which
contains a concept, there is a predication in regard to the
concept generally, and a predication in regard to a class
or individuals contained in it, and the conclusion is
necessitated by the two, or rather by the relation
of the two, the one embracing the other in its exten-
sion.

18. At this point it will be necessary to explain some
terms which are found in attributive (but not in equiva-
lent) reasoning. The subject of the conclusion is called
the Minor Term, and the predicate the Major Term :
this because the Minor Term (at least in affirmative
propositions, P. II., § 17) is the least extensive, and the
Major Term the more extensive. The premiss containing
the Major Term is called the Major Premiss — sometimes
also the Sumption ; that containing the Minor Term, the
Minor Premiss — or the Subsumption ; and this, which-
ever of the premisses is placed first.

From the time of Aristotle to that of Boethius, the minor premiss
was placed first — following the analytic mode ; from the time of
Boethius it has been customary to put the major premiss first — fol-
lowing the synthetic method.

19. The Dictum of Aristotle is the regulating princi-
ple of all reasoning in which there is a Concept. But in
order to secure that arguments be put in correct form,
logicians lay down certain rules derived from it. Those
rules are additional to those given above (§ 9-13), as
applicable to all reasoning.

20. (1) The middle term must be distributed at least
once (by being the subject of a universal or predicate of
a negative). For if it were taken only in part, it might
happen that in the one premiss we compared an extreme
with one part of the middle, and in the other premiss the
other extreme with another part of the middle, and thus
entirely failed to bring the extremes into comparison

RULES. 129

When this rule is violated, we have the fallacy of Undis-
tributed Middle :

All good men are sincere ;
Eousseau was sincere ;
.•. Rousseau was a good man.

Here the Middle Term is undistributed in both premi-
ses, being the predicate of two affirmatives (P. II., § 11).
What we have done is to declare that all good men are
among the " sincere," that Rousseau is among the " sin-
cere ;" but then Eousseau may be among the sincere, and
not among the good, of whom it is said that they are
among the sincere, but not that they are coextensive
with the sincere. But it is enough that the middle be
once distributed, for as one extreme has been compared to
the whole of the middle, even though the other be com-
pared to only a part, we have brought the two into com
parison.

21. (2) No term must be distributed in the conclu .
sion which has not been distributed in one of the premis-
ses. Otherwise we should be using a term in its entire
extent in the conclusion when we had only made a com-
parison of it in part of its extent in the premiss. The
violation of this rule is called an Illicit Process of the
Major or Minor Term, according as it is the major or
minor term which is thus illegitimately used.

Whatever gives pleasure is to be valued ;
The learning of logical formula? does not give pleasure ;

is not to be valued.
Here " to be valued " is taken only in part in the pre-
miss, being the predicate of an affirmative, whereas it is
taken in all its extent in the conclusion, and we have an
illicit process of the major term.

22. (3) From two particular premisses, no conclusion
can be drawn. For if they were both negative (0 O), yon
could get no inference (§ 11). If they were both affirm-

130 REASONING.

ative (II.), the middle would be undistributed in either
premiss (P. II, § 11). There is left only I O, where trie
negative conclusion makes the major term distributed,
which it is not in the major premiss ; and 01 with either
undistributed middle or illicit process of major.

23. (4) If one of the premisses be particular, the con-
clusion must be particular. By a like process to that fol-
lowed in Kule (3), it can be shown that the violation of
this rule implies an illicit process of the minor.

2d. It should be observed that these rules apply simply to reason-
ing in which we have a concept. The rules given from § 9 to § 13,
apply to all reasoning. The main rules are summed up by logi-
cians in the following mnemonic lines:

Distribuas medium ; nee quartus terminus adsit.
Ultraque nee prsemissa negans, nee particularis.
Sectetur partem conclusio deteriorem.
Et non distribuat, nisi cum prsemissa, negetve
To understand the third line, that the conclusion follows the
worse part, it is necessary to bear in mind that logicians reckon the
particular as worse than the universal, and the negative worse than
the affirmative.

23. MOODS. By Mood is meant the legitimate forms
of the syllogism indicated by the symbolic vowels A, E, I,
O, designating the quantity and quality of the proposi-
tions in then" respective order.

E No planet twinkles ;
A That body twinkles ;
.•. E It is not a planet.

As there are four kinds of propositions, and three
propositions in each syllogism ; and as any one of the
four may be the major premiss ; and each of the four
majors may have four different minors ; and each of the
sixteen pairs of premisses may have four different con-
clusions, it might look as if the possible moods might be
4 x 4 (= 16) x 4 = 64. But many of these moods are
illegitimate as violating the rules of the syllogism as
above laid down (§ 20-23) ; some from negative premisses.

FIGURES. 131

some from particular premisses, &c. When sifted it will be
found that there remain only eleven legitimate moods,
AAA, AAI, AEE, AEO, All, AOO, EAE, EAO, EIO, IAI,
OAO.

26. The rest are excluded for the following reasons :
EBA, EBB, EBI, EEO, EOA, EOE, EOI, EOO, OEA, OEE, OEI,

OEO, OOA, OOE, OOI, 000, = 16 for negative .premisses.

II A, HE, III, 110, IOA, IOE, 101, 100, 01 A, OIE, Oil, 010,
= 12 for particular premisses.

ABA, AEI, AOA, AOI, EAA, EAI, EIA, EII, IEA, IEI, OAA, 0A1,
= 12, because of a negative premiss without negative conclusion.

AIA, AIE, AOE, EIE, IAA, IAE, IEE, OAE, =.8, because of a
particular premiss without particular conclusion.

AAE, AAO, AIO, IAO, = 4, because of negative conclusion with
out negative premiss.

IEO is rejected for an illicit process of the major in every figure.

27. FIGURE. This consists in the position of the
middle term in reference to the extremes. As the middle
term is the very bond of the argument, syllogisms may be
divided very conveniently in respect of figure. In the
First Figure, the middle term is the subject of the major
premiss and predicate of the minor. In the Second Fig-
ure it is the predicate of both premisses. In the Third
Figure it is the subject of both. In the Fourth Figure it
is the predicate of the major premiss, and subject of the
minor. Let P stand for the major term (the predicate of
the conclusion) ; S for the minor term (the subject of the
conclusion) ; and M for the middle term.

28. Fig. I. M P A All human beings are responsible to God ;

S M A The negro race are human beings ;

S P A They are responsible to God.
The Dictum is applicable at once to an argument in
this figure. We affirm P (responsible) of M (human
beings), and M (human beings) of S (negroes), and in
the conclusion we affirm P (responsible) of S (negroes).
This figure admits of four moods, AAA, EAE, All, EIO.
From this it appears that it admits of conclusions in everv

132 REASONING.

kind of proposition, A, E, I, O ; and it is the only figure
in which a universal affirmative (A) can be drawn. We
shall see when we come to consider Reduction that every
kind of argument can be made to take this form ; but
there are arguments which fall naturally into other
figures.

29. There are Special Rules to guide us in detennining what are
legitimate moods in each figure. Thus for the first figure : (1) The
minor premiss must be affirmative ; for if it were negative the con-
clusion must be negative and distribute the major term (P), which
would not be distributed in the major premiss, whicb must be af-
firmative when the minor is negative. (2) The major premiss must
be universal ; for if it were particular, the middle term (M) would
not be distributed in the major premiss, and could not be distributed
in the minor premiss as being the predicate of an affirmative.

30. Fig. II. P M A Reptiles bring forth their young by eggs ;

S M E The rat does not bring forth its young by

eggs ;
S P E The rat is not a reptile.
Arguments fall naturally into this figure when we
have to disprove something which has been maintained
or believed (as when we prove that the rat is not a rep-
tile), or when we have to bring out the differences of
things, which we do by the negative premisses and con-
clusion.

31. The Special Rules are (1) One of the premisses must be
negative, to admit of M being distributed. (2) The conclusion
must be negative, because of the negative premiss. (8) The major
premiss must be universal, for the conclusion being negative dis-
tributes P, which must be distributed in the premiss. The special
regulating principle is the Dictum de Diver so, " if one term is con-
tained in, and another excluded from, a third term, they are mu
family excluded."

32. Fig. III. M P A The connection of soul and body is to be

believed ;
MSA The connection of soul and body is incom

prehensible ;
S P I Some things incomprehensible are to be

believed.

FIGURES. 133

Arguments fall into this form when the middle term is
singular, since a singular term is naturally the subject
when the predicate is a concept. It is, therefore, useful
in bringing in examples. It is also efficient in establish-
ing an exception to an opponent's premiss, when his argu-
ment requires the premiss to be universal. Thus, some
one maintains that certain Scripture doctrines are not to be
believed, as they are incomprehensible. In order to the
validity of his argument it is rsecessary to assume as his
major premiss, that " everything incomprehensible is not
to be believed " (E). Now we can, as in the example,
show iu opposition to him, that " some things incompre-
hensible are to be believed " (I), which is the contradic-
tory of his major premiss.

33. The Special Rules : (1) The minor premiss must be affirma-
tive. For if it were negative the conclusion would be negative, and
would distribute P, which cannot be distributed in the major pre-
miss, which must be affirmative when the minor is negative. (2)
The conclusion must be particular, otherwise there would be an
illicit process of the minor, which as the predicate of an affirmative
is not distributed in the premiss, and cannot therefore be distrib-
uted in the conclusion. Its special rule is the Dictum de exemplo,
" Two terms which contain a common part partially agree, or if one
contains a part which the other does not, they partially differ."

34. Fig. IV. P M A What is expedient is conformable to nature ;

M S E What is conformable to nature is not hurt-
ful to society ;
S P E What is hurtful to society is not expedient
The Special Rules are (1), Major premiss not 0, else illicit maj "i
(2) Minor premiss not 0, else middle not distributed. (3) Conclu
sion not A, else illicit minor.

35. The fourth figure is not found in Aristotle, and many logi-
cians have rejected it. In the minor premiss, S, the predicate is
more extensive than M, the subject ; and in the major premiss, M.
the predicate is more extensive than P; consequently S is more
extensive than P. But in the conclusion we find S, the more exten-
sive, the subject, and P, the less extensive, the predicate, which is
not agreeable to spontaneous thought, and should not have a place
in reflective thought. Figure fourth is perfectly valid, but is not a

134 REASONING.

form into which thought spontaneously falls. It is reached by con-
version or other forms of transposed judgments. To take the ex-
ample (Whately's) : the conclusion is not in the form which natu-
ral thought would use ; we should rather say, " What is expedient
is not hurtful to society." This makes "what is expedient " which
has been placed as if narrower than " conformable to nature "in the
first premiss, which has again been placed as if narrower than " hurt-
ful to society " in the second premiss, to take its proper place in the
conclusion as the subject, as narrower than " hurtful to society " in
the predicate. But in this collocation the reasoning is in the first
figure, which is its natural form.

What is conformable to nature is not hurtful to society ;
What is expedient is conformable to nature ;
What is expedient is not hurtful to society.

30. Mnemonic Lines, devised to exhibit the available
moods in each figure, and also to assist in Reduction.

Fig. I. bArbArA, cElArEnt, dArll, fErlOque prioris ;

Fig. II. cEsArE, cAmEstrEs, fEstlnO, bArOKO, secundte ;

Fig. III. tertia, dArAptl, dlsAmls, dAtlsI, fElAptOn,

bOkArdO, fErlsOn, habet ; quarta insuper addit.

Fig. IV. brAmAntlp, cAmEnEs, dlniArls, fEsApO, frEsIsOn.
Quinque subalterni totidem generalibus orti,
Nomen habent nullum, nee si bene colligis, usum

In these lines the vowels indicate the mood of the syl-
logism, e. g., AEE in Camestres (Fig. II.) denotes that
the major premiss is universal affirmative, and the minor
premiss and conclusion both universal negative. The
five subaltern moods which might be drawn, are AAI,
EAO, in Fig. I. ; EAO, AEO, in Eig. II., and AEO, in
Fig. IV. ; but they are useless, as universals can be
drawn, and they are comprised in AAA, EAE, EAE,
AEE, AEE.

37. REDUCTION. In this we bring a syllogism in
one Figure into the form of a syllogism in another. It is
possible to reduce syllogisms in the first figure to syllo-
gisms in the others. But the phrase is specially applied
to that process in which we turn syllogisms of the second,
third, and fourth figures into the first. The object of re

REDUCTION. 135

duction is first to show that the Dictum of Aristotle,
which is obviously the regulating principle in the firsi
figure, is truly the regulating principle in all reasoning —
in which a concept is involved. But it shows secondly,
and in a very interesting way, that the reasoning process,
whatever be the forms which it takes spontaneously, or
those in which it is made to appear by logicians in order
to bring out the nature and validity of the process, is in
all cases one and the same in substance and in principle.

38* The reduction is made in every instance by Im-
plied Judgments, specially by Conversion ; that is, we put
one or more of the propositions in a transposed form.
The mnemonic lines are meant to direct us in this. The
initial consonants b, c, d, f, show that the mood so marked
in the second, third, and fourth figures, is to be reduced
to the mood marked by the same letter in the first. Thus
c in camestres, shows that tbe syllogism is to be reduced
to celarent in the first. The consonants in the middle
of the words, show how the reduction is to be effected.
Thus s indicates that the proposition designated by the
vowel before it, is to be converted simply ; p, that it is to
be converted per accidens ; and m, that the premisses be-
tween which it stands are to be transposed. The k in
baroko and bokardo denotes that the mood is to be re-
duced per impossibile — a process to be explained forth-
with.

39. Ostensive Reduction is accomplished directly bj
Conversion and other Implied Judgments. We may give
an example from each figure :

Fig. II. cA All men have the power of speech ;

mEs Gorillas have not the power of speech;
trEs Gorillas are not men.

reduced to cE Beings having the power of speech are nol
gorillas :
1A All men have the power of speech ;
rEnt Gorillas are not men.

136

REASONING.

Fig. III. dA Theft is a crime ;

tls Some kinds of theft were encouraged by the
laws of Sparta ;
I Some of the things encouraged by the laws of
Sparta were crime ;
reduced to dA Theft is a crime ;

rl Some things encou raged by the laws of Sparta

were theft ;
I Some things encoura ged by the laws of Sparta
were crime.
Pig. IV. brA Political economy is a profitable study ;
mAn Profitable study sharpens the intellect ;
tip Among the things that sharpen the intellect is
political economy,
reduced to bAr Profitable study sharpens the intellect ;
bA Political economy is a profitable study ;
rA Political economy sharpens the intellect.
4i0. Reductio per Impossibile. In this process we pro-
ceed on the principle that of two contradictory proposi-
tions, one must be true and the other false. We prove
not that the original conclusion is true, but that its con-
tradictory must be false. By it the older logicians re-
duced the syllogisms AOO in the second figure, and OAO
in the third. The method of effecting it is indicated by
baroho and bokardo in the mnemonic lines, where the
letter k intimates that the proposition denoted by the
vowel immediately before it must be left out, and the con-
tradictory of the conclusion substituted :
bO Some poets are not wise ;
kAr Poets are men of genius ;
dO Some men of genius are not wise.
If this conclusion is not true, its contradictory must,
' all men of genius are wise." Let this be substituted for
the major premiss :

bAr All men of genius are wise ;
bA All poets are men of genius ;
rA All poets are wise.
This is the contradictory of the originally granted maioT

REDUCTION. 137

premiss, and must therefore be false. But one of the pre
misses which proves a falsehood must be false. This
cannot be the minor, which was one of the originally
granted premisses ; it must therefore be the major.
But this major thus shown to be false, is the contradictory
of the original conclusion, which must therefore be true.
The same mode of demonstration is employed for baroko,
and may be employed in the reduction of all the moods
of the second, third, and fourth figures. But it is not
necessary to resort to this method. For while baroko
and bokardo cannot be reduced by Conversion either
simple or per accidens, they may by the Implied Judg-
ments involved in Privative Conceptions, (Part II., 49J.

dA All true poets are men of genius ;
rl Some not wise are poets ;
I Some not wise are men of genius ;
or, Some men of genius are not wise.

If we adopt this method, which is perfectly legitimate,
quite as much so as that by conversion or contradictory
opposition, then we require to substitute fakoro and
dokamo in the place of baroko and bokardo in the mne-
monic hues.

4:1. Generally it may be remarked, that in all Mediate
Reasoning we may use what are called Immediate Infer-
ences. We may put either of the premisses or the con-
clusion in the form of any Implied Judgment, if thereby
we are enabled to see the relation of subject and predi-
cate more clearly. Thus in the last example the conclu-
sion may be expressed either " some men not-wise are
men of genius," or " some men of genius are not wise."
This enlarges indefinitely the number of forms in which
reasoning may be expressed and still be valid. It is not
necessary to spread out all the forms which reasoning
may thus be made to take. It is enough to know what

138 REASONING.

we are entitled to do, and how to do it legitimately, wlien
perspicuity of thought requires it.

