John Grier Hibben.

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LOGIC

DEDUCTIVE AND INDUCTIVE



BOOKS BY JOHN


GRIER HIBBEN, Ph.D.


PUBLISHED BY CHARLES SCRIBNER'S SONS


LOGIC, DEDUCTIVE


AND INDUCTIVE,




net $1.40


THE PROBLEMS OF PHILOSOPHY . 7iet 1.00


HEGEL'S LOGIC .


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INDUCTIVE LOGIC


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LOGIC



DEDUCTIVE AND INDUCTIVE



BY



JOHN GRIER HIBBEN, Ph.D.

STUART PROFESSOR OF LOGIC IN PRINCETON UNIVERSITY



NEW YORK

CHARLES SCRIBNER'S SONS

1905



COPYRIGHT, 1896, 1905, BY
CHARLES SCRIBNER'S SONS



NortoooO ipreaa

J. S. Gushing & Co. — Berwick & Smith Co.

^■o^wood, Mass., U.S.A.



JOHN DAVIDSON



IN APPRECIATION OF THE VALUABLE SUGGESTIONS

RECEIVED IN THE PREPARATION OF THIS BOOK,

AND OF THE KINDLY INTEREST EXPRESSED

IN MANY WAYS THROUGH YEARS OF

AN INTIMATE FRIENDSHIP



'O fxkv yap crvvoTrrtKo? SiaXeKTiKos, 6 8e fxrj ov.

— Plato : Republic VII, 537 C.



PREFACE

This book consists of two parts, — the Deductive and
the Inductive Logic. The former treats of the general
nature of our thought processes as well as the fundamental
principles and practice of deduction, and is now published
for the first time. The latter is my Inductive Logic which
was published in 1896, now revised and incorporated in
this volume. It has been my endeavor to present in con-
nection with the more formal and traditional treatment of
the deductive logic also some considerations which have
been contributed by the discussions of the modern logic
and which find expression in such works as those of Sig-
wart, Lotze, Erdmann, Green, Bosanquet, Venn, and others.

The illustrations and examples contained in the text are
taken as far as possible from the sphere of everyday expe-
riences, in order that they may represent modes of actual
reasoning pursued by the common run of mankind. With
this end in view, all the stock examples which have grown
old and infirm in the service of many generations of stu-
dents in logic have been omitted. Moreover, the material
as well as the formal significance of the judgments em-
ployed in reasoning has been emphasized in order that the
student may come to regard logic as a living process of
thought functioning in a normal and natural manner, and
not as an artificial manipulation of certain dead elements
mechanically adjusted one to another.

The illustrations which appear in the Inductive Logic,
and which are taken from the experiments of Faraday,
Tyndall, Darwin, Pasteur, Lubbock, and others, are quoted



viii PREFACE

for the most part at considerable length, not merely be-
cause in the concrete case the universal principles of rea-
soning and of method are often most forcibly discovered,
but also because the experiments of such pioneers in re-
search actually create these methods of investigation, or
at least serve to render them exact and definite.

In Chapter XIV, Part I, " A Generalization of Immediate
Inferences," I have presented some original material, — this
being an attempt on my part to summarize all the possible
transformations of any given proposition according to a
scheme suggested by the Aristotelian square of opposition,
and developed along similar lines. In addition to the
general field usually covered by writers on deductive logic,
there is appended a discussion on " Extra-syllogistic Reason-
ing," being Chapter XVIII, Part I.

I wish to avail myself of this opportunity to express my
appreciation of the suggestions and help which I received
from my colleagues. Dean Andrew F. West and Professor
Winthrop M. Daniels, in the preparation of the Logical
Exercises which appear at the end of Part II.

J. G. H.

Princeton, N.J.,
December 23, 1904.



CONTENTS

PART I

DEDUCTIVE LOGIC

CHAPTER I

PAGE

The Nature of Thought 3

Definition and nature of Logic, 3. Thought as reflection, 4.
The four functions of thought, 4. Concept, judgment, in-
ference, 10. Logic as a normative science, 11.



13



CHAPTER II

The Concept

Relation of identity to diversity in concepts, 13. The
natural history of the concept, 15. Logical and empirical
concepts, 16. Genetic concepts, 22. Thought and lan-
guage, 23.

CHAPTER III

The Judgment 25

The essential nature of judgment, 25. Universal and
singular judgments, 26. Relation of judgment to reality,
27. The element of necessity in judgment, 30. The uni-
versal element in judgment, 31. Judgment and language,
33. Subject, predicate, and copula, 33.

