AN INTRODUCTORY LOGIC
AN
INTRODUCTORY LOGIC
BY
JAMES EDWIN CREIGHTON
NEW EDITION', REVISED AND CORRECTED
THE MACMILLAN COMPANY
LONDON : MACMILLAN & CO., LTD.
I9O6
All rights reserved
COPYRIGHT, 1898, 1900,
BY THE MACMILLAN COMPANY.
Set up and electrotyped September, 1898. Reprinted July,
1899. New Edition, Revised and Corrected, March, 1900 ;
April, October, 1901 ; July, 1902 ! February, 1903 ; February,
August, 1904; January, October, 1905; September, 1906.
Staek
PREFACE
THIS volume is intended primarily as a text-book for
college students, and grew out of my lectures on Logic
to undergraduate classes in Cornell University. It
aims at being both practical and theoretical. In spite of
the obvious deficiencies of formal Logic as a theory of
the nature of thought, I am convinced that it is one
of the most valuable instruments in modern education
for promoting clear thinking, and for developing criti-
cal habits of mind. J. S. Mill, speaking in the Auto-
biography of the discipline which he received from
working logical exercises, expresses the following
opinion : " I am persuaded that nothing, in modern
education, tends so much, when properly used, to form
exact thinkers, who attach a precise meaning to words
and propositions, and are not imposed on by vague,
loose, or ambiguous terms." Although in treating the
syllogistic Logic I have followed to a large extent the
ordinary mode of presentation, I have both here, and
when dealing with the Inductive Methods, endeavoured
to interpret the traditional doctrines in a philosophical
way, and to prepare for the theoretical discussions of
the third part of the book.
The advisability of attempting to include a theory of
thought, or philosophy of knowledge, even in outline,
Vi PREFACE
in an elementary course in Logic, may at first sight
appear doubtful. It seems to me, however, that this
inclusion is not only justifiable, but even necessary at
the present time. Psychology is no longer a ' philoso-
phy of mind ' ; but, under the influence of experimental
methods, has differentiated itself almost entirely from
philosophy, and become a ' natural ' science. As a
natural science, it is interested in the structure of the
mental life, the characteristics of the elementary
processes, and the laws of their combination, and
not primarily in the function which ideas play in giving
us knowledge. It is clear that psychology does not
undertake to describe all that mind is and does. It
belongs to Logic to investigate intelligence as a know-
ing function, just as it is the task of Ethics to deal
-with the practical or active mental functions.
The practical question still remains as to whether
this side of Logic can be made profitable to students
who have had no previous philosophical training. I
am well aware of the difficulty of the subject, but my
own experience leads me to believe that the main con-
ceptions of modern logical theory can be rendered
intelligible even to elementary classes. Of the incom-
pleteness and shortcomings of my treatment I am quite
conscious ; but I have endeavoured to make the matter
as simple and concrete as possible, and to illustrate it
by means of familiar facts of experience,
For a number of the practical questions and exer-
cises, I am indebted to Professor Margaret Washburn
of Wells College ; others are original, or have been
collected in the course of my reading. I have also
PREFACE vii
taken a number of arguments from the examination
papers of different universities, and from various works
on Logic, especially from Jevons's Studies in Deductive
Logic, from the little volume entitled Questions on Logic
by Holman and Irvine (2d ed., London, 1897), and from
Hibben's Inductive Logic.
In writing the book, I have been under obligation to
a large number of writers and books. My heaviest
debt is doubtless to Bosanquet, and perhaps next in
order I am under obligations to Mill, Jevons, Sigwart,
and Bradley. I have also derived help from Minto's
Logic, Deductive and Inductive, the chapter on ' Rea-
soning' in James's Principles of Psychology, J. H. Hys-
lop's Elements of Logic, and from other works to which
reference is made throughout the book.
My colleagues in the Sage School of Philosophy
have kindly aided me from time to time with advice
and encouragement, and I have also received valuable
suggestions from other teachers of Logic with whom I
have talked and corresponded. In particular, I wish
to express my obligations to my former colleague, Pro-
fessor James Seth, who read nearly all of the book in
manuscript, and to Dr. Albert Lefevre, who kindly
assisted me in reading the proofs.
J. E. C.
CORNELL UNIVERSITY,
August, 1898.
TABLE OF CONTENTS
INTRODUCTION
CHAPTER I
THE STANDPOINT AND PROBLEM OF LOGIC
PACK
I. Definition of the Subject I
2. Relation to Psychology 4
3. Logic as a Science and an Art 8
4. The Material of Logic 13
CHAPTER II
IMPORTANT STAGES IN THE DEVELOPMENT OF LOGIC
5. The Logic of the Greeks : Aristotle 1 8
6. Logic during the Middle Ages 26
7. The Logic of Bacon 28
8. Logic since the Time of Bacon 29
PART I. THE SYLLOGISM
CHAPTER III
THE SYLLOGISM AND ITS PARTS
9. The Nature of the Syllogism
10. The Parts of the Syllogism
n. The Proposed Division of Mental Operations . . .
CHAPTER IV
THE VARIOUS KINDS OF TERMS
12. Singular, General, and Collective Terms . .
13. Abstract and Concrete Terms . > . , . .. .
TABLE OF CONTENTS
14. Positive and Negative Terms 52
15. Absolute and Relative Terms 54
1 6. Extension and Intension of Terms 55
' CHAPTER V
DEFINITION AND DIVISION
17. Fixing the Meaning of Terms 61
18. Definition 63
19. Division . . .'.''. 71
CHAPTER VI
PROPOSITIONS
20. The Nature of a Proposition 78
.21. The Quality and Quantity of Propositions . . . .80
22. Difficulties in Classification 83
23. Formal Relation of Subject and Predicate .... 85
CHAPTER VII
THE INTERPRETATION OF PROPOSITIONS
24. The So-called Process of Immediate Inference ... 92
25. The Opposition of Propositions 94
26. The Obversion of Propositions 98
27. The Conversion of Propositions loo
CHAPTER VIII
THE SYLLOGISM
28. The Nature of Syllogistic Reasoning 105
29. The Rules of the Syllogism 108
30. The Figures of the Syllogism . ... . ."3
CHAPTER IX
THE VALID MOODS AND THE REDUCTION OF FIGURES
31. The Moods of the Syllogism . . . . . . . 115
32. The Special Canons of the Four Figures . . . . 1 1 7
33. The Determination of the Valid Moods in Each of the Figures 120
34. The Mnemonic Lines 122
TABLE OF CONTENTS xi
CHAPTER X
ABBREVIATED AND IRREGULAR FORMS OF ARGUMENT
PAGE
35. Enthymemes 126
36. Episyllogisms and Prosyllogisms . . . . . . 127
37. Sorites, or Chains of Reasoning . . . . . .129
38. Irregular Arguments . . . . . . . .132
CHAPTER XI
HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
39. The Hypothetical Syllogism 136
40. Relation of Categorical and Hypothetical Arguments . .139
41. Disjunctive Arguments ' . . 145
42. The Dilemma . 148
CHAPTER XII
FALLACIES OF DEDUCTIVE REASONING
43. Classification of Fallacies . . . . . .
44. Errors in Interpretation .......
45. Formal Fallacies
46. Material Fallacies
PART II. INDUCTIVE METHODS
CHAPTER XIII
THE PROBLEM OF INDUCTION. OBSERVATION AND EXPLANATION
47. The Problem of Induction 172
48. Observation . . . . ~ 176
49. Explanation . . 182
CHAPTER XIV
METHODS OF OBSERVATION. ENUMERATION AND STATISTICS
50. Enumeration or Simple Counting . . . . . . 185
51. Statistics and Statistical Methods . . . . . . 189.
52. The Calculation of Chances . . . . . . .194
xii TABLE OF CONTENTS
CHAPTER XV
METHODS OF OBSERVATION. DETERMINATION OF CAUSAL
RELATIONS
fAGB
53. Mill's Experimental Methods 198
54. The Method of Agreement 200
55. The Method of Difference 205
CHAPTER XVI
METHODS OF OBSERVATION. DETERMINATION OF CAUSAL
RELATIONS (continued}
56. The Joint Method of Agreement and Difference . . . 209
57. The Method of Concomitant Variations . . . . .211
58. The. Method of Residues 213
CHAPTER XVII
METHODS OF EXPLANATION. ANALOGY
59. Explanation by Analogy 219
60. Analogy as Suggestive of Explanatory Hypotheses . . 223
6l. The Incompleteness of Analogical Reasoning . . . 226
CHAPTER XVIII
METHODS OF EXPLANATION. THE USE OF HYPOTHESES
62. Reasoning from Hypotheses 230
63. The Formation of Hypotheses 234
64. The Proof of an Hypothesis 237
65. Requirements of a Good Hypothesis 240
. CHAPTER XIX
FALLACIES OF INDUCTIVE REASONING
66. The Source of Fallacy
67. Fallacies due to the Careless Use of Language
68. Errors of Observation
69. Mistakes in Reasoning .......
70. Fallacies due to Individual Prepossessions . '-. .;.-/.> ' ,
TABLE OF CONTENTS xiii
PART III. THE NATURE OF THOUGHT
CHAPTER XX
JUDGMENT AS THE ELEMENTARY PROCESS OF THOUGHT
PAGE
71. Thinking the Process by which Knowledge grows or develops 260
72. The Law of Evolution and its Application to Logic . . 262
73' Judgment as the Starting-point ...... 266
74. Concepts and Judgment . . . . . . . 268
CHAPTER XXI
THE MAIN CHARACTERISTICS OF JUDGMENT
75. The Universality of Judgments 274
76. The Necessity of Judgments 276
77. Judgment involves both Analysis and Synthesis . . . 279
78. Judgment as constructing a System of Knowledge . . 284
CHAPTER XXII
THE LAWS OF THOUGHT
79. The Law of Identity 288
80. The Law of Contradiction 295
81. The Law of Excluded Middle 297
CHAPTER XXIII
TYPES OF JUDGMENT
82. Judgments of Quality 300
83. Judgments of Quantity 304
84. Judgments of Causal Connection 307
85. Judgments of Individuality 315
CHAPTER XXIV
THE NATURE OF INFERENCE. INDUCTION AND DEDUCTION
86. Judgment and Inference 318
87. The Nature .of Inference 324
88. Induction and Deduction ....... 329
xiv TABLE OF CONTENTS
CHAPTER XXV
RATIONAL AND EMPIRICAL THEORIES
PAGE
89. The Point of View of Rationalism 335
90. The Doctrine of Empiricism 337
91. Reasoning from Particular ta Particular .... 340
92. Reasoning from Particulars to a Universal .... 344
QUESTIONS AND EXERCISES 348
INDEX 389
AN INTRODUCTORY LOGIC
INTRODUCTION
CHAPTER I
THE STANDPOINT AND PROBLEM OF LOGIC
i. Definition of the Subject. Logic may be defined
as the science of thought, or as the science which in-
vestigates the process of thinking. Every one knows,
in a general way at least, what is meant by think-
ing, and has noticed more or less consciously some
of its peculiarities. Thinking is the intellectual act by
means of which knowledge is obtained. We do not
really know any fact until we think it ; that is, until the
mind sets it in its proper relation to the other parts of
its experience, and thus comes to understand its true
meaning. We make a distinction, for example, between
what has come to us through report or hearsay, and
conclusions which we have reached by our own think-
ing. ' I have heard,' we say, ' that A is dishonest, but
I do not know it.' That is, this fact has not been
reached as a result of our own thinking, and cannot
therefore claim the title of knowledge. On the other
hand, that the earth is round, is not a mere matter of
hearsay for an educated man. It is a piece of know-
ledge, because it is a conclusion which he has reached
by thinking, or by putting together various facts for
himself.
B I
2 THE STANDPOINT AND PROBLEM OF LOGIC
Logic, then, in dealing with thinking, is concerned
with the process by which knowledge is obtained. In
defining it as a science, we mean that it seeks to sub-
stitute exact and systematic knowledge regarding the
nature of thought for the popular notions to be found
in everyday life. Like all the sciences, logic has to
correct and supplement ordinary knowledge. It is its
mission to help us to understand more exactly and
completely the way in which thinking goes on, and
to discover the laws which are followed in gaining
knowledge.
But it is also the business of a science to system-
atize facts. Logic, then, cannot content itself with a
mere description of this or that kind of thinking, in
isolation from other ways in which we think. It must
also deal with the way in which the various kinds of
thinking are related. For example, we apply such
terms as 'conception,' 'judgment,' 'induction,' and 'de-
duction ' to different intellectual operations, and give
the distinguishing characteristic in each case. But it is
necessary as well to understand how these processes
are related. Since all thinking has one end, the dis-
covery of truth, the various intellectual operations must
mutually cooperate and assist in this result. All of
the logical processes, then, stand in relation to one
another. They are all parts of the one intelligence,
though they may well represent different stages or
steps in its work of obtaining knowledge. It becomes
the business of logic, then, to show us the organic
structure of thought. In other words, it must furnish
a comprehensive view of the way in which intelligence
i. DEFINITION OF THE SUBJECT 3
acts, and the part which processes like ' conception,'
'judgment,' 'induction,' etc., play.
(1) The word 'logic 1 is derived from the adjective corresponding
to the Greek noun Aoyos, which signifies either a complete thought,
or a word as the expression of that thought. The singular form of
the adjective Aoyuo/, from which the English word is derived, was
supposed to qualify either eTrtoT??/^ as applying to the theoretical
science of logic, or re'xv?? as referring to the practical application
of its rules and as affording guidance in the art of correct reason-
ing. We shall have to raise the question in a subsequent section
how far it is possible to regard logic as an art, or a system of rules
which teach us how to reason correctly.
(2) We have defined logic as the science of the operations and
processes of thought, or as the science of thinking. It is evident,
however, that this definition does not carry us very far unless we
know what thinking means. And to gain a clearer idea of this com-
mon term may be said to be the problem of logic. This is, however,
by no means as easy a task as may at first appear. Familiar words
and phrases often conceal difficulties. They are constantly repeated
without reflection, and this very frequency of repetition is likely
to prevent us from trying to gain any clear ideas regarding the
nature of the objects which they denote. It is only when we
become discontented with our knowledge regarding any subject,
when doubts arise whether we really understand the meaning of
the words which we use, that we attempt to make our knowledge
scientific, i.e., to gain clear, definite, and systematic ideas. This
can perhaps be made clearer by considering the main differences
between an educated and an uneducated man. The educated man
has, of course, a great deal more information than the other, and
his knowledge is more definite and systematic. But a second and
more important distinction is found in the attitude of mind which
education begets. The educated man is desirous of knowing more,
because he is sensible of his own ignorance. The uneducated
man, on the other hand, supposes that he knows all about things
whose names are familiar to him. He can settle puzzling theo-
logical or political problems off-hand in a way which is per*
4 THE STANDPOINT AND PROBLEM OF LOGIC
fectly satisfactory to himself, without study, and almost without
reflection.
It is clear that no intellectual salvation is possible for a man so
long as he remains in this state of mind. A sense of one's own
ignorance is the beginning of wisdom. Socrates, one of the great
pioneers of science among the Greeks, and especially of the sciences
of logic and ethics, was so firmly convinced of this that he made it
the business of his life to go about the streets of Athens and con-
vince those " who thought they were wise and were not wise," of
their ignorance. " And because I did this," he says naively, " many
of them were angry, and became my enemies."
2. Relation to Psychology. It may aid us in
obtaining a clearer view of what thinking is, if we
compare the general standpoint of logic with that of
psychology. Both of these sciences deal with what
goes on in mind or consciousness, and are thus opposed
to the so-called objective sciences, which are all con-
cerned with some group or field of external facts. But
in spite of this agreement, there is an important dis-
tinction between logic and psychology. In the first
place, psychology deals with all that there is in mind.
It describes pleasures and pains, acts of will, and the
association of ideas, as well as what is usually called
logical thinking. But logic does not differ from psy-
chology simply by being less inclusive than the latter.
It is true that, from the standpoint of psychology, the
thought-process is merely a part of the mental content,
which has to be analyzed and described like anything
else which goes .on in consciousness. Thinking has
doubtless for psychology peculiar marks or charac-
teristics which distinguish it from other related pro-
cesses like those of association; but when these have
2. RELATION TO PSYCHOLOGY 5
been found, and the psychological description of think-
ing is complete, the question with which logic deals has
not yet been raised. For logic, as we shall see pres-
ently, adopts a different standpoint, and investigates
with a different end in view.
The important difference is this : In psychology we
are interested in the content of consciousness for its
own sake, and just as it stands. We try to find out
what actually goes on in our minds, and to describe it
just as we should any event which occurs in the exter-
nal world. But in logic the question is not : What are
mental processes ? but rather : What knowledge do
they give us, and is this knowledge true or false?
Logic, in other words, does not regard the way in
which ideas exist, and is not interested in them for
what they are, but rather in the purpose which they sub-
serve in affording us knowledge of something beyond
themselves. Psychology, in its description of conscious
states, inquires regarding their quality, intensity, dura-
tion, etc., and the ways in which they combine with
each other to form complex ideas. The problem with
which logic is concerned, on the other hand, has refer-
ence to the value of ideas when they are taken to
represent facts in the real world. In other words, the
question which logic raises is not regarding the actual
character of ideas as existing processes, but regarding
their value or significance as pieces of knowledge.
(i) The relation between logic and psychology may perhaps be
illustrated by referring to that which exists between morphology
and physiology. Morphology deals with the form and structure
of living organisms, and physiology with the various acts and func-
tions which these organisms discharge. Thus we speak of the
former as the science of form or structure, and of the latter as the
science of function. In the same way, psychology may be said to
deal with the actual structure of mental processes, and logic with
the part which they play in giving us knowledge.
It must be noticed, however, that this is a distinction made for
purposes of investigation, and does not denote that structure and
function have nothing to do with each other. On the contrary,
some knowledge of the function is often necessary in order to under-
stand the structure of an organ ; and, on the other hand, it is usually
true that the nature of a function only becomes completely intelligi-
ble when the character of the mechanism with which it works is
known. And the same holds true, I think, of the relations between
psychology and logic. Although it has been found profitable when
dealing with consciousness, as in the biological realm, to investigate
the nature of structure and function separately, yet here, as there,
the two lines of inquiry cross each other ; for it is beyond question
that the knowledge we obtain by thinking is largely dependent upon
the character (quality, intensity, etc. ) of the actual processes in con-
sciousness. To understand the nature of a logical idea, then, it is
often necessary to refer to the psychological facts and their actual
mode of behaviour. And it is equally true that one cannot carry
on a psychological investigation into the nature of mental processes
without taking account, to some extent, of the part which they play
in giving us knowledge. No psychology is able to take ideas simply
as existing conscious processes to which no further meaning or
importance attaches ; it is only with reference to the function they
perform as knowing states that their own peculiar character can be
understood. In other words, the intellectual activities and purposes
of mind must be presupposed in psychology, though this science, for
the most part, goes its way as if the ideas were not cognitive at all.
At least this seems to be true of the 'new' or experimental psy-
chology as opposed to the philosophies of mind.
(2) It would of course be presumptuous, as well as utterly useless,
for any writer to draw a hard and fast line between logic and psy-
chology, and to forbid others to overstep it. In attempting to dis-
2. RELATION TO PSYCHOLOGY 7
cover the dividing line between two closely related sciences one
must be guided by the procedure of those who are working in the
fields which it is proposed to divide. Now, it must be admitted that
by no means all of the recent writers in psychology limit the sphere
of their science in the way above described ; that is, there are
certain psychologists who do not confine their attention to the mere
mental processes as such, but include in their investigations the fur-
ther problem regarding the part which these processes play in giving
us knowledge. Thus in Professor James's Principles of Psychology
there is an excellent chapter on ' Reasoning' which certainly con-
tains as much logical as psychological matter. In the same way,
one finds problems of knowledge discussed in the psychological
writings of Professor Ladd, and also, to some extent, in the recent
work by Mr. Stout entitled Analytic Psychology. In spite of this,
it is evident that the tendency of the ' new, 1 or laboratory psy-
chology, is towards a sharper differentiation of its problems from
those of logic. The ' natural science of psychology ' is interested
in the conscious process as an event in time with certain defi-
nitely ascertainable characteristics. It is perhaps not a matter of
great moment whether the name 'psychology' be limited to this
kind of inquiry, or whether philosophical inquiries regarding the
nature of knowledge be also included under it. I have assumed,
however, in this section, that psychology is now being differentiated
from the more general inquiries regarding the nature of mind, and
that it has taken for its field of investigation the nature of mental
processes regarded merely as mental processes.
Consider a little further the nature of the ideas with
which logic deals. Every idea, as we have seen, not
only exists in some definite fashion in some particular
consciousness, connected with certain other ideas, and
with a definite quality, intensity, etc., but it has a mean-
ing or significance as a piece of knowledge. It not
only is something, but it also stands for or signifies
something. Now it is not with the existence, but with
8 THE STANDPOINT AND PROBLEM OF LOGIC
the meaning side of ideas that logic has to do. A
logical idea, or piece of knowledge, is not merely a
modification of consciousness which exists in the mind
of some individual at a particular time. For example,
the proposition : ' The three angles of a triangle are
equal to two right angles,' will give rise to a number
of definite psychological processes (probably auditory
or visual in character) in the mind of any individual.
These processes would also probably differ in character
in the case of two persons. The meaning of the propo-
sition, however, is distinct from the definite processes
which arise in particular minds. The proposition has
a significance as an objective fact, or piece of know-
ledge, outside my mind ; the psychological images or
processes may differ for different persons, but the fact
expressed is the same for all minds and at all times.
$ 3. Logic as a Science and an Art. We have de-
fined logic as the science of thought, but it has often
been pointed out that there are equally strong reasons
for considering it to be an art. Jevons makes the
distinction between a science and an art very clear by
saying that " a science teaches us to know, and an art
to do." A science is interested in the discovery of facts
and laws without any thought of what use may be made
of this knowledge; an art, on the contrary, gives practi-
cal guidance and direction for some course of action.
The question before us, then, is this : Does logic merely
give us knowledge about the ways in which we think,
or does it also help us to think rightly ?
Before we attempt to answer this question, we must
3. LOGIC AS A SCIENCE AND AN ART 9
note that practical rules of action are based upon sci-
entific knowledge. An art, in other words, depends
upon science, and grows in perfection with the advance
of scientific knowledge. Thus medicine, as the art of
healing, is founded upon the sciences of chemistry,
physiology, and anatomy, and it is because of the great
discoveries which have been made in these fields within
recent years, that it has been able to advance with such
gigantic strides. Again, the art of singing, in so far as
it is an art which can be taught and learned, depends
upon a knowledge of the physical and physiological
laws of the vocal organs. An art, then, always pre-
supposes a certain amount of science, or knowledge,
and is simply the application of this knowledge to some
practical purpose. In some cases the application is
very obvious and direct; in others, it is much more
difficult to determine ; but, in general, there is always
this relation between theory and practice, between
knowing and doing.
From what has been already said, it will be evident
that logic must first be a science before it can become
an art. Its first business must be to investigate the
nature of thought, and to attempt to discover the differ-
ent forms which the latter assumes in the course of its
development. So that we were right in defining it as
primarily a science. But the further question remains:
How far is it possible to apply the laws of logic after
they have been discovered in such a way as to obtain
directions how to reason correctly in every case ? Can
we not apply our knowledge of the laws of thought in
such a way as to get a complete art of reasoning, just as
10 THE STANDPOINT AND PROBLEM OF LOGIC
the laws of chemistry and biology are applied in medi-
cine ?
It is no doubt true in logic, as everywhere, that scien-
tific knowledge is capable of practical application. But
I do not think that logic can be regarded as an art, in
the sense that it furnishes a definite set of rules for
thinking correctly. There is an important distinction
in this case which must not be left out of account. The
physical, and even the biological sciences, deal with
things whose way of acting is perfectly definite and
uniform. The character of any of the physiological
functions, as, e.g., digestion, may be comparatively com-
plex and difficult to determine, but it always attains its
end through the use of the same means. When once its
laws are understood, it is not difficult to prescribe just
how the proper means may always be secured for the
attainment of the desired end. But thinking has much
more flexibility in its way of acting. We cannot say
with the same definiteness as in the cases we have been
considering, that in order to reach a certain end we must
use a definite set of means. It is not possible, that is,
to say : If you would learn what is true about this sub-
ject, you must follow this rule and that in your thinking.
Logic, it seems to me, cannot be regarded as an art like
photography, or even like medicine ; for it is not possible
to lay down definite rules for the guidance of thinking
in every case. What we can do, is to show the method
by which new truths have been discovered, and the
general conditions which must always be fulfilled in
reasoning correctly. And it is also possible to point
out the more common errors which arise when these
3. LOGIC AS A SCIENCE AND AN ART 1 1
conditions are violated. But it is beyond the power of
logic to formulate any definite set of rules for the
guidance of thinking in every case.
We have found that we must give up all extravagant hopes
of the practical advantages to be gained from a study of logic.
There is no set of rules which will make us infallible reasoners.
That being admitted, the question may be raised as to the utility of
the study. What will it profit us to devote ourselves to this subject?
It might be a sufficient answer to point out that this question pre-
supposes that knowledge has always some ulterior motive. The
assumption upon which it is based is, in other words, that the prac-
tical advantages arising from any study furnish the only justification
for undertaking it. But it is scarcely necessary to say that this is not
an attitude which any student should adopt. A student is one who
prosecutes a study for its own sake, with no other motive than the
desire to know. And to such a person logic should not be without
interest. For as we have seen, it is an inquiry into the nature of
intelligence. Its results, therefore, are not in themselves less in-
teresting or less important than a knowledge of the various forms
of geological formation, or of plant or animal life. " If it is re-
garded as a valuable achievement," says Hegel, " to have discovered
sixty odd species of parrot, a hundred and thirty-seven species of
veronica, and so forth, it should surely be held a far more valuable
achievement to discover the forms of reason." 1
The necessity of devoting oneself to a science quite
unselfishly cannot be too strongly enjoined, nor the evils
which arise when one begins a study greedy ' for quick
returns of profit,' too often emphasized. Nevertheless,
since the question has been raised, it would not be just
to refuse altogether to speak of the particular results
1 Hegel, Werke, Bd. V., p. 139. Quoted by Bosanquet at the beginning
of his work on Logic.