42. REASONING IN COMPREHENSION. In rea-
soning, so far as we have considered it, the propositions
have been understood in extension, and Aristotle's Dic-
tum, which is a maxim in extension, has been considered
the regulating principle. But we have seen tnat all prop-
ositions have a meaning in comprehension. May there
not then be reasoning in comprehension also? In an-
swering this question fairly, it should be allowed that in
the greater number of propositions, the uppermost thought
is in comprehension rather than extension. When we are
saying " the boy plays," we are thinking of the boy as
engaged in the act of playing, rather than among the
class of things that play. But it is different when we con-
sider judgments so connected as to entitle us to draw a
conclusion. The uppermost spontaneous thought seems
now to be in extension. When we argue that " the Bed
Indian, having the power of speech, is a human being,"
we refer, in thought, the Bed Indian to a class composed
of those who have the power of speech. Of course the
possession of attributes is implied in each of the terms ;
but in the ratiocination we require to proceed on the
principle that there are classes possessing the attributes ;
and it is because this is recognized, that the conclusion is
seen to follow, If we argue that "man, being respon-
sible, is a free agent," the reasoning is conclusive only on
the condition that the whole class " man " is in the class
" responsible," which again is in the class " free agent."
That " brutes have no free will " cannot give the conclu-
sion that "the brutes are not responsible," unless we
proceed on the general principle that "those who are
without free will are not responsible."

43. But then all the propositions in a syllogism may
be understood in comprehension ; and a syllogism mav

IN COMPREHENSION. 139

be constructed in which the comprehension is the more
prominent, and the reasoning will be perfectly valid, and
the form accurate, though not the form expressing the
thought which the mind spontaneously follows. The
regulating principle will now be, " a part of a part of an
attribute will be part of the whole attribute."

Free will is an attribute of responsibility ;

Responsibility is an attribute of man ;
.'. Free will is an attribute ofmau.

Bringing forth its young by eggs is an attribute of reptiles,
Bringing forth its young by eggs is not an attribute of rats ;
. ' . Some attributes not of rats are attributes of reptiles.

It will be observed that the order of the terms in the
propositions, is here the reverse of what it is when we
express the thought in extension. In extension we say
in the major premiss "man is responsible," "reptiles
bring forth their young by eggs." In the form of exten-
sion, the subjects are the less extensive and the more
comprehensive ; and the predicates the more extensive,
and the less comprehensive. But in comprehension the
subjects are the more comprehensive and the less exten-
sive, and the predicates the less comprehensive and the
more extensive.

What do we mean when we say that in reasoning in comprehen-
sion the ruling principle is that " part of the part of an attribute
is a part of the whole attribute ? " We mean, on the principle that
the abstract implies the concrete, that whatever things contain a
part must also contain a part of that part, e. g., that men, having
the attribute of responsibility, have the attribute of free will in-
volved in that responsibility. We seem thus to be thrown back on
extension as the uppermost thought in reasoning.

4:4:. But if it be true that the mind reasons primarily
in extension, it is not necessary to draw out the forms in
comprehension, the more so as the forms in extension
embrace all cases of reasoning — except those proceeding
on the principle of Equivalence, which we have placed

140 REASONING.

under a separate head (§ 15). But the student should ha
able, on demand, to translate reasoning in extension, in
the way above indicated, into reasoning in comprehen-
sion.

45. THE TWO DICTA ARE COMBINED. We
have seen in our survey, that there is one rule so general,
that it may be held as regulating all reasoning that " no-
tions which agree with one and the same notion agree
with one another " (§ 14). But this rule is too vague, as
not specifying the nature of the agreement ; and so we
lay down two more specific rules, the one the rule of
Equivalence (§15), and the other the Dictum of Aris-
totle (§ 17) — to which we may add the rule of Comprehen-
sion— if we allow reasoning in comprehension (§42).
But there are cases in which the rule of Equivalence and
the Dictum are united :

A Locke lived in the seventeenth century ;
IT Locke is the greatest of English metaphysicians ;
A The greatest English metaphysician lived in the seventeenth
century.

This is in the Third Figure, and yet we legitimately
draw a universal conclusion, and the reason is that the
minor term being an abstract is distributed, is distributed
in the minor premiss, and may therefore be distributed
in the conclusion.

Both Dicta are involved in Mathematical reasoning, as
in the demonstration of Euclid, B. I., Prop. I.

(1) The radii of the same circle are equal to one another ;
A C and A B are radii of the same circle (B C D) ;

A C and A B are equal to one another.

(2) The radii of the same circle are equal to one another ;
B C and A B are radii of the same circle (ACE);

B C and A B are equal to one another.

(3) AC = AB;BC = AB/.AC = BC.

Under this head should be placed what is called a Per-
fect Induction, in which we argue that what we have

THE TWO DICTA COMBINED. 141

found true of each of the members of a class, must be true
of the whole class.

A Shein, Ham, and Japhet were in the ark ;

U Sheui, Ham, and Japliet were the whole sons of Noah .

A All the sons of Noah were in the ark.

In both these examples, two of the terms are singulars
involving a process of abstraction (but not of generali-
zation) ; the minor premisses are equipollent, with both
terms distributed ; and so the minor term is to be re-
garded as distributed in the conclusion, which is univer-
sal. Of the same description :

A Certain sciences are classificatory ;

U These sciences are Mineralogy, Botany, and Geology ,

A Mineralogy, Botany, and Zoology are classificatory.

46*. Sir W. Hamilton has an ingenious mode of exhibiting all
the possible forms of reasoning both in extension and comprehen-
sion. The scheme shows 36 moods in each of the first three figures
(the fourth is not allowed), or, in all, 108. Many of these moods
would never occur (so it appears to us) in spontaneous thought, and
arise from his giving Y, tj, and w, a place among propositions. Still
the scheme is worthy of being looked at as exhibiting along with
the forms arising in spontaneous thought, those that may be reached
by immediate inferences. The Table, with the explanations, is
taken from Thomson's Outlines of the Laws of Thought. (See p. 142.)

In this Table M denotes the middle term ; and C and T the two
terms of the conclusion. A colon (:) annexed to a term denotes that
it is distributed, and a comma (,) that it is undistributed. Where
the middle term has a : on the right side, and a , on the left, we
understand that it is distributed when it is coupled in a judgment
with the term on the right, and undistributed when coupled with
the other. The syllogisms actually represented are all affirmatives,
being twelve in each figure ; and the affirmative copula is the line
— — , the thick end denoting the subject, and the thin the predicate,
of extension. Thus C: ■- — , M would signify "All C is (some) M."
In reading off the intension, the thin end denotes the subject. But
from each affirmative can be formed two negative syllogisms, by
making each of the premisses negative in turn. The negation is
expressed by drawing a perpendicular stroke through the affirmative
copula; thus n ■ . j.. ■ In the negative modes the distribution of

142 HEA80N1NQ.

Fig. I. Fig. n. Fig. III.

ii. C, : M : , r C, : M : ■ , r C, ■■ : M : , r

, iii. C, : M , : r C, — : m , : r C, ■ : M , ■ : r

XXX

iv. C: — — , M:— — , r C:- , M : ,r C: — ,M:

v. C, — — : M , ■ , r C, — - — : M , , r C, ■ : M , , i

XXX

vi. C, , M : , r C, , M : , r C, — — , M :

XXX

viii. C, — : M : — : r C, : M : i : r C, : M :

Ix. C : : M , : r C : : M , — : r C : . ; M ,

XXX

xi. C : : M , , r C : : M , . , T C : — . : M , — — , r

X X X

xli. C, , M : — — : r C, . , M : ■ : I' C, — , M : : 1

■ .

MILL'S THEORY, 143

terms will remain exactly the same as it was in the affirmatives
from which they were respectively formed. The line beneath the
three terms is the copula of the conclusion ; and in the second and
third figures, as there may be two conclusions indifferently a
line is also inserted above, to express the second of them. The mark
s — y — ' under a mode denotes that when the premisses are converted,
the syllogism is still in the same mode. But a X between two
modes, signifies that when the premisses of either are converted, the
syllogism passes into the other. The middle is said to be balanced
when it is distributed in both premisses alike. The extremes, or terms
of the conclusion, are balanced, when both alike are distributed or both
undistributed ; unbalanced, when ©ne is and the other is not. Two
propositions, or two modes, are balanced, when the distribution of
terms is the same in both. A. 5. and ii. are balanced. B. The other
modes are unbalanced. Of these, iii. and iv. are unbalanced in terms
only, not in propositions ; the rest in both.

4:7* The author of this treatise has commented elsewhere on Mr. J.
S. Mill's theory of the reasoning process. " The ' really fundamental
axiom of ratiocination,' as announced by him is, ' Things which co-
exist with the same thing, co-exist with one another ; ' and ' a thing
which co-exists with another thing, with which other a third thing
does not co-exist, is not co-existent with that third thing.' But the
phrase ' co-exist,' if limited to co-existence in respect of time or
space, does not include most important cases of reasoning ; and if
widened beyond this it becomes meaningless. When we argue that
the man having committed murder deserves punishment, the pre-
misses and conclusion have reference, not to space or time, but to
far different relations. When we infer from A being equal to B, and
B to C, that A is equal to C, we are not making affirmations about
co-existence. In explanation, he tells us (Vol. I., p. 202, footnote, 6th
ed.), 'the co-existence meant is that of being jointly attributes of the
same subject.' This statement is still vague, and is not adequate,
for it does not specify what is 'the same subject,' and it does not
bring out that the attribution involves Extension : but it contains
partial truth, and it has a meaning, which we can examine.

This new Dictum gives him the following universal formula:

Attribute A is a mark of attribute B ;
A given object has the mark A;
.•. The given object has the attribute B.

But what does this first premiss mean when we translate it ffott'

144 REASONING.

abstractions into concrete realities ? As there cannot be an attri
bute existing separately, or apart from objects, it must mean, ' What
ever objects have the attribute A have the attribute B.' And wha'
is this but the major premiss of the old syllogistic formula 1 The
second premiss requires an explanation. "A given object has the
mark A:" this object may be one object or a class of objects. Id
order to give the formula a meaning, we must interpret it, ' What
ever individual or class has the attribute A has the attribute B ; a
given object or class C has the attribute A ; therefore it has the
attribute B.' The new Dictum and new Syllogistic formula arejust
bad versions of the old ones. I call them bad versions, for the
phrase "co-exist" does not bring out the precise relation of the
terms on which the thought proceeds ; and the phrase, " Attribute
A," requires to be interpreted in order to have a relevant significa-
tion."— Examination of Mr. J. 8. Mill's Philosophy.

4z8* Some eminent mathematical logicians are seeking
to introduce into Logic, reasoning founded on plurative
judgments :

Two-thirds of mankind are heathens ;

Two-thirds of mankind live in Asia ;
.•. Some who live in Asia are heathens.

Now there is no doubt that this reasoning is valid
But so also :

Lias lies above Red Sandstone ;
Red Sandstone lies above Coal ;
.'. Lias lies above Coal.

But all logicians allow that in the latter case there is a
major premiss implied, that " when one stratum lies above
a second, and that above a third, the first must be above
the third "; and then the minor premiss becomes, " there
is such a stratum (Lias), lying above a second stratum
(Red Sandstone), which lies above a third (Coal)" ; and
then the conclusion follows. It is the same in plurative,
and indeed in all arithmetical reasoning, there must be a
major premiss got from arithmetic, that is, from a region
without and beyond pure discursive thought.

CONDITIONAL REASONING. 145

CONDITIONAL SEASONING.

40' In this, one or both the premisses are conditional
propositions. The common form is that in which the
major premiss (so called) is a conditional, and the minor
a categorical.

ANTECEDENT. CONSEQUENT.

If this man has consumption he shall die ; major premiss.

He has consumption ; minor premiss.

.-. He shall die. conclusion.

This is called a Constructive Conditional Syllogism : it
proceeds on the rule (modus ponens), Affirm the antecedent
and we may affirm the consequent. In the Destructive form
the rule (modus tollens) is, Deny the consequent and we may
deny the antecedent.

If this man has consumption he shall die ;
He shall not die ;
.•. He has not consumption.

But we are not entitled by denying the antecedent to
deny the consequent, or by affirming the consequent to
affirm the antecedent ; for the consequent may follow
from some other antecedent. We cannot, by denying
that this man has consumption, deny that he shall die ;
or by affirming that he shall die, that therefore he has
consumption ; for he may die of some other disease.
Hence arise two fallacies in conditional reasoning : one
that of denying the antecedent and therefore denying the
consequent ; the other that of affirming the consequent
and therefore affirming the antecedent.

So far for reasoning in which the major premiss has
one or more concepts, and in which the proposition is
attributive or the relation one of joint extension and com-
prehension. But there are cases in which the notions are
singular or abstract, and in which the proposition is
10

146 REASONING.

equivalent, U ; and in these we can, from the denial of
the antecedent deny the consequent, and from the affirm-
ation of the consequent affirm the antecedent. " If Ho-
mer wrote the Iliad he is the greatest poet in antiquity "
From this we can infer not only (1) that as he wrote the
Eiad he is the greatest poet in antiquity ; and (2) that he
is not the greatest poet in antiquity if he did not write
the Iliad ; but farther (3), that if he did not write the
Iliad he is not the greatest poet in antiquity ; and (4)
that as he is the greatest poet in antiquity, he must have
written the Iliad.

50. The common forms with a conditional major and
categorical minor are :

1) If A is B, B is C (major).

Equivalent and attributive A is B .\ B is C. B is not C .". A is

notB.
Equivalent additional A is not B .-. B is not C. B is C .". A is B.

(2) If A is B, C is D ; A is B .-. C is D. C is not D .-. A is not B.

(3) If A is not B, C is not D ; C is D .-. A is B.

(4) If A is not B, C is D ; A is not B .-. C is D. C is not D.\ Ais B.

(5) IfAisnotB, CisnotD; A is not B .-. C is not D. CisD.\ AisB.

(6) If A is B, either C is D, or F is G.

A is B .-. either C is D, or P is G. Neither C is D, nor F is G,
.: A is not B.

(7) If either A is B, or C is D, either E is F, or G is H.
Either A is B, or C is D .-. either E is F, or G is H.
Neither E is F, nor G is H /. neither A is B, nor C is D.

Other conclusions may be drawn when the terms are
equivalent, but it is needless to formulize them.

51. Reasoning, being all the while one and the same,
will spontaneously take the conditional or categorical
form according to the case to which it is applied. We
reason and conclude that " a man guilty of murder should
be punished." If we know that a particular man com-
mitted the murder, the reasoning would take the categor-
ical form, " This man, having committed murder, should

CONDITIONAL REASONING 147

be punished." We may not know, however, whether the
man has committed the murder, and we simply assert
that " this man, if guilty of murder, should be punished,"
thus declaring the validity of the consequence. But we
come to know that he has committed the murder, and we
apply the reasoning, and the form spontaneously assumed
will be the categorical.

52. There is a sense in which all reasoning is regarded by lo-
gicians as hypothetical, that is, he does not, in looking at the valid-
ity of reasoning, examine the truth of the premisses. Assuming
them to be true, he inquires solely into the relation between them
and the conclusion. But in Hypothetical Reasoning Proper, there is
a hypothesis in the very enunciation of the argument. The relation
of categorical and hypothetical reasoning is analogous to that be
tween the original and derived propositions in Implied Judgments.

33* All conditional reasoning can be reduced to cate-
gorical form. This is accomplished by putting the major
premiss in a new shape by immediate inference : as " the
case of a man committing murder is a case in which he
should be punished," or more simply :

He who is guilty of murder should be punished ;
This man is guilty of murder ;
.•. He should be punished.

When in conditional form, the reasoning is to be tried
by the rules of conditionals ; when in categorical form by
the rules of the syllogism. It will be found that the fal-
lacy of denying the antecedent and thence denying the
consequent, corresponds to illicit process of the major or
negative premisses, or the introduction of more than three
terms. In conditional form, " If this man has consump-
tion he shall die ; he has not consumption ; therefore he
shall not die," becomes categorically, "He who has con-
sumption shall die ; this man has not consumption ; there-
fore he shall not die " (illicit major). The fallacy of as-
serting the consequent and thence inferring the antece-
dent corresponds to the fallacy of undistributed middle or

148 REASONING.

negative premisses. With the same majors, " This man
shall die, therefore he has consumption," is in conditional
reasoning the fallacy of affirming the consequent, and in
categorical of undistributed middle. It is evident from
these considerations and examples, that conditional rea-
soning is the same substantially in the relation of the
terms as categorical, and that it is governed in thought
by the principles expressed in the Dictum of Equivalence
and the Dictum of Aristotle.

DISJUNCTIVE EEASONBTG.