CHAPTER IV

The Universal Judgment ^^

The categories of Aristotle, 37. Heads of Predicates, 38.
Various types of judgment, 40. Extension and intension,
denotation and connotation, 42.
ix



CONTENTS



CHAPTER V

PAGE

Definition 44

Nature of definition, 44. Real and nominal definition, 44.
Rules of definition, 45. Definition by description, 47.
Definition for purpose of identification, 48. Genetic defi-
nition, 48.

CHAPTER VI

Division and Classification 50

Nature of division, 50. Rules of division, 51. Dichotomy,
51. Contrary and contradictory, 52. Trichotomy, 53.
Empirical and logical divisions, 54. Nature of classifica-
tion, 55. Artificial and natural classification, 56. Serial
classification, 58. Effect of the doctrine of evolution on
theory of classification, 59. Classification of the sciences,
61. Classifications of Bacon, Comte, and Spencer, 62.

CHAPTER VII
The Singular Judgment 67

Its relation to the universal judgment, 67. Impersonal,
perceptive, and demonstrative judgments, 67. Determinate
reference, 68. Indeterminate reference, 69. Judgment
concerning a proper name, 69.

CHAPTER VIII

The Negative Judgment 73

Nature of the negative judgment, 73. Its function of
exact determination, 74. Its positive ground, 75. Signifi-
cant negation, 75. Implication in negation, 76. Infinite
negation, 77.

CHAPTER IX

The Categorical, Hypothetical, and Disjunctive

Judgments 78

The nature of each, 78. Their relation to universal and
singular judgments, 79. Their relation to the progressive
stages of knowledge, 81. Modality of judgments, 83.



CONTENTS XI



CHAPTER X

PAGE

The Nature of Inference 85

Logical and psychological elements in inference, 85. Ob-
jective and subjective necessity, 87. Data of perception,
88. System as ground of inference, 89. The implicit and
explicit, 92. Inference mediated through the universal, 93.
Conceptual processes, 94. Explanation, 94. Relation of
inference to judgment, 95.

CHAPTER XI

The Laws of Thought 98

The law of identity, 98. The law of contradiction, 100.
The law of excluded middle, 101. The law of sufficient
reason, 102.

CHAPTER XII
Immediate Inference ........ 103

Immediate inference, a misnomer, 103. The processes of
implication and transformation, 103. The square of opposi-
tion, 104. Practical suggestions based on opposition, 108.

CHAPTER XIII
On Transformations of Judgment Forms . . . 110
Conversion, 110. Content and form in conversion, 113.
Obversion, 114. Contraposition, 114.

CHAPTER XIV
A Generalization of Immediate Inferences . . 117

Summary of possible transformations, 117. The A square,
118. The E square, 119. The / square, 120. The
square, 120.

CHAPTER XV
Mediate Inference — The Syllogism .... 122
Structure and functions of the syllogism, 122. Distribu-
tion of terms, 125. Rules for criticism of validity of syllo-



xii CONTENTS



PAGE



gisms, 126. Modification of these rules in special cases, 129.
Enthymeme, 130. Prosyllogism, episyllogism, and the
sorites, 132.

CHAPTER XVI

Mood and Figure 134

The valid moods, 134. Figure, 137. Mnemonic lines,
139. Reduction, 140.

CHAPTER XVn

The Hypothetical and Disjunctive Syllogisms . . 142
Hypothetical syllogism, 142. Disjunctive syllogism, 145.
Dilemma, 145. Trilemma, 148.



CHAPTER XVIII

Extra-syllogistic Reasoning . . o . . . 149
Reasoning from particulars to particulars, 149. The typi-
cal case a disguised universal, 151. Inference based upon
given relations, 152. Its relation to the underlying system,
154. The logic of relatives, 156.



-\- CHAPTER XIX

Fallacies 157

Formal fallacies, 157. Material fallacies, 158. Equivo-
cation, 158. Amphiboly, 159. Composition, 159. Divi-
sion, 160. Accent, 160. Figure of speech, 160. Accident,
161. Converse accident, 161. Ignoratio Elenchi, 162. Non
sequitur, 164. Petitio Princijni, 164. Non causa pro
causa, 165. Many questions, 165.



CONTENTS xiii

PART II

INDUCTIVE LOGIC

CHAPTER I



PAGE



Induction and Deduction 169

Various opinions concerning their relative importance,
169. Eegarded as different phases of one and same pro-
cess, 170. Their relation to the ground of inference as
system, 170. Their relation to the universal, 171. Truth
and fact, 171. Mutual dependence of deduction and induc-
tion, 172.