12 THE STANDPOINT AND PROBLEM OF LOGIC
arising from a study of logic. As we have seen, we
cannot hope to become infallible reasoners by its aid.
It is just as true here as in any other field, however,
that knowledge is power, and ignorance synonymous
with weakness. For even if one resolves never to look
inside a logic book, one must nevertheless have some
theory, or act upon some principle it may be quite
unconsciously in deciding what is true and what is
false. For instance, a man may act upon the principles
that those things are likely to be true which are favour-
able to his own interests, or which agree with his own
prejudices, or with the articles of his church or political
party. Or again, he may regard his senses as the
standards of truth. Mr. Bradley says that if dogs
reason, they proceed upon the principle, ' what smells,
exists, and what does not smell does not exist.' It is not
uncommon to hear it announced : What can be perceived
through the senses is true ; what cannot be sensed, or is
contrary to the testimony of the senses, is an absurdity.
This was the standard of truth adopted, for example, by
those who attempted to overthrow the Copernican theory
by declaring it to be in plain contradiction to the tes-
timony of the senses.
It seems evident, therefore, that intellectual beings
cannot escape some kind of logical theory, whether they
hold" it consciously or unconsciously. It is clear, too,
that the character of this theory will determine to a
great extent their thoughts and opinions. The only
question which remains is whether it is better to
leave this matter entirely to chance, or to attempt to
gain some clear ideas regarding the nature of thinking,
4- THE MATERIAL OF LOGIC 13
and the conditions under which knowledge arises. It
can scarcely be doubted that, even from a practical point
of view, a true theory is better than a false one. A
man who has reflected upon the nature of proof, and the
principles of reasoning, is much less likely to be deceived
than one who is guided unconsciously by assumptions
which he has never examined. It is always an advan-
tage to know exactly the nature of the result at which
we are aiming, and to be perfectly clear as to our own
purposes. And this is just what a study of logic aids
us in attaining. It helps us to understand the structure
of knowledge and conditions of proof. Moreover, it
engenders the habit of criticising propositions, and ex-
amining the evidence upon which they rest. Further,
the importance of this study for a theory of education
may well be emphasized. For education, at least so
far as it undertakes to train the knowing powers of
the individual, must be based upon a knowledge of the
necessary laws of intelligence, and of the steps or stages
which it passes through in its process of development.
4. The Material of Logic. The business of logic,
as we have seen, is to discover the laws of thought and
to show the differences which exist between real and
imaginary knowledge. Where now shall we find the
materials for this study ? Where are the facts which
are to be taken as a starting point ? It is, of course,
impossible to learn directly from one's own conscious-
ness all that thinking is, or everything of which it is
capable. For, quite apart from the difficulty of observ-
ing the process of thought while it is actually going on,
14 THE STANDPOINT AND PROBLEM OF LOGIC
no one can suppose that his own mind furnishes an
example of all that thinking has done, or can do. It is
necessary to take a broader view, arid learn how other
men think. Of course, we cannot look into the con-
sciousness of other men, but we can study the products
and results of their thoughts. The history of the way
in which truth has been discovered is of the greatest
importance for logic. It must not be forgotten that
thought is not a thing which can be described once for
all. It is rather a living activity, which is constantly
showing what it is in what it does. The history of the
various sciences furnishes a record of the steps by means
of which thought has built up knowledge. And, in this
record, we have also a revelation of the nature of the
thinking process itself, and of the stages through which
it has passed in the course of its development.
It is by a reflection, then, upon the nature of proposi-
tions which are universally regarded as true that the
laws of logic are obtained. There is always a permanent
body of knowledge which no one thinks of calling in
question. Both in everyday knowledge, and in the
sciences, there is always found a great number of propo-
sitions which appear true to everybody. And it is here
that logic finds its material. Taking the facts and propo-
sitions which are recognized as certain by everybody,
logic examines their structure in order to learn about
the nature of the intellectual processes by which they
have been discovered. What principles, it asks, are
involved in those pieces of knowledge, and what partic-
ular acts of thought were necessary to discover them ?
It is only by examining various pieces of knowledge
4- THE MATERIAL OF LOGIC 15
in this way, and attempting to trace out the conditions
of their discovery, that one can learn anything new
regarding the laws and character of thought. In other
words, there is no way of learning about thinking ex-
cept by studying what it has done. The best way of
getting information about what thought can do, is to
study what it has already accomplished.
Every piece of knowledge, as the product of thinking, is to some
extent a revelation of the nature of intelligence. But scientific
knowledge by this I mean the results of the philosophical and
historical sciences as well as of the so-called natural sciences^
exhibits perhaps most clearly the nature of thought. For the
history of these sciences enables us to see the process of know-
ledge, as it were, in the making. In tracing the history of philo-
sophical and scientific ideas, we are at the same time following
the laws of the development of thought. It is this fact which
makes the history of philosophy and of the various sciences so
instructive. It was with this object in view, to take but a single
example, that Whewell wrote his famous History of the Inductive
Sciences. He was interested, that is, not so much in the mere facts
and names with which he dealt, as in showing the nature of thinking
and the methods which had been employed in gaining a knowledge
of the world. This is made very clear in the introduction to another
work of Whewell from which I quote : " We may best hope to
understand the nature and conditions of real knowledge by studying
the nature and conditions of the most certain knowledge which we
possess ; and we are most likely to learn the best methods of discov-
ering truth by examining how truths, now universally recognized,
have really been discovered. Now there do exist among us doc-
trines of solid and acknowledged merit certainly, and truths of which
the discovery has been received with universal applause. These
constitute what we commonly term sciences ; and of these bodies of
exact and enduring knowledge we have within our reach so large a
collection that we may hope to examine them and the history of
1 6 THE STANDPOINT AND PROBLEM OF LOGIC
their formation with a good prospect of deriving from the study such
instruction as we need seek." 1
We have been insisting that the materials for the
study of logic are to be found mainly in the records
which we possess of what thinking has actually accom-
plished. Our own consciousness, it was said, can supply
but a very small quantity of material. To learn what
thinking is, one must have as broad a survey as possible
of its achievements.
But there is another side to the matter. It must never
be forgotten that it is the actual operations of thought
with which logic is concerned. The words and proposi-
tions which express the results of thinking must never be
allowed to take the place of the thoughts themselves.
Now, we cannot directly study the thoughts of any other
individual. It is only in so far as we interpret, through
our own consciousness, the records of what thinking has
done, that these records are able to throw any light
upon the problem of logic. So in this study, as else-
where, we must find the key to the material in our own
consciousness. If we are to gain any real ideas of the
character of the thinking processes by means of which
the sciences have been built up, we must reproduce
these in our own minds. One's own consciousness
must after all furnish the key which makes intel-
ligible the account of the various steps which the
thought of mankind has taken in building up science
or knowledge.
1 Whewell, History of Scientific Ideas, 3d ed., Vol. I., p. 4.
4- THE MATERIAL OF LOGIC I/
References
The following references may be given in connection with
I and 2 :
C. Sigwart, Logic, Vol. I., General Introduction.
F. H. Bradley, The Principles of Logic, pp. i-io.
B. Bosanquet, Logic, Vol. I., Introduction.
H. L. Mansel, Prolegomena Logica, Chap. I.
R. Adamson, The first part of the article ' Logic ' in the Encyclo-
pedia Britannica.
D. G. Ritchie, The Relation of Logic to Psychology, Philos.
Review, Vol. V., pp. 585-600, Vol. VI., pp. 1-17.
CHAPTER II
IMPORTANT STAGES IN THE DEVELOPMENT OF LOGIC
5. The Logic of the Greeks : Aristotle. In the
fourth and fifth centuries before Christ, a great interest
in debate and public controversy sprang up in Athens.
There were several reasons for this. In the first place,
the Athenians of this period were a very acute and intel-
lectual people ; they therefore required some outlet for
their mental activities. The various sciences of nature
which occupy so much of the thought of the modern
world did not exist at that time, nor did the interest exist
which was necessary to create them. For although the
Greeks of this period had the greatest love and rever-
ence for nature, their interest in natural objects was
rather like that of the poet and the artist, than that of
the modern man of science ; in other words, they were
content to enjoy the beauty of natural objects, and to
take delight in the harmonies of sound and color which
their senses presented to them. They had no desire to
pull things to pieces to see how they are made, or to
discover the laws according to which they act, and so
their mental energy and mental acuteness found its
chief outlet in argumentative controversy, and public
debating became one of their favourite diversions. The
Athenians of those days used to argue, from the pure
love of argument, wherever they met, in the market-
18
5. THE LOGIC OF THE GREEKS 19
place, in the groves and gardens, and at their meals and
banquets.
There was in addition, however, a very practical
reason why it was necessary and desirable for one to
be able to argue well. A man of property in Athens
was constantly exposed to lawsuits, and was obliged to
be his own lawyer and defend his cause by pleading
before the judges. It was of the utmost practical
importance, then, that he should be able to state his
cause well, and should be master of all the arts by
which the judges would be likely to be influenced.
Under these circumstances, it is not difficult to under-
stand why the art of public speaking came to be
regarded in Athens as a necessary part of education.
And, in response to this demand, there arose a class of
teachers called Sophists, who made it their business to
instruct young men in all the practical affairs of life,
and especially in the art of public speaking, or rhetoric,
as it was called. The Sophists do not seem to have
made it their object to teach truth to their pupils, or
to inculcate in them a love and reverence for truth;
they rather sought to make those whom they taught
clever men of the world. In teaching the art of argu-
mentation or public speaking they did not seek to point
out the methods by which true conclusions could be
reached, but rather taught the arts by which the judges
could be persuaded, and tricks for the discomfiture of
one's adversary. The rhetoric of the Sophists, in other
words, was not a science of reasoning, but an art of
persuasion and of controversy. It was not necessary
to have any real knowledge of the subject under dis-
2O DEVELOPMENT OF LOGIC
cussion in order to argue well, but only to be well
versed in all the arts of persuasion, and quick to take
advantage of the omissions of an opponent.
The theory on which the teaching of the Sophists
was based is usually known as scepticism. The
Sophists, that is, had come to the conclusion that it
is impossible to find any fixed standard of truth.
Looking at the diversity of individual opinions and
of individual feelings, they declared that knowledge
or truth as something objective, or the same for all,
is an illusion. Only individual opinions exist; there is
no standard by reference to which these opinions may
be measured. It is impossible, then, to distinguish
false opinions from true. Indeed, the words ' truth '
and ' falsehood ' can have no real meaning ; each indi-
vidual must be the measure of truth for himself.
Moreover, in the opinion of the Sophists, the same
state of things exists with regard to our moral ideas.
There is no standard of right and wrong, just as there
is no standard of truth and falsehood. Each man
has the right to choose what he regards as most
advantageous f or s_ himself. The traditional rules of
morality have no authority over the individual, nor is
it possible to discover any rules of morality which are
binding on all men. It is the part of wisdom to con-
sult one's own interest in acting, and to seek to secure
one's own advantage. Moral distinctions, like logical
distinctions, are purely relative and individual.
Socrates was the great opponent of the ethical scepti-
cism of the Sophists. They had concluded, from the
diversity of individual opinion on moral questions, that
5- THE LOGIC OF THE GREEKS 21
there is no real or absolute distinction between right and
wrong. Socrates, however, was convinced that, if one ex-
amined more carefully the nature of the judgments which
men pass on matters of right and wrong, one would find
common elements or ideas. It is possible, he believed,
to find a fixed standard, both in matters of theory and in'
matters of practice. This common element, however,
is not to be discovered in sensation, nor in feelings of
pleasure and pain; these are purely individual, and
can never serve as a universal standard. But beneath
the diversity of sensation and feelings there is the
thought, or concept, which is common to all men.
When rational beings come to understand each other,
they must agree as to the nature of the fundamental
virtues, justice, temperance, courage, etc. It is true
that few men have thought about these matters, and
are able to express their meaning clearly ; but every
man, as a rational being, carries these fundamental
notions in his mind. Now, in order to refute the
moral scepticism of the Sophists (and it was this side
of their teaching which Socrates especially opposed),
it is necessary that the ethical notions, or concepts,
which are implicit in the minds of men shall be drawn
out and carefully defined. How is this to be accom-
plished? Socrates did not undertake to teach men
what ideas they should hold regarding the nature of
any of the virtues ; he rather made them partners
in an investigation, and by means of skilful questions
tried to assist them' in discovering the real nature of
goodness for themselves. Another point to be noticed
is that the definition of the various virtues was reached
22 DEVELOPMENT OF LOGIC
as a result of comparing the views of a number of
individuals. In this way, by comparing the opinions
of many men, of different professions, and of different
grades of society, he was able to separate what was
merely individual and relative in these opinions, from
what was unchanging and absolute.
Plato, the disciple of Socrates, continued the work
of his master. He did not confine his attention wholly
to the moral conceptions, but showed that the Socratic
method could also be used to refute the intellectual scep-
ticism of the Sophists. In other words, he proved that
in the concept, or thought, as opposed to sensation, a
standard of truth is to be found, as well as a standard
of morality. Knowledge arises from thinking, and it
is possible to compare our thoughts, however impossi-
ble it may be to find any basis of comparison in our
sensations.
Plato's disciple, Aristotle, is of great importance in
the history of logic. He undertook a thorough investi-
gation of the process of reasoning, and sought to show
what conditions and principles are necessarily involved
in reaching certainty. Aristotle was thus the founder of
logic, as well as of psychology, zoology, and a number
of other sciences. His most important logical works
are the Categories, De Interpretation, Prior Analytics,
Posterior Analytics, Topics, and the Sophistical Elenchns,
a treatise on Fallacies. These writings came after-
wards to be known as the Organon (or scientific instru-
ment) of Aristotle. They contained, in the first place,
what we call theory of knowledge (a discussion of the
structure of knowledge, and of the scientific principles
s- THE LOGIC OF THE GREEKS 23
upon which it rests), which formed an essential part of
Aristotle's philosophical system. But they also fur-
nished the practical application of these principles. In
his doctrine of the syllogism, which is found mainly in
the Prior Analytics, he showed what are the only valid
forms of reasoning, and thus furnished the pattern or
type to which all proofs must conform. He also classi-
fied, in his work on Fallacies, the various species of
false reasoning ; and showed how false arguments could
be refuted and exposed by the principles which he had
discovered. The form to which Aristotle maintained that
all true reasoning can be reduced was as follows :
All men are mortal,
Socrates is a man,
Therefore Socrates is mortal.
This is called a Syllogism, and it is made up of three
propositions. The first two propositions are called
Premises, and the last the Conclusion. Every piece of
reasoning, all proof, can be reduced to this form. Of
course, the propositions which make up the syllogism
do not always stand in this order, and sometimes one of
them may be omitted. Thus in the argument : ' he
ought to be supported by the state, for he is an old
soldier,' the conclusion stands first, and one premise is
wanting entirely. It is easy to see, however, that the
real argument when properly arranged is equivalent to
this :
All old soldiers ought to be supported by the state,
He is an old soldier,
Therefore he ought to be supported by the state.
Now the part of Aristotle's logic which was best
24 DEVELOPMENT OF LOGIC
worked out, was a theory of proof or demonstration by
means of the syllogism. Here he showed clearly the
various ways in which different kinds of propositions
could be combined as premises to yield valid conclu-
sions, and proved that no conclusion could be drawn
from other combinations. This part of the Aristotelian
logic has c-ome down to us almost unchanged, and is
the subject of Part I. of the present volume.
It will be noticed that, in the doctrine of the syllogism,
Aristotle was dealing with that kind of reasoning which
undertakes to demonstrate the truth of some fact,
by showing its relation to a general principle which
every one admits. In other words, this part of his
work may be called the logic of proof or demonstra-
tion. Aristotle was at one time of his life a teacher of
rhetoric, and he seemed always to have aimed at putting
this art of reasoning on a scientific basis. That is, for
the rules of thumb and questionable artifices of the
Sophists, he wished to substitute general laws and
methods of procedure which were based upon a study
of the principles and operations of reason. By com-
plying with the rules which he laid down, an argument
will necessarily gain the assent of every rational being.
But we do not employ our reason merely in order to
demonstrate to ourselves or to others what we already
know. We seek to discover new facts and truths by
its aid. In other words, we not only wish to prove what
is already known, but also to discover new facts, and we
need a logic of Discovery, as well as a logic of Proof.
This distinction between proof and discovery corre-
sponds in general to that between Deduction and In-
5. THE LOGIC OF THE GREEKS 2$
duction. Deduction is the process of showing how
particular facts follow from some general principle which
everybody admits, while Induction shows the methods
by which general laws are obtained from an observation
of particular facts. Now Aristotle, as we have seen,
furnished a very complete theory of Deduction, or
method of proof. But he did not treat of Induction,
or the method of passing from particular facts to gen-
eral laws, with anything like the same completeness.
Moreover, what he did write on this subject received no
attention for many centuries. Aristotle was himself a
great scientific observer, and may well be regarded as
the father of the natural history sciences. But, in his
logical writings, his main object seems to have been to
present a true theory of argumentation, as opposed to
the false theories of the Sophists. Science, too, was
only in its beginning when Aristotle wrote, and it was
impossible for him to foretell the methods of discovery
which it has actually employed.
After Aristotle's death (322 B.C.), and after the loss
of Athenian independence, there was a great decline of
interest in matters of mere theory which had no direct
application to the practical affairs of life. The Stoic
school did make some slight additions to logical theory,
but like their opponents, the Epicureans, they regarded
practice, the art of living well, as. the supreme wisdom
of life. The Romans, who derived their knowledge of
Greek philosophy largely from the Stoics, were also in-
terested in the practical advantages of logic, rather than
in its theoretical side. It was the possibility of apply-
ing the laws of logic to rhetoric and public speaking
26 DEVELOPMENT OF LOGIC
which especially interested Cicero, who was the first to
make Latin paraphrases and adaptations of Greek logic
in his rhetorical works.
6. Logic during the Middle Ages. For more than
seven hundred years, during the Middle Ages, the Greek
language and literature was almost unknown in Western
Europe. During this time, almost the only sources of
information regarding logic were Latin translations of
Aristotle's Categories, and of an Introduction to the same
work by Porphyry, who lived 232-303 A.D. Both of these
translations were made by Boethius (470-525), who is best
known as the author of The Consolations of Philosophy.
Even when scholars again became acquainted with the
original works of Aristotle, in the latter part of the
Middle Ages, they did not really understand their true
significance. They took the husk, one may say, and
neglected the kernel. They adopted the Aristotelian
logic as an external and arbitrary set of rules for the
guidance of thinking, and neglected entirely 'the sci-
entific theory upon which these rules were based. A
great deal of ingenuity was also shown in subdividing
and analyzing all possible kinds of argument, and giv-
ing the particular rule for each case. This process of
making distinctions was carried so far that scholastic
logic became extremely cumbersome and artificial. Its
pretensions, however, rapidly increased ; it claimed to
furnish a complete instrument of knowledge, and a sure
standard for discriminating between truth and false-
hood.
It is not very difficult to understand why this set of logical rules
6. LOGIC DURING THE MIDDLE AGES 27
seemed so satisfactory to the age of Scholasticism. The men of this
period had no desire to increase their knowledge ; they supposed
that they were already in possession of everything which was worth
knowing. Their only object was to weave this knowledge into a
system, to show the connection and interdependence of all its parts,
and thus to put it beyond the possibility of attack. And for this
purpose, the school logic was admirably adapted ; it was always
possible to bring every case which could arise under one or other of
its rules.
There is no doubt that the Aristotelian logic had
a real value of its own, and that it exercised a very
important influence upon Western civilization, even in
the form in which it was taught by the Schoolmen;
but there is, of course, nothing complete or final about
it. Its main purpose, as we have already seen, was to
furnish a method by means of which the knowledge we
already possess may be so arranged as to be absolutely
convincing. But the centre of intellectual interest has
changed since mediaeval times. We are not content
merely to exhibit the certainty and demonstrative char-
acter of the knowledge which we already have, but we
feel that there is a great deal of importance still to be
discovered. So that, in modern times, one may say the
desire to make discoveries, and so add to the general
stock of knowledge, has taken the place of the medi-
aeval ideal of showing that the traditional doctrines
taught by the church are absolutely certain and con-
vincing. And when men became conscious of the
importance of gaining new knowledge, and especially
knowledge about nature, they at once saw the neces-
sity for a new logic, or doctrine of method, to aid them
in the undertaking.
28 DEVELOPMENT OF LOGIC
7. The Logic of Bacon. All the great thinkers
of the sixteenth and seventeenth centuries saw clearly
that the school logic is simply a method of showing the
certainty of the knowledge we already possess, and
does not aid us at all in making new discoveries. A
new method, they all declared, was an absolute neces-
sity. The new point of view was put most clearly and
eloquently by the famous Francis Bacon (1561-1626),
at one time Lord Chancellor of England. Bacon called
his work on logic the Novum Organum, thus contrast-
ing it with the Organon, or logical treatises of Aristotle.
An alternative title of the work is, True Suggestions for
the Interpretation of Nature. Bacon begins this work
by showing the advantages to be gained from a know-
ledge of nature. It is man's true business, he tells us,
to be the minister and interpreter of nature, for it is only
by becoming acquainted with the laws of nature that we
are ever able to take advantage of them for our own
ends. " Knowledge and human power are synonymous,
since ignorance of the cause prevents us from taking
advantage of the effect." The discovery of the laws of
nature, which is therefore of so great practical impor-
tance, cannot be left to chance, but must be guided by
a scientific method. And it is such a method which
Bacon endeavours to supply in the Novum Organum.
The method which Bacon proposed seems to us very
simple. If we would gain new knowledge regarding
nature, he says, and regarding natural laws, we must
go to nature herself and observe her ways of acting.
Facts about nature cannot be discovered from logical
propositions, or from syllogisms ; if we would know the
8. LOGIC SINCE THE TIME OF BACON 29
law of any class of phenomena, we must observe the par-
ticular facts carefully and systematically. It will often
be necessary, also, to put pointed questions to nature
by such experiments as will force her to give us the
information we want. Knowledge, then, must begin
with observation of particular facts ; and only after we
have made a great number of particular observations,
and have carefully classified and arranged them, taking
account of all the negative cases, are we able to discover
in them the general law. No hypotheses or guesses are
to be made ; but we must wait until the tabulations of
the particular phenomena reveal the general ' form ' or
principle which belong to them all.
It will be frequently necessary to refer to Bacon's
work in what follows. At present, it is sufficient to
note that Bacon showed that a knowledge of nature
cannot be attained through general propositions and
logical arguments, but that it is necessary to begin
with the observation of particular facts. He empha-
sized, also, the importance of systematic observation
and carefully planned experiments, and showed that
knowledge must begin with facts of perception. This
is the method of induction, and Bacon is usually said
to have been the founder of the inductive sciences of
nature.
8. Logic since the Time of Bacon. Another and
quite different method of extending knowledge was pro-
posed by the great Frenchman, Descartes (1596-1650),
who took mathematics as the type to which all know-
ledge should conform. That is, he supposed that the
30 DEVELOPMENT OF LOGIC
true method of extending knowledge was to begin with
general principles, whose truth could not be doubted,
and to reason from them to the necessary character
of particular facts. Descartes and his followers thought
that it was possible to discover certain axiomatic propo-
sitions from which all truth could be derived through
reason. They thus emphasized Deduction rather than
Induction, and reasoning rather than observation and
experiment. The spirit of Bacon's teaching was, how-
ever, continued in England by John Locke, in the
Essay Concerning Human Understanding (1690). Dur-
ing the next centuries, philosophical thinkers were
divided into two great schools, Rationalists, or those
who agreed in the main with Descartes, and Empiricists,
or Sensationalists, who followed the teachings of Bacon
and Locke.
Although the natural sciences made great advances
during the seventeenth and eighteenth centuries, there
seems to have been no effort made to analyze and
describe the methods which were actually being em-
ployed. In England, at least, it seems to have been
assumed that all discoveries were made by the use of
the rules and methods of Bacon. One of the first
writers to attempt to explain the method used by the
natural sciences was Sir John Herschel (1792-1871).
His work, Discourse on the Study of Natural Philosophy,
was published in 1832. A little later, and with the
same object in view, William Whewell (1794-1866),
afterwards Master of Trinity College, Cambridge, un-
dertook his History of the Inductive Sciences, which
was followed some time after by the Philosophy of the
8. LOGIC SINCE THE TIME OF BACON 3 1
Inductive Sciences, The man, however, who did most
towards putting the study of logic on a new basis was
John Stuart Mill (1806-1873), the first edition of whose
Logic appeared in 1843. We shall have frequent occa-
sion to refer to this work in future discussions. It is
sufficient to say here that Mill continues the empirical
tradition of the earlier English writers in his general
philosophical position. Mill's book gave a great im-
pulse to the study of logic. Before it was published,
writers on the subject had confined their attention
almost exclusively to the syllogistic or deductive rea-
soning. Mill, however, emphasized strongly the impor-
tance of induction ; indeed, he regarded induction as
the only means of arriving at new truth, deduction
being merely a means of systematizing and arranging
what we already know. Though few logicians of the
present day adopt this extreme view, the importance of
inductive methods of reasoning, and the necessity of
studying them, have now become generally recognized.
Most modern writers on logic devote a considerable
amount of attention to induction. The reader will find
that Part II. of the present volume deals with this
subject.