54z. In it one premiss is a disjunctive proposition, and
the other is categorical. The disjunctive proposition
proceeds on the principle that the notion is divided into
subordinate species, and is governed by the rules of Log-
ical Division (P. I., § 58, 59) : that the species must make
up the genus, and that the species must exclude one an-
other. In it there are two or more judgments which
cannot all be true, but one or some of which must. In
the categorical premiss (called the minor) we make a
predication as* to one or other of the species, and in the
conclusion, we draw an inference as to the other or
others :

Lines are either straight or curved ;

The line A B is not straight ;
.*. It must be carved.

Here we find " line " divided into two exclusive species
we affirm that it is not in the one species and so infer it
must be in the other. There is the same process when
the members are three :

The Apostles must either have been deceivers, or deceived, or thej

spake the truth ;
They were not deceivers nor deceived ;
•. They spake the truth.

DISJUNCTIVE REASONING. 149

Or with four members :

The season must have been spring, or summer, or autumn, 01

winter ;
It was winter ;
.•. It could not have been spring, or summer, or autumn,

A fallacy often creeps into disjunctive reasoning in con-
sequence of the division in the disjunctive premiss not
being exhaustive. Thus it is argued " either that all our
ideas are had from experience, or that there are innate
ideas." Then it is shown that " there are no innate ideas,"
i. e., that the child is not born with ideas ; and the con-
clusion follows that " all our ideas are from experr
ence." But there is a third supposition, which seems the
true one, that " there are innate laws or principles in the
mind, ready to be called forth by experience." "We have
given other examples in treating of Logical Division,
(P. I., § 58.) The detection of such fallacies requires us
to look beyond Formal Logic, but Logic tells us where
they lurk.

55. The following are the principal forms (Fowler's
Logic) :

Either A is B, or C is D (major).
(1) A is B .-. C is not D. (2) A is not B .-. C is D.
(3) C is D .-. A is not B. (4) C is not D .-. A is B.

Either A is B, or C is not D (major).
(1) A is B .-. C is D. (2) A is not B .-. C is not D.
(3) C is not D .-. A is not B. (4) C is D .-. A is B.

Either A is B, or C is D, or E is F (major).
(1) A is B .-. neither C is D, nor E is P. (2) A is not B .-. either 0

is D, or E is F.
(3) Neither C is D, nor E is F .-. A is B. (4) Either C is D, or E is

F /. A is not B.
(5) Either A is B, or C is D .-. E is not F, &c, &e.

56. Disjunctive reasoning can be reduced to categor-
ical in changing by immediate inference the disjunctive
proposition according to the rule of logical division.

150 REASONING.

All lines not-straight are crooked ,
A B is not-straight ;
•.It is crooked.

This shows that ultimately disjunctive reasoning is
founded on the same principle as categorical, that is, on
the principle of subalternation of the species to the genus,
implied both in logical division and in the Dictum of
Aristotle.

DILEMMA.

S7. There are spontaneous exercises of thought in
which we draw a conclusion from disjunctive premisses,
or reach a disjunctive conclusion without determining
which of the alternatives is to be preferred ; and in these
the reasoning takes the form of a dilemma. In it we
have a conditional premiss, in which either the antece-
dent or consequent is disjunctive, and in the other pre-
miss we make a predication in regard to the exclusive
nature of the disjunctive in the premiss, and thence draw
a conclusion.

Major. If a man can help a thing he should not fret about it : if

he cannot help a thing he should not fret about it
Minor. But he can either help a thing or not help it ;
.*. He should not fret about it.

He who opposes this must set himself against one or
other of the alternatives — must, as it is said, choose his
horn, and if the alternative is exhaustive, he will be trans-
fixed by either. If a dilemma is accurate in form, the
conclusion follows, and the only way of meeting it is by
showing that the alternatives in the premisses are not
exhaustive — that there may be another supposition.

If that narrative be true you must believe it ; if it be false you

must disbelieve it ;
But it must either be true or false ;
. You must either believe it, or not believe it.

DILEMMA. 151

But there may be a third supposition, that it is partly
true and partly false. The rules are (1), The antecedent
being affirmed, either disjunctively or not, as the case
may be, the consequent must be admitted; (2) The conse-
quent being denied, either disjunctively or not, the ante-
cedent must be denied.

58. (1) There are cases in which the first premins
consists of one antecedent and several consequents. The
conclusion is destructive.

If A is B, C is D, and E is F ;
But either C is not D, or E is not F ;
.*. A is not B.

(2) In which the major consists of several antecedents
and one consequent ; and we draw the common conse-
quent in the conclusion. The argument is constructive •

If A is B, or if C is D, E is F ;
But either A is B, or C is D ;
.-. E is F.

(3) In which each of the antecedents has a different
consequent, and we can draw the consequent only disjunc-
tively. The argument may be constructive or destructive :

Major. If A is B, C is D, and if E is F, G is H ;
Minor. But either A is B, or E is F ;

.-. Either C is D, or G is H.
Minor. But either C is not D, or G is not H ;

.-. Either A is not B, or E is not F.

59. There may be Trilemma or a Tetralemma, &c, when tb.6
number of antecedents or consequents, one or both, is three, four
&c. Trilemma. If the universe is not the best possible, we must
suppose that God did not know a better, or that he could not make
a better, or that he did not desire a better. The first supposition
cannot be true (for it is inconsistent with His wisdom) ; and the
second (because it limits His power) ; and the third (because against
His goodness) ; therefore the universe must be the best possible.

60. A Dilemma being a condition a] with a disjunctive
proposition, may be reduced to categorical syllogistic
form, like conditionals and disjunctives.

152 REASONING.

CHAINS OF REASONING— THE SORITES.

01. Prosyllogism and Episyllogism. Hitherto we have
been considering single arguments. But ratiocination
is commonly conducted in a train, and the single
argument has a connection with what goes before and
with what follows. The major or minor premiss, one or
both, of any syllogism, may have been established by a
previous act of reasoning, which in relation to that syl-
logism is called a Prosyllogism. Or a syllogism may be
employed to establish a position to be used as a premiss
in a subsequent syllogism called an Episyllogism. The
conclusion in the Prosyllogism is a premiss to the syUo-
gism which it precedes ; the Episyllogism uses the con-
clusion of the syllogism which goes before as a premiss.
It is evident that the same syllogism may be a Pro-syllo-
gism in one connection, and an Epi-syUogism in another.

Pro-Syllogism. He who administers arsenic administers poison ;

The prisoner administered arsenic ;
. . The prisoner administered poison.
Given Syllogism. He who administers poison is guilty of murder ,
The prisoner administered poison ;
.•. He is guilty of murder.
Epi-Syllogism. He who is guilty of murder should bo executed ,

The prisoner is guilty of murder ;
.•. He should be executed.

This may become a Prosyllogism to a farther act of
reasoning :

He who is to be executed should not be executed in publie ;
This man is to be executed ;
.•. He should not be executed in public.

This may be taken as an example of a chain of reason-
ing. It is not to be understood that in spontaneous
thought, the mind constructs the reasoning into syllo

CHAINS OF REASONING, ETC. 153

gisms. It is enough, that it perceives the relations in-
volved in the terms. The formal unfolding of the rela-
tions is left to the logician.

02. Logicians have drawn the form of one of these
chained trains of reasoning, and call it the Sorites (from
acopoc, a heap — the Germans call it chain argument, Ket-
tenschluss) : — The prisoner administered arsenic to the
man who died ; he who administers arsenic administers
poison ; he who administers poison is guilty of murder ;
he who is guilty of murder should be executed ; he who
is executed should not be executed in public ; .'. the pris-
oner should not be executed in public. The Sorites con-
sists of a series of propositions, the predicate of each be- '
coming the subject of the one following, till in the last -
step the predicate of the last is affirmed or denied of the
subject of the first, which is the conclusion. In the pro-
cess there are as many middle terms as there are prop-
ositions between the first and the last ; and the mind in
reasoning sees the connection between these middles and
the other terms, and thus passes on from the first pre-
miss to the final conclusion. The Dictum of Aristotle
slightly modified, is the regulating principle. " Whatever
is affirmed or denied of a whole class, may be affirmed or
denied of whatever is comprehended in any class that is
wholly comprehended in that class," — the words in Italics
being an addition. In the Sorites the first proposition,
and that alone (with the last), can be particular ; because
in the first figure the minor may be particular but not the
major (§ 29), and all the other propositions on to the con-
clusion are major premisses. There can be one and only
one negative premiss, and that the last ; for if any others
were negative, one of the syllogisms would have a nega-
tive premiss, which cannot be in the first figure.

03. The reasoning is perfectly valid, but we may in
the way of testing it, and to show that this form oJ

154 REASONING.

reasoning is founded on the same principle as the syllo-
gism, draw out the process in a series of syllogisms.
These will all be in the first figure ; the same in number
as the middle terms ; and the first will have for its major
premiss the second proposition of the Sorites, and for its
minor the first. Syllogisms thus drawn out, will take the
form of syllogism, pro-syllogism, and epi-syllogism, given
above :

The form is, All (or some) A is B ;

All B is C ;

All C is D;

All (or no) D is E ;
.-. All (or some) A is (or is not) E.

Keduced to syllogisms :

All B is C ; All C is D ; All (or no) D is E ;

All (or some) A is B ; All (or some) A is C ; All (or some) A is D ;
.*. All (or some) A is C. .\ All (or some) A is D. .'. ALL (or some) A is (01

is not) E.

Trie Sorites may take another form called Goclenian (from Gocle-
nius who noticed it). The subject of each premiss becomes the
predicate of the next ; the conclusion predicates the first predi-
cate of the last subject ; the first premiss only cau be negative and
the last particular. When expanded into syllogisms the conclusion
of each becomes the major premiss of the next. The form is :
All (or no) E is F ; All B is C ;

All D is E ; All (or some) A is B ;

All C is D ; .*. All (or some) A is (or is not) F.

He who is executed should not be executed in public ; he who is
guilty of murder should be executed ; he who administers poison is
guilty of murder ; and he who administers arsenic administers
poison ; the prisoner administered arsenic ; therefore the prisoner
should be executed, but not in public. These two forms differ from
each other only as a syllogism with the major premiss put first, and
the minor premiss second, differs from a syllogism with the minor
premiss put first and the major last (see § 18). A series of Con-
ditional arguments may in the same way be abridged into a Sorites
[f A is B C is "D ; if C is D, E is F. But A is B .-. E is F.

REMARKS ON REASONING PROCESS. 155

GENERAL REMARKS ON THE REASONING PROCESS.

64. We have seen that in all reasoning there is in-
volved a comparison of two terms by means of a third,
and that when the process is fully unfolded, there will be
three propositions, that is, two premisses and a conclu-
sion. The question arises, whence do we get the premis-
ses ? The answer is, that they may be obtained either by
intuition or by experience. First there are premisses
gained by an immediate intuition of objects. It is thus
that I know that these two parallel lines will not meet
however prolonged ; that these two straight lines cannot
enclose a space ; that this deed of ingratitude to God and
cruelty to man is a sin. We reach these truths by no
process of inference ; we perceive them to be true on the
bare contemplation of the objects. But a far greater
number of premisses are attained by ordinary obser-
vation— in the case of general truths by a gathered obser-
vation. It is thus we know that fire burns, that all bodies
attract other bodies, that plants and animals need nourish-
ment, and that animals feed on other organized matter.

65. This gathered observation may be made by the
individual for himself, or by the combined experience of
others. Of these, the individual experience, so far as
it goes, is by far the more valuable ; as with the results
we have the processes which guide and restrain in the
application of the general maxim. It is for this reason
that a mere school or book learning can never serve the
ends of a practical education ; and that a dear-bought
personal experience is often worth all the labor and suf-
fering which may have been expended in gaining it. But
on the other hand, individual observation, however en-
larged, must always be limited, and unless widened by
intercourse with mankind and by reading, tends to be*

156 REA80N1JS(*.

come narrow and exclusive. By far the greater part of any
man's knowledge is derived from the experience of others,
and is conveyed to him by oral instruction and hooks ;
and the most valuable jjart consists in nice distinctions
and scientific laws, some of which embody the results of
the thoughts of the greatest men who have appeared on
our earth, and of a hundred generations.

00* Some of these have been written out and pro-
claimed to the world ; such, for instance, are ascertained
natural laws, as the three laws of motion, the classifications
of natural history, the chemical affinities of bodies, and
certain laws of the mind, such as those of the logical pro-
cesses, of intuition, and the association of ideas. It is one
of the advantages which the modern reasoner has over
the ancient, that he has provided for him and placed at
his disposal, an immense number and variety of general
principles handed down from the ages precedent. Others
of the published maxims are of a moral and practical
nature, such as proverbs and wise saws handed down
from father to son and from one generation to another,
as " Evil communications corrupt good manners," " Sec-
ond thoughts are best." Others of the maxims have not
been embodied in words and never will be. For example,
you have discovered of a certain man that you can trust him,
and you confide in his statements, and coidd place your
property in his hands. Or, you have found of a certain
look and manner, which you know but could not describe,
that they are signs of deceit and dishonesty. Such media
axiomata, as Bacon calls them, equally removed from high
generalizations and minute particulars, are most useful
of all in the arts and the practical business of life. And
observe wherein lies their utility. They form, as we shall
immediately see, the major premisses in that reasoning
which the mind is ever conducting in regard to the cases
that cast up — these cases supplying the minors. One

REMARKS ON REASONING PROCESS. 157

grand use of education in the higher sense of the term,
of travel, and of an acquaintance with the world, is to
supply such majors for continual use and application in
the varied circumstances of life.

07. Many of the maxims are absolutely certain. Such
are established scientific laws, as those of chemical affin-
ity, of physiology, and psychology. Such are also aL
moral maxims, as that it is wrong to lie, to thieve, tc
kill. In other cases, the maxim is true only in most
cases. For example, the rule that netted-leaved plants
are exogenous is true only as to most plants ; foi
there is a tribe called dictyogens by Lindley, which have
netted-leaves and yet are endogenous. The general ob-
servation that solanacese are poisonous, has a still greater
number of exceptions — for the potato is a solanaceous
plant ; and all that such a rule can do is to guard
against eating the flowers or berries of this tribe of
plants when they come in our way. Of this character
are the loose maxims which float in the world as to races
and nations. Acting on them we are commonly right,
while we should greatly err if we insisted on applying
them rigidly. " One of themselves, even a prophet of
their own, said, the Cretans are always liars, evil beasts,
slow bellies," " Frenchmen are lively," " The Irish are
witty," " The Scotch are cautious."

08. When all the new steps in the reasoning process
are seen to be true intuitively, we have what is called
Demonstration (a-rrodet&g). The fittest example is to be
found in Mathematics. Here we start with things defined,
that is, with points, lines, squares, ellipses, &c, and look-
ing to these things, on the bare contemplation of them,
we discover certain truths regarding them. This is what
is to be understood by intuitive truths — truths seen on
the bare inspection of the things. Having thus obtained
certain truths, we compare two truths by means of a

158 REASONING.

third — which is reasoning — and rise to farther and far-
ther truths. Finding that the line AB = the line C D,
and C D = E F, we conclude that A B = E F. The things
we thus compare are all abstracts, and the notions are all
distributed both in the subject and the predicate. This
kind of reasoning all falls under the head in which the
law of Equivalence is the regulating principle. We may
arrange the terms as we please as subject and predicate
in the proposition, and the propositions as we please in
the syllogism — there being, properly speaking, no major
and no minor. We do not require to announce a gene-
ral principle, as that things which are equal to the same
things are equal to one another ; on the bare contem-
plation of A B and E F being equal to G D, we conclude
them to be equal to one another. This reasoning is
also found to a limited extent in Formal Logic, as when
we draw the rules of the syllogism (§ 20-23) and the spe-
cial rules of the figures (§ 29-34) from the Dictum of Aris-
totle. It cannot, however, be employed in any of those
departments of knowledge in which we deal with scat-
tered facts. In such branches, the only available method
is that of Induction — a subject which does not fall under
Formal Logic, but that Secondary department which
treats of discursive thought as applied to certain classes
of objects.