CHAPTER II

The Essentials of Induction 175

The inductive hazard, 175. Basal postulate of induction,
176. Its epistemological nature, 177. Reduction, 177.
Law and rule, 180. Law as a hypothetical universal,
181. Induction in practical affairs of life, 181. Scientific
spirit, 182.

CHAPTER III

Types of Inductive Inference 183

Method of enunciation, 183. (a) Perfect induction, 184.
(h) Incomplete induction, 186. (c) Probability, 186.
Method of Analogy, 187. Method of Scientific Analysis,
188. The causal element in these various methods, 189.



CHAPTER IV

Causation 195

Phenomenal significance of causal concept, 196. Philo-
sophical significance, 197. Logical significance, 198. Origin
of belief in uniformity of nature, 199. Popular and scien-
tific idea of cause, 201. Causal analysis, 202. Limitations
of knowledge, 203,



xiv CONTENTS



CHAPTER V

PAGE

The Method of Causal Analysis and Determination 206

Sequence, 206. Concurrence, 207. Coexistence, 208.
Collocations, 209. Transfer of energy, 211. Quantitative
determination, 211. Observation and experiment, 213.
Negative determination, 217. Pseudo-causal connections,
219.

CHAPTER VI

Mill's Inductive Methods — The Method of Agree-
ment 222

The five methods, 222. Agreement, 224. Symbolical
representation, 225. Variation of instances, 227. Obser-
vation, 228. Simple enumeration, 228. Sequence and
coexistence, 229. Criticism of this method, 229. Agree-
ment as a method of suggestion, 232. Illustrations, 232.

CHAPTER VII
The Method of Difference 236

Its relation to agreement, 236. Its characteristic features,
236. Symbolical representation, 238. Relation to negative
determination, 239. Difference and combinations, 239.
Criticism of the method, 240. Practical difficulties, 242.
Illustrations, 245. Blind experiments, 247.

CHAPTER VIII

The Joint Method of Agreement and Difference . 248

Relation to method of difference, 248. Its characteristics
and symbolical representation, 249. Illustrations, 250.
Advantages of this method, 257.

CHAPTER IX

The Method of Concomitant Variations . . . 258

Characteristics and symbolical representation, 258. Quan-
titative determination, 259. Graphical representation, 260.
Advantages in its psychological impressions, 261. Illustra-
tions, 262, Comprehension of unknovs^n forces by this
method, 266. Precautions in using this method, 267.



CONTENTS XV



CHAPTER X

PAQB

The Method of Residues 271

Characteristics and symbolical representation, 271. A
deductive method, 272. Its function suggestive, 273. Illus-
trations, 273. Its practical value, 277.

CHAPTER XI

Prediction and Verification ... = .. 278

The inducto-deductive method, 278. Illustrations, 279.
Bacon's anticipations of nature, 283. Scientific thought,
284. Indirect method of prediction, 286. Exceptional
phenomena, 288. Generalization, 289. Mathematical
method, 290.

CHAPTER XII

Hypothesis 291

Its relation to induction, 291. Illustrations, 292. Func-
tion of the imagination in hypothesis, 299. Analysis and
synthesis, 300. Requirements of a logical hypothesis, 301.
Consilience of inductions, 309. Experimentum Crucis, 310.
Mill and Whewell controversy, 312.

CHAPTER XIII

Analogy 314

Analogy and induction, 314. Natural kinds, 314. Anal-
ogy and classification, 315. Teleological analogy, 317.
Suggestion the chief function of analogy, 323. Require-
ments of true analogy, 325. Analogy and probability, 329.

CHAPTER XIV

Probability . 330

Probability and causal determination, 330. Relation to
enumerative induction, 332. Various kinds of inference in
sphere of probability, 333. Coincidence and cause, 345.
Circumstantial evidence, 346. Probability and method of
residues, 350.



>



XVI CONTENTS

CHAPTER XV

PAGE

Empirical Laws 351

Various degrees of probability in inference, 351. Various
kinds of empirical laws, 352. Empirical uniformity result-
ing from the method of agreement, 357. Empirical laws
and laws of an ultimate nature, 357.

CHAPTER XVI

Inductive Fallacies 359

Errors of perception, 360. Errors of judgmen', 362.
Errors of imagination, 366. Errors of the concept al pro-
cesses, 369. The psychological nature of these fallac es, 372.

CHAPTER XVII

The Inductive Methods as applied to the Various

Sciences 374

Method varies with different kinds of phenomena, 374.
Difficulties in method due to complexity of phenomena, 378.
Phenomena of one science interpreted in the light of others,
380. Deductive method of some sciences replaced by the
inductive, 381.