There is still another side of logic which has been
developed in the English-speaking world since the time
of Mill, though it is a direct continuation of the move-
ment started in Germany by Kant more than a hun-
dred years ago. The so-called ' modern ' logic has laid
aside the formalism and paradoxical mode of expression
adopted by Hegel, but the fundamental conceptions
with which it works are essentially the same as those
32 DEVELOPMENT OF LOGIC
employed by the latter in his Wissenschaft der Logik
(1816-1818). It has been within the last twenty years
that the results of German idealism the doctrines of
Kant, Fichte, Schelling, and Hegel have become
naturalized in England and America. And largely as
a consequence of these teachings, a new conception of
the nature of thought has grown up, and given rise to
investigations which may be said to have created a
'modern' logic that is fairly entitled to rank beside
its sister science, the ' new ' psychology.
The Aristotelian doctrine of the syllogism is a purely
formal science. In the form in which it is represented
in ordinary text-books, it might perhaps be more prop-
erly described as the art of arranging our knowledge
in such a way as to compel assent. The ' matter ' with
which thought is supposed to work is supplied to it in
form of concepts and judgments. The problem which
formal logic has to solve is to define and classify the
various kinds of concepts with which thought operates,
and to determine the various relations in which these
stand when combined into judgments. Similarly, it
has to show what combinations of judgments can be
employed as premises leading to valid conclusions in
the syllogism. The criterion of truth employed in these
investigations is the principle of non-contradiction or
consistency. Inconsistent combinations of concepts,
that is, are ruled out ; but so far as the doctrine of
the syllogism goes, anything is true which is not self-
contradictory.
Now, without questioning the practical value of its
canons, it is obvious that formal or syllogistic logic does
8. LOGIC SINCE THE TIME OF BACON 33
not take any account of many of the processes of every-
day thought, and that its rules go but a little way in
helping us to distinguish the true from the false. For,
in the first place, to think is not merely to combine and
arrange ideas already in our possession. This might
enable us to render clearer and more definite what we
already know, but would never enable us to gain new
knowledge. The real movement of thought as op-
posed to its merely formal procedure consists in the
formation of new ideas and new knowledge through
actual contact with the world of experience. A com-
plete account of the intellectual process, then, must
deal with the relation of the mind to objects; it must
investigate the various activities by means of which
thought interprets the world and builds up the various
sciences of nature and of man.
The recognition of the importance of induction, and
of the necessity of studying the methods of the induc-
tive sciences which was brought about by Whewell,
Mill, and others, was a step in the right direction, for
it called attention to a kind of thinking which occupies
a large place in our intellectual life, and also gave rise
to a truer conception of the nature of thought itself.
But even Mill did not reach the idea which guides
modern logicians, that thought or intelligence is one
from beginning to end, and that the various logical
processes are all parts of one whole, or rather ways in
which intelligence operates in different circumstances,
or at different stages of its development. He still
treats of logical processes, like conception, judgment,
and reasoning, as if they were quite separate from
D
34 DEVELOPMENT OF LOGIC
each other ; and, as has already been noticed, in his
zeal for induction, he fails completely to do justice to
syllogistic reasoning.
As opposed to the division of mind into separate
faculties, the thought by which modern logic is domi-
nated is that of the unity and continuity of all intel-
lectual life. Thought is regarded as an organic, living
function or activity, which remains identical with itself
throughout all its developing forms and phases. The
problem, accordingly, which logic must set before itself
is to show the unity and interrelation of all of the
intellectual processes. No one of the steps or stages
in this process can be completely understood when
viewed by itself : each is what it is only in and through
its connection with the whole of which it forms a part.
No hard and fast boundary lines are to be drawn be-
tween the different stages of the reasoning process, but
it must be shown that the whole nature of intelligence
is involved more or less explicitly at each step. So
far only the broad outlines of this theory have been
filled in ; but the conception of an organism whose
parts are developing in mutual relation and inter-
dependence, promises to be as fruitful when applied
to logic as it has already shown itself to be in the
other sciences.
Besides the ordinary histories of philosophy the reader may con-
sult for the history of logic : Prantl, Geschichte der Logik im Abend-
lande, 4 vols., Leipsic, 1855-1870; which extends, however, only to
the dose of the mediaeval period. Harms, Geschichte der Logik,
Berlin, 1881. Ueberweg, System der Logik, 4th ed., 1874; Eng.
trans, of 3d ed., London, 1874. Adamson, article 'Logic,' in tha
8. LOGIC SINCE THE TIME OF BACON 35
Encyl. Brit., gth ed. Sir William Hamilton's Lectures on Logic,
also contain much historical information.
Among modern works on logic, the following may be mentioned :
J. S. Mill, A System of Logic, London, ist ed., 1843; Qth ed., 1875.
W. S. Jevons, The Principles of Science, London, 1874; 2d ed.,
1877. Also, by the same author, Studies in Deductive Logic, 1880 ;
and Pure Logic, 1890. H. Lotze, Logik, 1874; Eng. trans., Lon-
don, 1 88 1 and 1888. W. Wundt, Logik, 2d ed., 1896. C. Sigwart,
Logik, 2d ed., 1889-1893 ; Eng. trans., London and New York, 1895.
The newer development of logic is well represented by F. H. Brad-
ley, The Principles of Logic, London, 1886. B. Bosanquet, Logic,
or the Morphology of Knowledge, London, 1888 ; and The Essentials
of Logic, London and New York, 1895. L. T. Hobhouse, The Theory
of Knowledge, London, 1 896, may also be mentioned in the same
group of writers, although he has been, perhaps, more influenced by
Mill than by any other writer.
The following works, among others, have proved useful as text-
books : W. S. Jevons, Elementary Lessons in Logic, London and
New York, 1870. A. Bain, Logic, Deductive and Inductive, New
York, 1883. J. H. Hyslop, The Elements of Logic, New York, 1892.
W. Minto, Logic Inductive and Deductive, New York, 1894. J. G.
Hibben, Inductive Logic, New York, 1 896.
PART I. THE SYLLOGISM
CHAPTER III
THE SYLLOGISM AND ITS PARTS
9. The Nature of the Syllogism. The theory ol
the syllogism, as has been already stated ( 5), was
first worked out by Aristotle. And it stands to-day
in almost the same form in which he left it. A few
additions have been made at different points, but these
do not affect materially the main doctrine. In deal-
ing with the nature of the syllogism, we shall first
try to understand its general aim and purpose, or the
results which it seeks to bring about. We shall then
have to analyze it into the parts of which it is com-
posed, and to examine and classify the nature of these
elements. Finally, it will be necessary to discover
what rules must be observed in order to obtain valid
conclusions, and to point out the conditions which
most commonly give rise to error or fallacy.
In the first place, it is to be noticed that syllogistic
logic deals with the results of thinking, rather than
with the nature of the thought-process. Its object is
not to give an account of the way in which thinking
goes on, but to show how the ideas and thoughts which
we already possess may be combined so as to compel
36
9. THE NATURE OF THE SYLLOGISM 37
assent. The ideas which it uses as material are fixed
by having been expressed in language. Indeed, it is
largely with words, as the expression of thoughts, that
syllogistic logic deals. Many of the discussions with
which it is occupied have reference to the meanings
of words and propositions ; and the rules which it fur-
nishes may be taken as directions for putting together
propositions in such a way as to lead to a valid conclu-
sion. Nevertheless, it is important to remember that
these rules are not arbitrary and external, but find their
justification in the nature of thought. Indeed, the
theory of the syllogism, when rightly understood, may
be said to reveal the fundamental characteristics of the
process of intelligence. For it brings together facts
in such a way as to make evident their relation and
dependence. It connects a judgment with the grounds
or reasons which support it, and is thus a process of
systematization. In order to understand the signifi-
cance of the rules of syllogistic logic, then, it will
frequently be necessary to look beyond words and
propositions to the act of thought whose result they
express.
A great deal has been written regarding the princi-
ples, or laws of thought, which are employed in syllo-
gistic reasoning. , It seems better, however, to postpone
the definite consideration of this subject until the student
has learned more about the various kinds of syllogisms,
and has had some practice in working examples. In
dealing with the nature and principles of thought in the
third part of this book, it will be necessary to discuss
this question at length. Even at the present stage of
38 THE SYLLOGISM AND ITS PARTS
our inquiry, however, it is important to notice that syl-
logistic reasoning presupposes certain simple and fun-
damental principles of thought whose nature we shall
have to examine hereafter. In particular, the regular
syllogism is founded on a principle which we may call
the law of Identity, or the law of Contradiction, according
as it is stated affirmatively or negatively. Stated affirm-
atively, this so-called ' law ' simply expresses the fact
that every term and idea which we use in our reason-
ings must remain what it is. A is A, or has the same
value and meaning wherever employed. The law of
Contradiction expresses the same thing in negative
language. A cannot be both B and not B. If any
term is taken to be the same as another in one connec-
tion, it must always be taken to be so ; if it is different,
this relation must everywhere be maintained. .The
data or materials which are employed in the syllogism
are ideas whose meaning is supposed to be perma-
nently fixed, and expressed in words which have been
carefully defined. It would be impossible to reason, or
to determine the relation of our ideas, if their mean-
ing were to change without notice, or if the words by
means of which they are expressed were used now in
one sense, and now in another. It is of course true
that our ideas regarding the nature of things change
from time to time. And, as is evident from one's own
experience, as well as from the history of language, a
corresponding change takes place in the meaning of
words. But the assumption upon which syllogistic
reasoning proceeds, is that the ideas which are to be
compared are fixed for the mean time, and that the
io. THE PARTS OF A SYLLOGISM 39
words by which they are expressed are used in the
same sense throughout the course of the argument.
In this kind of reasoning, then, just as in geometry, it
is essential that the terms which enter into the argu-
ment be clearly and precisely defined, and that when
thus determined they shall be taken as fixed and un-
changeable until further notice is given.
It is quite possible that all the requirements of the
syllogism may be met without its conclusions being
true of reality. In other words, an argument may be
formally true, but really false. It is not difficult to
understand why this may happen. The syllogism ac-
cepts the ideas and judgments which it compares with-
out criticism. These data are of course the product of
previous acts of thinking. But in proceeding to ar-
range them in syllogistic form, we do not inquire
whether or not they are true ; i.e. adequate to express
the nature of the things for which they stand. For
the purposes of the syllogism it is only essential that
their meanings be clearly understood, and that these
meanings be regarded as fixed and permanent.
io. The Parts of a Syllogism. The syllogism may
be said to express a single comprehensive act of thought.
We may define inference as a judgment which has been
expanded so as to exhibit the reasons by which it is
supported. In the syllogism
The geranium has five pointed sepals,
This plant has not five sepals,
Therefore it is not a geranium.
we may say that we have the judgment, 'this plant is
40 THE SYLLOGISM AND ITS PARTS
not a geranium,' supported by the propositions which
precede it, and that the whole syllogism taken together
expresses a single thought, which is complete and self-
sufficient. It is possible, however, even when one is
dealing directly with the process of thinking, to dis-
tinguish in it different subordinate steps, various stages
which serve as resting places, in the course of its passage
to the complete and comprehensive form represented
by "the syllogism. But it is usual, in dealing with the
syllogism, to take a more external view of its nature,
and to regard it primarily as made up of words and
propositions.
In this sense, a syllogism can, of course, be divided
into parts. In the first place, it is composed of three
propositions. In the example given above the two
propositions which stand first are called the premises,
since they furnish the grounds or reasons for the propo-
sition which stands last, and which is known as the
conclusion. However, it is not true that we always
find the two premises and the conclusion arranged in
this regular order in syllogistic arguments. Oftentimes
the conclusion is given first. Frequently, too, one of
the premises is not expressed, and has to be supplied in
order to complete the argument. Thus the statement,
'he must be more than sixteen years of age, for he
attends the university,' is an incomplete syllogism.
The conclusion, as will be readily seen, stands first.
There is also only one premise expressed. To put this
statement in the regular syllogistic form we have to
supply the missing premise and arrange it as fol-
lows :
io. THE PARTS OF A SYLLOGISM 4!
All students of the university are more than sixteen years of age,
He is a student of the university,
Therefore he is more than sixteen years of age.
When one premise of an argument is lacking, the name
of enthymeme is applied to it. When an argument is
defective in this way, it must be remembered that the
missing proposition is to be regarded as in consciousness,
though not expressed. It is of great importance to form
the habit of making clear to oneself the premises by
which any conclusion claims to be supported. In this
way groundless assumptions are often brought to light,
and the weakness of an argument exposed. Whenever
words like 'therefore,' 'for,' 'because,' 'it follows,' etc.,
are used in their proper signification, it is possible to
find an argument composed of two premises and a con-
clusion. But one must not allow oneself to be imposed
upon by the mere words, but must insist on understand-
ing exactly what are the premises in the case, and how
the conclusion follows from them.
It is possible to carry the division of a syllogism still
further. Every logical proposition may be divided into
two terms, and a copula or connecting link. The terms,
which are the extremes of the proposition, are named
the subject and the predicate. Thus in the proposition,
' the fields are covered with snow,' ' the fields ' is the
subject, 'are,' the copula, and, 'covered with snow,'
the predicate. To reduce a proposition to the logical
form in which it is most conveniently treated, it is neces-
sary to express it in such a way that the two terms are
united by some part of the verb 'to be,' preferably 'is'
or ' are.' Thus the sentence, ' No plant can grow with-
42 THE SYLLOGISM AND ITS PARTS
out light and heat,' would be expressed as a logical
proposition in the following, or some similar, form : ' No
plant is an organism which can grow without light and
heat.' ' Men have strong passions,' may be written,
' Men are beings having strong passions.' It is always
well to reduce a sentence to some such form, by substi-
tuting for the verb of predication some part of the verb
' to be.'
The analysis of the syllogism gives us the divisions
under which it is convenient to treat this part of logic.
We shall accordingly deal (i) with Terms, (2) with
Propositions, and (3) with the Syllogism as a whole.
These divisions, however, are only made for the sake
of convenience in treatment. It must not be forgotten
that a term is a. part of a proposition. To understand
the nature of a term, it is necessary to consider the
part which it plays in the judgment which the propo-
sition expresses. In other words, the function of the
term, rather than the form of the word or words em-
ployed, must be considered. It is, of course, true that
we naturally and commonly use certain word forms to
express certain kinds of ideas, just as in the grammati-
cal sentence the different 'parts of speech' nouns,
verbs, etc., have each a definite and comparatively
permanent function. But even in the sentence, it is the
part which the word in its grammatical function plays,
rather than its form, which determines whether it is to
be classified as a noun or an adjective, a preposition or
a conjunction. In dealing separately with terms, as we
propose to do in the next chapter, we shall be occupied
to a large extent with the form of words in which cer-
II. PROPOSED DIVISION OF MENTAL OPERATIONS 43
tain kinds of ideas are usually expressed. But, as the
same word or group of words may be used for different
purposes, it will be necessary, in order to understand
the meaning of terms, to refer frequently to the various
ways in which they are used in a proposition.
The same difficulty exists when propositions are con-
sidered by themselves, the relation to the complete
argument of which they form a part being thus ig-
nored. In this case, however, the results of the isola-
tion are not so apparent, for a proposition forms, in
a certain sense, a whole by itself. It is the expression
of a judgment which, as we shall see later, is the unitary
process of thought. It has thus a significance of its
own, as expressing a more or less complete and inde-
pendent act of thought. Nevertheless, it must not be
forgotten that its independence and completeness are
only partial and relative. A single proposition cannot
stand alone. Taken strictly by itself, a proposition is
only a fragment. In order to make it intelligible, it
must be brought into relation with the other proposi-
tions which state the grounds or reasons upon which
it rests, or the conclusion which it helps to support.
The logical nature of a proposition will, therefore, de-
pend upon its function in an argument, and in treating
of propositions this fact must not be forgotten.
ii. The Proposed Division of Mental Operations.
It is frequently stated in text-books on logic that corre-
sponding to the division into Terms, Propositions, and
Syllogisms, there must be a division of the different kinds
of thought, or of operations of the mind. These differ-
44 THE SYLLOGISM AND ITS PARTS
ent operations are usually called Simple Apprehension,
Judgment, and Reasoning. " The first of these, Simple
Apprehension, is the act of mind by which we merely
become aware of something, or have a notion, idea, or
impression of it brought into the mind. The adjective
simple means apart from other things, and apprehension,
the taking hold by the mind. Thus the name or term
' iron ' instantaneously makes the mind think of a very
strong and very useful metal, but does not tell us any-
thing about it, or compare it with anything else." 1
Judgment, the account continues, is an entirely dif-
ferent action of mind, and comes later than Simple
Apprehension. It consists in comparing two notions
or ideas derived from simple apprehension in order to
ascertain whether they agree or differ. In order to
judge, we must have two notions or ideas ready in the
mind. The judgment results from comparing these,
and affirming, that they agree or do not agree. In
the sarne way, having already made judgments, we
can combine them into arguments or processes of
reasoning by a new and still different activity of mind.
Apprehension, judgment, and reasoning are thus sup-
posed to be separate and distinct mental operations.
It is true that the later forms employ as their mate-
rial the finished products of the earlier. But from this
point of view, apprehension, judgment, and reasoning
simply succeed one another. The real unity which
belongs to these operations as forms of intelligence is
not set forth.
1 Jevons, Lessons on Logic, pp. n, 12.
II. PROPOSED DIVISION OF MENTAL OPERATIONS 45
The whole of Part III. of the present book may be
regarded as an argument against this point of view.
We shall there endeavour to show that thinking is not
a process of externally joining on part to part, but
consists in a development or expansion of knowledge
from within. And, in particular, we shall try to ex-
hibit the essential unity of intellectual processes by
whatever name they may be called, and at whatever
stage of development they may be found. Without
anticipating too far our future discussions, we may point
out that the primary process of thought is not ' Simple
Apprehension,' but Judgment. In other words, it is
impossible to apprehend or passively receive ideas.
'To get an idea/ or to understand the meaning of a
term, is only possible when the mind judges or inter-
prets things for itself. To have an idea or concept
of anything, then, is to be able to judge more or less
clearly and confidently regarding it. I have an idea
of 'iron' when I judge that it is 'black' and 'heavy'
and 'malleable.' And the more complete and exact we
can make our judgments, the better is the idea or appre-
hension which we obtain of the thing in question. In-
telligence or thought must not be regarded as at first
merely receptive. It does not begin by laying hold of
separate ideas or terms, and afterwards call in judg-
ment as a new kind of process to bring the former into
relation. But it is from the first a systematizing and
relating activity which proceeds from the less perfect
to the more perfect form of judgment (cf. 73, 74).
CHAPTER IV
THE VARIOUS KINDS OF TERMS
12. Singular, General, and Collective Terms. A
logical term, as we have already seen, is an element of
a proposition. In dealing with terms apart from prop-
ositions, we shall be concerned mainly with different
classes of words and the meanings which they usually
express. It will be impossible, however, to fix ths
meanings of terms absolutely without reference to the
way in which they are used in propositions. The first
division which we have to notice is that into Singular or
Individual, General, and Collective terms.
(i) A Singular or Individual term is one which can
be applied in the same sense to but a single thing.
The main purpose of Singular terms is to refer to,
or identify, some individual object. Proper names are
all singular. It is true that proper names are some-
times used to denote a class of objects, as, e.g., 'a
Daniel,' ' a Mephistopheles.' But when thus employed
they lose their real character as proper names. That
is, their function is no longer merely to identify certain
individuals by naming them, but to describe them by
mentioning certain qualities or characteristics which
they are supposed to possess. But the ordinary pur-
pose in using a proper name is to indicate some indi-
vidual to whom the name belongs. In this sense, then,
proper names are Singular.
46
12. SINGULAR, GENERAL, AND COLLECTIVE TERMS 47
In addition, any word or group of words which is
applied to a single thing may be regarded as singular.
And by 'single thing,' we mean anything which is
thought of as one, as well as objects which are per-
ceived through the senses. Thus, 'the waterfall just
below the bridge,' ' the centre of the earth,' are singu-
lar terms, and so also are words like 'justice,' 'good-
ness,' 'the chief end of man.' It is perhaps more
doubtful whether we should call terms such as ' white-
ness,' ' sweetness,' singular, since we speak of differ-
ent degrees and kinds of whiteness and sweetness.
The question would have to be decided in every case
by reference to the way in which the terms are em-
ployed in propositions.
(2) A General term is a name which applies to a
whole group of objects. It is not limited, like the sin-
gular name, to a single thing, but applies to a number
of different things. All class names like ' metal,'
' man,' ' works on logic,' are of this character. The
general name belongs to each and every individual
of a whole class. Thus iron, gold, silver, etc., are
' metals ' ; and A, B, and C, ' men.'
(3) A Collective term, on the other hand, is a name
applied to a number of individuals when taken together
and treated as a whole, as 'an army,' 'an audience.'
It is important to distinguish carefully between general
and collective terms. A general term is a name which
applies equally to each individual of the group ; or, in
other words, it is used of the individuals distributively.
A collective name belongs to the whole, but not to the
separate parts of the whole. Thus we say that 'sol-
48 THE VARIOUS KINDS OF TERMS
dier ' is a general name, and is used distributively of
each man in a regiment. ' Regiment,' however, is a
collective name, for it applies only to the whole group,
and not to the individual soldiers.
Ambiguity sometimes arises from the fact that the
English word 'all' is used in both of these senses.
That is, it may rnean ' all taken together/ or ' each and
every.' Thus we can say : ' All the angles of a tri-
angle are less than two right angles ' ; and ' all the
angles of a triangle are equal to two right angles.' In
the former sentence, the word ' all ' is used distribu-
tively ; in the latter, collectively. In Latin two different
words are used : cuncti expresses the collective sense
of ' all,' and omnes its distributive signification.
It is worth noticing in this connection that it is the use which
is made of terms, rather than the form of the words composing
them, which determines their logical character. Thus terms which
are collective in one connection may be general in another. ' Regi-
ment,' for example, is a collective term with reference to the soldiers
which compose it, but general when used as a common term for a
number of similar divisions of an army. The same is also true of
terms like ' grove,' 'mob/ 'class/ etc. Again, collective terms
may be very properly regarded as singular when the proposition
in which they are used emphasizes the unity and solidarity of the
group. A proper name is sometimes applied to a collection of in-
dividuals that are permanently united or that have acted together
on some historic occasion, as, for example, ' The Fifth Cavalry regi-
ment/ < The Charge of the Six Hundred.'
13. Abstract and Concrete Terms. Terms are fur-
ther divided into abstract and concrete terms. The
word ' abstract ' is often used popularly to describe
anything which is difficult to understand. Etymologi-
13. ABSTRACT AND CONCRETE TERMS 49
cally, it signifies drawn off, separated (abstraho, to
draw off, take away). We may distinguish two senses
in which the word is used, both, however, being derived
from its etymological signification.
(i) A term is called abstract when it refers to some
object which cannot be directly perceived through the
senses, and concrete when such perception is possible.
Thus 'a beech tree,' ' a tall man,' 'a sweet taste,' being
names of things which can be perceived, are concrete.
Words like 'sweetness,' 'hardness,' etc., have no objects
of sense directly corresponding to them, and are for
this reason called abstract. The same is true of terms
like 'individuality,' 'equality,' 'justice,' etc. These
words represent objects of thought, rather than ob-
jects of sense. There may be cases or instances of
'equality,' 'justice,' etc., which fall under our percep-
tion, but the real object to which these words corre-
spond is not a thing which can be perceived through
the senses at all. Their reality is conceptual, or for
thought, not something directly revealed through the
senses.
It is important to notice that there are degrees of abstractness in
terms, according as the objects for which they stand are nearer to, or
further removed from ordinary sense-perception. All general or
class names are abstract. One cannot point to a single object, to
which the term 'metal,' for example, or the term ' man 1 corresponds.
But although such terms have no direct sensuous object, yet we feel
that they stand nearer to sense-perception, and are therefore tess
abstract, than words like 'animal,' 'inorganic substance.' These
terms, again, are perhaps less abstract than 'energy,' or 'spirit,' or
even than singular terms like 'justice,' 'the ground of the universe,'
etc.
50 THE VARIOUS KINDS OF TERMS
(2) Again, the word ' abstract ' is applied to any ob-
ject which is treated apart from the whole to which it
belongs. Thus it would be an abstraction to attempt
to represent the nature of a leaf in complete isolation
from the plant to which it belongs, or to consider the
nature of a man without regard to the social institu-
tions family, church, state, etc. of which he is a
member. Of course, it is essential when dealing with a
complex whole to analyze it into its parts, and to under-
stand just what is the nature of each part when taken
by itself. But in order to comprehend fully the nature
of the parts, it is necessary to restore them to their
proper setting, and to see their relation to the concrete
whole. In this sense of the word, then, ' abstract '
applies to what is taken out of its proper setting, broken
off, and considered apart from the things to which it is
organically related. Concrete, on the other hand, means
what is whole and complete, a system of things which
mutually support and explain one another.
Since science has to analyze things into their elements,
and to investigate and describe these elements in detail,
it is impossible entirely to avoid abstraction. But it is
necessary, in order to completely understand the nature
of a complex object, that the abstractions of analysis
shall be corrected. In other words, the concrete rela-
tions in which things stand must not be ignored in
investigating them. The conception of evolution in
recent times has done much to render the biological
sciences more concrete in the sense in which we are
now using the term. For it has substituted, for the old
method of treating each species of plant and animal as
13- ABSTRACT AND CONCRETE TERMS 51
distinct and separate, ' cut off from each other as if by
a hatchet,' the view that all organic beings are members
of one family, and can be properly understood only in
their relations to one another.