SOo When the evidence is gained from a gathered ex-
perience, it is called Experiential, also Probable, and
Moral. It is of importance that we should know the
difference between this and Demonstrative or Apodictive
evidence. (1) The essential distinction is that the one
is derived exclusively from intuition, and the other partly
or wholly from experience. In order to discover th<. truth,
the mind in the former case looks simply at the object ;
whereas in the latter there is need of observation, com-
monly of observation upon observation. There is no

REMARKS ON REASONING PROCESS. 159

ueed of trial in order to convince us that two parallel
lines will never meet ; the truth is discovered at once by
the bare contemplation of parallel lines. But we cannot
by thus inspecting the things say whether the planets do
or do not move in ellipses, whether the earth is or is not
hot in the centre. "A clever man shut up alone and
allowed an unlimited time, might reason out for himself
all the truths of mathematics, by proceeding from those
simple notions of space and number of which he cannot
divest himself without ceasing to think ; but he could
never tell by any effort of reasoning what would become
of a lump of sugar in water, or what impression would be
produced on his eye by mixing the colors yellow and
blue." (Sir J. Herschel.) (2) The one does not, the other
does, admit of degrees. Demonstration does not allow of
degrees. Every one proposition so substantiated, is as
certain as any other, as every other. Nor can we add to
the evidence of a proposition demonstrated. That the
opposite angles formed by the crossing of two straight
lines are equal, this cannot be rendered more certain by
any addition of proof. It is different with observational
evidence which admits of all degrees of certainty. That
it will rain to-morrow is a vastly more uncertain propo-
sition than that the sun will rise to-morrow. This kind of
evidence may have additions made to it ; the probability
of there being rain may be increased by the fall of the
barometer and the threatening aspect of the sky. It may
rise at last to moral certainty, which ought to carry our
full conviction and lead to corresponding action. (3) In
the one there is not, in the other there commonly is, a
balancing of seemingly opposite proofs. In Demonstra-
tion there never is anything contrary, even in appearance,
to what has been established. But in Probable evidence
there is often one fact or argument which seems to in-
cline one way, and another which seems to tend the

160 HEASOxVIWG.

other way ; and in order to arrive at a satisfactory conclu-
sion, we must look at both, and give to each its proper
weight. What a number of considerations require to be
estimated before a merchant makes an extensive purchase
of certain goods ; before a statesman proposes a measure
with far-reaching consequences ; before a general ventures
on a perilous campaign ! The most useful of all kinds
of practical sagacity is that which enables a man, in
the midst of complicated circumstances, to determine on
which side the balance of probability lies. (4) The one
does not, the other does, involve responsibility. There
is no sort of accountability attaching to intuitive evidence ;
a man must believe it, whether he will or not. We have
no credit, or the reverse, in believing that if we take equals
from unequals that the remainders are unequals ; or that
the angles at the basis of an isosceles triangle are equal
to one another. As soon as any one understands these
propositions and the evidence advanced in their behalf —
if they need proof — he is obliged to yield his assent to
them. It is different with Experiential Evidence. A man
may or may not listen to it ; he may, but he also may not,
act upon it. There is room here for the influence of a
spirit of candor, or for the opposite temper of prejDosses-
sion and prejudice. It is on this account, that experien-
tial evidence is often called Moral, because it is possible
for us either to attend to it or not to attend to it, and the
act to be morally right or morally wrong.

tO. It is vain to expect Demonstration in every line of
inquiry. Demonstration is confined to a limited class of
objects, and these characterized by their simple and ab-
stract nature. In most of the sciences it is not available ;
it cannot be had in chemistry, in natural history, in psy-
chology, in political economy. In the practical affairs of
life no man looks for it. If a man's house is on fire, he
will proceed to pour water upon it, though it cannot be

REMARKS ON REASONING PROCESS. 161

demonstrated in the technical sense of the term, that
water will quench the flame. The evidence adduced in
behalf of the existence of God, of the immortality of the
soul, of a day of judgment, and of the truth of the Chris-
tian religion, is all of this moral character. It is addressed
to an understanding capable of weighing it, and a heart
supposed to be ready to receive it. There may be excel-
lence implied in the faith that receives it ; and guilt
involved in the perverseness which rejects it.*

71> To return from this seeming digression. It is to
be observed that all reasoning proceeding on experiential
evidence falls under the Dictum of Aristotle, and in order
to its validity we must have a major as well as a minoi
premiss. The major may not always be expressed ; the
argument often takes the form that is vulgarly called an
Enthymeme, that is, with one premiss suppressed. But
one reason for its being so often unnoticed is that we are
so familiar with it ; and whether expressed or not, it is" in
all cases implied, and we proceed upon it in our reason-
ings.

72. It has been disputed whether there is reasoning
involved in the Inductive Method of inquiry, by which all
discoveries have been made in physical and mental
science. In that method two steps are involved : one is
the gathering of the facts ; the other the gathering of the
law out of the facts. In the former there may be no
special exercise of ratiocination ; but in the latter there
is ; we proceed from something given to something de-
rived from it, from the facts to the law of the facts. And

* " I receive mathematics as the most sublime and useful science as long as
they are applied in their proper place ; but I cannot commend the misuse of
them in matters which do not belong to their sphere ; and in which, noble
science as they are, they seem to be mere nonsense ; as if, forsooth, things only
exist when they can be mathematically demonstrated. It would be foolish for
a man not to believe in his mistress's love because she could not prove it to him
mathematically. She can mathematically prove her dowry, but not her love."-
Goethb's Conversations with Eckermann.

162 REASONING.

this reasoning can be reduced to syllogistic form. In the
inference there are two things involved ; one is the facts
gathered, and the other some general principle on which
we proceed in reaching the law from the facts. Attempts
have been made to enunciate the principles which entitle
us to rise from the particulars to the laws and causes.
The first systematic attempt was made by Bacon, who
enumerated a number of Prerogatives of Instances (Pre-
rogativse Instantiarum), which enable us to proceed
from the facts to what he called axioms, causes, and
forms. In this past age these have taken a better form
in what are called Canons of Induction. Now these Pre-
rogatives of Instances, or Canons of Induction, are in
fact the major premisses, while the observed facts consti-
tute the minor premisses in the process by which we rise
from the facts to the law. To give an example. The an-
cients referred the rising of water in a pump, and of mer-
cury in a tube, to nature's horror of a vacuum. Toricelli
and Pascal referred it to the weight of the atmosphere.
The case was decided by taking a barometer to the top of
a mountain, when it was found that the mercury de-
scended as the instrument was carried up to a higher
elevation. One of Bacon's Prerogatives of Instances
guarantees the process, what he calls the Experimentum
Crucis : When there are two rival theories, let us produce
a phenomenon which can be explained by the one and not
by the other, and it will prove the truth of the theory
which furnishes the explanation. This constitutes the
major premiss, and the minor premiss is the fact that the
mercury sinks as the atmosphere becomes lighter, — a fact
which cannot be explained on the theory of nature's hor-
ror of a vacuum, but can on the other. The process may
be unfolded still more clearly by that Canon of Induction
called the Method of Difference. " If in comparing one
ease in which the effect takes place, and another in which

REMARKS ON REASONING PROCESS. 1G3

it does not take place, we find the latter to have every an-
tecedent in common with the former except one, that one
circumstance is the cause of the former, or at least, part of
the cause of it." This is the major premiss in the argu-
ment. The minor is, that at the foot of the mountain
where the atmosphere was heavy the mercury was high,
while it was low at the top where the atmosphere was
light. The two together guarantee the conclusion that
the weight of the atmosphere is the cause, or part of the
cause, of the rise of the mercury.

73, The best exposition of the Canons of Induction is by Mr.
Mill (Logic, B. III., c. viii.). He states and illustrates five : — that ol
the Method of Agreement, of the Method of Difference, of the Joint
Method of Agreement and Difference, of the Method of Residues,
and of Concomitant Variations. But he does not perceive that
their Canons are the major premiss, while the facts are the minor
premiss, in the process by which we reason from the facts to the
law. We are prevented from enlarging on this subject only by the
circumstance that it would carry us into Particular Logic. It is
enough to show here how the reasoning involved in Induction can
be reduced to syllogistic form.

74. When the premisses are only probably true, the
conclusion is also only probably true. " Bash actions lead
to evil consequences," is true only in a general way —
there are cases in which rash deeds have led to brilliant
results. But in dealing with such general maxims, we
are not to allow to the conclusion a certainty not found
in the premisses — to use a graphic illustration of Whate-
ly's — " The chain is not stronger than its weakest part."
It is evident that if both the premisses in an argument,
and still more if all the premisses in a chain of argument,
be only probably true, the conclusion is more uncertain
than any one of them. If a story has reached us through
a number of persons detailing it the one to the other, it
may come in the end to be very doubtful, even though
each narrator be probably trustworthy. It is thus that
events, handed down from age to age by tradition, be

164 REASONING.

come in the end very uncertain — the stream may at first
have been pure, but it receives a polluting mixture in
every region through which it passes. Sometimes we
can, in a loose way, numerically estimate the probability
attaching to each premiss in the chain of proof, and then
we can state the conclusion numerically. The incident,
we may suppose, has reached us through three persons :
one trustworthy, and we value his testimony at T90, re-
garding 1 as absolute certainty ; the testimony of another
we reckon f , and of the other i ; the probability of the
story being true is now T90 x f x ! = |^ ; and we see that
the story is more likely to be false than true. The suc-
cess of a scheme depends, we may suppose, on the com-
bined character and ability and wisdom of the person who
manages it. His character we estimate y9^ ; his ability,
y7^ ; and his wisdom, fV) ; the probability of his success
will be y9^ x T7o x T% = y3o7o8o5 or the scheme is more likely
to fail than to succeed. It is seldom that in the practical
affairs of life we can get numerical estimates of any value.
When, however, the data are derived from such occur-
rences as the average number of deaths taking place an-
nually among a definite number of persons, and of fires
occurring in a certain description of property, Insurance
Companies can make calculations which are rigidly cor-
rect as to averages. But in all such cases the calculation
belongs rather to the arithmetician than the logician.
The shrewd man of the world, without expressing his
premisses or conclusion in numbers, can commonly ob-
tain sufficient data to enable him to reason and reach a
sound conclusion, as to the side on which the probability
lies, in departments falling under his habitual notice. He
may err in regard to a given proposal made to him, and
lose much by acting or not acting ; but in the long run
he will be found in acting on the rules (majors) which he
has laid down for himself, to have acted judiciously. He

REMARKS ON REASONING PROCESS 165

who proceeds habitually on such principles as that "rash
actions are to be avoided," " honesty is the best policy,"
will be found in the end to have acted a prudent part in
this world. Swayed by other and moral principles, he
will be found to have acted a good and a geneious part.

7«>. When there is a concurrence of evidence towards
a particular point, the conclusion is more probable than
any of the premisses. An incident is detailed to us by three
independent witnesses known to us to be trustworthy, and
we have now quite as certain proof as is to be had in this
world. We estimate the probability of each of them
speaking the truth as T% ; this makes the probability of
each of them speaking falsely as only T^3 and the proba-
bility of the three concurring in a falsehood as fa x fa x
fa, or only T fa „. Of this description is the evidence in be-
half of the great doctrines of natural and revealed religion.
Thus in behalf of the existence of God, we have the argu-
ment from the evident design in the structure and adap-
tations of animal and plant, the native disposition to trace
the seen effects to their unseen cause, and the conscience
or law in the heart pointing to a lawgiver. In favor of
the Christian religion we have the deposition of witnesses
that Jesus performed miracles and rose from the dead ;
and we have the character of Jesus and the doctrines he
taught, the spirit he inculcated and the precepts he en-
joined. Evidence of this kind is called Cumulative, and
may amount, as in the cases just mentioned, to the highest
moral certainty. There is still, to be sure, a bare possi-
bility of error, but it is as one to a thousand, a million, or
a million millions. Only diseased minds will allow them-
selves to dwell on it — only the fool will say in his heart.
There is no God. But healthy minds will brush it aside,
will in fact not feel it in the view of the overwhelming
evidence on the other side.

¥6. When there is a concurrence of facts towards a

166 REASONING.

conclusion, the point may be regarded as established when
no one of the proofs is itself sufficient. This is what is
called Circumstantial Evidence. A murder has been
committed, a person is charged with the crime, and the
proof runs as follows :

The murderer may very likely have blood on his clothes ;

This man had blood upon his clothes ;
. . He is the murderer.

The murderer must have been prowling about the premises;

This man was prowling about the premises ;
'. He is the murderer.

The murderer will have some of the goods of the murdered man

This man had some of the goods of the murdered man ;
•. He is the murderer.

No one of these arguments is in itself conclusive. The
syllogisms are all in the second figure ; the premisses are
both affirmative ; in neither is the middle term distribu-
ted, and so no conclusion can be drawn. But by such
considerations we reach a general major premiss, that the
person thus found with blood on his clothes, thus seen
prowling about the premises, and caught with the prop-
erty of the murdered man in his possession, must be the
murderer, and the conclusion follows syllogistically.

77. Whence the rapidity and the unreflective nature of
the process ? It is acknowledged by all logicians, that in
spontaneous reasoning we have not before us consciously
the distinction between major, minor, and middle, the
moods and the figures of the syllogism. I hold, indeed,
that in all reasoning, the mind has before it the terms, and
perceives the relations between them ; but having this,
it proceeds with amazing quickness and without analyz-
ing or even reflecting on the process. This rapidity pro-
ceeds from the laws of the association of ideas. These
laws are those of Coexistence and Correlation. Things
which have been together in the mind tend to suggest
each other, as do also things that are related, say by re-

REMARKS ON REASONING PROCESS. 1G7

semblance, or means and end, or by cause and effect. Now
in subjects with which we are familiar, we have laid up an
immense store of such associations, partly by the things
having been brought together in our experience, and
partly by our being ever called on to notice relations.
What a number of such associations are formed in the
mind of the mathematician, the mechanic, the politician,
and the student of the fine arts, each in his own depart-
ment. And when he is meditating on any one topic, his
thoughts flow on with amazing speed from one point to
another. In this flow the terms of an argument or a
train of reasoning come up, and he perceives the relations
between them, and goes on from premiss to conclusion,
and from one conclusion to a farther. Meanwhile he
might be quite incapable of unfolding the process, or
even of recalling the steps. At the same time it is ever to
be understood that the train of ideas raised by association
does not amount to reasoning. I believe that much of
what is called reasoning in brutes, and even among chil-
dren, proceeds from mere association. When the burnt
child, and we may add the burnt dog, dreads the fire, it
is from the mere law of coexistence. All their lives men
are, more or less, under the influence of mere association,
in cases in which we imagine them to be reasoning. They
are led, not by a concatenated train of argument, but by
mere impulse — as it is said, that is, by the suggestion that
comes up. Hence the mistakes into which they are ever
falling — mistakes not to be referred to the reasoning
power. In all judgment, and in reasoning as implying
judgment, there is a perception of the relations of the
notions to each other ; and it is only thus we can reach a
sound and safe conclusion. Association is to be allowed
to aid us as an assistant, and to suggest terms for com-
parison. But above it, as a master, there is to be an
understanding to judge of the relations of the terms thus

168 REASONING.

brought before the mind ; not that we should adopt them
or follow them, but that we should judge of them, and
believe and act accordingly.

78. In what sense are the truths reached by the rea-
soning process new truths, and in what sense old truths ?
They are old truths, inasmuch as they all depend upon,
and are derived from, the truths with which the mind has
started in the reasoning process. That this man will die,
may depend on two other truths, that he has consump-
tion, and that consumption produces death. That man
will have to appear before the Judgment-seat, may depend
on other truths, as that he is a moral being, possessing
intelligence, conscience, and free will. The truths of the
sixth book of Euclid are all obtained from the definitions,
axioms, postulates assumed at the beginning, and from
the reasonings of the first five books. But in another and
an important sense they are new truths. They are not
truths at all to us, till they are reasoned out ; they may
not be known to us till they have been unfolded by
the reasoning process. There are truths, especially in
morals, but also in the fine arts, in geometry itself, and
indeed in every department of knowledge, thus bursting
upon us with all the freshness of novelty, because in fact
they are now brought out by us for the first time, from
premisses — it may be known to us for years. Such
truths, it is often said, come to us by intuition ; but in fact
they are obtained by a rapid reasoning process aided by
association ; and we forget the steps we have taken in
climbing, in the joy we experience because we have
gained the height.

FALLACIES. 169

FALLACIES.

70. A fallacy is defined " any unsound mode of argu-
ing, which appears to demand our conviction and to be
decisive of the question in hand, when in fairness it is
not." Its genus is " any unsound mode of arguing ; " but
every unsound mode of arguing is not a fallacy ; it is so
only when " it seems to demand our conviction and to be
decisive of the question in hand when " — we prefer saying
— " it is not according to the laws of thought." In order to
its being a fallacy, it is not needful that it should be stu-
diously constructed for deceitful purposes. The man who
uses it may himself be deceived by it ; or more frequently
he has first been deceived by the influence of selfishness
or passion, and " the wish becomes father of the thought,"
and the argument occurs to him and he advances it in his
justification. Some logicians call a fallacy a Paralogism,
wLen the man who employs it is deceived by it, and a
Sophism when, being aware of its unsoundness, he uses
it to deceive others. We need to be warned not only
against the sophistry of designing men, but against the
fallacies laid in our way by persons who believe what they
say ; and, as still more dangerous, against those which
originate in thoughts that favor our own selfish and
crooked aims.