CHAPTER XVIII

Historical Sketch of Induction ..... 385

Socrates, 385. Plato, 385. Aristotle, 386. Roger Bacon,
387. Leonardo da Vinci, 388. Telesius, 389. Campa-
nella, 389. The experimental investigators, 390. Francis
Bacon, 390. Locke, 392. Newton, 393. Herschel, 394.
Whewell, 395. Mill, 396.

Logical Exercises 399

Index 435



PART I
DEDUCTIVE LOGIC



CHAPTER I

THE NATURE OF THOUGHT

Logic is a word derived from the Greek \6yos, whicli
means thought or reason; and in this origin may be found
the essential significance of logic, — that it treats of the
nature and of the laws of thought. Before it is possible
to appreciate the characteristic features of the laws of
thought, it is necessary to understand the general nature
of the processes of thought themselves. While the process
of thought is various, its most common and conspicuous
manifestation may be described as that phase of the mind's
activity which regards any specific object which may be
presented to it in the light of the general body of knowl-
edge. For example, a person may chance to pick up a stone,
which he holds in his hand for a moment and immediately
throws away. It has been in the focus of his attention for
a fleeting moment only, and has excited no activity of
thought whatsoever. He has observed but has not thought
about it. Suppose, however, it does arrest his attention and
he begins to think about it, what is the nature of this
thinking which goes on in his mind ? If his knowledge of
geology is meagre, the result of the application of it to the
special object of inquiry may be merely the assertion that
the stone which he holds in his hand is some kind of a
fossil. If, however, his knowledge is more extensive and
has grown out of a wide experience, he will be able no
doubt to refer the fossil in question to its proper geological
age, and to give some satisfactory description of the general
nature and habits of that species of animals to which it

3



4 DEDUCTIVE LOGIC

belongs, thus, in a measure more or less explicit, recon-
structing its probable life history. Thinking, therefore,
may be defined in one of its aspects at least as the process
of interpreting the special by the general, or the new expe-
rience by the old.

This definition of thought may be further illustrated by
the word reflection, which is often used as synonymous
with thought. Thus we say that we will reflect about a cer-
tain proposition, which is equivalent to saying we will think
about it. The process of reflection is essentially one of
illumination. The very word reflection suggests the light
ray which flashes from one object of vision to another ; so,
also, in a figurative sense, it signifies the illumination which
one object of knowledge sheds upon another. In the reflect-
ing mind, the new element of experience, whatever it may
be, is held in the focus of the light rays which converge to
that point from all the surrounding parts of the general body
of knowledge until its essential nature is fully revealed.

In this process which we call thinking, or reflecting, there
are in all four functions involved.

1. The first function of thought consists in the trans-
formation of the crude data of knowledge furnished by
the senses into forms of such a nature that they can be
readily used in the various operations of our thinking
processes. The form which thought necessarily assumes
for the prosecution of its own activity is always that of
a universal idea; that is, an idea which possesses a one-
ness of meaning but admits of an indefinite variety of
application. The universal is sometimes called a group
idea, or a class idea, by which a number of individuals are
embraced under some one general designation. If our body
of knowledge consisted merely in the total number of par-
ticular experiences arranged in the form of a series wherein
each separate term remained distinct and completely uncon-
nected with any other term, then obviously new experiences
could be added to, but never could be assimilated with,



THE NATURE OF THOUGHT 5

such a body of knowledge. Indeed, a disconnected array of
isolated experiences would hardly merit the name of knowl-
edge at all. On the contrary, the elements constituting the
body of our knowledge must be so related and coordinated
that similar elements fall together in such a manner that
a single thought form shall be able to express them all.
Thus, when a geologist says that a certain stone is a fossil,
he means that in his general body of knowledge he has
framed an idea known by the word symbol " fossil," which
embraces under it innumerable special cases, and that one
of these is the stone in question. Thus objects of per-
ception can be grasped by the mind and become definite
objects of thought. This grasp of the mind by which a
number of special cases are held together by a single idea
of a nature so universal as to comprehend them all is known
as the process of conception, and the universal idea itself
which is the result of that process is known as the concept.
This word is from the Latin concapio, to take together. The
corresponding German word is Begriff, which has the same
root as our English word " grip." In the concept the mind
grasps all the essential features which characterize a given
group or class of objects, and holds them together in such a
manner as to constitute an elemental thought form. The
process of thinking, therefore, is fundamentally a conceptual
process, and this primary function of thought consists in
constructing whatever is given through the processes of
perception into the forms of concepts.