It is interesting to notice that, from this point of view, sense-
perception is more abstract than thought. For the senses represent
things in isolation from each other. Each thing is known in sense-
perception as a separate individual, occupying its own space and
time, and in this way, cut off from its fellows. It is the business of
thought, on the other hand, to discover the relations between things,
and the principles according to which they are united. Thinking
thus overcomes the abstract point of view of sense-perception by
showing that what appear to the latter as separate objects are
really closely and necessarily connected as members of a com-
mon unity or system. Each science takes as its province certain
facts which resemble one another, but which nevertheless appear
to sense-perception to be quite independent. It attempts by
thinking to bring these facts into relation, to show that they are
all cases of some law, that there is a common principle which unites
them as parts of a whole or system. The law of gravitation, for
example, expresses the unity which thought has discovered in
things which appear to sense-perception as different as the falling
of an apple, the movements of the heavenly bodies, and the ebb
and flow of the tides. Scientific knowledge, then, is more con-
crete than the facts which we learn from ordinary sense-percep-
tion, because it brings to light real unity and connection in facts
which appear to be entirely isolated and independent from the
latter point of view.
In employing the terms 'Abstract' and 'Concrete' it
is of the utmost importance to distinguish the two sig-
nifications of the words. From one point of view, as we
have seen, all thought terms are abstract, as opposed to
words which refer directly to objects of sense-perception.
52 THE VARIOUS KINDS OF TERMS
In another sense, ' abstract ' denotes what is partial and
incomplete, what is taken by itself and out of relation
to the system of things to which it belongs. And since
the real connection and relations of things are not given
by perception, but have to be discovered by thought,
the knowledge which the latter yields is more concrete,
in this latter sense of the term, than that afforded by
the former.
14. Positive and Negative Terms. The distinction
between Positive and Negative terms is very obvious.
Positive terms express the existence of some quality, or
group of qualities, in the objects which they denote; as,
e.g., ' happy,' ' good/ ' equality,' ' organism,' etc. A Neg-
ative term, on the other hand, indicates the absence
of qualities or properties in some object; 'bad,' 'un-
happy,' 'inorganic,' 'injustice,' for example, are negative
terms. Negative terms are often formed from positive
by means of the affix, less, as in ' hopeless/ or by means
of certain prefixes, of which the more common are un, in,
dis, a, anti. Words which are positive in form are, how-
ever, often negative in meaning, and are used as the
contradictories of other terms. Thus 'ignorant' is
generally regarded as the negative of ' learned/ ' dark-
ness ' is the negative of ' light/ etc. It is not always
possible, however, to find a separate word to express the
exact opposite of every positive term. Words are used
primarily to express the presence of qualities, and the
negative idea may not be referred to so frequently as
to require a separate word to express it. Thus there
is no independent term to express the opposite of ' trans-
H. POSITIVE AND NEGATIVE TERMS 53
ferable,' but by employing ' not ' as a negative prefix we
obtain ' not-transferable.'
It is always advisable when we wish to limit a term strictly to its
negative application to employ not or non as a prefix. Words
which are negative in form frequently have a more or less definite
positive signification. Jevons points out that words like 'unloosed'
and ' invaluable, 1 though negative in form, have a positive meaning.
But, in addition, terms like 'unhappy,' 'immoral,' do not merely
indicate the absence of positive qualities, but also express some
positive properties of the objects to which they are applied. We
speak of a person ' being positively unhappy ' ; and we employ
'non-moral' to express the simple negative relation rather than
' immoral.'
On the other hand, there are certain terms which are positive in
form that express the absence of qualities or attributes. Words like
'blind,' 'dumb,' 'maimed,' 'orphaned,' may be given as examples.
These are often called Privative terms, rather than Negative, the
distinction being that they refer to qualities or attributes which the
objects to which they are applied naturally and usually have, but of
which they have been deprived, or which they have never possessed.
Thus ' blind,' as applied to a man, implies that he has lost or is desti-
tute of the ability to see which naturally belongs to a human being.
Again, other terms seem to be positive and negative solely in
relation to each other. ' Element ' and ' compound ' are related as
negatives or contradictories. It is difficult, however, to say which
term is in itself negative or positive.
It is important to notice the distinction between the
relation in which positive and negative terms stand to
each other, and that expressed by words which have
to do with opposite extremes of something which pos-
sesses quality or degree. Positive and negative terms
are mutually contradictory. An element is what is not
a compound, ' dishonest ' is the contradictory of ' honest,'
54 THE VARIOUS KINDS OF TERMS
and as contradictories there is no middle ground be-
tween them. What is not an element, is a non-element
or a compound. Opposite or contrary terms, on the
other hand, express a great difference of degree in the
objects to which they refer. Thus 'foolish' is the op-
posite of ' wise,' ' cold ' the opposite of ' hot,' and ' bitter '
of 'sweet.' But there is always the possibility of a
middle ground between opposites. We cannot say that
a man must be either wise or foolish, a taste either
sweet or bitter. The logical contradictory of ' wise ' is
'not-wise,' of 'bitter,' is 'not-bitter,' etc. Opposite or
contrary terms, then, must be carefully distinguished
from contradictories.
15. Absolute and Relative Terms. Another classi-
fication of terms, which is usually given by logicians,
is that into absolute and relative terms. An absolute
term is one which refers to an object which exists by
itself, and has an intelligible meaning when taken alone.
Thus, 'tree,' 'house,' 'the State of New York,' are ex
amples of absolute terms. A relative term, on the con-
trary, is a name which only derives a meaning from its
relation to something else. The term ' parent,' for ex-
ample, cannot be thought of except in relation to 'child.'
Similarly, 'teacher' is relative to 'pupil,' and 'cause' to
'effect.' Relative terms usually go in pairs and are
known as Correlatives. Adjectives, as well as nouns,
may be related in this way. The presence of one
quality or characteristic in a thing frequently implies
the presence of others. Thus, ignorance and super-
stition, sympathy and tolerance, are necessary correla-
16. EXTENSION AND INTENSION OF TERMS 55
tives, because the one involves the other, or is invariably
connected with it.
It is of course true that no finite thing is completely absolute or
independent of other things. The nature of everything is largely
determined by the nature of the other things with which it stands
in relation. A tree, for example, is relative to the seed from which
it sprang, the soil in which it grew, the sunshine, rain, etc., which
accompanied its growth. All finite things have a beginning and an
end, and are also influenced throughout the whole period of their
lives by the action of other things. They are therefore not com-
pletely absolute or independent. It is, however, possible to make a
distinction between words which are the names of things that are
comparatively independent, and may for ordinary purposes be con-
sidered by themselves, and those which have only a meaning when
regarded as correlatives.
1 6. Extension and Intension of Terms. In the
foregoing sections of this chapter we have explained
the nature of the various kinds of terms with which
logic deals. It is now necessary to notice two different
purposes for which terms are employed. In the first
place, terms are used to refer to things, to name and
identify them. Thus ' man ' refers to the different
individual men, John Smith, Thomas Brown, etc., as
well as to the various classes of men, Caucasians,
Indians, Mongolians, etc. As denoting or naming ob-
jects, whether these be individual things or classes of
things, terms are said to be employed in Extension.
But words are also used to describe as well as to name.
That is, they represent the qualities or attributes be-
longing to things for which they stand. They are not
bare names without signification, but as the expression
56 THE VARIOUS KINDS OF TERMS
of ideas they stand for certain qualities or character-
istics which things are judged to possess. ' Man,' for
example, is not merely a name which may be applied
to individual human beings or races of men, but it
implies that the objects so named have certain qualities,
such as animal life, reason, and the power of com-
municating with their fellows. When words are used
in this way to define or describe things, rather than
merely to name them, they are said to be employed in
Intension.
The terms ' Denotation ' and ' Connotation ' were used by Mill
instead of Extension and Intension, respectively, and have been
adopted pretty generally since his time. To 'denote,' is to point
out or specify the objects for which a term stands ; and to 'connote'
is to take account of the attributes or qualities which a name implies.
The words 'breadth,' and 'comprehension,' are also sometimes used
as synonymous with Extension, and ' depth,' or ' content,' instead of
Intension. The terms to be remembered, however, are Extension
or Denotation, and Intension or Connotation.
It is useful to accustom ourselves to distinguish these
two functions or uses of a term, to notice, that is, the
things or classes of things to which the name applies,
and also to reflect upon the signification, or ways of judg-
ing about these things, for which the name stands. The
Extension of a term, as has been said, indicates the
objects to which a name applies, and the Intension the
qualities or attributes which it signifies. From the point
of view of extension, therefore, ' planet ' may be defined
by mentioning the names of the various planets, Mer-
cury, Venus, the Earth, Mars, etc. Similarly, a term
like 'carnivora' might be given in extension by nam-
1 6. EXTENSION AND INTENSION OF TERMS 57
ing seals, bears, weasels, dogs, wolves, cats, lions, etc.
Usually, however, we define from the point of view of
intension, that is, by stating the qualities or character-
istics for which the term stands. Thus we give the
intensive meaning of ' planet,' as a heavenly body which
revolves in an elliptical orbit round the sun. ' Car-
nivora,' defined from the same point of view, are mam-
malian vertebrates which feed upon flesh. It is not
unusual, however, to supplement an intensive definition
by turning to extension and enumerating examples.
Thus we might add to the definition of 'carnivora' just
given, the words, ' as lions, tigers, dogs, etc.'
It is sometimes said that the intension and extension
of terms vary inversely. This is simply an attempt to
give a mathematical form of statement to the fact that
the more a term is defined, or limited, by the addition of
attributes, the fewer are the objects to which it applies.
' As the intension of a term is increased its extension is
diminished, and vice -versa,' is the form in which the
relation is often stated. For example, let us begin
with some class-name like 'animal,' which has a great
extension, and add a new attribute, 'rational.' We get
' rational animal ' = man. This term now applies to a
much smaller number of individuals than 'animal.' The
extension of the former term has been diminished, that
is, by increasing the intenJ\i.. If we add to 'man' still
another attribute like 'vinte,' we .again lessen the num-
ber of individuals to which the term applies. In gen-
eral, then, it can be seen that the extension of a term
is lessened as it is made more definite by the addition
of new attributes. And, conversely, by stripping off
58 THE VARIOUS KINDS OF TERMS
attributes, by ' decreasing the intension,' the number
of individuals to which a term applies is increased.
There is, however, no exact ratio between the increase
or decrease of intension and the corresponding change
in extension. Indeed, the extension of a class may
increase greatly without any loss of intension on the
part of the term by which the idea is expressed. Thus
the meaning or intension of the term ' man ' has not
lost, but rather gained, during the last hundred years by
the increase of population throughout the world.
Extension and intension, according to the view just
given, represent two different uses or functions of terms.
Every term denotes some object or group of objects
more or less directly, and at the same time connotes or
signifies certain qualities or attributes. Sometimes the
one purpose, sometimes the other, is the predominant
one. Proper names, for example, are used primarily
to denote or mark out things, and do not directly
qualify or describe them. In the proposition, 'these
animals are all vertebrates,' the predicate term ' verte-
brates ' is employed less as a name of a number of
animals, than as a description of their qualities. Never-
theless, in both these cases the terms employed have the
double function of naming or denoting objects, and of
connoting qualities.
Mill, however, and certaVpother logicians who follow
him, make a distinction betftsim connotative and non-
connotative terms. " A non-connotative term is one
which signifies a subject only, or an attribute only. A
connotative term is one which denotes a subject, and
implies an attribute. By a subject is here meant any-
16. EXTENSION AND INTENSION OF TERMS 59
thing which possesses attributes. Thus ' John,' or ' Lon-
don,' or ' England ' are names which signify a subject
only. 'Whiteness,' 'length,' 'virtue,' signify an attribute
only. None of these names, therefore, are connotative.
But 'white,' 'long,' 'virtuous,' are -connotative. The
word ' white ' connotes all white things, as snow, paper,
the foam of the sea, etc., and implies or, as it was termed
by the schoolmen, connotes the attribute whiteness. . . .
All concrete general names are connotative. The word
'man,' for example, denotes Peter, James, John, and an
indefinite number of other individuals, of whom, taken
as a class, it is the name. But it is applied to them
because they possess, and to signify that they possess,
certain attributes." 1
There is no real ground, I think, for such an abso-
lute distinction between connotative and non-connota-
tive terms. When we consider the use or function of
terms, we find that they are never used merely to name
things, or merely to connote attributes, though in cer-
tain cases the former purpose is the primary one, and
in other cases the latter object is more prominent.
Even when proper names are employed, the qualities or
characteristics of the objects named are indirectly im-
plied. The very fact that a proper name is given to
an object implies that it possesses a certain definitely
marked individuality. And a proper name when used
intelligently carries with it some still more definite im-
formation regarding the qualities of the thing to which
it is applied, as, for example, whether it is a name of a
person, an animal, or a place.
1 Mill, System of Logic, Bk. I. Ch. II. 5.
6O THE VARIOUS KINDS OF TERMS
The reader may consult, in connection with this
chapter :
J. S. Mill, Logic, Bk. I. Ch. II.
F. H. Bradley, The Principles of Logic, pp. 155-173.
B. Bosanquet, Logic, Vol. I., pp. 46-71.
" " The Essentials of Logic, Lecture V.
CHAPTER V
DEFINITION AND DIVISION
17. Fixing the Meaning of Terms. --We have al-
ready referred to the necessity of definitely fixing the
meaning of the terms which we employ in reasoning.
In ordinary life, words are frequently used in a loose
and shifting way, without any clear conception of the
qualities or properties which they connote, or of the
objects to which they apply. Logic demands, in
the first place, that we shall have clear and definite
ideas corresponding to our words, and that the signifi-
cation and scope of the latter shall be carefully deter-
mined. But this is a demand to which little attention
is paid in the ordinary affairs of life. To define our
terms in explicit language, or even to make clear to
ourselves the ideas and things for which they stand, is
by no means a natural or a universal mode of proced-
ure, but something which requires a distinct, conscious
effort.
Bacon, Hobbes, Locke, Hume, and nearly all of the
older philosophical writers have warned us against the
abuse of words. The whole matter has been expressed
very clearly by Locke, from whom I quote the follow-
ing passage :
" For he that should well consider the errors and
obscurity, the mistakes and confusion, that are spread
61
62 DEFINITION AND DIVISION
in the world by an 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 amongst mankind. How
many are there, that when they would think on things
fix their thoughts only on words, especially when they
would apply their minds to moral matters ; and who
then can wonder if the result of such contemplations
and reasonings, whilst the ideas they annex to them
are very confused and very unsteady, or perhaps none
at all ; who can wonder, I say, that such thoughts and
reasonings end in nothing but obscurity and mistake,
without any clear judgment or knowledge ?
" This inconvenience in an ill use of words men suffer
in their own private meditations ; but much more
manifest are the discords which follow from it in con-
versation, discourse, and arguments with others. For
language being the great conduit whereby men convey
their discoveries, reasonings, and knowledge from one
to another; he that makes an ill use of it, though he
does not corrupt the fountains of knowledge which are
in things themselves ; yet he does, as much as in him
lies, break or stop the pipes whereby it is distributed to
the public use and advantage of mankind." l
The remedy for the obscurities and confusions of
words is to be found in clear and distinct ideas. We
must endeavour to go behind the words and realize
clearly and distinctly in consciousness the ideas for
which they stand. Now the means which logic re-
1 Essay concerning Human Understanding, Bk. III. Ch. XI.
i8. DEFINITION 63
commends for the attainment of this end is definition.
The first requirement of logical reasoning is that terms
shall be accurately defined. There are, however, two
ways in which the meaning of a term may be defined
or explained. Every term, as we have already seen
( 1 6), may be regarded either from the point of view
of intension, or from that of extension. To define in
the narrower sense is to explain from the standpoint
of intension, to state the attributes or qualities which
are connoted by the term. The process of explaining
terms with reference to the objects, or classes of objects,
for which they stand is known as Division. We may
include, then, under the general term definition, (i) In-
tensive definition, or definition in the narrower sense,
and (2) Extensive definition or division.
1 8. Definition. To define a term is to state its
connotation, or to enumerate the attributes which it
implies. Thus we define a parallelogram as a quadri-
lateral figure whose opposite sides are parallel. A
distinction is often made between verbal and real defi-
nition. When we merely wish to explain the mean-
ing in which we intend to employ some term, we have
verbal definition. But when it is the purpose of our
assertion to state the real nature or essential character-
istics of some object, the proposition employed is said
to constitute a real definition. This distinction, though
not without importance, cannot, I think, be regarded as
ultimate. For we never define a word or term for its
own sake merely, but in order to understand the nature
of the objects to which it refers. Indeed, a mere word,
64 DEFINITION AND DIVISION
apart from the things for which it stands, has no inter-
est for us. In denning a term, then, we are always
attempting to explicate or explain, more or less directly,
the nature of a thing, or our idea about a thing.
Nevertheless, there is an advantage in distinguishing
propositions whose immediate purpose is to expound
the meaning of a word, from those which assert some-
thing directly of an object. ' Monarchy consists in the
authority of one man over others,' may be regarded as
a verbal definition, because the purpose of the propo-
sition is simply to explain the meaning of the subject
term. On the other hand, ' iron is malleable ' is a real
definition (though not a complete one), because it does
not primarily refer to the signification of the word
' iron,' but to the real object to which the name is ap-
plied.
In this connection, it is interesting to notice that a proposition
which amounts to nothing more then a verbal definition, is some-
times put forward as if it were an assertion which contained some
real knowledge. The solemn commonplaces in which ignorant per-
sons delight are often of this character. ' A republic is a govern-
ment by the people, 1 ' a just man will do what is right, 1 ' if it rains,
the ground will be wet, 1 may serve as examples. The mistake in
such cases consists in supposing that these assertions are anything
more than verbal.
There are two points of view from which the subject
of definition may be considered. We might either
discuss the best method of obtaining real definitions of
the nature of things^ or might confine our attention to
the requirements which a good definition has to fulfil.
A person's ability to define either a term, or the thing
1 8. DEFINITION 65
for which the term stands, depends, however, upon the
possession of clear and distinct ideas on the subject.
The problem, then, as to the best method of finding
definitions, resolves itself into an inquiry concerning
the means to be used in obtaining and classifying our
ideas in general ; and the answer to this question, so
far as an answer can be given, must be found in the
theory of logic as a whole. In our treatment of the
subject we shall, therefore, confine our attention mainly
to a consideration of the requirements of a logical
definition, and the rules which must be observed in
stating it in language.
Before entering upon the subject, however, it is in-
teresting to refer briefly to the method proposed by
Socrates for obtaining definitions. Socrates, as we
have already seen ( 5), was the first to emphasize
the necessity of defining and fixing the meaning of
familiar terms. He found that, though the people of
Athens were constantly using terms like 'good,' 'beau-
tiful,' 'justice,' and 'temperance,' none of them, not
even those with the greatest reputation for wisdom, were
able to give any clear and consistent statement of what
these terms implied. Socrates himself did not profess
to be wiser than the rest, but he had a genuine spirit
of inquiry, and made it the business of his life to try to
arrive at clear conceptions, especially with regard to
certain fundamental ethical virtues, like justice, and
temperance, and wisdom, which he regarded as of the
utmost practical importance. It was by means of con-
versation with others that he sought to gain clear
ideas regarding the nature of these virtues. By a
r
66 DEFINITION AND DIVISION
series of questions and answers, by comparison of
any definition proposed with particular facts which are
admitted, he led his interlocutors to expose and refute
the inadequacies of their earlier statements. In the
Republic, for example, the question is regarding the
nature of justice. The first definition suggested is,
that it is just 'to speak the truth, and to restore to
each man his own.' But supposing that a man were
out of his mind and demanded his weapons which had
been placed in the hands of a friend, would the friend
be an unjust man if he refused to return the weapons,
or abstained from telling the whole truth ? Evidently
not. The definition is then modified to read, ' It is just
to give to each man what is his due.' Socrates then
questions further, What is due to each man ? What is
due to a friend, and what to an enemy ? This leads to
the further modification that 'justice means doing good
to our friends and harm to our enemies.' By referring
again to particular instances and familiar analogies,
Socrates leads the person maintaining this definition
to admit that to injure a person is to make him less
virtuous, and therefore less just. But how can justice
render the character of another less just than it was
before ? The idea is absurd ; therefore the definition
has to be abandoned, and a fresh start made.
This method of proceeding by means of question and
answer, and thus compelling a speaker to admit par-
ticular facts which refute the general thesis which he
is maintaining, is called Dialectic. This was the means
by which Socrates constantly strove to advance to consis-
tent and adequate definitions. Apart from the dialectical
1 8. DEFINITION 6/
and dramatic form which the Socratic argument took,
the method employed is essentially that of induction.
For the definition, or conception, is derived from a com-
parison of particular instances, both positive and nega-
tive. By a consideration of individual cases, Socrates
sought to obtain a definition which would be a complete
and adequate expression of the nature of all the individ-
uals which share in the class name. Aristotle says that
it is to Socrates we owe the method of induction and
logical definitions. Clear and distinct conceptions, for-
mulated in exact definitions, constituted the scientific
goal for Socrates, and the inductive procedure of ob-
serving and classifying particular instances was the
means which he employed for reaching this goal.
The second question has reference to the formulation
of a definition in language. Suppose that we already
possess a clear conception of the meaning of the terms
to be defined, what are the conditions which a logical
definition must fulfil ? The answer to this question is
usually given in logical text-books by means of a set
of rules for definition. Before stating these rules, how-
ever, it is necessary to explain the meaning of the terms
'genus,' 'species,' and 'differentia,' which will be fre-
quently employed throughout the remainder of this
chapter. These terms, together with ' property ' and
'accident,' constitute what the older logicians call the
predicables, and to which a great deal of importance
was supposed to belong. It will only be necessary,
however, for us to consider briefly the signification of
the first three terms.
68 DEFINITION AND DIVISION
In logic, any term may be regarded as a genus which
contains two or more subordinate classes or species.
A species, on the other hand, is simply a subdivision or
subordinate class of some larger whole. Thus ' metal '
is a genus with reference to iron, gold, silver, etc.,
which are its species. ' Rectilinear figure ' is the genus
to which belong the various species, triangle, quadri-
lateral, pentagon, etc. The differentia of any term is
made up of the qualities or characteristics which dis-
tinguish it from other terms, from the genus to which
it belongs, as well as from the species which are co-
ordinate with it. Thus the logical differentia of a
triangle, is the property of having three sides, the dif-
ferentia of man, is that which distinguishes him from
other animals, whether this be the power of speech and
reason, or some other characteristic either physical or
mental.
The use of the terms 'genus' and 'species' in logic is
entirely relative. That is, any term may be considered
either as a species or a genus, according as it is regarded
as forming a part of some more comprehensive class, or
as itself including other classes. Thus man, for example,
is a species of the genus ' animal ' ; but the same term
also may be regarded as a genus including various species
of men, Caucasians, Negroes, Mongolians, etc. In the
same way, ' animal ' may be considered a species of the
still more comprehensive class 'organized being,' and
this latter term again as a species of the genus ' material
being.' A still higher or more comprehensive term
which includes as its species material and spiritual
beings alike is 'being.' Since this term includes every-
i8. DEFINITION 69
thing which exists, and can therefore never be included
in any more ' general class, it is sometimes called the
highest genus ' (summum genus}. On the other hand,
we might proceed downwards until we come to a class
which did not admit of division into any subordinate
classes. Such -a term is called in logic the lowest
species (infima species}.
It is important to notice that the terms ' genus ' and ' species ' have
not the same signification in logic as in the natural sciences. In
classifying objects in natural history, we use the terms 'variety,'
' species, ' genus, 1 ' family,' and ' order,' to denote varying degrees of
relationship between certain groups or classes of objects. These
terms, as thus employed, also indicate certain relatively fixed divi-
sions, or permanent ways of grouping the various forms of plant and
animal life. But in logic the terms ' genus' and 'species' are em-
ployed to indicate the relationship between any higher and lower
class whatsoever. Moreover, as we have seen, any term (excepting
only the highest genus and the lowest species) may be regarded
from different standpoints, as either a genus or a species.
We shall now proceed to state the requirements of a
logical definition :
(l) A definition should state the essential attributes
of the thing to be defined. This is done by stating the
genus to which the object belongs, and also the pecul-
iar marks or qualities by means of which it is distin-
guished from other members of the same class. Or
as the rule is usually stated : A logical definition
should give the next or proximate genus, and the dif-
ferentia of the species to be defined. Thus we define
a triangle as a rectilinear figure (genus), having three
sides (differentia) ; and man as an animal (genus), which
has the power of speech and reason (differentia).
70 DEFINITION AND DIVISION
(2) A definition should not contain the name to be
defined, nor any word which is directly synonymous with
it. If, for example, we were to define justice as the
way of acting justly, or life as the sum of vital pro-
cesses, we should be guilty of a violation of this rule.
(3) The definition should be exactly equivalent to the
class of objects defined, that is, it must be neither too
broad nor too narrow. In other words, the definition
must take account of the whole class and nothing but
the class. ' A sensation is an elementary state of con-
sciousness,' for example, is too broad a definition, since
it applies equally to affective and conative elementary
processes. On the other hand, the definition of gov-
ernment as 'an institution created by the people for
the protection of their lives and liberties,' is too nar-
row. For it takes no account of absolute forms of
government which do not depend upon the will of the
people. Both of these cases may be regarded as a
failure to give the true differentia of the class to be
defined, and hence as violations of the first rule.
(4) A definition should not be expressed in obscure,
figurative, or ambiguous language. The reasons for
this rule are at once evident. Any lack of clearness
or definiteness in a definition renders it useless as an
explanation. Sometimes the words used in defining
may be less familiar than the term to be explained
(ignotum per ignotius\ The definition which was once
given of the word 'net' as 'a reticulated texture with
large interstices or meshes,' may serve as an example.