80. In order to avoid all seeming exaggeration, we
may state precisely what Logic cannot do, and what it
can do, in the way of preventing us from being led astray
by fallacious reasoning. It should be allowed at once
that the best safeguard against error of every kind, is to
be found in a sincere desire to discover the truth, which
keeps the mind open to facts and arguments from what-
ever quarter they come — " When the eye is single the whole
body s full of light." Without this, no dialectic skill can

170 REASONIM*.

protect us from so insidious a foe as a deceitful heart. It
may be farther admitted that native shrewdness can de-
tect fallacies without the aid of logical rules. But freely
granting all this, it may yet be maintained that many valu-
able practical as well as scientific ends are to be gained
by an acquaintance with logical principles and the viola-
tions of them. It is most important, for the guidance of
our thoughts, that we should know what are the essential
steps involved in inference ; that we should be aware, for
example, that there are always three terms, and a com-
parison of two of these by the third ; and that in most
reasoning there is a major premiss implied in the form of a
general principle. By a logical training the mind is led to
look keenly into the meaning of terms and the relation of
terms one to another, to place the case fairly before it, to
sift the proof which may be proffered, and to determine
how far it is fitted to support the conclusion. How use-
ful, too, to know what are the common forms of invalid
reasoning, to be aware of the places where error lurks, that
so we may be on our guard against its insidious attacks,
or ready if need be to seek it out, and expose it to view
and hunt it to death. By such a discipline the mind may
acquire a habit which will lead it spontaneously to reason
accurately, and gender a spirit of penetration, scrutiny, and
caution, which will save it from being carried along by im-
pulse, by plausible statement and clap-trap oratory. We
find the correct speaker and writer coming to speak and
write accurately without construing his sentences, but it is
because he has previously studied grammar ; and the arith-
metician makes his calculations without referring to rules,
because the habit has become part of his nature. In like
manner the correct thinker can conduct a long chain of
ratiocination, without thinking of syllogistic formulee, but
all the while the skill may be the result of logical train-
ing, and there may be throughout an unconscious use of

fallacies. 171

the principles of reasoning. And just as an author when
a dispute arises about his language, is obliged to resort
to the rules of grammatical construction, and as the mer-
chant's clerk when his accounts will not balance has to
fall back on arithmetical rules to correct his blunders, so
the reasoner may find it convenient when he hag any
cause to doubt of his own arguments, or to dispute those
of his neighbor, to have logical rules ready for applica-
tion. In this way, any one who has a sincere desire to
discover the truth, may be guided aright in his own cogi-
tations, and kept from aberrations on cither side, and
enabled to use any natural shrewdness which God mav
have given him, in detecting the sophistries laid in his
way by others.

81. Psychology can explain how the heart sways the head. In
all judgment, immediate or mediate, there is comparison ; the com
parison of objects, two or more, represented to the intelligence and
apprehended by it. But the representation may be a misrepresen-
tation, the apprehension a mistaken one, and the judgment become
in consequence a perverted one. A prejudiced heart presents a par-
tial, an exaggerated, a distorted case to the judicial power. This is
effected through the influence of the will on the train of association.
We have already noticed the fact (§ 76) that while reasoning is not
the same as the association of ideas, it is yet greatly dependent on
it. It is by the laws of the succession of our ideas that the notions
compared are suggested. Now the will has a direct and an indirect
power over the train of thought and feeling. It has a direct power
in retaining the present idea, for as long as the will to retain it
exists, it keeps the idea before the mind ; and it is apt to detain
oniy what pleases and gratifies vanity, pride, and passion, and it
turns away from all that would reprove or humble. And then it
has a more important indirect influence. In detaining the present,
it collects around it a great many other thoughts connected with it
by the laws of suggestion, say by the law of co-existence, or the law
of correlation. In doing this, it calls into operation certain second
ary laws, such as when we bestow a great amount of energy of any
kind — say of thought, feeling, or attention — on any object, it will
come up more frequently before the mind. The heart thus sends up
to the head an immense number of ideas, all of one complexion ; and

172 REASONING.

the will seizes eagerly on those that please it, and as it lodges then?
they gather other ideas of a like description, till at last the man is
bound in a fellowship from which he cannot extricate himself. This
we believe to be the main source of our erroneous judgments and
invalid reasonings. They spring not so much from the understand-
ing as from the prepossessions of the heart, calling up only one kind
of ideas, and tempting us to look at them exclusively and carelessly,
keeping us from distinguishing between the things that differ, lead-
ing us to trace effects to wrong causes, and deceiving us by fail
appearances and specious analogies.

82. Fallacies from the days of Aristotle have been
logically divided into those In Dictione and those Extra
Dictionem, or, to use a better mode of expression, into
those in Form and those in Matter. The former are
found in the very form or expression, and we need look
no farther ; the latter can be detected only when we look
to the matter or objects of thought. Whately introduced
a third division, intermediate between the two others,
what he calls semi-logical, lying partly in the form, and
partly in the matter. The division is a very convenient
one, but cannot be consistently carried out. For Logic
cannot look at mere material errors ; if it did it would
have to look at all errors, and therefore at all knowledge,
historical, ethical, theological, scientific, practical. When
confined to its proper province, it can look at mistakes
only so far as they imply violations of the laws of thought.
But then in order to detect them, it is often necessary to
look at the matter, at least to the extent of understanding
what is meant by the propositions and the argument.
Fallacies of the latter kind constitute what are properly
called Material fallacies, which, however, must always be
logical, inasmuch as they imply a disregard of the laws of
thought, but which may be more or less logical according
as we have to look less or more to the matter, that is, the
objects.

S3, FORMAL FALLACIES. These can be detected

FALLACIES. 173

from the expression apart from the meaning or the ob-
jects. They are simply violations of the fundamental
laws of reasoning, and may best be exposed by an appli-
cation to them of the rules of the syllogism.

Undistributed Middle. Some one proves that Mohammed
was sincere, and thence quietly infers that he was a good
man. The reasoning is :

All good men are sincere ;
Mohammed was sincere ;
.•. Mohammed was a good man.

This violates the general rule that the middle must be
distributed at least once in the premisses, which is not
done here, as both premisses are affirmative with the mid-
dle term in their predicates undistributed. It also vio
lates the special rule of the second figure, which requires
one of the premisses to be negative. To legitimate the
conclusion, the reasoning must take a form in which it
will be at once seen that the major premiss is not true :

All sincere men are good men ;
Mohammed was sincere ;
.*. Mohammed was a good man.

Some one shows that religious professors have been
hypocrites, and thence argues that this man who is a re-
ligious professor is a hypocrite. This conclusion is valid
only when he has distributed his middle by showing that
all, and not merely some, religious professors have been
hypocrites.

84. Illicit Process of Major or Minor Term. Thus some
one allows that all studies are useful which tend to pre-
pare a man for the practical and professional duties of
life, but shows that the study of Latin and Greek does
cot accomplish this end, and thence argues that it is use-
less. Put the reasoning in proper form, and it is at onco
seen that there is an Illicit Process of the Major, which ia
distributed in the conclusion and not in the premiss.

174 REASONING.

The studies which prepare for professional life are useful ;
The study of Latin and Greek does not prepare for such ;
• It is not useful.
Whatever represses the liberties of mankind is to be resisted ;
Among the things which do so are governments ,
.'. Governments are to be resisted.

Here is an illicit process of the Minor. All that we can
argue is that some governments are to be resisted.

83. Negative Premisses. Some one is arguing against
a doctrine he dislikes, and lays down a number of neg-
ative positions in the way of objection, and imagines that
he has established a positive truth. Thus he shows that
Christianity cannot be proven to be true by its success —
for Mohammedanism succeeded ; nor by its alleged mira-
cles— for false religions have had alleged miracles. But
he is not entitled thereby to draw any positive conclusion,
certainly not to conclude that Christianity cannot be
proven by evidence.

80- Arguments with more than Three Terms. Thus
when it is argued, " Every one desires happiness ; virtue
gives happiness; therefore every one desires virtue," we
have no fewer than five terms : " every one," " desirous
of happiness," " virtue," " gives happiness," " desirous of
virtue." It might be possible, no doubt, to express the
thought so as to exhibit only three terms ; but then the
fallaciousness of the whole would be evident. When it
is argued that " as idolatry is a sin ; and as magistrates
should punish sin ; so they should punish idolatry," the
fallacy may be concealed by not seeing that there are
more than three terms, and will at once become visible
when the comparison is distinctly stated:

Sin (some sin) should be punished by magistrates ;
Idolatry is a sin.

We can draw no conclusion as the middle is not dis-
tributed.

FALLACIES. 175

S7» Fallacies of Conditionals, in denying the antecedent
and thence denying the consequent, or affirming the con-
sequent and thence affirming the antecedent. " Prayer
may be regarded as useful, if indeed we can regard
our prayers as announcing to Deity what he does not
know, or changing his eternal purposes ; but as we can-
not tell the Omniscient what he does not already know, or
change his plans, we may regard prayer as useless."
Here we deny the antecedent and can draw no conclusion
—as prayer may be useful on other grounds. " If this
man has been much injured, he is unfit to travel ; but he
is unfit to travel ; so he has been much injured." Here
we affirm the consequent, but can thence draw no con-
clusion as to the antecedent, as the man may have been
unfit to travel from other causes.

Fallacies in Disjunctives arise chiefly from the dividing1'
members not making up the whole. But in order to dis-
cover this, we must look at the objects ; and so this class
of fallacies falls under the head of Material.

88. MA TERIA L FALL A GIFS. All fallacies must im-
ply a violation of the laws of thought in order to bring
them within the domain of Formal Logic ; but in those
now to be considered we have to look to the matter in
order to discover this.

Ambiguous Teems, specially Ambiguous Middle, in which
a term is used in different senses in the premiss and
conclusion, or in the middle as it appears in the two
premisses. This is the Material Fallacy which approaches
nearest the Formal Fallacies. In fact it falls under the
head of Fallacies involving more than three terms. It
is called semi-logical by Whately. It is logical in that
it violates the law of thought which requires that there
be only three notions compared in the three proposi-
tions. But so far as the language is concerned, there
seem to be onlv three notions, and we have to look

176 REASONING.

beyond the expression to find that under the same phrase
two notions have been introduced.

80. In Part First we have dwelt at considerable
length on the incidental disadvantages of language, and
specially on those which spring from the ambiguity of
terms. No evil would arise from the double meaning of
a word provided we always had a clear apprehension of
the two senses, and never slid from the one signification
to the other in the course of the argument. When Paul
concludes (Rom. iii. 28), that " a man is justified by faith
without the deeds of the law,'"' he is using the word 'jus-
tify' consistently throughout, as meaning 'treated by
jod as free from guilt.' When James says (ii. 24), " Ye
see then how that by works a" man is justified, and not by
faith only," he too is using the phrase consistently,
meaning ' seen to be just before God,' which, he says,
requires the evidence of works. All candid minds will
see and acknowledge that in such a case the two state-
ments are not contradictory, and that both arguments
may be conclusive. Were we steadily to bear in mind
that some, as Locke and Kant, understand ' reason ' as
including ' reasoning,' and that others employ it to signify
intuitive reason, which excludes ' reasoning,' no mischief
could arise from the word having two meanings. The
evil arises from the circumstance that people, both those
who employ the argument and those te> whom it is ad-
dressed, are apt to pass from the one sense to the other
without being aware of it.

00. Paul says (Col. ii. 16), "Let no man judge you
in meat, or in drink, or in respect of an holyday, or of the
new moon, or of the Sabbath-days," meaning by Sabbath-
day, the seventh day of the week kept at that time by
many Jewish Christians. But from this some have ar-
gued that Christians are not now bound to keep the Sab-
bath-day, meaning the Lord's day, or first day of the

FALLACIES. 177

week. Certain of the ancient philosophic sects of Greece,
as the Stoics, laid down the general maxim, whatever is
conformable to nature is virtuous and should be attended
to. The Stoics approved of the principle, understanding
by nature what is godlike within and without us. Bishop
Butler says it can be justified only when we properly un-
derstand our nature, and give to the moral power the
highest and an authoritative commanding place. But
some have understood by it, all that is in our nature ; and
that therefore addictedness to pleasure in youth and to
gain in old age are allowable, as being agreeable to na-
ture. Many have argued in former ages that, as a coun-
try is prosperous according to its wealth (which is true
in the political-economy use of the phrase), and as a cer-
tain nation has much wealth (meaning coin or precious
metals), it must therefore be in a prosperous condition.
There has been a great deal of logomachy in the dispute
as to whether there is a reality in heat, light, and color :
some meaning by these phrases the sensation in our
frame ; others, the external qualities exciting the sensa-
tion. Many are puzzled in the present day when they
hear heat described as a mode of motion, understanding
by heat the feeling in our organism which, they say truly,
cannot be a mode of motion, whatever the exciting
cause may be. There is an ambiguity in the phrases
' obliged,' ' necessitated,' which has led to false conclu-
sions being drawn ; some understanding by the phrases
an external physical compulsion, and others, a moral in-
clination in the will. Thus some argue that since no man
has any discredit in what he is necessitated to do, and as
certain men are necessitated by their nature to do base
deeds, so they are not to be blamed nor punished. An
unsatisfactory ethical discussion has been encouraged by
the uncertain meaning of the word ' good,' which some-
times means 'morally good,' and sometimes is so widened
12

178 REASONING.

as to include happiness. There are writers who deceive
themselves as they pass from one of the meanings to the
other. They show that happiness is a good thing and
to be promoted, and then go on to speak of it as moral
good. The words ' conceivable ' and ' inconceivable ' have
helped much to confuse the controversy between the a
priori and a posteriori philosophies. Descartes maintained
that whatever is clearly and distinctly conceived, is to be
at once believed ; and many have argued that what is
inconceivable is to be rejected. It is shown in opposition
to them, that we can clearly and distinctly conceive, in
the sense of picture or image, many things, such as ghostSj
in the existence of which we have no faith ; and that
there are things, such as antipodes, which were reckoned
inconceivable in one age, and believed in a later age. If the
defenders of intuitive truth would not render themselves
the easy prey of their opponents, they should abandon all
such vague language, and show that there are truths
which man perceives at once. There is a like ambiguity
in the statement that all man's ideas are got by expe-
rience : it is true in the sense that experience is neces-
sary in order to the ideas springing up ; but it is not true
that experience apart from an intuitive capacity, can give
us such ideas as those of moral good and infinity.

91, Fallacia Accidentis, with its converse, Fallacia a
dicto secundum quid ad dictum simpliciter. In both, a
term is used in one of the propositions of the syllogism
to signify a thing in itself, or in its substance, and in the
other with certain adjuncts or accidents : as in the hack-
nied example, " What is bought in the market is eaten ;
raw meat is bought in the market ; therefore it is eaten.'"'
It is thus that orators and devotees deceive others and
are deceived themselves, while they use the phrases loy-
alty, authority, liberty, faith, religion. These are noble
qualities in themselves, but men confound the accompaui-

FALLACIES. 179

inents with the essence : and they comraend loyalty to a
person which is disloyalty to a nation ; and obedience to
a power which has no rightful authority ; and a liberty
which is licentiousness as being without law ; and a faith
which is credulity ; and a religion which is superstition.
It was thus that the cavaliers denounced the covenanters
and puritans as disloyal, though no set of men ever so
meant to be loyal. It is thus that some denounce as in-
fidels all who will not understand as they do the first
chapter of Genesis, or account as they do for the for-
mation of the strata of the earth's surface, or the origin
of animal species.

92* Equivocation, embracing in it Amphiboly. A mem-
ber of the House of Commons was supposed to have called
another member a liar, and a confused dispute arose
whether that member had been called a liar, or had told
a lie, when the gentleman charged rose and said sol-
emnly, " It is quite true and I am sorry for it," meaning,
" It is quite true he is a liar ; " but understood, " it is
quite true I said it." To this head may be referred the
response of the oracle, " Aio te, Aeacida, Romanos
vincere posse," and the prophecy "The Duke yet lives
that Henry shall depose." But there are far worse in-
stances of equivocation than these, in common use. A
person is charged with having struck another with a stick
to the danger of his life, and he replies that he did not
injure him with a stick, though he is conscious all the
while that he did so with a bar of iron. Or' some one is
charged with having done a base act on a certain day in
the forenoon, and he denies it, because he did it after
twelve o'clock. It is a weapon which has been employed
in all ages in politics, in courtship, in commercial trans-
actions : language is employed which is capable of being
understood in a just sense, but which is meant to leave
a different impression on those to whom it is addressed.

180 REASONING.

The person who resorts to these mean tricks may imagine
that he is free from the sin of lying ; but the fact is, his
lying is of a peculiarly aggravated character, as with the
falsehood there is low and deceitful cunning. Closely
allied is the fallacy of what is called

OS. Oblique Expression. It is used by the courtier and
the flatterer, who keep within the limits of truth in their
statement, but intend that their words should suggest
much more to those whom they address. It is employed
by the calumniator when he does not bring a direct
accusation — which might be met ; but he hints and in-
sinuates certain dark charges fitted to raise our worst
suspicions. We see it exhibited by the guilty man when
he puts on a look of injured innocence ; or affects a vir-
tuous indignation because such an offence could be
charged against him. There are certain speakers guilty
of it in every sentence, and certain writers exhibit it in
every page, for they can say nothing clearly and plainly.
It has been said of Hume, as a historian, that, " without
asserting much more than can be proven, he gives prom-
inence to all the circumstances which support his case, or
glides lightly over those which are unfavorable to it."