2. The second function of thought consists in the reduc-
tion of the total mass of concepts to some kind of systematic
order. Every concept as it is formed must be received into
the general body of knowledge and assigned to its proper
place and position. The concepts must be arranged in their
due rank and order according to their natural relations of
coordination or subordination. In order that our concepts
may be used as instruments of knowledge, they must admit
of a constant and consistent reference to the general system

f



6 DEDUCTIVE LOGIC

of which they form constituent parts. These elemental
forms of thought must have their origin in order and not in
chaos. They must be subject to underlying laws of relation,
and not to accident or caprice. Thus the botanist not only
possesses an idea of the general nature of a certain species
of plant, that is, a concept of it, but he knows also definitely
its particular relation to the classified system of plants as
a whole. He is able therefore to describe the species in
question by the relative position which it occupies in the
system itself. Knowledge of the species is obtained not
merely through an understanding of what it is, but also of
what its proper setting may be.

3. The third function of thought consists in referring
whatever may be before the consciousness as the object of
thought to its appropriate concept. Such a reference is a
process of interpretation, and represents the central and
most essential feature of all thinking. This mode of inter-
pretation may be brought about in several ways.

(a) In the first place, any one portion of our general
body of knowledge may be interpreted in the light of some
other. Thus by way of interpretation or explanation I may
refer one concept to another concept which embraces it as
a smaller class or group within a larger one ; e.g. the Trap-
pists are a Roman Catholic brotherhood.

(5) Again, the concept lends itself to a further use as an
instrument of knowledge, by revealing the various charac-
teristics which constitute its nature according as the trend
of thought at the moment may happen to emphasize one or
another of them. In the ordinary processes of thought we
never use a concept in the totality of its significance. We
attend only to a single phase of the concept's meaning at a
time ; and our thought selects always that particular phase
of the meaning which is pertinent to the special object of
thought under consideration. Thus the concept, govern-
ment, is an exceedingly complex idea, and may be consid-
ered from various points of view, — as to its general nature,



THE NATURE OF THOUGHT 7

whether democratic, monarchial, despotic, etc. ; or as to its
special functions, whether that of the judicial, legislative, or
executive. The concept as a complex idea may always be
subjected to a more precise determination by the concentra-
tion of thought upon one or more of its special attributes or
relations.

(c) In the third place, a particular experience in the
field of sense perception may be interpreted by referring it
to the appropriate concept of which it may be regarded as a
special case. The knowledge given through the senses is
rendered more definite by this reference of it to a concept
which serves to illumine it.

This process of thought which renders the elements of
consciousness more definite by a reference in any one of the
three ways mentioned above to some interpreting concept
is known as the judgment. There is a universal tendency
of thought to transform every concept into the form of a
judgment, because the very presence of a concept in con-
sciousness challenges our thought to express some definite
assertion concerning it, and such an assertion is itself a
judgment. As long as there is sustained interest in any
concept which occupies the focus of attention, there is a
constant play of thought about it ; we turn it over in our
minds ; we examine it on all sides ; we put questions to
ourselves about it ; and the result is a series of judgments
as regards its nature and the several relations which it sus-
tains to cognate concepts. Thus our general knowledge
serves to illumine the specific portion of it which is the
special object under contemplation. So also when the
object of consciousness is a particular object of sense per-
ception, we form a judgment by referring it to its appropri-
ate concept. Thus in the judgment. Arsenic is a poison, we
have as it were a cross-section of our knowledge in general ;
but in the judgment, this substance which is in the test-
tube before me contains arsenic, the reference is to a special
object in the field of vision which is interpreted by means
of its appropriate concept.



8 DEDUCTIVE LOGIC

Every new experience which is more than a fleeting im-
pression, and which is drawn into the field of our attention,
gives rise to one or more judgments of this latter kind. As
I am writing, I look out from a hillside which commands a
wide prospect; and as I observe the various objects in the
field of vision, my thought immediately refers them to their
appropriate concepts by way of more definite characteriza-
tion. There is the winding road through the valley, sepa-
rating the green meadow from the wood beyond; in the
meadow cows are grazing; by the side of the road flows a
stream, rushing over its rocky bed and losing itself in the
dark shadows of the wood ; in the distance are the uplands
again bounded by the horizon line, above which the clouds
are hanging low and threatening. Such a description of the
various objects of perception within a field of vision forms a



Online LibraryJohn Grier HibbenLogic : deductive and inductive → online text (page 1 of 35)