(5) A definition should, whenever possible, be affirma-
tive rather than negative. A definition, that is, should
19. DIVISION 71
state what a term implies rather than what it does not
imply. Sometimes, however, the purpose of a defini-
tion may be best attained by a negative statement of
what is excluded by the meaning of the term. Thus,
for example, we may define a spiritual being as a being
which is not material, that is, unlike a material body
made up of parts extended in space.
A logical definition, as has been said, requires us to mention the
proximate genus or next higher class to which the species to be defined
belongs, and also the specific or characteristic differences which dis-
tinguish it from other species. Now it is clear that there are certain
cases in which these conditions cannot be fulfilled. In the first
place, no logical definition can be given of the highest genus, be-
cause there is no more general class to which it can be referred.
And again, although it is possible to give the differentia of any
species such as ' man ' or ' metal,' it is not possible to state indi-
vidual characteristics by means of a logical definition. An indi-
vidual thing may be perceived, and its various properties pointed
out. But it is never possible to state in a logical definition wherein
the individuality of a particular thing consists. The uniqueness of
a particular object cannot be summed up in a -general definition, but
must be learned through perception. We may perhaps say that the
highest genus is above, and the individual thing below, the sphere of
logical definition.
There are, moreover, other terms such as 'space,' 'time, 1 'life,'
'thought,' which are not readily referred to any higher class, and
for which therefore logical definitions cannot be given. These
terms are sometimes said to denote objects which are sui generis,
or of their own class.
19. Division. We have already spoken of divi-
sion as a process of defining a term from the point of
view of extension. This is to enumerate the objects
or classes of objects which the term denotes. This
72 DEFINITION AND DIVISION
enumeration must, however, be guided by certain prin
ciples which we have now to consider.
It is usual to begin this subject by speaking of Di-
chotomy, or the division of a term into two parts (S/%a
re/jiveiv, to cut in two). This is a purely formal process,
and is based on the so-called law of Excluded Middle,
which is regarded as one of the fundamental laws of
thought. This law may be stated as follows: There
is no middle ground between contradictories. Any term,
a, is either b or not-. A triangle is either equilateral or
not-equilateral. Of two contradictory predicates, one or
the other must belong to every possible subject.
Now it is clear that this is a purely formal principle
of division. Some positive knowledge of the particular
facts involved is always necessary, in order to enable
one to determine what things do stand in this relation
of logical opposition. The logical law, in other words,
does not help us at all in deciding what may be re-
garded as not-a in any particular case. It is not, there-
fore, a means of increasing our knowledge, but merely
a principle of order and arrangement. This fact, obvi-
ous as it seems, was not understood by the Schoolmen
who busied themselves with logic in the latter part of
the Middle Ages. They clung firmly to the belief that
it was possible to discover the nature of particular facts
by purely formal operations of this kind. Accordingly,
they spent a great deal of time in classifying and arrang-
ing terms as contradictions, contraries, etc. This work
was doubtless of much service in fixing the meaning of
terms, and in preventing confusion in their employment.
But it was a purely verbal investigation, and of course
ig. DIVISION 73
could not lead to any discoveries regarding the nature
of things.
Moreover, it must be noticed that we do not always
get propositions to which any meaning can be attached
by uniting subjects and predicates in this way. If the
law of Dichotomy is not guided by knowledge of the
particular facts, it will give absurd propositions like,
'virtue is either square or not-square/ 'iron is either
pious or not-pious.' Unmeaning propositions of this
kind being left out of account, however, we may proceed
to divide everything according to this principle. All
geometrical figures are either rectilinear or not-rec-
tilinear ; all rectilinear figures either triangular or not-
triangular ; all triangles, equilateral or not-equilateral, etc.
This method of division may be represented thus :
Substance
Material non-material
I
r^ j
Organic not-organic
I I
mineral not-mineral
gold not-gold
If it were desirable, the terms 'non-material,' 'organic,'
and 'not-mineral' might also be further subdivided in
the same way.
Now it is not difficult to see that the practical use of
this principle will depend upon our ability to find some
positive value for the negative not-a. That is, to make
the law of more than formal value, we must know what
74 DEFINITION AND DIVISION
concrete term excludes a, or is its logical contradictory.
And knowledge of this kind comes, as already said, only
from experience of the particular facts. The strictly
logical contradictory of a is always not-a ; of wise, not-
wise, of cold, not-cold, etc. Mistakes frequently arise in
stating contradictories in a positive form. The difficulty
is that terms are chosen which are not true logical con-
tradictories. Thus, if we say that every man is either
wise or foolish, our terms are not contradictory, for a
middle ground between them is possible. The same
would be true of divisions like, 'large or small,' 'rich or
poor,' 'saint or sinner,' 'idle or diligent.' In general,
it is safe to scrutinize all dichotomic divisions very
sharply to see that the alternatives are really contra-
dictories.
The method of dichotomy depends, as we have seen,
upon the law of Excluded Middle. But there is also
another process called Division in logic, which is per-
haps better known by its less technical name of Classi-
fication. In classification, there is no necessary limit
to the number of classes or divisions which may be ob-
tained. In this respect, it of course differs fundamentally
from the twofold division which we have been exam-
ining. Furthermore, a classification is always made
according to some principle which is retained through-
out the whole process. Any common characteristic of
the group of individuals to be divided may be taken as a
principle of classification. If, however, the characteristic
chosen is merely an external and accidental one, the
classification based upon it will be regarded as artificial,
and made for some special or temporary purposes,
19- DIVISION 75
Thus we might divide all flowering plants according to
the color of the flowers, or the persons in any company
according to the pattern of their shoes. A classification
which proceeds upon such surface distinctions has, of
course, no real or scientific value. It does not attempt
to discover fundamental or deep-lying resemblances be-
tween the individuals with which it deals.
A scientific or natural classification, on the other hand,
has for its purpose the discovery of real likeness or resem-
blance. It seeks to find and group together, the things
which are related in some essential point. Consequently,
it selects as its principle of division some property which
appears to be a real mark of individuality, and to be
connected with changes in other properties. Such a
real principle of natural classification is rarely found
by comparison of merely one property or set of prop-
erties in the things to be compared. To classify accord-
ing to a single property may be a convenient method
of giving names to any group of individuals, and of
arranging them in such a way as to be useful to the
student. It does not, however, give any adequate idea
of the properties and true relations of the individuals
compared. A really scientific, or natural, classification
must be based upon a study and comparison of all
the discoverable properties of the different individuals
to be classified. It is only in this way that their real
resemblance and affinities can be brought to light.
(i) The classification of plants proposed by the famous Swedish
botanist, Karl Linnaeus (1707-1778), was based upon the comparison
of a single feature : the structure of the sexual organs of plants. This
method proved of the greatest convenience in indexing plants in a
76 DEFINITION AND DIVISION
convenient way into genera and species so that they could be named
and described. Yet since the classification adopted was based upon
a single property or feature of the plant, it was considered (even by
Linnaeus himself) as merely artificial. Of course it is not so obvi-
ously artificial as the examples of what we may perhaps call merely
accidental or trivial classification given above. But Linnnsus's
system did not aim at setting forth the true relations of plants, and it
was not based upon any systematic study of all their properties. It
is useful merely as a stepping-stone to the real study of plants which
is presupposed in natural classification.
Certain rules for division are usually given in con-
nection with the treatment of this subject. It is not,
of course, supposed that by their help one can properly
divide any subject without special knowledge. The
purpose of these rules is rather to warn against the
logical errors to which one is most liable in the process
of division.
(1) Every division is made on the ground of differ-
ences in some attribute (or attributes) common to all
the members of the whole to be divided.
(2) Every division must be based on a single prin-
ciple or ground (fundamentum divisionis).
(3) The constituent species (or groups into which the
whole is divided) must not overlap, but must be mutually
exclusive.
(4) The division must be exhaustive, i.e., the con-
stituent species must be equal, when added together,
to the genus.
The first rule requires no remark. It simply states
that it is only possible to divide any whole on the basis
of differences in something which is common to all its
parts. The second rule warns against changing the
i 9 . DIVISION 77
principle of division while the process is being carried
out. This law would be violated, if, for example, one
were to divide mankind into Caucasians, Negroes, Mon-
golians, Europeans, Australians, and Americans. The
principle of division which was first adopted in this
example was obviously that of the color of the skin.
But this principle was not carried through, and another
principle, that of geographical distribution, was substi-
tuted for it. In dividing one must be clearly conscious
of the principle which one is using, and keep a firm
hold of it until the division is completed. The example
which we have just given also violates the third rule.
For not all of the groups, European, Caucasian, etc.,
exclude one another. Similarly, it would not be good
logic to divide animals into vertebrates, mammals, in-
sects, birds, molluscs, and fishes. The fourth rule
simply insists that the division must be complete. The
whole must be completely included in its divisions. It
would not be a complete division to say that books may
be divided into folios, quartos, and duodecimos ; or
vertebrates into mammals and birds. For in neither
of these examples are the divisions enumerated equal
to the whole class.
References
J. S. Mill, Logic, Bk. I. Chs. VII. and VIII.
W. Minto, Logic Inductive and Deductive, Pt. II. pp. 82-130.
C. Sigwart, Logic, Vol. I. 42-44.
J. H. Hyslop, The Elements of Logic, Ch. VI.
CHAPTER VI
PROPOSITIONS
20. The Nature of a Proposition. A proposition is
the expression in words of an act of judgment. It is
composed, as we have already seen, of two terms, a
subject and a predicate, connected by a copula. From
the point of view of formal logic the predicate is affirmed
(or denied) of the subject. When we come to consider
the nature of judgment (cf. especially 74, 77), we
shall find reasons for questioning whether this analy-
sis of the proposition can be taken as furnishing a cor-
rect account of what actually takes place in judgment.
When we judge, we do not begin with words or terms
which are not yet judgments, and then pass on to judg-
ment by joining together the former in an external way.
The conclusions which we shall have to adopt are, that
terms represent ways of judging, that the simplest
act of thought is already a judgment, and that thinking
develops by advancing from incomplete to more com-
plete and comprehensive judgments. The theory of
the syllogism is, however, worked out on the view of
the proposition already indicated. This is sufficiently
accurate for practical purposes, and is not likely to
lead to any serious mistakes so long as we remember
that it is the proposition, rather than the actual nature
of judgment, with which we are dealing.
78
20. THE NATURE OF A PROPOSITION 79
The logical proposition, as the expression of an act of
thought, corresponds to the grammatical sentence. Not
every sentence, however, is a logical proposition. Sen-
tences which express a wish or an interrogation do not
directly enter into the process of argument at all, and
may therefore be neglected for the present The same is
true of exclamatory sentences. Again, even indicative
sentences frequently require to be rewritten in order to
reduce them to the form of a logical proposition, which
demands two terms and a copula. The sentence, ' the
sun shines,' must, therefore, for purposes of logical
treatment, be reduced to, 'the sun is a body which
shines.' ' On the hillside deep lies the snow ' is ex-
pressed as a logical proposition in some such form as
this : ' The snow is a covering lying deep on the hill-
side.' It is very important to change the grammatical
sentence to the regular form of a proposition before
attempting to treat it logically.
The most general division of propositions is that
which classifies them as Categorical and Conditional. A
categorical proposition asserts directly, and without any
condition. The predicate is either affirmed or de-
nied unconditionally of the subject. 'A is B,' 'this
room is not cold,' ' New York is the largest city in
America,' are examples of categorical propositions.
Conditional propositions, on the other hand, make a
statement which is not immediately and directly true>
but only claims to be true under a condition ; as, e.g.,
'we shall go to-morrow, if it does not rain.' 'It will
either rain or snow to-morrow,' is also a conditional prop-
osition ; for neither rain nor snow are asserted directly
80 PROPOSITIONS
and absolutely, but in each case the appearance of the
one is dependent upon the non-appearance of the other.
The first of these conditional propositions is known as
a Hypothetical, and the latter as a Disjunctive proposi-
tion ; but for the present we shall deal only with cate-
gorical propositions, and with the form of syllogistic
argument to which they give rise. After we have com-
pleted the account of the categorical syllogism, however,
it will be necessary to return to a consideration of
conditional propositions, and to the class of arguments
in which they are employed.
21. The Quality and Quantity of Propositions. We
shall now consider the various kinds of categorical prop-
ositions. Such propositions are classified with regard to
quality and quantity. From the standpoint of quality,
propositions are either affirmative or negative. An
affirmative proposition is one in which an agreement is
affirmed between the subject and predicate, or in which
the predicate is asserted of the subject. The proposi-
tion, ' snow is white,' for example, indicates such an
agreement between the subject and predicate, and is
therefore affirmative in quality. A negative proposition
indicates a lack of agreement or harmony between the
subject and predicate. The predicate does not belong
to the subject, but all relation or connection between the
two is denied. 'The room is not cold,' 'the trees are not
yet in full leaf,' are examples of negative propositions.
The quantity of a proposition is determined by the
extension of the subject. When the proposition refers
to all of the individuals denoted by the subject, it is said
21. THE QUALITY AND QUANTITY OF PROPOSITIONS 8 1
to be universal in quantity. When, on the other hand,
the proposition affirms that the predicate belongs only
to a part of the subject, it is said to be particular. For
example, ' all metals are elements ' is a universal propo-
sition, because the assertion is made of the subject in
its widest or fullest extent ; ' some metals are white ' is
a particular proposition, because reference is made to
only a part of the subject 'metal.'
We divide propositions, then, with regard to quantity,
into Universal and Particular propositions. Universal
propositions are often indicated by adjectives like 'all,'
' the whole,' ' every,' etc. It frequently happens, how-
ever, that no such mark of universality is present. A
scientific law is usually stated without any explicit
statement of its quantity, though from its very nature it
is meant to be universal. Thus we say, 'the planets
revolve around the sun,'' 'comets are subject to the law
of gravitation.' Propositions which have a singular or
an individual name as subject are often called Individual
propositions, as, e.g., 'the earth is a planet,' 'knowledge
is power.' But since it is impossible to limit a singular
subject, individual propositions are to be regarded as
universal. They belong, that is, to the class of propo-
sitions which employ the subject term in its complete
extent.
Another class, called Indefinite or Indesignate propo-
sitions, has sometimes been proposed. This class is
usually said to include propositions in which the form
of the words does not give any indication whether the
predicate is used of the whole, or only of a part of the
Subject.- ' Men are to be trusted,' ' animals are capable
o2 PROPOSITIONS
of self-movement,' may serve as examples. This classi-
fication may be useful in illustrating the evil of making
indefinite or ambiguous statements. Otherwise there
is nothing to be learned from it. A really indefinite
proposition has no place in an argument, and logic
rightfully refuses to deal with it. The first demand of
logic is that our statements shall be clear and precise.
A proposition is not necessarily indefinite, however,
because it has no qualifying words like 'all' or 'some.'
It is the meaning of a proposition as a whole, rather
than the form of its subject, which renders it definite
or indefinite. Where, on the other hand, it is really im-
possible to decide whether the proposition is universal
or particular, logic forbids us to proceed with the
argument until this point has been made clear.
Particular propositions are usually preceded by some
word or phrase which shows that the subject is limited
in the extent of its application. The logical sign of
particular propositions is 'some,' but other qualifying
words and phrases, such as 'the greatest part,' 'nearly
all/ ' several,' ' a small number,' etc., also indicate par-
ticularity. Here again, however, it is the meaning of
the proposition, rather than its form, which is to be
considered. ' All metals are not white,' for example, is
a particular proposition, although introduced by 'all,'
since it is clearly equivalent to 'some metals are not
white.' 'Every mark of weakness is not a disgrace,'
again, is a particular proposition, and signifies that ' not
all, or some marks of weakness are not disgraceful.'
The words ' few ' and ' a few ' require special atten-
tion. The latter, as in the proposition, ' a few persons
22. DIFFICULTIES IN CLASSIFICATION 83
have spoken to me about it,' is equivalent to 'some,'
and introduces a particular affirmative proposition.
' Few,' on the other hand, is negative in character.
Thus, ' few were saved from the shipwreck ' implies that
only a few were saved, or that the greater number did
not escape, and the proposition is therefore to be con-
sidered as a particular negative. Propositions, then,
are classified as affirmative and negative in Quality,
universal and particular in Quantity. When these classi-
fications are combined, we get four kinds of propositions,
to symbolize which the vowels A, E, I, O are employed.
A and I, the vowels contained in affirmo, stand for
affirmative propositions ; E and O, the vowels in nego,
for negative propositions. This may be represented as
follows :
Affirmative: All S is P A
Negative: No S is P. E
Affirmative : Some S is P. I
Negative : Some S is not P. O
We shall henceforth use A, E, I, and O to represent
respectively a universal affirmative, a universal negative,
a particular affirmative, and a particular negative propo-
sition. In dealing with propositions logically, the first
step is to reduce them to one or other of these four
types. This can be accomplished readily by noticing
the distinctions previously laid down. There are, how-
ever, certain grammatical forms and sentences which
present some difficulty, and it may therefore be useful
to consider them separately.
22. Difficulties in Classification. In the first place,
we may notice that in ordinary language the terms
Universal <
Particular <
84 PROPOSITIONS
of a proposition are frequently inverted, or its parts
separated in such a way that it requires attention to
determine its true logical order. In the proposition,
'now came still evening on,' for example, the subject
' still evening ' stands between two portions of the
predicate. As a logical proposition, the sentence would
have to be expressed in some such form as the follow-
ing : ' Still evening is the time which now came on.'
Similarly, we should have to write an inverted sentence
like, ' deep lies the snow on the mountain/ as ' the snow
is something which lies deep on the mountain.'
If a subject is qualified by a relative clause, the verb
of the latter must not be confused with the main asser-
tion of the proposition. Take the sentence, ' he is brave
who conquers his passions.' Here it is evident that the
relative clause describes or qualifies ' he.' Logically,
then, the proposition is of the form A, and is to be
written, ' he who conquers his passions is brave.' The
reader will notice that all propositions which begin with
pronouns like 'he who,' 'whoever,' etc., are universal
in quantity, since they mean all who belong to the
class in question.
(i) We have reduced grammatical sentences to logical propo-
sitions by changing the form in such a way as to have two terms
united by ' is ' or ' are ' as the copula. Such a proposition, however,
does not express time, but simply the relation existing between
subject and predicate. When the grammatical sentence does
involve a reference to time, and especially to past or future time,
the reduction to logical form is somewhat awkward. Perhaps the
best method is to throw the verb expressing time into the predi-
cate. Thus 'the steamer will sail to-morrow' = 'the steamer is
a vessel which will sail to-morrow ' ; ' we waited for you two hours
23. RELATION OF SUBJECT AND PREDICATE 85
yesterday ' = ' we are persons who waited for you two hours yes-
terday.'
(2) Exclusive propositions exclude all individuals or classes
except those mentioned by the use of some such word as ' except,'
' none but,' ' only.' ' None but the guilty fear the judge ' ; ' only
citizens can hold property'; 'no admittance except on business.'
These propositions may all be reduced to the form E by writing
'no' before the negative si the subject term. Thus 'none but the
guilty fear the judge ' = <<? one who is not guilty fears the judge ' ;
' only citizens can hold property ' = ' no one who is not a citizen,
etc ' ; ' no admittance except on business ' = '#<? person who has not
business is to be admitted. 1
23. Formal Relation of Subject and Predicate. We
have now to consider how the relation existing between
the terms of a proposition is to be understood. In 16
it was shown that every term may be interpreted in two
ways : either from the point of view of extension, or
from that of intension. Extensively, terms are taken
to represent objects or classes of objects ; while their
meaning in intension has reference to the attributes
or qualities of things. Now the interpretation of the
categorical proposition given by formal logic is based
entirely on extension. That is, the subject and predi-
cate are regarded as standing for individual objects
or classes of objects. The question to be considered,
then, concerns the extensive relation of these groups of
objects in the propositions A, E, I, and O.
This mode of interpreting propositions must not be
taken as furnishing an adequate theory of the nature of
the act of judgment which is expressed in the proposi-
tion. It leaves entirely out of account, as we have
seen, the connection of attributes asserted by the propo-
86 PROPOSITIONS
sition, which in many cases is the most prominent
part of its signification. Thus the proposition, 'all
metals are elements,' implies that the quality of being
an element is united with the other qualities connoted
by the term ' metal.' Indeed, this interpretation is
perhaps more natural than the one given by formal
logic, namely, that the class of metals is included in
the class of elements. It must be admitted that the
extensive way of reading propositions, as affirming or
denying the inclusion of one class of objects in another
class, frequently seems artificial. Nevertheless, it is
the view upon which the historical account of the
syllogism is founded. And the fact that this mode of
representing the meaning of propositions leads in
practice to correct conclusions, proves that it is not
wholly false. It represents, as we have seen, one side
or aspect of the meaning of propositions.
From the point of view of formal logic, then, a logical
proposition signifies that a certain relation exists be-
tween the class of things denoted by the subject, and
that denoted by the predicate. This relation may be
one of inclusion or of exclusion. For example, the prop-
osition ' all good men are charitable ' is interpreted to
mean that ' good men ' are included in the class of
'charitable men.' On the other hand, 'no birds are
mammals,' signifies that the two classes, 'birds' and
'mammals,' are mutually exclusive. The meanings of
the four logical propositions A, E, I, and O may be
represented by means of a series of diagrams, which
were first used by the celebrated German mathematician
Euler, who lived in the eighteenth century.
23. RELATION OF SUBJECT AND PREDICATE 87
To represent the meaning of a proposition in A, like
'all good men are charitable,' we draw a circle to sym-
bolize the class of charitable beings, and then place
inside it a smaller circle to stand for men. The propo-
sition, that is, signifies that ' good men ' are included in
the class of 'charitable beings.' The subject belongs
to, or falls within, the larger class of objects represented
by the predicate.
FIG. i.
/
It must be carefully noted that proposition A does
not usually assert anything of the whole of its predicate.
In the example just given, no assertion is made regard-
ing the whole class of ' charitable beings,' but only in so
far as they are identical with ' good men.' There may
possibly be other charitable beings who are not good
men, or not men at all. The meaning of the proposition,
then, is that ' all good men are some charitable beings.'
In other words, the predicate of the ordinary universal
affirmative^ proposition is taken only in a partial, or
limited extent : nothing is affirmed of the whole of the
circle of charitable beings. We denote this fact by
saying that the predicate of proposition A is undis*
88 PROPOSITIONS
tributed. The subject, on the other hand, as a universal
term, is employed in its fullest extent, or is distributed.
In some cases, however, the predicate is not a broader
term which includes the subject, but the two are equal
in extent. In the proposition, ' all equilateral triangles
are equiangular,' for example, this is the case. If we
were to represent this proposition graphically, the circle
of equilateral triangles would not fall inside that of
equilateral triangles, but would coincide with it. The
same relation between subject and predicate holds in
the case of logical definitions. For example, in the
definition, ' monarchy is a form of political government
where one man is sovereign,' the subject is coextensive
with the whole of the predicate. In examples of this
kind, it is of course obvious that the predicate, as well
as the subject, is distributed.
As an example of proposition E, we may take the
example, 'no birds are mammals.' The meaning of
this proposition is represented graphically by means
of two circles falling outside each other as in Fig. 2.
FIG. 2.
The proposition asserts that the class of birds falls
completely without the class of mammals, that the two
classes are entirely distinct, and mutually exclusive.
23. RELATION OF SUBJECT AND PREDICATE 89
With regard to quantity, the subject is of course uni-
versal or distributed. And, in this case, the predicate is
also distributed. For the proposition asserts that the
subject ' birds ' does not agree with any part of ' mam-
mals.' Or, in terms of the diagram, we deny that the
circle representing 'birds' corresponds with any portion
of the circle 'mammals.' But to exclude the former circle
completely from the circle which represents ' mammals,'
it is necessary that we know the whole extent of the
latter. Otherwise we could not be sure that the sub-
ject had not some point in common with it. Proposition
E, therefore, distributes, or uses in their widest extent,
both subject and predicate.
FIG. 3.
The meaning of a proposition in I, as, e.g., 'some
birds are web-footed,' is shown by means of two circles
intersecting or overlapping as in Fig. 3. A part of the
class of birds corresponds with a part of web-footed
animals. The proposition has reference to the common
segment of the two circles, which may be large or small.
The two circles correspond in part at least. In proposi-
tion I, both subject and predicate are undistributed. The
90 PROPOSITIONS
subject is, of course, a particular or limited term. And,
as will be clear from what has already been said in the
case of proposition A, reference is made to only a
limited portion of the predicate. In the example used,
the assertion refers only to those web-footed animals
which are also birds. Or we may say that the proposi-
tion has reference only to the common segment of the
circles representing subject and predicate. Nothing is
asserted of the other portions of the two circles. In
other words, both subject and predicate are employed
in a limited extent, or are undistributed.
' Some metals are not white,' may serve as an example
of proposition O.
FIG. 4.
This proposition may be represented graphically as
in Fig. 4. Though this is the same form of diagram
as that employed in the last figure, the proposition
refers now to the outlying part of the circle 'metals.'
Some metals, it asserts, do not fall within the sphere of
white substances. A larger or smaller section of the
circle representing the former term, falls completely
without the circle of white substances.
23. RELATION OF SUBJECT AND PREDICATE 91
It is necessary to notice carefully that although the
subject of O is undistributed, its predicate is distributed.
For, as we have seen, a part of the subject is completely
excluded from the class of 'white substances.' But in
order to exclude from every part of the predicate, the
full extent of the predicate must be known. Or, in
terms of the diagram, the proposition excludes a portion
of the circle of metals (some metals) from each and
every part of the circle of white things. The latter
term must therefore be used in its full extent, or be
distributed.
It is absolutely necessary, in order to comprehend
what follows, to understand the distribution of terms
in the various propositions. It may help the reader to
remember this if we summarize our results in the follow-
ing way :
Proposition A, subject distributed, predicate undistributed.