94. FALLACIES OF CONFUSION. Almost all
paralogisms might be put under the head of Confusion of
Thought. It is the office of Logic to correct error by ex-
hibiting the various kinds of confusion into which the
mind may fall in apprehending, judging, and reasoning.
The phrase, Fallacy of Confusion, might be restricted to
those errors which arise from confounding in our minds
the nature of the notions and the relation of the notions.
Thus we may be employing in argument a notion of
which we have a very obscure apprehension. It is a con-
cept, and we do not know what are the common qualities
which join the objects in the concept, and in the process
we suppose these qualities now to be one thing and no^v

FALLACIES. 181

another. We are reasoning about the 'good,' and now
we suppose it to be the morally good and now to be hap-
piness. Or we use abstract and general terms as if they
were singulars, and after making jjroper enough predi-
cations of them, we reach a conclusion in which they are
to be understood as individual existing things. Plato is
right in saying that there are ideas in and before the
Divine Mind ; that these Ideas exist as model forms or
laws in nature ; and that the human mind may rise to
the contemplation of them. But he is wrong when he
speaks of them as existences, like God, the world, and
the human mind. Scientific men are right when they
say that the planets are held in their spheres by gravita-
tion, but they err when they give gravitation a being and
a power different from the bodies themselves of which
gravitation is a property. Under this head we may place
the fallacy of husteron proteron, of placing that which is
first last, and last first. The good woman mentioned in
the " Guesses after Truth," had a truth in her mind, but
expressed it very confusedly, when she thanked God that
he had placed the Sabbath at the beginning of the week
instead of the middle of it, as thereby everything was
kept in order.

95. Fallacy of Division and Composition, in which a
term is used in one judgment collectively, and in another
distributively. In Division, a term is used collectively in
the major premiss and distributively in the minor, and
in Composition, the reverse. The liability to fall into
this fallacy is much furthered by the ambiguity of the
word "all," which may signify the whole collectively, ot
may mean every one ; and we fall into a fallacy when we
use it in one proposition of the syllogism in one sense,
and in another proposition in the other. It is thus that
when an army gains a victory, every regiment and soldiei

182 REASONING.

in it is apt to claim a share of the credit, though he
may in no way have helped to produce the result.
Many a one reasons thus :

What is no uncommon occurrence may reasonably be expected ;
To be successful in play is no uncommon occurrence ;
.•. To be successful in play may be reasonably expected.

This fallacy is involved in the reasoning of the youth,
who says or feels : — I may lay oat a certain sum on fine
clothes and not be in difficulties, and a like sum in jewels
and not he in debt, and as large a sum in travelling with-
out spending all my money, and concludes that he may
procure all these enjoyments. The same error is involved,
but in an opposite way, when the greedy man being asked
to subscribe to one charity after another, and finding that
if he gives to all he will be ruined, determines to give to
none. " Two distinct objects may, by being dexterously
presented again and again in cuiick succession to the
mind of a cursory reader, be so associated together in his
thoughts as to be conceived capable, when in fact .they
are not, of being actually combined in practice. The fal-
lacious belief thus induced, bears a striking resemblance
to the optical illusion effected by that ingenious and
philosophic toy called the Thaumatrope, in which two
objects painted on opposite sides of a card — for instance,
a man and a horse, a bird and a cage — are, by a quick
rotatory motion, made to impress the eye in combination
so as to form one picture, of the man on the horse's back,
the bird in the cage." ( Whately.)

96. Imperfect Division. This fallacy specially appears
in Disjunctive Reasoning, in which it is implied in order
to the validity of the reasoning, that the members make
up the whole, and that they exclude one another. But it
often happens that the parts named do not make up the
whole :

FALLACIES. 183

If it is decreed that you will recover from this disease you do not
need a physician ; if it is decreed that you will not recover
you do not need a physician ;

But you will either recover or not recover ;
. You do not need a physician.

Whereas there may be a third supposition ; that it is de-
creed that you are to recover by means of a physician.

Quite as frequently the divisions are not exclusive, in
other words, cross each other. In the famous con-
troversy between the a priori and a posteriori philoso-
phies, the supporters of the latter shut their opj)onents
up into the dilemma, that such ideas as those of power
and moral good are to be had either from some innate
power exclusively or from experience, and then show
that experience has to do with their formation ; but the
truth may be that the two combine ; the native power
may work in our experience, and on the occasion of our
experience.*

i)7. We now come to consider fallacies arising, not so
much from the terms, as from their relation to one an-
other in the reasoning.

Fallacy of Shifting Ground, as when the advocate or
opponent of a cause begins as if he were about to prove
it to be good and right, and as he proceeds shows that
some good may be derived from it ; or that it is wrong
and bad, and shows that it has led to certain supposed
evil results. Under this head may be placed the common
practice of persons professing to prove that a certain
deed has been done, but dwelling chiefly on the enormity
or the excellence of the deed, with the view of rousing

* Triptolemus Yellowley thought there were two ways of draining Braebaster
Loch, one down the Linklater Glen, the other by the Scahnester burn. But the
Udaller saw the imperfection of his division. " There is a third way ; let each
of us start an equal proportion of brandy, lime juice, and sugar, into the loch,
and let us assemble all the jolly TJdallers of the country, and in twcnty-foni
hours you shall see dry ground where the loch of Braebaster now is."

184 BEA80MJS/U.

the feelings and to prevent it being seen that they have not
established their point. Francis Bacon is charged with
having received an estate from his Mend the Earl of Essex,
and afterwards being unkind to him ; and the strength of
the writer is expended in dwelling on the evil of ingrati-
tude, especially on the part of so great a man, instead of
proving the alleged facts. In oral controversy how often
is it found that you combat "both your opponent's pre-
misses alternately, and shift the attack from the one to the
other, without waiting to have either of them decided
before you quit it. ' And besides ' is an expression one
may often hear from a disputant who is proceeding to a
fresh argument, when he cannot establish, and yet will
not abandon, his first." Under this head may be placed :

98. Fallacia Plurium Interrogalionum consists in ask-
ing two or more questions as if they were one and the
same, and when one of them is answered it is interpreted
as applied to the other. It is a trick of a low kind often
resorted to by lawyers in examining witnesses, with the
view of puzzling tliem, and turning their answers to a
wrong account. " You were swayed by the love of money
in the transaction?" (meaning exclusively,) to which the
witness answers " yes," (meaning in part.) Another ques-
tion follows : "Iu being swayed by money you were
acting selfishly in the transaction ? " The fallacy appears
in higher matters. Thus the utilitarian puts to us the
questions : " You deny that virtue consists in utility ? "
" Yes." " Then you deny that utility is a good thing."
The faUacy is to be met by accurately answering each
question separately.

99. PETIT10 PRINGIPII, or BEGGING OF THE
QUESTION, "in which one of the premisses either is
manifestly the same in sense with the conclusion, or is
actually proved from it." A man may prove that the
Bible comes from God because it contains certain ele-

FALLACIES. 185

vated doctrines which could not be discovered by the
natural sagacity of the writers ; but after he has done
this he cannot turn round and prove that these doctrines
are true because they are contained in the Bible. We
ought not to prove the existence and unity of God from
its being contained in Scripture, and then prove the truth
of Scripture from its giving us such high views of the ex-
istence, unity, and nature of God.

100. And here it may be proper to remark that the Syllogism or
Syllogistic reasoning is not, as has often been alleged, a Petitic
Principii. As put in syllogistic form, the premiss does not in any
sense depend on the conclusion; and the conclusion follows, not
from one of the premisses, but from the two, or rather from the re-
lations between the things compared in the premisses. It is when
the relations predicated in the two propositions are brought before
the mind that it sees the force of the inference.

101. Arguing in a Circle is the common manifestation
of the Petitio Principii. The person covertly, it may be
ignorantly, assumes a fact or principle, and by means of
it reaches a conclusion, which he is found after a while to
be employing to establish the fact or principle with which
he set out. Thus we find persons arguing that their church
is the true one because sanctioned by God ; and that since
it is the true church, God has sanctioned it. Or they reach
the truth of the Bible from the authority of the Church,
and infer the authority of the Church from the Bible. A
man maintains that his party is good because it promotes
good measures ; and that a measure is good because pro-
moted by his party. Malebranche is believed by many
to have become involved in this circle, when he proved
the existence of an external world by the authority of
Scriptare ; and he certainly did so, if it be impossible to
establish the authority of Scripture unless you assume
the existence of an external world. Much of the elabo-
rate reasoning employed in the discussion of intricate
subjects — for example, that of Spinoza in his Ethics — is a

186 REASONING.

movement in a circle — like that of a man who, after toiling
for hours in the dark, comes to the place from which he
started. It is evident that the more involved the chain, the
more difficult to detect the unsatisfactory junctions. The
most effective way of exposing the whole, is to insist on
narrowing the circle, and so spreading out the links that
we may see the feeble place, where the conclusion is em-
ployed to support the premiss, and the whole chain made
to hang on nothing.

102. IGNORATIO ELENGHI, or IRRELEVANT
CONCLUSION. Logicians suppose that in discussion
the opponent should prove the elenchus or contradictory
of your doctrine ; and when he fails to do this, and es-
tablishes a different proposition, he is said to be guilty of
an Ignoratio Elenchi. But the language may be so
widened as to include under it all cases of Irrelevant
Conclusion — that is, in which persons establish, not the
conclusion which they ought, but another which may be
mistaken for it. The dispute is, whether any one has a
right to compel a father to educate his child in a way dif-
ferent from what he is doing, in religion or in something
else, and one of the disputants thinks he has settled the
whole question when he has shown that the father is
educating his child wrong. Locke in showing that the
syllogism is of little or no value, proves that man can
reason without the use of syllogisms. " There are many
men that reason exceeding clear and rightly, who know
not how to make a syllogism." " God has not been so
sparing to men to make them barely two-legged crea-
tures, and left it to Aristotle to make them rational."
Macaulay in his Article on Bacon, thinks he has proven
that a knowledge of the canons of induction is of little
use, since men, without knowing them, are practising
them from morning to night. Under this general head
may be placed several other fallacies.

FALLACIES. 187

103. The Fallacy of proving only Part of the Question,
A.s wlien a man is charged with murder, and the prose-
cutor proves that he killed a man. The judge and jury
will insist that it be farther shown that he did the deed,
not in self-defence, or from provocation at the moment,
but with malicious intent. A person is denounced as a
liar, and his accuser when asked for his evidence shows
that he did make certain misstatements, it may be from
misapprehension or misinformation. "When the agri-
culturist objected to the Shetland plough with only one
handle, Magnus Troil proved part of his point when he
replied, " Tell me how it were possible for Neil of Lup-
ness, that lost one arm by his fall from the crag of Nek-
brekan, to manage a plough with two handles ? "

104. Fallacy of Objections, that of concluding that a
proposal is to be set aside because there are objections to
it — as if the captiousness of men were not prepared to
object to anything, even to the existence and worship of
Grod. It is not enough to show that there are objections ;
it must be shown that there are stronger reasons against
it, than for it. Thus in one of the rising cpiestions of the
day, when it is proposed to appoint young men to public
offices by competitive examination, an opponent thinks it
sufficient to object that at times you might thus get a
person who has no great business capacity ; whereas it
properly devolves on him to show that by this mode of
appointment you would not get young men of such high
business talents and character as by the method now
practised of political patronage.

103. Argumentum ad Hominem. As all reasoning is
ex concessis, we are entitled in reasoning with any one to
proceed on the principles avowed by him, though these
might not just be the principles to which we might appeal
in dealing with others or with mankind generally. Our
Lord often employed this method in dealing with the

188 REASONING

cavils of the Pharisees. The argument, however, will not
be acknowledged as valid by those who do not admit the
principles on which it proceeds. That loose appeal made
to faith in the last age by so many German and British
writers, is not allowed to be legitimate by those who in-
sist on your proving by the proper tests that a faith must
be intuitive, or that it is supported by sufficient mediate
evidence, before they are inclined to yield to it. It is not
an honest use of the argumentum ad hominem, when we
take advantage of premisses which those with whom we
are arguing allow, but which we do not ourselves believe,
— except, indeed, when our aim is simply to make them
doubt of their premisses by showing the consequences to
which they lead.

106. Argumentum ad Populum, or an appeal to prin-
ciples cherished by the great body of the people. It is
allowable only when the principles are right and proper
in themselves, and are conscientiously entertained by
those who advocate them. It is not legitimate when
they are wrong in themselves, or when he who urges
them is doing so hypocritically. It will commonly hap-
pen in the end that such a deceitful use of the argument
will turn against the person enjoying it. In no case is
it allowable to employ this argument to stir up a malig-
nant spirit or violent acts.

107. Argumentum ad Verecundiam. It consists of an
appeal to antiquity, to the opinions of ancestors, to the
religion of the country. This line of argument may prove
that we are not rashly to disturb the established order of
things ; but it goes no farther. It does not tend to prove,
that if we are constrained otherwise by truth or by duty,
we must believe as our forefathers did, or decline to dis-
turb the present order of things.

108. Argumentum ad Ignorantiam, as when you insist
on a man believing a thing because he knows nothing to

FALLACIES. 189

the contrary. It is thus that people have been frightened
by horrid pictures, drawn by priests or pretenders, of the
world to come. It is thus that some would have us be-
lieve in animal magnetism, in clairvoyance, and the like,
because they exhibit phenomena which we cannot explain.
The legitimate conclusion in such cases is, that we should
suspend our judgment, and wait for light to come from
true religion, or scientific research.

109 '. Fallacy of Pretension. We are inclined to intro-
duce some such head as this, to include certain very
common cases of wrong inference. It would embrace, for
instance, the Fallacy of References, in which there is an
appeal by authors or speakers to passages or to authorities
which are not expected to be very narrowly searched, or
which, if narrowly scrutinized, do not bear out the con-
clusion. It is thus that Buckle, in his work on Civili-
zation, has deceived (we do not say intentionally) many
by numerous quotations which, if narrowly sifted in their
historical connection, are not fitted to bear up all that he
would rear on them. It is thus that a dogmatic air over-
awes many who are not inclined to think for themselves
or institute an independent inquiry. Many feel as if such
men as Hobbes and Comte must be speaking truly and
with a profound knowledge of their subject, when they
utter their statements so clearly and so confidently — where-
as all this may have arisen fi'om their never having looked
at anything more than one side of a very complex ques-
tion. Under this head we place the Idola TJieatri of
Bacon, or the deceiving influence exercised by great
doctors, heads of sects, and leaders of opinion.

110. Argument from Consequences. This is allowable
in questions of pure expediency, as, for example, in con-
sidering a proposal to pass a law for the suppression of
intemperance, or gambling, or licentiousness ; we ought
to inquire whether it would effect the end in view. But

190 REASONING.

when the question is one of truth or right, we should not
in the first instance appeal to results. There is a con-
stant tendency on the part of some, when a new scientific
truth is divulged, to reject it because it may produce evil
consequences by undermining religious beliefs, or good
social sentiments. But if a doctrine be true, and a deed
be right, the consequences must be good whether we see
it or not. After we have established the truth or false-
hood of a doctrine on independent evidence, then we may
allowably trace the consequences — always, however, in a
spirit of candor and fairness.

Ill, Mistakes as to the Onus Probandi. When any one
makes a positive affirmation, the Burden of Proof un-
doubtedly lies on him, and his evidence should be such
as can stand the laws of evidence in the particular de-
partment. If it be a mathematical truth, he must dem-
onstrate it by principles self-evident, necessary, univer-
sal. If it be a scientific truth, he should bring evidence
that can stand the tests of the canons of induction. If
it be a historical event, he must show that it can stand the
tests of historical criticism. If it be reached by deduc-
tion, it may be tried by the syllogism. But if he has
failed to give sufficient proof, he is not entitled to insist
on those who may not give in to his affirmation, proving
the contradictory of it. They may very properly content
themselves with suspending their judgment till proof is
adduced. For example, if a man says a particular plant
is to be found in a certain country — say azaleas in Scot-
land— we expect him to produce the plant. But he is not
entitled to demand of us that we go round the whole
country and show that there is no such plant. It is often
easy to disprove a general statement by an individual
case. If a man were to say that all the blessings which
God sends are universal or common to the whole race,
you could confute him by showing (in the third figure of

FALLACIES. lyl

the syllogism) that certain blessings, such as the means of
education, had not been placed within the power of all
mankind. But to prove a general negative is often dim-
cult or impossible ; for you would have to go round all
possible cases, and show that no one of them admits of a
positive affirmation being made regarding it.

112. We now come to consider certain Fallacies
usually treated of in works of Formal Logic, but conduct-
ing us into Particular or Objective Logic, which looks at
thought as directed to special classes of objects. No
doubt there are violations of the laws of discursive
thought involved, but in order to find out what they are,
and how they are to be remedied, we must go to other
departments of knowledge.

Fallacies of Analogy. By analogy we are to understand,
not the resemblance of one thing to another, but the re-
semblance of ratios or relations. Thus the sovereign of a
country is said, by analogy, to be the head of the country,
because he bears the same relation to the country as the
head does to the body. Two fallacies may spring from
the use or abuse of analogies. First we may suppose
that the things related resemble each other because their
relations do. The wing of a bird and the wing of a but-
terfly are said by naturalists to be analogous, for they
serve the same purpose, that of flight ; but the two
members do not resemble each other in their structure.
We are exhorted by our Lord in praying to God, to imi-
tate the importunity of the woman who continued to
apply to the judge till she gained her case ; but we are
not to understand that Grod resembles that judge in
character, or the motives by which he is swayed. An-
other fallacy arises from carrying the analogy too far.
Thus some have argued that since all nations resemble ani-
mals, in having a period of childhood, youth, and maturity,
they will therefore resemble them in having a time of de-

192 REASONING.

creptitude and death — whereas there may be causes al
work in certain nations, such as education and Christian-
ity, which will save them from the latter stages. The
argument from Analogy is : " Things resemble each other
in certain known respects ; they will therefore resemble
each in certain other and unknown respects." This is an
argument which is often conclusive. Thus the connois-
seur argues : this painting resembles the paintings of
Rubens in certain characteristic marks, and must resem-
ble them in this respect also, that it has been produced
by the same hand. Thus it is that the anatomist finding
one fossil hind leg of an animal, concludes that the other
must have been like it. It is in a great measure by this
principle that the palaeontologist can construct the whole
animal from a few bones found in the dust of the earth.
It is the province of Inductive Logic to lay down some
rule to guide us as to when the conclusion is valid, and
when it is invalid. Formal Logic can assist us no way at
this place. All that it can do is to show where error may
lurk, and insist on our seeking to obtain some general
principle (as a major) to guide and guard us.

113, Imperfect Enumeration. In all departments of
science and practical knowledge, general laws are gained
by the observation of particular facts. But what number
and what kind of observations are sufficient to entitle us to
declare that we have discovered the law V A sailor reasons :
' Three times did I set sail on a Friday, and in each of
the voyages I encountered a storm ; it is clear that Fri-
day is an unlucky day.' Another met once or twice with
a calamity after sitting at a table where there was a com-
pany numbering thirteen, and resolves always to leave a
company when he discovers it to be composed of this
number. A third met with calamities on several occa-
sions when he persevered in a journey after a hare had
crossed his path, and he now turns back whenever that

FALLACIES. 193

animal crosses the road on which he is travelling. Every
enlightened man sees that these are cases of narrow enu-
meration. But what is a sufficient enumeration ? It can
easily be shown that the sufficiency does not depend on
the number of the cases. Mr. Mill puts the question :
" Why is a single instance in some cases sufficient for a
complete induction, while in others myriads of concur-
ring instances, without a single exception known or pre-
sumed, go such a very little way towards establishing a
universal proposition?" and declares that he who will
answer this question is wiser than the ancients. Bacon,
followed by Sir J. Herschell, Mr. Mill, and others, have
tried to answer it by means of Prerogative Instances
( § 71) and Canons of Induction, and have been so far
successful. The Logic of Induction is seeking to lay
down principles which may decide for us when we have
such an enumeration as to authorize us to say that we
have reached a law. But Formal Logic can do nothing
more than warn us against trusting in imperfect enumer-
ations, and require us to look out for some principle to
authorize the conclusion we would draw.

111. Non Causa pro Causa. The inquiry into Causes
is not the same as the inquiry into Laws, referred to in
last section. In the inquiry into Laws, we are seeking a
mere co-ordination of facts ; in the inquiry into Causes we
are seeking after antecedent agents having a producing
power. The one inquiry, as well as the other, carries us
beyond Formal Logic into Inductive Logic, and indeed
into the Natural Sciences which treat of objects. Formal
Logic, however, can guard us against certain errors, and
draw our attention to some important distinctions.

115. Post Hoc ergo propter Hoc. A remarkable meteor

was seen in the sky, and followed by a dreadful national

calamity : a conjunction among the planets was followed

by a royal marriage which issued in far-reaching conse-

194 REASONING.

quences; and the superstitious conclude that one oi
the facts had some kind of causal connection with the
other. "We have outlived these weaknesses of past ages :
but we have not outgrown the fallacies on which they
proceeded. A country or college has prospered under a
certain government or management, and some conclude
that it was because of the government or management,
and oppose all projected improvements.

116. Fallacy of mistaking Sign for Cause. The quack
doctor falls into this, when on seeing certain spots on the
body he attacks and removes them, thereby, it may be,
sending the malady farther into the frame, instead of
curing it in its seat. The quack statesman is guilty of the
same error, when discovering the existence of ignorance
and crime in a country he contents himself with punish-
ing them, instead of trying to remove the deep moral
causes from which they spring. Buckle has, as it ap-
pears to us, fallen into the fallacy ; he traces all civiliza-
tion to mere intellectual power, excluding moral causes :
whereas the intellect in many cases, as in Scotland and
the United States, was awakened by moral causes of
which the intellectual life was, properly speaking, the
effect.

117* In order to keep us from falling under the power
of these fallacies, Logic calls our attention to two im-
portant distinctions. There is the distinction between
the Causa Essendi and the Causa Cognoscendi. The for-
mer is the objective cause in the powers of nature or of
God ; the latter, the facts or means by which we come to
know the objective cause of the occurrence. The two are
often confounded by much the same language being em-
ployed by us to denote them. Thus we speak of the
ground being wet because it has rained ; and of its hav-
ing been rain because the ground is wet. It is evident
that the Causa Cognoscendi is often an effect indicating

FUNDAMENTAL LAWS OF THOUGHT. 195

the Causa Essendi; thus the melting of snow may be a
proof or a sign of the rise of temperature which has made
the snow to melt. Of very much the same character is
the distinction between Reason and Cause ; the Reason
being that which brings conviction to us, and the Cause
that which produces the phenomenon. The increase of
temperature is the cause of the melting of the snow, but
the melting of the snow as being an effect may, on being
contemplated by us, be the means of revealing the action
of the Cause.

FUNDAMENTAL LAWS OF DISOUKSIVE THOUQHT.

118. It now only remains to try to enunciate the
fundamental laws which lie at the basis of all Logical op-
erations. These work in our minds without our being
conscious of them — we are as little conscious of them, as
we are of the physiological laws involved in our breathing.
We can discover them only by careful observation and
analytic generalization of the operations of discursive
thought. A knowledge of them does not assist us in
spontaneous reasoning, but it is of great value to all who
would reflectively acquaint themselves with the processes
of thinking. They are such as the following :

110. I. The Law of Identity, which may be expressed,
"the same is the same, perceived it may be at different
times and with different concomitants." This rules all
cases in which we draw an affirmative proposition from a
proposition or propositions, in which the relation of the
two terms is one of identity. Thus it being given that
" Jonathan Edwards is the greatest American metaphy-
sician," we get the Implied Judgment " the greatest
American metaphysician was Jonathan Edwards ; " or, it
being farther allowed that " Jonathan Edwards was the

196 G0NGLU8I0N.

Missionary to the Indians at Stockbridge,' we get bj
reasoning the Conclusion that " the Missionary to the
Indians at Stockbridge, was the greatest A meriean meta-
physician."

120. II. The Law of Contradiction. This law is " it
is impossible for the same thing to be and not to be at the
same time." Or bringing out a farther aspect of the same
truth, it may take the form : " A thing cannot have, and
not have, the same attribute at the same time." It rules
in all cases in which we get a negative proposition from a
negative proposition by implication, or from negative
propositions by reasoning, as when it is given us that,
" Francis Bacon is not the same as Boger Bacon," we say
that " Koger Bacon was not the same as Francis Bacon,"
or, with another proposition allowed, that " Francis Ba-
con was the expounder of the Inductive Method," so
" Roger Bacon was not the expounder of the Inductive
Method."

121. III. The Law of Excluded Middle, Lex Exclusi
Tertii aut Medii ; that is, either a given judgment is true,
or its contradictory — there is no middle course or third
supposition. Thus it must either be true or not true
that " God exists ; " and it must either be true or false
that " this man was ignorant of the deed ; " and if it
can be shown that he was not ignorant of it, you cannot
look upon him as if he was ignorant.

122. TV. The Principle of Equality, " things which
are equal to the same things, are equal to one another."
It is thus we argue that 2 + 2 = 4; and 2 x 2 = 4;
therefore 2 + 2 = 2x2.

In all cases in which the propositions are Equivalent
(P. II., § 14), these are the sole regulating principles.
But where the propositions imply Extension and Compre-
hension, other Laws come in and act along with these.

123. V. The Dictum of Aristotle, " whatever is predi-

FUNDAMENTAL LAWS OF THOUGHT, 197

cated of a Class Notion, may be predicated of all that ia
contained in it." This is seen to be true on, the bare con-
templation of the nature, of the extension, of a concept.
Combine this principle with that of Identity, and we get
Affirmative Judgments implied or inferred. Thus as " all
plants die," so " some plants die," and as " Coniferae are
plants," so " Coniferee die." Combine this principle with
that of Contradiction, and we draw negative propositions.
As " no men are perfect," so " some men are not perfect,"
and " the Greeks " " who were some men," " were not
perfect." These principles, the Dictum combined with
the Law of Identity in affirmatives, and of Contradiction
in negatives, rule all ordinary syllogistic and conditional
reasoning.

Combine the Dictum with the principle of Excluded
Middle, and we get a number of Implied Judgments.
Thus we argue that if it be false that " no metal is heavier
than water," it must be true that " some metals are heavier
than water." Eeductio per Impossibile (P. III., § 40), pro- -
ceeds on these two principles.

124:. VI. The Principles of Attribution, " every at-
tribute implies a thing of which it is an attribute." Or,
it may take a subordinate form, " All that is in an attribute
is in the thing that contains the attribute," or, as Leib-
nitz expresses it, " Nota notse est nota rei ipsius." This
law has a place in Abstraction (P. I., § 11) ; in Imme-
diate Inferences from Privative Conceptions (P. IT., § 49),
and in all reasoning in Comprehension (P. III., § 42), that
is, reasoning in which we specially look at the attributes.
Thus we argue that as intelligence, conscience, and free
will, make the beings who possess them moral and re-
sponsible agents, so man, as possessing these, must be
regarded as a moral and responsible agent.

125. VII. The Law of Division, " the dividing mem-
bers make up the whole class." This is the principle — al-

198 CONCLUSION.

ways along with the Dictum — regulating Disjunctive Rea-
soning, as when we argue that if a man has not taken
two of three possible roads, he must have taken the third.
Combined with the principle of Excluded Middle, it regu-
lates reasoning in which we argue on the supposition
that the members exclude one another. " If this man
must be either a fool or a knave," it follows if he is not a
fool, " he must be a knave."

12(>. VDII. The Principles of Whole and Parts.
" What is true of the whole is true of each of the parts."
This holds good of parts whether they be sub- classes or
attributes. This principle helps to guide us in Subalter-
nation, and in all reasoning involving Extension and Com-
prehension. Another Principle to be placed under the
same head is, " The parts make up the whole ; '' a prin-
ciple involved in all reasoning which proceeds on the
completeness of Division.

127- I" looking at the discursive operations of the mind, we
have constantly come to such principles as these. The consider-
ation, however, belongs not to Logic, but to Metaphysics (P. I., § 1),
or the science of First or Fundamental truths. The author of this
treatise has treated of them, of their nature and mode of develop-
ment, in First and Fundamental Truths. He has there shown that
such principles are Intuitive, that is, are seen to be true at once ;
and this not by any form in the mind, but by the capacity which the
mind has to contemplate objects, and by the exercise of that capacity
in looking at objects. He has shown that the Law is not consciously
before the mind when it is exercising it, and that it is in looking at an
individual object, or judgment, that it is called forth. The mind has
not consciously before it the Law of Equality Avhen it declares that if
A is equal to B, and B to C, then A must be equal to C. It reaches
the conclusion at once on the contemplation of the equal lines. The
Law of Equality is discovered by us by a generalization of the individ-
ual judgments.

APPENDIX.

I.-EXERCISES AS TO FORMS.
The Notion.

1. Are the following Singulars, Abstracts, or Universals, ana
if Universals, are they Generalized Abstracts or Generalized Con ■
cretes, viz. : Aristotle, Rationality, Rational, Man, Beauty, Good,
The Good, Homeless, The Creator, Creature, Resolute, Plant,
Mammal, Substance, Mind ?

What sort of terms are the following, viz. : Multitude, Thii
Regiment, David King of Israel, The First King of Rome, Th*
greatest living Sculptor, The Dog Cesar, This Dog, That Bird
Flying, The most distinguished Soldier in the Army, Husband ,
Husband and Wife,

" The glass of fashion and the mould of form,
The ohserved of all ohservers."

2. What are the Terms in the following, and what sort ot
Terms ? " Thou (FalstafF) didst swear to me upon a parcel gilt
goblet, setting in my Dolphin Chamber, at the round table, by
a sea-coal fire, upon Wednesday in Whitsunweek, when the
prince broke thy head for liking his father to a singing man of
Windsor ; thou didst swear to me then, as I was washing thy
wound, to marry me and make me my lady thy wife. Canst
thou deny it ? Did not good wife Keech, the butcher's wife,
come and call me Gossip Quickly ? Coming in to borrow a me«9
of vinegar; telling me she had a good dish of prawns, whereby
thou didst desire to eat some ; whereby I told thee they were ill
for a green wound ? And didst thou not, when she was gone
down stairs, desire me to be no more so familiarity with such
poor people, saying, that ere long they would call me madam."

200 APPENDIX.

" Because A F is equal to A G, and A B to A C, the two sidea
F A, A C are equal to the two G A, A B, each to each ; and they
contain the angle FAG common to the two triangles AFC,
A G B ; therefore the base F C is equal to the base G B, and
the triangle AFC to the triangle A G B ; and the remain-
ing angles of the one are equal to the remaining angles of the
other, each to each, to which the equal sides are opposite, viz. :
the angle A C F to the angle A B G, and the angle A F C to the
angle A G B,'1 &c.

" To be, or not to be, tbat is the question ;
Whether 'tis nobler in the mind to suffer
The stings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And, by opposing, end them ? To die— to sleep —
No more : and, by a sleep, to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to — 'tis a consummation
Devoutly to be wished. To die ? to sleep 1
To sleep— perchance to dream ; aye, there's the rub,
For in that sleep of death what dreams may come,
When we have shuffled off this mortal coil,
Must make us pause."

S. Are the following pairs of Notions Contrary or Contradictory
viz. : Sweet and Bitter, Organic and Inorganic, Greek and Bar-
barian, Wise and Foolish, Animate and Inanimate, Finite and Infi-
nite, Alive and Dead, Short or Long, Existent and Non-existent ?

4. What sort of reality is there in the following, viz. : Popu-
larity, The Rose Tribe of Plants, Gravitation, The Vine, Love of
Fame, Imagination, Roman Citizen, Heat, Cold, Blue, Substance,
Body?

5. Logically Define Notion, Percept, Abstract, Concept, Genus,
Species, Differentia, Judgment, Equivalent Proposition, Attribu-
tive Proposition, Conditional Proposition, Disjunctive Proposi-
tion, Implied Judgments, Conditional Reasoning, Disjunctive
Reasoning, Reasoning in Comprehension, Sorites, Fallacy, Am-
biguous Middle, Petitio Principii, Irrelevant Conclusion.

6*. Logically divide and subdivide Notion, Judgment, Reason-
ing, Fallacy.

7- Analyze General Notion, Collective Notion, Judgment,
Argument, A Horse Galloping, Unappeasable Revenge, Remorse
of Conscience.

APPENDIX 201

Judgment.

8, Point out Subject and Predicate aud designate the Quality
and Quantity of following, viz. :

A soft answer turnetb away wrath.

The man's heart is not in the right place. -

Dogs bark.

Great is the work of life.

Sailors are needed for the vessel.

It is wrong to put an innocent man to death.

It is the duty of every man to fear God and honor the

king.
Man is capable of living in a greater variety of climates than

any of the lower animals.
There was no possibility of substantiating the allegations.
The evidence proves that Phalaris was not the author of thn

Epistles.
Few patriots have been disinterested.
All gold mines cannot be wrought with profit.
The eagle lost much time when he submitted to learn ot thi .

crow.
The English can scarcely be said to be humble-minded.
Nothing is so easy as to object.
" In jewels and gold men cannot grow old."
There is no place like home.
None but the brave deserve the fair.
None but whites are civilized.

9. What is the Nature of the Terms in the following '{ Ate
the Propositions Equivalent or Attributive ?

The crocodile is a reptile.