Proposition E, subject distributed, predicate distributed.
Proposition I, subject undistributed, predicate undistributed.
Proposition O, subject undistributed, predicate distributed.
References to 23
W. S. Jevons, Elementary Lessons in Logic, pp. 71-75.
J. S. Mill, Logic, Bk. I. Ch. V.
C Sigwart, Logic, 5.
B. Bosanquet, The Essentials of Logic, Lectures V. and VI,
CHAPTER VII
THE INTERPRETATION OF PROPOSITIONS
24. The So-called Process of Immediate Inference. -
Many logicians speak of two kinds, or processes of reason-
ing, to which they give the names of mediate, and imme-
diate inference. Mediate inference, it is said, asserts
the agreement or disagreement of a subject and predi-
cate after having compared each with some common
element or middle term. The conclusion is thus reached
mediately or indirectly. The syllogism is the best
example of mediate inference. In the syllogism,
All M is P,
All S is M,
Therefore S is P,
the conclusion is reached through the medium of M,
with which both S and P have been compared. It will
be noticed that to obtaii? a conclusion in this way two
propositions or premises are necessary.
We sometimes are able, however, to pass directly
or immediately from one proposition to another. For
example, the proposition that 'no men are infallible,'
warrants the statement that ' no infallible beings are
men.' Or, if we know that it is true that ' some birds are
web-footed,' we perceive at once that the proposition,
' no birds are web-footed,' is false. It is this process of
passing directly from one proposition to another which
has been named by many logicians immediate inference.
92
24. PROCESS OF IMMEDIATE INFERENCE 93
Can we be properly said to infer at all when we pass
from one proposition to another, as in the above ex-
amples ? As we have already shown, inference is a pro-
cess of exhibiting the relation of facts to one another by
discovering some common element, or connecting prin-
ciple by means of which they are united (cf. also 87).
Wherever we can discover a connecting thread, or com-
mon element between two facts or groups of facts, we
are able to infer with greater or less certainty from the
nature of the one what the nature of the other must be.
But it is essential to inference that there shall be a real
transition from one fact to another that the conclu-
sion reached shall be different from the starting-point.
The point at issue, therefore, is whether a new fact
or truth is reached in the so-called processes of imme-
diate inferences, or whether we have the same fact
repeated in the form of a new proposition. When we
pass from ' no men are infallible,' to ' no infallible beings
are men,' can we be said to infer a new truth ? In this
case it is evident, I think, that there has been no real
development or extension of the original proposition
so as to include a new fact. The new proposition is the
result of a verbal interpretation of the original one, and
restates the same fact in a different way. Inference
always completes or enlarges the truth from which it
sets out by showing the reasons which support it, or the
consequences which follow from it. But when we pass
directly from one proposition to another, as in the exam-
ples given above, it will be found, I believe, that nothing
has really been added to the original statement no new
facts have been brought into connection in the process.
94 THE INTERPRETATION OF PROPOSITIONS
It is of course true that the claims of each of the
different types of so-called immediate inference should
be examined separately. But it will be found, I think,
that the conclusion which we have reached is equally
true of all of the forms to which this name is applied.
It seems better to regard these processes as acts of
verbal interpretation, or explication of the meaning of
propositions, rather than as inferences in the true sense
of the word. They render important service in helping
us to understand what is implied or involved in the
propositions we use, but they do not lead the mind on
to any new truth. We may consider three ways in
which propositions may be transformed as a result of
the interpretative process Opposition, Obversion, and
Conversion.
25. The Opposition of Propositions. We have seen
that all categorical propositions have to be reduced to
one of the four forms, A, E, I, O, in order to be dealt
with by logic. Now, when these propositions have the
same subject and predicate, certain relations exist be-
tween them, to which the general name of Opposition
has been given. It is clear that the truth of some of
these propositions interferes with the truth of others.
Thus if it be true that 'no professional gamblers are
honest,' it is impossible that ' all professional gamblers
are honest,' or even that some are honest. The propo-
sition E is thus inconsistent with both A and I. Again,
if it be false that ' all politicians are dishonest,' it must be
true that ' some politicians are not dishonest,' though it
by no means follows that ' no politicians are dishonest'
25. THE OPPOSITION OF PROPOSITIONS
95
That is, when A is false, O is necessarily true, while E
may or may not be true. Propositions A and E are
called contrary propositions. 'All A is B,' and 'no A
is B,' express the greatest possible degree of contrariety
or opposition. If one proposition be true, the other is
necessarily false. It is to be noticed, however, that we
cannot conclude that if one is false, the other is true.
For both A and E may be false. Thus, for example,
the propositions, 'all men are wise,' and 'no men are
wise,' are both false. But, on the other hand, proposi-
tions A and O, E and I, are pairs of contradictory prop-
ositions : if one is false, its contradictory is necessarily
true ; and if one is true, the other is manifestly false.
The relation of the four logical propositions is clearly
shown by arranging them in the following way :
&s^ ./-v^^A* > i-^'cttu^ J r\3\ / V*^%M -6-<
A Contraries
Sub-Contraries
FIG. 5.
96 THE INTERPRETATION OF PROPOSITIONS
A and E are known as contraries ; I and O as sub*
contraries ; A and O, I and E, as contradictories ; A
and I, E and O, are subalterns.
The relations of these propositions may now be
summed up in the following statements :
(1) Of contrary propositions, one is false if the other
is true, but both may be false.
(2) Of contradictory propositions, one is true and the
other necessarily false.
(3) If a universal proposition is true, the particular
which stands under it is also true ; but if the universal
is false, the particular may or may not be true.
(4) If a particular proposition is true, the correspond-
ing universal may or may not be true ; but if the par-
ticular is false, the universal must be false.
(5) Subcontrary propositions may both be true; but
if one is false, the other is necessarily true.
The knowledge that any one of these propositions is
either true or false enables us to determine the truth or
falsity of at least some of the others.
For example, if A is true, E is false, O is false, and
I is true. If A is false, E is doubtful, O is true, and
I doubtful.
If I is true, E is false, A is doubtful, and O doubtful.
If I is false, E is true, A is false, and O true.
Similarly we are also able to determine what follows
when we suppose that E and O are either false or true.
It ought to be carefully noted that when we affirm the truth of
the particular proposition I, we do not deny the truth of the universal
proposition A. The proposition, 'some students are fond of recre-
ation,' for example, does not exclude the truth of ' all students are
25. THE OPPOSITION OF PROPOSITIONS 97
fond of recreation. 1 Similarly, the truth of O does not exclude the
corresponding proposition in E : the statement, 'some men are not
generous,' for example, does not interfere with the truth of the uni-
versal proposition, ' no men are generous.' A particular proposition,
in other words, asserts something of a limited part of a subject ;
it neither affirms nor denies anything of the same term taken
universally.
The reader will remember that propositions which
have the name of some singular or individual thing as
subject, have been classified as universal. ' New York
is the largest city in America,' ' charity is not the only
virtue,' are examples of such propositions. Now it is at
once evident that in cases of this kind there are no cor-
responding particular propositions. What has just been
said regarding the relation of universal and particular
propositions, applies therefore only to propositions which
have a general term or name as subject. Moreover,
we must notice that when A and E propositions have
a singular or individual name as subject, the relations
between them are somewhat different from those just
stated. A and E, we said, are contrary, but not contra-
dictory propositions. By that it was implied that al-
though we can proceed from the truth of the one to the
falsity of the other, it is not possible to go in a converse
direction, from falsity to truth. We cannot conclude,
for example, from the falsity of the proposition that
' all men are selfish ' the truth of the corresponding
negative proposition, 'no men are selfish.' 'With contra-
dictory propositions, however, we can go from a denial
to an affirmation. Now the point to be observed, with
regard to propositions with a singular term as subject,
98 THE INTERPRETATION OF PROPOSITIONS
is that although only contraries in form, they have yet
the force of contradictories. ' Socrates is wise ' (A),
and ' Socrates is not wise ' (E), are contradictory as well
as contrary, propositions.
26. The Obversion of Propositions. The terms ' Ob-
version ' and '^Equipollence ' were formerly used to
denote any process by which the form of a proposition
is changed without an alteration in meaning being
involved. The name ' Obversion ' is, however, now gen-
erally employed to describe the change which a propo-
sition undergoes in passing from the affirmative to the
negative, or from the negative to the affirmative form
while still retaining its original meaning.
Every fact is capable of expression either in the form
of an affirmative or of a negative proposition. Whether
the affirmative or negative form is chosen in any par-
ticular case, is partly a matter of convenience. It is
also determined largely by the psychological interest of
the moment, i.e., by the purpose which we have in view
in making the assertion. When, for example, we wish
to repel some suggestion which may have occurred to
us, or to deny something which our companions appear
to believe, we naturally choose the negative form of
statement. But the meaning of the proposition is the
same whether we say, ' all men are fallible,' or, ' no men
are infallible.' Similarly, we can say, 'not one of the
crew escaped,' or, 'all of the crew perished.'
Obversion, then, is the process of substituting for
any affirmative proposition its equivalent in negative
form, or of expressing the meaning of a negative prop-
26. THE OBVERSION OF PROPOSITIONS 99
osition as an affirmative. To obtain the obverse of
proposition A, we proceed on the principle that two
negatives are equal to an affirmative. Instead of 'all
animals digest food,' we may write, ' no animals are
beings that do not digest food'; for, 'every man has
his own troubles,' ' there are no men who have not
their own troubles.' Instead of affirming the predicate
of the subject, the obverse of A takes the negative of
the original predicate and denies it universally.
Proposition I may be obverted in the same way,
though it yields a particular, instead of a universal
negative proposition. Thus the obverse of, 'some of
the houses are comfortable,' is ' some of the houses are
not not-comfortable,' i.e., uncomfortable. We deny the
negative predicate in the obverse proposition, instead of
affirming the positive.
We obtain the obverse of the propositions E and O
by changing the negation contained in them to its
equivalent affirmation. This is done by attaching the
negative to the predicate, and then affirming it of the
subject. For example, to obtain the obverse of, ' no one
who was present can forget the scene,' we first write the
proposition in logical form, ' no one who was present is a
person who can forget the scene.' Now the negative of
the predicate term, ' a person who can forget the scene,'
is, ' a person who can not forget the scene.' Affirming
this universally we get, ' all persons who were present
are persons who cannot forget the scene.' As an exam-
ple of how the obverse of O is obtained, we may take the
proposition, 'some metals are not white.' Now if we
change the quality of the proposition by attaching the
100 THE INTERPRETATION OF PROPOSITIONS
negative to the predicate, we obtain ' some metals are not-
white.' That is, instead of denying, we affirm the neg-
ative of the original predicate. When the predicate is
made up of several words, it is important that the logical
contradictory of the whole term be taken. For example,
in the proposition, 'some men are not fond of work/ the
predicate fully expressed is, ' persons who are fond of
work.' Now the negative or contradictory term corre-
sponding to this is, ' persons who are not fond of work.'
The obverse of the original proposition therefore is,
'some men are persons who are not fond of work.'
27. The Conversion of Propositions. To convert a
proposition is to transpose its subject and predicate so
that each shall occupy the place previously held by the
other. Thus the proposition, 'no men are infallible,' is
converted by writing it, 'no infallible beings are men.'
The original proposition is called the convertend, and the
proposition obtained by conversion the converse. By
conversion, then, a new proposition is derived directly
from an old one. It is for this reason that conversion is
usually ranked as a process of immediate inference.
But, as we have already seen, the process of interpreta-
tion which results in conversion seems to fall wholly
within the proposition. In other words, it makes clear
what is involved in the original proposition, but does not
lead to any new fact with which the latter is connected.
We therefore reached the conclusion that it might more
.properly be regarded as a process of formal interpreta-
tion, than as one which involves real inference.
It is evident that in proceeding to convert propositions
2^. THE CONVERSION OF PROPOSITIONS IOI
it will be necessary to notice whether the predicate of
the convertend, or proposition to be converted, is dis-
tributed or undistributed, otherwise we should not know
what extension to apply to this term when used as
the subject of the converse proposition. The rules
usually given to limit the process of conversion are as
follows :
(1) No term must be distributed in the converse prop-
osition which was not distributed in the convertend.
(2) The quality of the converse proposition must
remain the same as the quality of the convertend.
The reason for the first rule is at once evident from
what has been already said. The second rule is not one
which is always observed. Of course, the meaning of
a proposition must not be altered by changing the qual-
ity simply or directly. But, in converting by Contrapo-
sition, as we shall see later, it is first necessary to obtain
the equivalent of the convertend by obversion, and this
necessarily involves a change of quality.
There are three kinds of conversion usually recog-
nized : {a) Simple Conversion ; () Conversion by Limi-
tation or per accidens ; (c) Conversion by Contraposition.
(a) By Simple Conversion is meant the direct trans-
position of the subject and predicate without any other
change in the form of the proposition. Both propositions
E and I can be converted in this way. Thus the
converse of, ' none of the books on this shelf are novels,'
is another proposition in E, ' no novels are books on this
shelf.' From ' some dicotyledons are exogens ' we obtain
by conversion another particular affirmative proposition,
' some exogens are dicotyledons.'
IO2 THE INTERPRETATION OF PROPOSITIONS
(b) Conversion by Limitation or per accidens is applied
to proposition A. In this process A loses its univer-
sality, and yields as a result only proposition I. To
illustrate this mode of conversion we may take the propo-
sition, 'brown hematite is an iron ore.' As we already
know, the term 'an iron ore,' being the predicate of
proposition A, is undistributed. When used as the sub-
ject of a new proposition, therefore, it must be limited
by the adjective 'some.' We thus obtain the converse
proposition, ' some iron ore is brown hematite.' Simi-
larly, the converse of the proposition, ' all sensations are
mental .processes,' is ' some mental processes are sensa-
tions.' When proposition A is converted by limitation,
then, it yields proposition I as a result. And it is evident
that the proposition has really lost something in the
process. For it is impossible by converting again to
obtain anything more than a particular proposition.
It is, however, sometimes possible to convert proposition
A without limiting the predicate. In formal definitions,
for example, the subject and the predicate are of equal
extent, and may be transposed simply without any
limitation of the latter. Thus the converse of, 'an
equilateral triangle is a plane figure having three equal
sides,' is 'a plane figure having three equal sides is an
equilateral triangle.'
(c) In Conversion by Contraposition the negative or
contradictory of the original predicate is taken as the
subject of the converse proposition. This method of
conversion is usually applied only to propositions A
and O.
When applied to A, it means that from a proposition
27. THE CONVERSION OF PROPOSITIONS 103
in the form, All B is C, we are able to assert something
of what is not C. If we know, for example, that ' all
the planets are bodies revolving around the sun,' we
can obtain by contraposition the proposition, ' no bodies
which do not revolve around the sun are planets.' The
rule for contraposition is, first obvert, and then convert
simply. Thus, the obverse of, 'aluminium is a white
metal,' is the proposition in E, 'aluminium is not a
metal which is not white ; ' and converting this simply,
we get as the contrapositive of the proposition from
which we started, 'no metal which is not white is alu-
minium.'
Proposition O can be converted only by contraposi-
tion. If we were to convert simply, as, e.g., ' some
metals are not white,' 'some white things are not
metals,' we should fall into error ; for the term ' metal '
is distributed in the converse proposition without having
been distributed in the convertend.
To obtain the converse of O by contraposition, the
rule given above, first obvert and then convert simply,
applies once more. The obverse of the proposition in
O, ' some men who make loud professions are not to be
trusted,' is the equivalent in I, 'some men who make
loud professions are persons not to be trusted.' Con-
verting this simply, we obtain the contrapositive, ' some
persons not to be trusted are men who make loud pro-
fessions.'
For the sake of convenience we may sum up the
treatment of Conversion as follows :
IO4 THE INTERPRETATION OF PROPOSITIONS
Proposition A is converted (i) by Limitation, and (2) by Contra
position.
All S is P. (A)
(1) Converting by Limitation, Some P is S. (I)
i.) Obversion yields, No S is
(2) Converting by Contraposition
not-P. (E)
ii.) The Simple Converse of this
is, No not-P is S. (E)
Proposition I is converted Simply.
Some S is P. (I)
Converting Simply, Some P is S. (I)
Proposition E is converted Simply.
No S is P. (E)
Converting Simply, No P is S. (E)
Proposition E may also be converted by Contraposition, but the
result is the same as the Contrapositive of O. Thus for example :
No S is P. (E)
f i.) Obversion yields, All S is not-
1P. (A)
v '
11.) Converting this by Limitation,
Some not-P is S. (I)
Proposition O is converted by Contraposition.
Some S is not P. (O)
f i.) Obversion yields, Some S is
Converting by Contraposition \ ..
11.) The Simple Converse of this
1 is, Some not-P is S. (I)
References
B. Bosanquet, Logic, Vol. I. pp. 310-319.
W. Minto, Logic Inductive and Deductive, Pt. III. pp. 130-166.
J. H. Hyslop, The Elements of Logic, Ch. X.
CHAPTER VIII
THE SYLLOGISM
28. The Nature of Syllogistic Reasoning. The syl-
logism, as we have already seen ( 10), presents a con-
clusion together with the reasons by means of which
it is supported. A single proposition taken by itself
is dogmatic : it merely asserts without stating the grounds
upon which it rests. The syllogism, on the other hand,
justifies its conclusion by showing the premises from
which it has been derived. It thus appeals to the
reason of all men, and compels their assent. To do
this, it is of course necessary that the truth of the
premises to which appeal is made should be granted.
If the premises are disputed or doubtful, the argument
is pushed a step further back, and it is first necessary
to show the grounds upon which these premises rest.
The assumption of syllogistic reasoning and, indeed,
of all reasoning whatsoever is that it is possible to
reach propositions which every one will accept. There
are certain facts, we say, well known and established,
and these can always be appealed to in support of our
conclusions. In syllogistic reasoning, then, we exhibit
the interdependence of propositions ; i.e., we show how
the truth of some new proposition, or some proposition
not regarded as beyond question, follows necessarily
105
106 THE SYLLOGISM
from other propositions whose truth every one will
admit.
The question which arises in connection with the
syllogism, therefore, is this : Under what conditions
do propositions which are accepted as true contain or
imply a new proposition as a conclusion? Or we may
put the question in this form : In what ways may the
four logical propositions, A, E, I, O, be combined so as
to yield valid conclusions ?
We pointed out in a previous chapter that a syllogism
has always two premises. It is, however, impossible to
obtain a conclusion by combining any two propositions
at random, as e.g.,
All A is B.
No X is Y.
It is evident that any two propositions will not yield a
conclusion by being taken together. In order to serve
as premises for a syllogism, propositions must fulfil
certain conditions, and stand in certain definite relations
to each other. To determine some of the most apparent
of these conditions, let us examine the argument :
All mammals are vertebrates,
The whale is a mammal,
Therefore the whale is a vertebrate.
"Vv^r-<rx MJsfV^ . \
It will be noticed that the term ' mammal ' is common
to both premises, and that it does not occur at all in the
conclusion. Moreover, it is because the other terms
are compared in turn with this common or Middle Term
and found to agree with it, that they can be united in
the conclusion. It is only propositions which have a
middle term, therefore, which can be employed as the
28. THE NATURE OF SYLLOGISTIC REASONING 10?
premises of a syllogism. The syllogism is thus essen
tially a process of comparison. Each of the terms
entering into the conclusion is compared in turn with
the same middle term, and in this way their relation
to each other is determined. We reach the conclusion
not directly or immediately, but by means of the middle
term. The conclusion is therefore said to be mediated,
and the process itself is sometimes called mediate
reasoning.
It will be interesting to compare what has just been said regard-
ing the function of the middle term, with what has been previously
stated regarding the nature of inference. When we infer one fact
from another, it was said, we do so by discovering some identical link
or connecting thread which unites both. We may say that to infer
is to see that, in virtue of some identical link which our thought has
brought to light, the two facts, or groups of facts, are in a certain
sense identical. Now the middle term in a syllogism is just the
explicit statement of the nature of this identical link. It is true that
in the syllogism we seem to be operating with words or terms rather
than with the thought-process itself. When we go behind the
external connection of the terms, however, we can see that the middle
term represents the universal principle, by means of which the con-
clusion is reached. In the example given above, for instance, we
reason that the whale, being a mammal, is a vertebrate.
The terms which enter into the conclusion of a
syllogism are sometimes called the Extremes, as opposed
to the middle term. Of the Extremes, the predicate of
the conclusion is known as the Major Term, and the sub-
ject of the conclusion as the Minor Term. The premise
which contains the major term is called the Major Premise,
and stands first when the syllogism is arranged in logical
form. The Minor Premise, on the other hand, is the
108 THE SYLLOGISM
premise which contains the minor term, and stands
second in the arrangement of the syllogism. The prop-
ositions of which the syllogism is composed may occur,
however, in any order in actual reasoning ; either
premise, or even the conclusion, may stand first. To
arrange an argument, therefore, it is necessary to
determine which is the major, and which the minor
premise. This can be done only by turning to the
conclusion, and distinguishing the major and minor
terms. For example, take the syllogism :
The whale suckles its young,
No fish suckles its young,
Therefore the whale is not a fish.
By turning to the conclusion we see that ' fish ' (being
the predicate) is the major term. The proposition
which contains this term, ' no fish suckles its young/
is, therefore, the major premise, and should stand first.
Before proceeding to examine the syllogism further
it would be necessary to arrange it as follows :
No fish is an animal which suckles its young,
The whale is an animal which suckles its young,
Therefore the whale is not a fish.
29. The Rules of the Syllogism. It is customary
to give a number of rules or canons to which the syl-
logism must conform in order to yield valid conclusions.
We shall first enumerate the rules, and afterwards
remark on their meaning and importance.
(i) In every syllogism there should be three, and
only three, terms, and these terms must be used
throughout in the same sense.
29. THE RULES OF THE SYLLOGISM 109
The terms, as we have already remarked, are known
as the major term, the middle term, and the minor term.
(2) Every syllogism contains three, and only three,
propositions.
These are called the major premise, minor premise,
and conclusion.
(3) The middle term must be distributed in at least
one of the premises.
(4) No term must be distributed in the conclusion
which was not distributed in one of the premises.
(5) From negative premises nothing can be inferred.
(6) If one premise be negative, the conclusion must
be negative ; and, conversely, to prove a negative con-
clusion one of the premises must be negative.
As a consequence of the above rules there result two
additional canons which may be set down here.
(7) No conclusion can be drawn from two particular
premises.
(8) If one of the premises be particular, the conclu-
sion must be particular.
The reason for the first and second rules will be
evident from what has been already said about the struct-
ure of the syllogism. We saw that a logical argument
is a process of comparison ; that two terms are united
through comparing them with a common or middle
term. If the meaning of the terms does not remain
fixed, there are more than three terms, and no com-
parison is possible. The second rule follows as a corol-
lary from the first.
The third rule, that the middle term must be dis-
tributed once, at least, is extremely important, and its
110 THE SYLLOGISM
necessity will be readily perceived. For, since the
middle terra is the standard of comparison, it must be
used in at least one premise in its universal extent.
Otherwise we might compare the major term with one
part of it, and the minor term with another part. Such
a comparison would of course not warrant us in either
affirming or denying the connection of these terms in
the conclusion. For example, the two propositions,
Sedimentary rocks are stratified substances,
Some metamorphic rocks are stratified substances,
do not distribute the middle term, ' stratified sub-
stances,' at all, being both affirmative propositions. It
FIG. 6.
is clear that the term, 'sedimentary rocks,' agrees with
one part of the stratified substances, and ' metamorphic
rocks' with another part. We are, therefore, not able
to infer that ' some metamorphic rocks are sedimentary
rocks.' This may be clearly shown by representing the
propositions by Euler's method of circles as in Fig. 6.
We know from the second proposition that the circle
representing ' metamorphic rocks ' falls partly within the
29. THE RULES OF THE SYLLOGISM III
circle of ' stratified substances.' But it is impossible to
determine from the statement whether it corresponds at
all with the circle of sedimentary rocks, or falls, as in
the figure, entirely without it.
The fourth rule states that no term must be dis-
tributed in the conclusion which was not distributed in
one of the premises. That is, the conclusion must be
proved by means of the premises, and no term which
was not employed in its universal signification in the
premises can, therefore, be used universally or dis-
tributively in the conclusion. This rule may be violated
by using either the major or the minor term in a wider
sense in the conclusion than in the premise in which it
occurs. The resulting fallacies are then known as the
Illicit Process of the major and minor terms respec-
tively. As an illustration of the illicit process of the
major term, we may consider the following argument :
All rational beings are responsible for their actions,
Brutes are not rational beings,
Therefore brutes are not responsible for their actions.
It will be at once seen that the major term, 'beings
responsible for their actions,' is distributed in the con-
clusion, but was not distributed when it appeared as the
predicate of an affirmative proposition in the major
premise. The fallacious nature of this argument may
also be shown by representing the proposition by
circles.
The illicit process of the minor term is usually more
easily detected. We may take as an example of this
fallacy :
112 THE SYLLOGISM
All good citizens are ready to defend their country,
All good citizens are persons who vote regularly at elections,
Therefore all who vote regularly at elections are ready to defend
their country.
It is clear that the minor term, ' persons who vote
regularly at elections,' is undistributed when used as
the predicate of the minor premise. In the conclusion,
however, it is wrongly taken universally, and it is this
unwarranted extension to which the name of illicit
minor is given. Students are advised to draw circles
to illustrate the nature of this fallacy.
The fifth and sixth rules have reference to negative
premises. It is not difficult to understand why two
negative premises cannot yield any conclusion. For,
from the fact that S and P are both excluded from M, we
can conclude nothing regarding their relation to each
other. Two negative premises afford us no standard by
means of which we can determine anything concerning
the relation of major and minor terms. Again, where
one premise is negative and the other affirmative, it is
asserted that, of the major and minor terms, one agrees,
and the other does not agree, with the middle term.