Alexander was a great conqueror.

Alexander was the greatest conqueror of antiquity.

Logic is the science of the Laws of Discursive Thought.

" The most sublime act is to put another before thee."

3x3 = 9.

If the clouds rise from the hill-top it will be a fine day.

If A = BthenC = D.

The event must have occurred either on Saturday or Sunday

202 APPENDIX.

" Man is endowed with the capacity of laughter." Undei
what head of Predicables would this be put by Aris-
totle ? By Porphyry ? And in this Treatise ?

10. Convert the following :
Every circle is a conic section.

Two straight lines cannot enclose a space.

No brutes are responsible.

Some students are diligent.

Some students do not fail in anything.

Perseverance is a condition of success.

Perseverance is the condition of success.

Washington was the first American President.

11. Put the following in the forms of Opposition :

The Duke of Wellington was the conqueror at Waterloo.
Dogs bark and bite.
What are the Contradictories ?

12. Interpret the following as to Denomination, Extension,
and Comprehension :

Man is fallible.

David was the sweet Psalmist of Israel.

The man who slanders his neighbor is not innocent."

13. What Implied Judgments can be derived from " Benevo-
lent actions are commendable."

14. Put the following in correct form as a Conditional, anu
indicate the Terms, the Antecedent, and Consequent : " This
patient will recover if he takes care of himself." Put it in Cate-
gorical Form, and indicate the Subject and Predicate.

Reasonikg.

15. Examine the following, and say if they are valid ; and if
so, according to what principle :

David was the youngest son of Jesse ;
David was the youth who slew Goliath ;
.*. The youngest son of Jesse was the youth who slew Goliath.
Logic is the Science of the Laws of Discursive Thought ;
Metaphysics is not the Science of the Laws of Discursive
Thought ;
*. Logic is not Metaphysics.

APPENDIX. 203

10. Put the following in Syllogistic Form. ; indicate the
Major, Minor, and Middle Terms ; the Major, and Minor
Premisses, and conclusion; and the Mood and Figure:

No one is free who is enslaved by his appetites ; a sensual-
ist is enslaved by his appetites ; therefore a sensualist
is not free.
Heavy dews fell last night and so it has not been cloudy.
From the case of the soul and body we see that there are
some things to be believed which cannot be compre-
hended.
17. Supply the wanting proposition in the following :
No branch of science has reached perfection ;
All branches of science deserve to be cultivated.

All horned animals are ruminant,
.•. The elk is ruminant.

The adaptation in the shoulder-joint is effected;
.•. It must have had a cause.

18. Put the following in Syllogistic Form, supplying Premis-
ses when necessary, and indicating Mood and Figure :

When Columbus was sailing the ocean in search of a new
world, he fell in with a flock of land birds and con-
cluded that he could not be far from land.

It has been argued by some that electricity is the agent by
which the nerves act upon the muscles. But that this
is not the case appears from the fact that electricity may
be transmitted along a nervous trunk when a string i?
tied lightly round it ; while the passage of ordinary ner-
vous power is as completely checked by this process as
if the nerve had been divided.

His imbecility of character might have been inferred from
his proneness to favorites ; for all weak princes have
this failing.

'•' Suppose ye that these Galilaeans were sinners above all
the Galilseans because they suffered such things ? "

204 APPENDIX.

The Scriptures cannot come from God because they contain
some things which cannot be comprehended by man.

That persons may reason without language is proven by
the circumstance that infants reason and yet have no
language.

Bolingbroke, in arguing against the truth of the Christian
religion, shows that the Christian religion has bred
contentions. Burke answered him by showing that
civil government had bred contentions.
"The barbarians of the isle of Melita, when they saw the
venomous beast hang on Paul's hand, said among them-
selves, No doubt this man is a murderer, whom though
he hath escaped the sea, vengeance sufifereth not to live
Howbeit, they looked when he should have swollen or
fallen down dead ; but after they had looked a great
while and saw no harm in him, they changed their
mind and said, he is a god."

The dervis who told the merchants that they had lost a
camel, blind in his right eye, lame in his left leg, with-
out a front tooth, loaded with honey on one side and
wheat on the other, describes the steps which had
passed through his mind, " I knew that I had crossed
the track of a camel which had strayed from its owner,
because I saw no mark of human footsteps on the same
route ; I knew that the animal was blind in one eye,
because it had cropped the herbage only on one side of
its path ; and I perceived that it was lame in one leg
from the faint impression that particular foot had pro-
duced on the sand ; I concluded that the animal had
lost one tooth, because wherever it had grazed a small
tuft of herbage was left uninjured in the centre of its
bite," etc.

If it can be shown that there are two or more persons, it
follows that all is not one, that all is not God. Accord-
ing to every scheme of pantheism, I, as part of the uni-
verse, am part of God, part of the whole which con-
stitutes God. In all consciousness of self we know our-
selves as persons ; in all knowledge of other objects.

APPENDIX. 205

we know them as different from ourselves and ourselves
as different from them. God then must be different from
one part of his works. He must be different from me.
19. If the Major Term be the Predicate of the Major Propo-
sition, prove that the Minor Premiss must be Affirmative. Id
what Figures does this happen ?

Prove that the Major is Universal in the First Figure, and the
conclusion Particular in the Third Figure.

If the Middle Term be the Predicate of both Premisses, prove
that one of the Premisses must be negative.

Given the Minor Term the Predicate of Minor Premiss, prove
that A cannot be a Conclusion.

Given the Major Term the Subject of Major Premiss, prove
that A cannot be a conclusion.
Prove that A can be drawn only in the First Figure.
Prove that the Minor Premiss cannot be Negative in First
and Third Figures.
If the Minor Premiss be E or O, the Major must be Universal.
Given I as the Major Premiss, determine the Mood and Figure."
Prove that O cannot be a Premiss in First Figure ; that it can-
not be the Major in the Second Figure ; or the Minor in the
Third Figure ; and that it cannot be a Premiss in the Fourth.
20- Reduce the following to First Figure :
Every virtue promotes the general happiness ;
Cunning does not promote the general happiness ;
.*. Cunning is not a virtue.
All men are liable to sorrow ;

Some men are in the enjoyment of great prosperity ;
,\ Some in the enjoyment of great prosperity are liable to guf
fering.
All men are sinners ;
Some men are not cruel ;
.*. Some not cruel are sinners.
Every liar is mean ;

No mean man should have a public office ;
.*. No man should be elected to public office who is a liar.
21. Put the following in the form both of Extension and
Comprehension :

206 APPENDIX.

Deceit, being a sin, will be detected and punished.
Cause and effect, not being a law of Discursive Thought,
does not corne within the province of Logic.

22. Psychology, Logic, Ethics, ./Esthetics, all tend to give a
power of internal observation and of analysis to the student ;
and these being all the mental sciences, we may conclude that
all the mental sciences tend to give a power of internal obser-
vation and analysis.

Oxygen, chlorine and steam, etc., are all the gases ; and as
they are elastic, it follows that all the gases are elastic.

23. Dr. Reid says, " This simple reasoning, A is equal to B,
and B to C, therefore A is equal to C, cannot be brought into any
syllogism in mood and figure."

The narrative is trustworthy because the author has means
of knowing about what he writes, and trustworthy
authors must have means of knowing about what they
write ; the narrative is trustworthy because it is evi-
dently sincere and candid, and trustworthy writers are
sincere and candid ; the narrative is consistent, and
trustworthy narratives are consistent.
24:. Elephants are stronger than horses ;
Horses are stronger than men ;
.•. Elephants are stronger than men.

A is greater than B, and B than C, therefore A is greater than 0.
Plato lived after Socrates, and Aristotle after Plato, and so

Aristotle lived after Socrates.
Three-fourths of the fruit in the garden were apples;
Three-fourths of the fruit were blown down ;
.*. Some of the fruit blown down were apples.
25. The fact that I defended him is a proof that I held him
innocent (stated both as Conditional and Categorical).

"When about to prove the equality of two given Figures,
Euclid shows that if the one is not equal to the other, it must
either be greater or less ; and he points out the absurdity cf both
these suppositions :

It is known that a rider proceeding along a road and coming
to a place where other three roads meet, must have
taken one or other of the three ; we examine two of

APPENDIX. 207

them, and find that he had not gone by them, and we
at once conclude that he must have gone on the third.

h i man is not a brute or a divinity, he is capable of making
progress.
26. Put the following in form of Sorites and draw it out in a
series of Syllogisms :

A demagogue must hold the populace in contempt ; for
being a favorite with the populace, he must know how
to manage them, and in doing so he understands their
weaknesses, and understanding these must hold them in
contempt.

1L— EXERCISES AS TO VIOLATIONS OF THE LAWS OF THOUGHT.
In Notions.

27- Examine the following :

A line is said to have length without breadth. There can
• be no such line ; it is a mere abstraction, a ghost, a
nonentity ; and all that is demonstrated regarding it
can have no objective value.

" What follows from a definition follows in reality from an im
plied assumption, that there exists a real thing conform
able thereto. This assumption in the case of the defini-
tions of geometry is false. There exist no real things
exactly conformable to the definition. There exist no
points without magnitude, no lines without breadth and
perfectly straight, no circles with all their radii exactly
equal, nor squares with all their angles perfectly right."

" Concreta vere res sint : abstracta non sunt res sed reruin
modi ; modi antem nihil aliud sunt quam relationes rei
ad intellectum " (Leibnitz).

M A concept cannot in itself be depicted to sense or imagina
tion."
28. TJniversals have an existence prior to things and above
tilings.

The One, the Good, are the highest realities, are the only
realities, and the mind is in its highest exercise when
it is contemplating them.

208 APPENDIX

29. Try the following by the Rules of Definition, and amend

A square is a four-sided figure.

(Amended) A square is a four-sided rectilinear figure witl
its sides equal.

A deer is an animal with branching horns.

The judicial power is not the legislative.

A newspaper is a printed paper appearing periodically.

Words are the signs of thought.

A general notion is an inadequate notion of an individual.

Judgment compares notions.

Conversion is the changing of terms in a proposition.

Opposed propositions are those which differ in quantity and
quality.

Contradictory opposition is the opposition of contradictories.

A conditional proposition consists of two categorical propo-
sitions connected with each other.

A disjunctive proposition consists of two or more categori-
cals connected by the prepositions either and or.t

Reasoning is the deriving of one truth from another.

A fallacy is an unsound mode of arguing.

Ambiguous middle is a fallacy in which the terms admit oi
more than one meaning.

Ignoratio Elenchi is drawing a wrong conclusion.

Petitio Principii is a begging of the question.

50. Try the following by the Rules of Division :
Discursive Thought may be divided into the Term, Judg

ment, and Syllogism.
Animals may be divided into Quadrupeds, Birds, Fishes,
Reptiles, and Invertebrata.

Literature consists of History, Biography, Tales, Theol-
ogy, Poetry.

Notions are Concrete, Singular, and Universal.

Propositions are Affirmative, Negative, Universal.

All our ideas must be had either from Experience or a
priori.

51. Analyze Pleasure, the Sensation of Heat, the Idea of tna
Color White, Consciousness.

APPENDIX. 209

in Judgments.

32. Criticise the following : " Every notion holding the place
01 a predicate in a proposition must have a determinate quantity
in thought." " TW relation between the terms of a propositioi
is one not only of similarity, but of identity." " The terms of a
proposition are of an absolute equality, and all propositions an
equation of subject and predicate."

33. What is conducive to happiness is good, and so
The good is that which is conducive to happiness.

All equilateral triangles are equiangular, and therefore

All equiangular triangles are equilateral.

That God is infinite implies that the Infinite is God.

We are not entitled to say that because Raphael was the
greatest painter which Italy has produced, that there-
fore the greatest painter which Italy has produced wast
Raphael ; but simply that among the greatest paintem
which Italy has produced was Raphael.
3d. Since it is false that all men are liars, its contrary must
be true, that no men are liars.

Since it is true that some men are very designing, it cannot
be true that some men are not designing.

35. If Alexander was the son of Philip, we can surely argue
by Immediate Inference that Philip was the father of Alexander.

In Reasoning.

36. Are the following allowable, EAI, AEI, EAE? Is
A A I admissible in Fig. I. ? Or I A I or A E E ? In what Fig-
ures are A A I and I A I admissible ?

37. Why is I E O to be rejected ? A person urged that there
might be a valid syllogism in I E O, and gave the following :

I Some X is Y;
E Every T is not Z ;
O Some X is not Z.

38. All wise legislators suit their laws to the genius of theil

nation ;
Lycurgus did so ;
.*. Lycurgus was a wise legislator

210 APPENDIX.

"Whatever is universally believed must be true ;

The existence of God is not universally believed ;
.'. It cannot be true.

Cloven feet being found universally in homed animals, we
may conclude that this fossil animal, since it appears to
have had cloven feet, was homed.

He must be an atheist, for all atheists hold these opinions.

You see that men who are indifferent to all religion do not
seek to compel others to believe as they do ; and as
this man does not seek to compel others to believe as
he does, we may conclude that he is indifferent to reli-
gion.
30. Liberty is a good thing, provided it is not abused; bu4
it is abused, so it is not a good thing.

All those who say that Logic can teach man to reason must
approve of Logic ; but as you cannot say that Logic
teaches man to reason, you cannot approve of it.

This world would be a happy one if all men were good ; but
all men are not good, so our world is not a happy one.

40. Examine the following, both as Categoricals and Condi-
tionals :

All must approve of this student who consider him diligent;
and as you approve of him, you must consider him dili-
gent.

There is always discontent in a country when it is ill-gov '
erned ; and as there is always discontent in Ireland, we
may conclude that it is ill-governed.

Provided the differences between one political party and
another, and one religious sect and another, are of no
moment, they ought to tolerate each other : but the
differences are important, so they ought not to tolerate
each other.

41. Honors and rewards by the government or private patrons
are useless ; they cannot influence the stupid, and men of geniua
rise above them.

There is and can be no revelation of His Will by God : for
if the matter of it cannot be received and comprehended
by the human faculties, it is no revelation ; and if, or

APPENDIX. 211

the other hand, it can be compassed and comprehended
by the human faculties, it could be attained by them,
and is no revelation.
&2. If it be a good thing to have faith, surely he who believes
la the £oran has faith, and must have a good thing.

It is absurd to maintain that when we cannot avoid think-
ing or conceiving of a thing, it must be true ; for some
persons cannot be in darkness without thinking of
ghomtSj in which they do not believe.
45. I think the government should punish this man, as he
hi told a flagrant falsehood, wh'ch is wrong, and he who does
w *ng deserves to be punished, aud government is appointed
f< the punishment of evil doers.

\4. The Irish are witty, and this man being an Irishman, must
\ witty.

Epimenides the Cretan says, that ' all the Cretans are liars ;"
but Epimenides is himself a Cretan : therefore he is
himself a liar. But if he be a liar, what he says is un-
true, and consequently the Cretans are veracious : but
Epimenides is a Cretan, and therefore what he says is
true.
If I buy this piece of land it will be profitable ; if I engage
in this mercantile speculation it will be profitable ; if I
buy this house it will be profitable ; and so I may do
all these and find it profitable.
To lay restriction on the importation of iron is profitable to
all home iron masters and iron workers ; to lay restric-
tion on the importation of linen goods is profitable to all
in the linen trade ; and so to lay restriction on woollen
goods, to all who are in the woollen trade, etc. ; and so to
lay restrictions on all these and other articles will be
favorable to the nation composed of such traders.

45. I believe this on the authority of my church, which is
founded on the Word of God, which all the Church believes in.

46. It is clear that the United States do not acknowledge
God as King of Nations, for they have no Established Church. ■

Some one proposes what seems a good measure for the
country at large ; and it is shown that it will cause some

212 APPENDIX.

people to grumble and a number of persons in the pub
lie service to be discharged.
Our forefathers, the wise and good in former generations,
all believed this and acted on it, and I am satisfied to
follow their example.

47. The theories of geologists cannot be true, for they tend to
undermine our belief in Scripture.

48. I charge you with having started this calumny against
me ; and if you deny it, you must disprove the allegation.

49. I know that this man, that man, and others, all gained
large sums at play ; and surely I may do the same.

I have found on three occasions, when I had a dream of this
kind, I heard soon after of the death of a friend. So
when I dream in this way, I expect to hear of a death.

50. The institution has flourished under these rules ; and if
would be wrong in any one to attempt to change tbem.

51. Aut Sirius ardor ;

Hie sitim morbosque ferens mortalibus asgria
Nascitur, et laevo contristat lumine ccelum.
The weather cannot be warmer till the snow is off the

ground.
A.S long as the interest of money is so low, trade cannot be
prosperous.

52. This story is likely to be true, for I had it from a man of
fair character, who lived soon after the event (estimated value of
testimony T97), who probably had it from his father (J).

As each of the witnesses may possibly be wrong, we may
believe them both to have been in error.

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