The necessary inference from these premises, then, is
that major and minor terms do not agree with each
other. That is, the conclusion must be negative.
It is worth noticing that it is sometimes possible to obtain a con-
clusion from premises which are both negative in form. For ex-
ample :
No one who is not thoroughly upright is to be trusted,
This man is not thoroughly upright,
Therefore this man is not to be trusted.
30. THE FIGURES OF THE SYLLOGISM 113
In this example, although the form of both premises is negative,
the minor premise supplies a positive basis for argument, and is
really affirmative in character. Or we may say that the ' not ' in the
predicate of the minor premise belongs to the predicate, and not to
the copula. The proposition may therefore be said to affirm, rather
than to deny.
The seventh and eighth rules, which refer to particular premises,
can be proved by considering separately all the possible cases. If
this is done, it will be found that these rules are direct corollaries
from the third and fourth, which are concerned with the proper dis-
tribution of terms. It is impossible to secure the necessary distri-
bution with two particular premises ; for either the distribution of
the middle term will not be provided for, or if this has been secured
by means of a negative premise, the conclusion will show a case of
the illicit major term. By means of the same rules, it may be
shown that a particular premise always requires a particular con-
clusion. The truth of these two subordinate canons may be also
readily shown by the use of circles.
30. The Figures of the Syllogism. We have seen
what an important part the middle term plays in the
syllogism. It constitutes the mediating link between
the major and minor terms, and makes possible their
union. Now upon the position of the middle term in the
premises depends the Figure of the syllogism. There
are four possible arrangements of the middle term in
the two premises, and therefore four figures of the
syllogism. If we let P represent the major term, S the
minor, and M the middle term, the form of the different
figures may be represented as follows :
SECOND FIGURE
P M
.-. S P
114 THE SYLLOGISM
THIRD FIGURE FOURTH FIGURE
M P P M
M S M S
.-. S P .-. S P
In the first figure, the middle term is the subject of
the major premise, and the predicate of the minor
premise.
In the second figure, the middle term is predicate of
both major and minor premises.
The third figure has the middle term as the subject
of both premises.
In the fourth figure, the middle term occupies just the
opposite position in the two premises from that which
it held in the first figure ; i.e., it is the predicate of the
major premise, and the subject of the minor premise.
CHAPTER IX
THE VALID MOODS AND THE REDUCTION OF FIGURES
31. The Moods of the Syllogism. By the Mood of
a syllogism we mean the combination of propositions
A, E, I, and O, which goes to make it up. Thus, when
a syllogism is made up of three universal affirm ative
propositions, we speak of it as the mood AAA ; if it
is composed of a universal negative, a particular affirma-
tive, and a particular negative proposition, we name it
the mood EIO.
Every syllogism, as has been already stated, is made
up of some arrangement of the four propositions
A, E, I, O, taken three at a time. Now, there are in
all sixty-four possible permutations of these four propo-
sitions taken three at a time. We might then write
out these sixty-four moods, and proceed to determine
which of them are valid. But this would be a long and
somewhat tedious undertaking. Moreover, if we can
determine what are the valid premises, we can draw the
proper conclusions for ourselves. Since, then, there
are but two premises in each syllogism, we shall have to
deal only with the possible permutations of A, E, I, and O,
taken two at a time, or with sixteen combinations in all.
The following, then, are the only possible ways in
which the propositions A, E, I, and O can be arranged
as premises :
"5
Il6 VALID MOODS AND THE REDUCTION OF FIGURES
AA
EA
IA
OA
AE
EE
IE
OE
AI
El
II
01
AO
EO
IO
OO
Some of these premises, however, cannot yield conclu-
sions, since they plainly violate certain rules of the syllo-
gism. The combinations of negative premises EE,
EO, OE, and OO can be at once struck out. Again,
since no conclusion follows from two particular prem-
ises, we can eliminate II, IO, and OI. There remain,
then, for further consideration the combinations:
AA EA IA OA
AE IE
AI El
AO
At this point we must recall the fact that every
argument must belong to one of the four figures. We
must now therefore ask this question : Which of the
above combinations of premises will yield valid con-
clusions in the first, second, third, and fourth figures,
respectively ? By examining the form of the syllogism
in each of these figures, we shall be able to discover
what conditions must be fulfilled in each case, and
to lay down special canons for each figure. We shall
first proceed to state and prove the special canons of
the different figures. It will not, however, be necessary
for the student to commit these rules to memory, as he
can always derive them for himself by a consideration
of the form of the argument in the different figures.
32. THE SPECIAL CANONS OF THE FOUR FIGURES 1 1 7
32. The Special Canons of the Four Figures. In tht
first figure ', the minor premise must be affirmative, and
the major premise universal.
The first figure is of the form :
M P
S M
.-. S P
To show that the minor premise is affirmative, we
employ the indirect method of proof. Let us suppose
that the minor premise is not affirmative, but negative.
Then since one premise is negative, the conclusion must
be negative. But if the conclusion is a negative propo-
sition, its predicate, P, must be distributed. Any term
which is distributed in the conclusion must, however,
have been distributed when it was used in the premise.
P must be distributed, therefore, as the predicate of the
major premise. But since negative propositions alone
distribute their predicates, the major premise, M P,
must be negative. But by hypothesis the minor prem-
ise, S M, is negative. We have, therefore, two
negative premises, which is impossible. Our suppo-
sition, that the minor premise is negative, is therefore
false; or, in other words, the minor premise must be
affirmative.
This having been established, we can very easily
prove that the major premise must be universal. For
the middle term, M, must be distributed in at least one
of the premises. But it is not distributed in the minor
premise, for it is there the predicate of an affirmative
proposition. It must, therefore, be distributed as the
Il8 VALID MOODS AND THE REDUCTION OF FIGURES
subject of the major premise, that is, the major premise
must be universal.
If we turn now to the second figure, we shall find
that the following rules may be deduced from a con-
sideration of its form :
(1) One premise must be negative, and the conclusion
therefore negative.
(2) The major premise must be universal.
The second figure is in the form :
P M
S M
/. S P
The reason for the first rule is at once evident. If one
premise is not negative, the middle term, M, is not
distributed, and no conclusion is therefore possible.
The only means of securing distribution of the middle
term in the second figure is by means of a negative
premise. And if one premise is negative, it of course
follows that the conclusion must be negative.
This having been established, the proof of rule 2
follows almost immediately. For, since the conclusion
is negative, its predicate, P, must be distributed. And
since P is distributed in the conclusion, it must have
been used distributively when it occurred as the subject
of the major premise, or, in other words, the major
premise must be universal.
The third figure is of the form :
M P
M S
.-. S P
32. THE SPECIAL CANONS OF THE FOUR FIGURES 119
From an analysis of this, the two following rules may
be obtained :
P(i) The minor premise must be affirmative.
(2) The conclusion must be particular.
The minor premise is here shown to be affirmative
by the method employed in proving the same rule in
the first figure. That is, we suppose the minor premise
negative, and show that, as a result of this hypothesis,
the conclusion is negative, and the major term dis-
tributed. It follows, then, that this term must be dis-
tributed as the predicate of the major premise. But
this could happen only if this premise were negative.
The hypothesis that the minor premise is negative thus
leads to the absurdity of two negative premises. The
conclusion that the opposite is true, that the minor
premise is affirmative, is therefore proved indirectly.
Since the minor premise is affirmative, its predicate
S is undistributed. This term must therefore be used
in an undistributed, i.e., particular sense in the conclu-
sion. And, as this term forms its subject, the conclu-
sion is particular.
In the fourth figure the terms are arranged in the
following way :
P M
M S
From a consideration of the form of this figure we can
obtain the following special canons :
(i) If either premise be negative, the major premise
must be tiniversal.
120 VALID MOODS AND THE REDUCTION OF FIGURES
(2) If the major premise be affirmative, the minor must
be universal.
(3) If the minor premise be affirmative, the conclusion
must be particular.
The student will be able to prove these canons for
himself by applying the rules of the syllogism in the
same way as has been done in the proofs already given.
33. The Determination of the Valid Moods in Each of
the Figures. We have now to apply these special
canons in order to determine what moods are valid in
each of the four figures. It has already been shown
(p. 1 1 6) that the premises which are not excluded by
the general rules of the syllogism are :
AA EA IA OA
AE IE
AI El
AO
Now we have proved that in the first figure the major
premise must be universal, and the minor affirmative.
The only combinations of premises which will stand
these tests are, AA, EA, AI, and El. Drawing the
proper conclusion in each case, we have as the four
valid moods of the first figure :
AAA, EAE, All, EIO_
It will be noticed that the first figure enables us to
obtain as conclusion any one of the four logical propo-
sitions, A, E, I, and O.
The special canons of the second figure state that
33- THE DETERMINATION OF THE VALID MOODS 121
the major premise must be universal, and one premise
negative. Selecting the combinations of premises
which fulfil these conditions, we obtain EA, AE, El,
and AO. These give, when the conclusions have been
drawn, the following four moods of the second figure :
EAE, AEE, EIO, AGO.
By means of the second figure, therefore, we are able
to establish the truth only of the negative propositions,
E and O.
In the third figure the minor premise must be affirma-
tive, and the conclusion particular. Taking all the
combinations in which the minor is affirmative, there
result, AA, IA, AI, EA, OA, El. It must be remem-
bered that the third figure yields only particular con-
clusions, even where both premises are universal. The
valid moods in this figure are therefore as follows :
AAI, IAI, All, EAO, OAO, EIO.
The canons of the fourth figure, which have to do
with the premises, state that where either premise is
negative, a universal major is necessary, and that an
affirmative major premise must be accompanied by a
universal minor. The combinations of propositions
which fulfil these conditions are A A, AE, I A, EA,
and EL In drawing conclusions from these premises,
however, it is necessary to pay attention to the third
canon of this figure, which states that where the minor
premise is affirmative, the conclusion must be particular.
Accordingly, the valid moods of this figure may now
be written :
122 VALID MOODS AND THE REDUCTION OF FIGURES
AAI, AEE, IAI, EAO,_EIO___
Here we are able to obtain a universal negative as a
conclusion, but not a universal affirmative. It is inter-
esting to notice that the first figure alone enables us
to prove a proposition of the form A.
It may also be pointed out that the combination IE,
although not excluded by the general rules of the syl-
logism, cannot be used at all as premises, since it vio-
lates the canons of all four figures. There remain in
all, then, nineteen valid moods of the syllogism, four
in the first figure, four in the second, six in the third,
and five in the fourth figure.
34. The Mnemonic Lines. It is not necessary to
commit to memory the valid moods in each figure. By
applying the general rules of the syllogism to the figure
in question, the student will be able to determine for
himself in every case whether or not an argument is
valid. The Latin Schoolmen in the thirteenth century,
however, invented a system of curious mnemonic verses
for the purpose of rendering it easy to remember the
valid moods in each figure. Although it is not neces-
sary for the student to burden his memory with these
barbarous names, it is interesting to understand the use
of the lines :
Barbara, Celarent, Dariz, Fertoque prioris ;
Cesare, Camestres, Fcstino, Baroko, secundae;
Tertia, Darapti, Disainis, Datist, Felapton,
Bokardo, Ferison, habet ; Quarta insuper addit
Bramantip, Came ties, Dimaris, Fesapo, Fresison.
The words printed in ordinary type are real Latin
34- THE MNEMONIC LINES 123
words, indicating that the four moods represented by
Barbara, Celarent, Darii, and Ferio are the valid moods
of the first figure, that the next four are valid in the
second figure, that the third figure has six valid moods
represented by as many artificial names, and that the
fourth figure adds five more. Each word represents a
mood, the vowels A, E, I, and O indicating the quality
and quantity of the propositions which go to compose
them. Thus, Barbara signifies the mood of the first
figure which is made up of three universal affirmative
propositions A A A ; Cesare, a mood of the second
figure, composed of the three propositions E A E.
These lines, then, sum up the results reached on
pages 1 20-22 regarding the valid moods in each figure.
But certain consonants in these mnemonic words also
indicate how arguments in the second, third, or fourth
figures may be changed to the form of the first figure.
The first figure was called by Aristotle the perfect
figure, and the second and third the imperfect figures,
since he did not regard an argument in these forms as
so direct and convincing as one of the first-mentioned
type. The fourth figure was not recognized by Aris-
totle, but is said to have been introduced into logic by
Galen, the celebrated teacher of medicine, who lived in
the latter half of the second century. The process of
changing an argument from one of the so-called imper-
fect figures to that of the first figure is known as Reduc-
tion. And, as we have said, these curious but ingenious
mnemonic words give rules for carrying out this process.
For example, s indicates that the proposition represented
by the preceding vowel is to be converted simply. Thus
124 VALID MOODS AND THE REDUCTION OF FIGURES
an argument in the second figure of the mood Cesare
is changed to Celarent in the first figure, by converting
the major premise simply. Again, / denotes that the
preceding vowel is to be converted by limitation, or per
accidens ; m is supposed to stand for mutare, and indir
cates that the premises are to be transposed ; k, which
is used in the moods Baroko and Bokardo, shows that
an indirect method of proof or reduction is necessary
to reduce the arguments to the first figure.
Further, the initial consonants of the moods of the im-
perfect figures correspond with those of the moods in the
first figures, to which they can be reduced. Cesare and
Camestres of the second figure, for example, and Ca-
menes of the fourth are reducible to Celarent ; and,
similarly, Festino, Felapton, Fesapo, and Fresison may
all be reduced to Ferio.
The student who understands the structure of the syllogism will
be able to arrange an argument in one figure or another, as may be
most convenient, without the aid of any mechanical rules. It may
be interesting, however, to give a single example for the sake of
illustrating the workings of this most ingenious device. Let us take
the following argument in the second figure of the mood AEE, or
Camestres :
All members of the class are prepared for the examination.
No idle persons are prepared for the examination,
Therefore no idle persons are members of the class.
Now the m in Camestres shows that the major and minor premises
are to be transposed ; the first s indicates that the minor premise is
to be converted, and the second that the same process must be per-
formed on the conclusion.
Converting the minor premise and transposing, we obtain :
34- THE MNEMONIC LINES 12$
No persons prepared for the examination are idle,
All members of the class are prepared for the examination,
Converting the conclusion,
Therefore no members of the class are idle persons.
This result, as will at once be seen, is an argument in the first
figure of the mood EAE, or Celarent.
References
Sir W. Hamilton, Lectures on Logic. Lectures XX., XXI.
A. Bain, Logic, Part First, Deduction, Bk. II. Ch. I.
NOTE. It would be interesting to work out, in connection with
the various forms of Inductive reasoning treated in Part II., the
organic relation of the syllogistic Figures, and their natural applica-
bility to various purposes of argument. This task, however, seemed
to lie beyond the proper limits of this book. All of the investiga-
tions on this point start from Hegel's treatment in the second part
of the Wissenschaft der Logik (Werke, Bd. 5, pp. 115 ff.). Those
interested in this subject may consult W.-T. Harris, The Psychologic
Foundations of Education, Ch. IX. -XL, and the same author's
Logic of Hegel. See also B. Bosanquet, Logic, Vol. II., pp. 44 ff.,
88 ff., and The Essentials of Logic, Lecture X.
CHAPTER X
ABBREVIATED AND IRREGULAR FORMS OF ARGUMENT
35. Enthymemes. The term ' enthymeme ' seems to
have been used by Aristotle for an argument from
signs or from likelihood, without complete proof.
From this sense of logical incompleteness, the name
has come to be applied in modern times to an argument
in which some part is omitted. We have already
noticed, in dealing with the syllogism ( 10), that one
premise is often omitted. Indeed, it is but seldom in
ordinary reasoning that we arrange our arguments in
the strict syllogistic form. We hurry on from one fact
to another in our thinking without stopping to make all
the steps definite and explicit. We feel it to be a waste
of time, and a trial to the patience, to express what is
clearly obvious, and so we press on to the conclusion
which is, for the time being, the central point of in-
terest.
But the more rapid and abbreviated the reasoning,
the more necessary is it to keep a clear head, and to
understand what conclusion is aimed at, and what
premises are assumed in the argument. To bring to
light the hidden assumption upon which an argument is
based, is often the best means of refuting it.
126
36. EPISYLLOGISMS AND PROSYLLOGISMS 127
Enthymemes are sometimes said to be of the first,
second, or third order, according as the major premise,
the minor premise, or the conclusion is wanting. As a
matter of fact, an enthymeme of the third order is a
rhetorical device used to call special attention to a con-
clusion which is perfectly obvious, although suppressed.
Thus, for example, ' all boasters are cowards, and we
have had proofs that A is a boaster.' Here the con-
clusion is at once obvious, and is even more prominent
than if it were actually expressed.
It is usually easy to complete an enthymeme. If the
conclusion and one premise are given, the three terms
of the syllogism are already expressed. For the con-
clusion contains the major term and the minor term;
and one of these again, in combination with the middle
term, is found in the given premise. From these data,
then, it will not be difficult to construct the suppressed
premise. When the premises are given without the
conclusion, there is no way of determining, except from
the order, which is major and which is minor. It is
therefore necessary to assume that they are already
arranged in proper logical order, and that the subject
of the conclusion, or minor term, is to be found in the
second premise, and the predicate of the conclusion, or
major term, in the first premise.
36. Prosyllogisms and Episyllpgisms. In deductive
reasoning it is often necessary to carry on the argument
through several syllogisms, using the conclusion first
reached as a premise in the following syllogism. For
example, we may argue :
128 FORMS OF ARGUMENT
All B is A
All C is B
.-. All C is A.
But all D is C
.-. All D is A.
It is clear that we have here two arguments in the first
figure. The first is called the Prosyllogism, and the
latter the Episyllogism. If the argument were carried
on further, so as to include three or more syllogisms, the
second would form the Prosyllogism with respect to
the third, while the third would be the Episyllogism of
the second. A concrete example of this kind of reason-
ing may now be given :
All timid men are suspicious,
All superstitious men are timid,
Therefore all superstitious men are suspicious.
But some educated men are superstitious,
Therefore some educated men are suspicious.
It will be noticed that in these examples the argument advances
from the premises of the Prosyllogism, to the conclusion of the
Episyllogism. It proceeds, that is to say, in a forward direction,
developing the consequences of the premises which form its starting-
point. This mode of investigation is therefore called the Progres-
sive or Synthetic, since it goes steadily forward building up its results
as it advances. To state the same thing in different words, we may
say that the Progressive or Synthetic method advances from the
conditions to what is conditioned, from causes to effects.
But it is often necessary to proceed in the opposite way. We
have often to go back and show the grounds upon which our prem-
ises rest, instead of going forward to show what consequences
follow from them. And when we do this we proceed Regressively
or Analytically. To take an example which will illustrate both
ways of proceeding :
37- SORITES, OR CHAINS OF REASONING 1 29
No man is infallible, for no man is omniscient,
Aristotle was a man,
Therefore Aristotle was not infallible.
.n advancing from the premises to the conclusion in this argument
our procedure is progressive or synthetic. Instead of reasoning out
the consequences of the premises, however, we may go back and
show the grounds upon which the major premise rests. It is evident
that this premise is itself the conclusion of a syllogism which may
be expressed as follows :
All infallible beings are omniscient,
No man is omniscient,
Therefore no man is infallible.
The regressive method goes backward from conclusions to premises,
or from the conditioned to its necessary conditions. In scientific
investigation it reasons from effects to causes, while the synthetic
method advances from causes to effects.
37. Sorites, or Chains of Reasoning. A Sorites is
an abbreviated form of syllogistic reasoning in which
a subject and predicate are united by means of several
intermediate terms. Such a train of reasoning repre-
sents several acts of comparison, and therefore several
syllogistic steps. But instead of stopping to draw the
conclusion at each stage, the sorites continues the
processes of comparison, and only sums up its results
at the close. We may define the sorites, therefore, as
a series of prosyllogisms and episyllogisms in which all
of the conclusions, except the last, are suppressed. It
is usually stated in the following form :
All A is B
All B is C
All C is D
All D is E
.. All A is E.
K
I3O FORMS OF ARGUMENT
It is evident that this train of reasoning fully expressed
is equivalent to the following three syllogisms :
FIRST SYLLOGISM SECOND SYLLOGISM THIRD SYLLOGISM
All B is C All C is D All D is E
All A is B All A is C (i) All A is D (2)
.-. All A is C (i). .-. All A is D (2). .-. All A is E (3).
There are two rules to be observed in using this form
of the sorites : (i) The first premise may be particular, all
the others must be universal ; (2) the last premise may
be negative, all the others must be affirmative. It is
evident from an examination of the syllogisms given
above that if any premise except the first were partic-
ular, the fallacy of undistributed middle would be com-
mitted. For, in that case, the middle term in one of the
syllogisms would be the subject of a particular propo-
sition, and the predicate of an affirmative proposition.
And if any premise but the last were negative, the
major term in the syllogism following that in which this
occurred would be disturbed in the conclusion without
having been distributed in the major premise. We
may now give some concrete examples of this kind of
reasoning :
Misfortunes sometimes are circumstances tending to improve
the character,
Circumstances tending to improve the character are promoters
of happiness,
What promotes happiness is good,
Therefore misfortunes are sometimes good.
In some cases the different terms of an argument of
this kind are expressed in the form of hypothetical
37- SORITES, OR CHAINS OF REASONING 131
propositions. Thus, for example, we might argue : If
a man is avaricious, he desires more than he possesses ;
if he desires more than he possesses, he is discontented ;
if he is discontented, he is unhappy ; therefore if a man
is avaricious, he is unhappy. This argument is hypo-
thetical in form only, and may be easily reduced to
categorical type as follows :
An avaricious man is one who desires more than he possesses,
A man who desires more than he possesses is discontented,
A discontented man is unhappy,
Therefore an avaricious man is unhappy.
It will be noticed that the subject of the first premise
in this form of argument is taken as the subject of the
conclusion, and that the predicate of the conclusion is
the predicate of the last premise. This is usually called
the Aristotelian sorites. But there is another form
which unites in the conclusion the subject of the last
premise, and the predicate of the first, and which is
known as the Goclenian sorites. 1 This may be thus
represented :
All A is B
All C is A
All D is C
All E is D
.-. All E is B.
Since B is the predicate of the conclusion, the prem-
ise in which it appears is always to be regarded as the
major. As a result of this, it is to be noticed that the
1 Rudolf Goclenius (1547-1628), Professor at Marburg, first explained
this form in his hagoge in Organum Aristotlis, 1598.
132 FORMS OF ARGUMENT
suppressed conclusions in this argument form the major
premise of the following syllogism, instead of the minor
premise as in the Aristotelian sorites. We may, there-
fore, expand the reasoning into the three following
syllogisms :
FIRST SYLLOGISM
All A is B
All C is A
SECOND SYLLOGISM
All C is B
All D is C
THIRD SYLLOGISM
All D is B
All E is D
.'. All C is B. .'. All D is B. /. All E is B.
A little consideration of the form of these syllogisms
will lead the student to see that the rules given for the
Aristotelian sorites must be here reversed. In both
forms of the sorites there cannot be more than one
negative premise, nor more than one particular premise.
In the Aristotelian form, no premise except the last can
be negative, and no premise except the first particular.
In the Goclenian sorites, on the other hand, the single
premise which can be negative is the first, and it is the
last alone which may be particular.
38. Irregular Arguments. There are a large num-
ber of arguments employed in everyday life which are
valid and convincing, and yet which cannot be reduced
to the syllogistic form. The difficulty with these argu-
ments is that they appear to have four terms, at least in
the form in which they are most naturally stated. We
may discuss such irregular forms of reasoning under
two headings: (i) Arguments which deal with the
relations of things in time and space, or with their
quantitative determinations; (2) arguments which are
38. IRREGULAR ARGUMENTS 133
largely verbal in character, and may be said to depend
upon the principle of substitution.
. (i) As an example of the first class of argument we
may take the following :
A is greater than B,
B is greater than C,
Therefore A is still greater than C.
It is obvious that, although we have here four terms,
the conclusion is valid, and the form of argument per-
fectly convincing. The truth seems to be that in rea-
soning about quantities we do not proceed upon the
syllogistic principle of the inclusion and exclusion of
terms. But knowing the continuous nature of quantity,
we take as our principle that, ' what is greater than that
which is greater than another is a fortiori greater than
that other.' It would not, however, make the matter
any clearer to write this as our major premise, and
bring the real argument under it in this way :
What is greater than that which is greater than another is
still greater than that other,
A is that which is greater than that which is .greater than C,
Therefore A is still greater than C.
What we have here given as the major premise is
simply a statement of the nature of quantity, not a
premise from which the conclusion is derived. We find
the same irregularity in arguments referring to the rela-
tions of things in space and time :
A is situated to the east of B,
B is situated to the east of C,
Therefore A is to the east of C.
134 FORMS OF ARGUMENT
In spite of the formal deficiency of four terms the
argument is valid. It will be observed, too, that it is
in virtue of the comparison of the position of A and
of C with that of B, that these relative positions have
been determined. The principle upon which we pro-
ceed may be said to be that, ' what is to the east of B
is to the east of that which B is to the east of.' Or
perhaps it would be truer to fact to say that we proceed
in such cases upon what we know regarding the nature
of space, and the relations of objects in space.
(2) The second class of irregular arguments are
largely verbal in character, and may be dealt with very
briefly. As an example we may consider :
Men are willing to risk their lives for gold,
Gold cannot buy happiness,
Therefore men are willing to risk their lives for what cannot buy
happiness.
It is doubtful, I think, whether these propositions rep-
resent any real inference. The whole process may
be regarded as a verbal substitution in the major prem-
ise of 'what cannot buy happiness' for the word 'gold.'
By a slight change in the form of the proposition, how-
ever, the argument may be expressed as a regular
syllogism of the third figure :
Gold is something for which men are willing to risk their lives,
Gold cannot buy happiness,
Therefore something which cannot buy happiness is something
for which men are willing to risk their lives.
Another example which also appears to be irregular
at first sight is added :
38. IRREGULAR ARGUMENTS 135
The men of the Middle Ages were ready to undertake any expe-
dition where glory could be won,
The crusades were expeditions in which glory could be won,
The crusades, therefore, were readily undertaken by the men of
the Middle Ages.
This argument seems to be irregular in form only, and
by a slight change in form may be expressed in the first
figure :
All expeditions in which glory could be won were readily under-
taken by the men of the Middle Ages,
The crusades were expeditions in which glory could be won,
Therefore the crusades were readily undertaken by the men of
the Middle Ages.
References, especially for 38
W. S. Jevons, Elementary Lessons in Logic, p. 152.
" " " The Principles of Science. Introduction.
F. H. Bradley, The Principles of Logic, pp. 348-360.
CHAPTER XI
HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
39. The Hypothetical Syllogism. We have hitherto
been dealing with syllogisms composed entirely of cate-
gorical propositions, and have not referred to the use
which is made of conditional propositions in reasoning.
A conditional proposition is sometimes defined as the
union of two categorical propositions by means of a
conjunction. It is the expression of an act of judg-
ment which does not directly or unambiguously assert
something of reality. We have already pointed out
( 20) that there are two classes of conditional propo-
sitions: the hypothetical and the disjunctive, and corre-
sponding to these we have the hypothetical and the
disjunctive syllogism. The hypothetical syllogism has
a hypothetical proposition as a major premise, and a
categorical proposition as a minor premise. The dis-
junctive syllogism in the same way is composed of a
disjunctive proposition as major, and a categorical
proposition as minor, premise. In addition to these,
we shall have to treat of another form of argument
called the ' dilemma,' which is made up of hypothetical
and disjunctive propositions.
A hypothetical proposition asserts something not di-
rectly, but subject to some limitation or condition. It
is usually introduced by some word or conjunctive
136
39- THE HYPOTHETICAL SYLLOGISM 137
phrase, like 'if,' 'supposing,' or 'granted that'; as, e.g. t
'if he were to be trusted, we might give him the mes-
sage'; 'suppose that A is B, then C is D.' The part of
a hypothetical proposition which expresses the suppo-
sition or condition is known as the Antecedent ; the
clause stating the result is called the Consequent. Thus,
in the proposition, ' he would write if he were well,' the
consequent, ' he would write,' is stated first, and the
antecedent, ' if he were well,' follows.
The hypothetical syllogism, as has been already re-
marked, has a hypothetical proposition as its major, and
a categorical proposition as its minor, premise :
If justice is to prevail, his innocence will be proved,
And justice will prevail,
Therefore his innocence will be proved.
It will be noticed that in this argument the minor
premise affirms the antecedent, and that, as a result,
the conclusion affirms the consequent. This form is
known as the constructive hypothetical syllogism, or the
modus ponens.
In the following example it will be observed that the
consequent is denied, and the conclusion obtained is
therefore negative.
If he were well, he would write,
He has not written,
Therefore he is not well.
This is called the destructive hypothetical syllogism^ or
modus tollens.
The rule of the hypothetical syllogism may therefore
be stated as follows : Either affirm the antecedent or
138 HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
deny the consequent. If we affirm the antecedent, i.e.,
declare that the condition exists, the consequent neces-
sarily follows. And, on the other hand, if the conse-
quent is declared to be non-existent, we are justified
in denying that the condition is operative.
The violation of these rules gives rise to the fallacies
of denying- the antecedent, and of affirming tJie consequent.
Thus, for example, we might argue :
If he were well, he would write,
But he is not well,
Therefore he will not write.
Here the antecedent is denied, and the argument plainly
false. For we cannot infer that his being well is the
only condition under which he would write. We do
not know, in other words, that the antecedent stated
here is the only, or essential condition of the conse-
quent. We know that if there is fire, there must be
heat; but we cannot infer that there is no heat when
no fire is present. Of course, if we can be certain
that our antecedent expresses the essential condition, or
real sine qua non of the consequent, we can go from
the denial of the former to that of the latter. For
example :
If a triangle is equilateral, it is also equiangular,
This triangle is not equilateral,
Therefore it is not equiangular.
Usually, however, when the hypothetical form of ex-
pression is employed, we cannot be certain that the
antecedent expresses the sole, or essential condition, of
the consequent. At the ordinary stages of knowledge
40. CATEGORICAL AND HYPOTHETICAL ARGUMENTS 139
we have to content ourselves with reasoning from ante-
cedent conditions, without being able to show that no
other condition is possible.
To illustrate the fallacy of affirming the consequent,
we may take the following example :
If perfect justice prevailed, the rich would not be permitted to rob
the poor,
But the rich are not permitted to rob the poor,
Therefore perfect justice prevails.
Here it will be noticed that the consequent states only
one result of the prevalence of 'perfect justice.' Be--
cause the consequent is declared to exist, it by no
means follows that it exists as a consequence of the
operation of this condition. It is also worth noting
in this example that the consequent of the major prem-
ise is negative. The minor premise which affirms the
consequent also takes a negative form. To. deny the
consequent we should have to say, 'the rich are
permitted to rob the poor.' Or, to put the matter gen-
erally, it is necessary to remember that the affirmation
of a negative proposition is expressed by a negative
proposition, and that the denial ' of a negative the
negation of a negation is, of course, positive in form.
40. Eolation of Categorical and Hypothetical Argu-
ments. It is evident that the form of the hypothetical
syllogism is very different from that of the categorical.
But, although this is the case, it must not be supposed
that with the former we have passed to a new and
wholly distinct type of reasoning. In hypothetical
I4O HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
reasoning, as in categorical, it is the presence of a
universal principle which enables us to bring two facts
into relation which formerly stood apart. Indeed, in
many cases, it is a matter of indifference in which form
the argument is stated. Thus, we may argue in hypo-
thetical form :
If a man is industrious, he will be successful,
A is an industrious man,
Therefore A will be successful.
The same argument may, however, be expressed equally
well in categorical form :
All industrious men will be successful,
A is an industrious man,
Therefore A will be successful.
It is clear that, in spite of the different forms in which
the argument is expressed, the reasoning is essentially
the same in both cases. The middle term, or general
principle which makes it possible to unite the subject
and predicate of the conclusion, in the hypothetical as
well as in the categorical syllogism, is 'industrious.' A
will be successful, we argue, because he is industrious,
and it is a rule that industrious men are successful.
Moreover, if an argument is fallacious in one form, it
will also be fallacious when expressed in the other.
The defects of an argument cannot be cured simply
by a change in its form. When a hypothetical argu-
ment, in which the antecedent is denied, is expressed
categorically, we have the fallacy of the illicit major
term. Thus, to state the example of denying the ante-
cedent given on page 138, we get:
40. CATEGORICAL AND HYPOTHETICAL ARGUMENTS 14!
The case of his being well is a case of his writing,
The present is not a case of his being well,
Therefore the present is not a case of his writing.
Similarly, when an argument in which the consequent
is affirmed is changed to the categorical form, the
defect in the reasoning appears as the fallacy of un-
distributed middle :
If this tree were an oak, it would have rough bark and acorns,
This tree has rough bark and acorns,
Therefore it is an oak.
When this argument is expressed in categorical form,
it is at once clear that the middle term is not distributed
in either the major or minor premise :
All oak trees are trees having rough bark and acorns,
This tree is a tree having rough bark and acorns,
Therefore this tree is an oak.
The change from the categorical to the hypothetical
form of argument, then, does not imply any essential
change in the nature of the reasoning process itself.
Nevertheless, it is important to note that hypothetical
propositions and hypothetical arguments emphasize one
aspect of thinking, which is entirely neglected by the
theory of the categorical syllogism. When dealing with
the extension of terms ( 16), we pointed out that every
term, as actually used in a proposition, has both an ex-
tensive and an intensive function. That is, the terms of
a proposition are employed both to name certain objects
or groups of objects, and to connote or imply certain
attributes or qualities. In the proposition, 'these are
oak trees,' the main purpose is to identify the trees.
142 HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
given in perception with the class of oak trees. When,
on the other hand, we say, ' ignorant people are super-
stitious,' the proposition does not refer directly to any
particular individuals, but states the necessary con-
nection between ignorance and superstition. Although
the existence of ignorant persons who are also super-
stitious is presupposed in the proposition, its most
prominent function is to assert a connection of at-
tributes which is wholly impersonal. We may perhaps
say that, in spite of the categorical form, the proposition
is essentially hypothetical in character. Its meaning
might very well be expressed by the statement, 'if a man
is ignorant, he is also superstitious/ What is here
emphasized is not the fact that ignorant persons exist,
and are included in the class of superstitious persons,
but rather the general law of the necessary connection
of ignorance and superstition. The existence of indi-
viduals to whom the law applies is, of course, presup-
posed by the proposition. It is not, however, its main
purpose to directly affirm their existence.
We have reached, then, the following position :
Every judgment has two sides, or operates in two ways.
On the one hand, it asserts the existence of individual
things, and sets forth their qualities and relations to
other things. But, at the same time, every judgment
seeks to go beyond the particular case, and to read off a
general law of the connection of attributes or qualities
which shall be true universally. In singular and par-
ticular propositions, the categorical element the direct
assertion of the existence of particular objects is most
prominent, although even here the hint or suggestion
40. CATEGORICAL AND HYPOTHETICAL ARGUMENTS 143
of a general law is not altogether absent. When we
reach the universal proposition, however, the reference
to real things is much less direct, and the meaning
seems capable of expression in hypothetical form.
Now in the chapters on the categorical syllogism
this latter aspect of judgments has been left out of
account. Propositions were there interpreted as refer-
ring directly to objects, or classes of objects (cf. 23).
The proposition, S is P, for example, was taken to
affirm that some definite object, or class of objects,
S, falls within the class P. And the fact that it
is possible to apply this theory shows that it repre-
sents one side of the truth. But the student must
sometimes have felt that, in this procedure, the most
important signification of the proposition is lost sight
of. It seems absurd to say, for example, that in the
proposition, ' all material bodies gravitate,' the class of
'material bodies' is included in the wider class of
'things that gravitate.' The main purpose of the judg-
ment is evidently to affirm the necessary connection
of the attributes of materiality and gravitation. The
judgment does not refer directly to things, or classes of
things at all, but asserts without immediate reference to
any particular object, if material, then gravitating. The
propositions of geometry are still more obviously hypo-
thetical in character. 'The three angles of a triangle
are equal to two right angles,' for example, cannot,
without violence, be made to mean that the subject is
included in the class of things which are equal to two
right angles. The main purpose of the proposition
is obviously to assert the necessary connection of
144 HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
the ' triangularity ' and the equality of angles with
two right angles, and not to make any direct asser-
tion regarding any actually existing object or group
of objects.
We reach, then, the following conclusion : Our
thought is at once both categorical and hypothetical.
As categorical, it refers directly to objects and their
relations. The terms of the proposition are then taken
in extension to represent objects or groups of objects,
and the copula to assert the inclusion of the subject in
the predicate, or, in cases of negative propositions, to
deny this relation. As hypothetical, the reference to
things is much more indirect. The terms of the propo-
sition are no longer regarded as representing objects or
classes, but are interpreted from the point of view of
intension. The judgment affirms or denies the con-
nection of the qualities or attributes connoted by the
terms, and not that of the objects which they denote.
Sometimes the one aspect of thought, sometimes the
other, is most prominent.
In sense-perception and in simple historical narra-
tion, assertions are made directly and categorically
regarding things and events. The main interest is in
particular objects, persons, or events, and our judgments
refer directly and unambiguously to them. But, as we
have already seen, our thought from its very beginning
attempts to get beyond the existence of particular things
and events, and to discover what qualities of objects are
necessarily connected. We pass from perception and
observation to explanation, from the narration of events,
to the discovery of the law of their connection. And,
4 i. DISJUNCTIVE ARGUMENTS 145
as a result of this advance, our judgments deal no longer
exclusively with particular objects and events, and the
fact of their relation, but with the general laws of the
connection between attributes and qualities. There is,
of course, no fixed point at which we pass from the
categorical to the hypothetical aspect of thinking. But,
in general, as we pass from judgments of sense-percep-
tion and memory, to a statement of theories and laws,
the hypothetical element comes more and more clearly
into the foreground. We have seen that it is almost
impossible to interpret propositions regarding geometri-
cal relations as referring directly to classes of objects.
In the same way, it is evident that propositions which
state general laws are more truly hypothetical than cate-
gorical. When we assert that ' all men are mortal,' the
proposition does not intend to state a fact in regard to
each and every man, or to refer directly to individuals
at all, but to express the essential and necessary relation
between humanity and mortality. A proposition which
is essentially hypothetical in character, may then be
expressed in categorical form. It must be remembered
that it is not the form, but the purpose or function of a
proposition, which determines its character. The hy-
pothetical form, however, does justice to an aspect of
thought which is especially prominent in the universal
laws and formulas of scientific knowledge, and which
is not adequately represented by the theory of subsump-
tion, or the inclusion of the subject in the predicate.
41. Disjunctive Arguments. A disjunctive propo-
sition, as we have already seen, is of the form, *A is
x.
146 HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
either B, or C, or D ' ; or, when expressed negatively,
'A is neither B, nor C, nor D.' It is sometimes said to
be the union of a categorical and a hypothetical propo-
sition. On the one hand, it asserts categorically regard-
ing A, and without reference to any external condition.
But the disjunctive proposition is not simple like the
categorical proposition : it states its results as a series
of related conditions and consequences. If A is not B,
it tells us, it must be either C or D ; and if it is C, it
follows that it cannot be B or D.
A disjunctive proposition may at first sight appear to
be a mere statement of ignorance, and, as such, to be
less useful than the simple categorical judgment of per-
ception. And it is true that the disjunctive form may
be employed to express lack of knowledge. ' I do not
know whether this tree is an oak or an ash ' ; ' he will
come on Monday or some other day.' A true disjunc-
tive proposition, however, is not a mere statement of
ignorance regarding the presence or absence of some
fact of perception. It is an attempt, on the part of
intelligence, to determine the whole series of circum-
stances or conditions within which any fact of percep-
tion may fall, and to state the conditions in such a
way that their relations are at once evident. And to
do this implies positive knowledge. In the first place,
the enumeration of possibilities must be exhaustive,
no cases must be overlooked, and no circumstances
left out of account. Secondly, the members of the
proposition must be taken so as to be really disjunc-
tive. That is, they must be exclusive of one another.
We cannot combine disjunctively any terms we please
41. DISJUNCTIVE ARGUMENTS 147
with each other. But it is only when we understand
the systematic connections of things in the field in ques-
tion, that we are able to express them in the form either
B or C, and thus assert that the presence of one ex~
eludes the other.
A disjunctive proposition, then, presupposes syste-
matic knowledge, and is consequently the expression of
a comparatively late stage in the evolution of thought.
It is true that disjunction may involve doubt or igno-
rance regarding any particular individual. We may
not be able to say whether A is B or C or D. But,
before we can formulate the disjunctive proposition,
we must be already acquainted with the whole set of
possible conditions, and also with the relation in which
those conditions stand to each other. Our knowledge,
when formulated in the disjunctive major premise of
an argument, is so exhaustive and systematic, that
the application to a particular case effected by the
minor premise appears almost as a tautology. This
will be evident in the disjunctive arguments given
below.
There are two forms of the disjunctive syllogism.
The first is sometimes called the modus tollendo ponens,
or the mood which affirms by denying. The minor
premise, that is, is negative, and the conclusion affirma-
tive. The form is,
A is either B or C,
A is not C,
Therefore A is B.
The negative disjunctive argument has an affirmative
minor premise. It is known as the modus ponendo
148 HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
tollens, or the form which, by affirming one member of
the disjunctive series, denies the others,
A is B or C or D,
But A is B,
Therefore A is neither C nor D.
It is, of course, a very simple matter to draw the con-
clusion from the premises in these cases. As we have
already indicated, the real intellectual work consists in
obtaining the premises, especially in discovering the
relations enumerated in the major premise. It is in
formulating the major premise, too, that errors are most
likely to arise. As already pointed out, it is essential
that the disjunctive members shall be exhaustively
enumerated, and also that they shall exclude each other.
But it is not always easy to discover all the possibilities
of a case, or to formulate them in such a way that they
are really exclusive. If we say, ' he is either a knave
or a fool,' we omit the possibility of his being both the
one and the other to some extent. A great many state-
ments which are expressed in the form of disjunctive
propositions are not true logical disjunctives. Thus we
might say, 'every student works either from love of
learning, or from love of praise, or for the sake of some
material reward.' But the disjunction does not answer
the logical requirements, for it is possible that two or
more of these motives may influence his conduct at
the same time. The disjunctive members are neither
exclusive nor completely enumerated.
42. The Dilemma. A dilemma is an argument
composed of hypothetical and disjunctive propositions.
42. THE DILEMMA 149
As the word is used in ordinary life, we are said to be in
a dilemma whenever there are but two courses of action
open to us, and when both of these have unpleasant
consequences. In the same way, the logical dilemma
shuts us in to a choice between alternatives, either of
which leads to a conclusion we would gladly avoid.
The first form, which is sometimes called the Simple
Constructive Dilemma, yields a simple or categorical con-
clusion,
If A is B, C is D ; and if E is F, C is D,
But either A is B, or E is F,
Therefore C is D.
It will be noticed that the minor premise affirms dis-
junctively the antecedents of the two hypothetical prop-
ositions which form the major premise, and that the
conclusion follows whichever alternative holds. We
may take as a concrete example of this type of argu-
ment :
If a man acts in accordance with his own judgment, he will be
criticised ; and if he is guided by the opinions and rules of others,
he will be criticised.
But he must either act in accordance with his own judgment, or
be guided by the opinions of others.
Therefore, in any case, he will be criticised.
The hypothetical propositions which make up the
major premise of a dilemma do not usually have the
same consequent, as is the case in the examples just
given. When the consequents involved are different,
the dilemma is said to be complex, and the conclusion
has the form of a disjunctive proposition. In the Complex
150 HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS
Constructive Dilemma, the minor premise affirms disjunc-
tively the antecedents of the major, and the conclusion
is consequently affirmative. We may take, as an ex-
ample, the argument by which the Caliph Omar is
said to have justified the burning of the Alexandrian
library : -
If these books contain the same doctrines as the Koran, they are
unnecessary ; and if they are at variance with the Koran, they are
wicked and pernicious.
But they must either contain the same doctrines as the Koran or
be at variance with it.
Therefore these books are either unnecessary or wicked and per-
nicious.
A third form, the Complex Destructive Dilemma, obtains
a negative disjunctive proposition as a conclusion, by
denying the consequents of the hypothetical proposi-
tions which form the major premise of the argument.
We may take the following example :
If a man is prudent, he will avoid needless dangers ; if he is bold
and courageous, he will face dangers bravely.
But this man neither avoids needless dangers nor does he face
dangers bravely.
Therefore he is neither prudent nor bold and courageous.
By taking more than two hypothetical propositions
as major premise, we may obtain a Trilemma, a Tetra-
lemma, or a Polylemma. These forms, however, are
used much less frequently than the Dilemma.
The dilemma is essentially a polemical or contro-
versial form of argument. Its object, as we have seen,
is to force an unwelcome conclusion upon an adversary,
by showing that his argument, or his conduct, admits of
42. THE DILEMMA I 5 I
one or other of two unpleasant interpretations. We
sometimes speak of the horns of the dilemma, and of
our adversary as 'gored,' whichever horn he may choose.
Dilemmas, however, like all controversial arguments,
are more often fallacious than valid. The minor pre-
mise of a dilemmatic argument, as we have already
seen, is a disjunctive proposition with two members.
But it is very rarely that two alternatives exhaust all
the possible cases. The cases enumerated, too, may
not exclude each other, or be real alternatives at all.
The dilemma is thus subject to all the dangers which
we have already noticed in the case of the disjunctive
argument. In addition, it is necessary to see that the
canon of the hypothetical syllogism, 'affirm the ante-
cedent or deny the consequent,' is observed. If this
rule is not observed, the logical form of the argument
will not be correct.
References, especially for 40
J. S. MiU, Logic, Bk. I. Ch. V.
C. Sigwart, Logic, Pt. I. Ch. VII.
W. Minto, Logic Inductive and Deductive, pp. 129-138, and
pp. 214-225.
F. H. Bradley, The Principles of Logic, Bk. I. Ch. 2.
B. Bosanquet, The Essentials of Logic, Lecture VI.
CHAPTER XII
FALLACIES OF DEDUCTIVE REASONING
43. Classification of Fallacies. We shall hereafter
treat of the fallacies or errors to which inductive reason-
ing is most subject (Ch. xix.). At present, however,
it is necessary to consider the fallacies which are likely
to attend the employment of the syllogistic form of
reasoning. In considering the subject, we shall find
that many fallacies belong equally to both kinds of
reasoning. This is especially true of errors which arise
from the careless use of words.
The first systematic account of fallacies is given in
Aristotle's treatise, On Sophistical Difficulties (irepl a-ofaa--
TIKWV e\eyx<ov). In this work, Aristotle divides falla-
cies into two classes : those which are due to language
(Trapa rrjv \%iv, or, as they are usually called, fallacies
in dictione\ and those which are not connected with lan-
guage (ea> TT}<? Xefeta?, extra dictioneni). Under the first
head, he enumerates six kinds of fallacies, and under
the second, seven. Aristotle's principle of classification
is, however, not entirely satisfactory. We must try to
find some positive principle or principles of classification
which will render us more assistance in understanding
the relations between the various fallacies than is
afforded by Aristotle's division into those which belong
to language, and those which do not.
43- CLASSIFICATION OF FALLACIES 153
In the strict sense of the word, a fallacy is to be
defined as an error in reasoning. In the syllogism,
however, propositions or premises form the data or
starting-point. If, now, these propositions are not
properly understood, the conclusions to which they
lead are likely to be false. We may then first divide
fallacies into Errors of Interpretation, and Fallacies in
Reasoning. Errors in interpreting propositions might,
perhaps, be more properly treated in a work on rhetoric
than in a chapter on logical fallacies. But it has been
the custom ever since the time of Aristotle to include
in the enumeration of logical fallacies a number of
errors which are likely to arise in interpreting propo-
sitions. Moreover, as we saw in Chapter VII., there
are certain processes of interpretation, like Obversion
and Conversion, which are sometimes called immediate
inference, and which require a knowledge of the logical
structure of propositions.
The Fallacies which arise in the process of reasoning,
we may again divide into Formal Fallacies, or violations
of the syllogistic rules, and Material Fallacies. The
latter class may be further divided into Fallacies of
Equivocation (including Ambiguous Middle, Composi-
tion, Division, and Accident) and Fallacies of Presump-
tion (including Petitio Principii, Irrelevant Conclusion,
Non Sequitur, and Complex Questions). The following
table will summarize this classification :
154
FALLACIES OF DEDUCTIVE REASONING
FALLACIES
Errors in Interpretation
(1) Illogical Obversion or
Conversion
(2) Amphiboly
(3) Accent
Mistakes in Reasoning
Material
In Categorical
Arguments
In
Hypothetical
rco
(2)
(3)
(4)
1(5)
f(6)
Formal
Four Terms
Undistributed
Middle
Illicit Major
Illicit Minor
Equivocation
(1) Ambiguous
Middle
(2) Composition
(3) Division
(4) Accident
Negative Premises
Arguments [
ic Antecedent
Affirming the Consequent
Presumption
(1) Petitio Prin-
cipii
(2) Complex
Question
(3) Irrelevant
Conclusion
(4) Non Sequitur
In Disjunctive
Arguments
(8) Imperfect Disjunction
44. Errors in Interpretation. This class of fallacies
results from imperfect understanding of the meaning
of propositions. They are not, then, strictly speaking,
errors of reasoning at all. If, however, the propositions
employed as premises in an argument are not correctly
understood, the conclusions founded upon them are
likely to be erroneous. And even if the proposition,
which is wrongly interpreted, is not made the basis of
further reasoning, it is in itself the result of an intel-
lectual error against which it is possible to guard. We
do not, of course, profess to point out all the possible
sources of error in interpreting propositions. The only
44- ERRORS IN INTERPRETATION 155
rule applicable to all cases which can be given is this :
Accept no proposition until you understand its exact
meaning, and know precisely what it implies. Delib-
eration and attention, both with regard to our own
statements and those of others, are the only means
of escaping errors of this kind.
(i) Illogical Obversion or Conversion. In a previous
chapter (Ch. vii.), we have treated of Obversion and
Conversion, and shown the rules to be followed in stating
the obverse or the converse of a proposition. In Obver-
sion, we interpret or show what is involved in a proposi-
tion, by stating its implications in a proposition of the
opposite quality. And unless we have clearly grasped
the meaning of the original proposition, mistakes are
likely to arise in changing from the affirmative to the
negative form of statement, or from the negative to the
affirmative. Thus, we should fall into an error of this
kind if we should take the proposition, 'honesty is
always good policy,' to be the equivalent of, or to imply,
the statement, 'dishonesty is always bad policy.' Nor
can we obtain by obversion the proposition, ' all citizens
are allowed to vote,' from, ' no aliens are allowed to
vote.'
In Conversion, we take some proposition, A is B, and
ask what assertion it implies regarding the predicate.
Does ' all brave men are generous ' imply also that ' all
generous men are brave ' ? This is, perhaps, the most
frequent source of error in the conversion of proposi-
tions. I do not mean that in working logical examples
we are likely to convert proposition A simply, instead of
by limitation. But in the heat of debate, or when using
156 FALLACIES OF DEDUCTIVE REASONING
propositions without proper attention, there is a natural
tendency to assume that a proposition which makes a
universal statement regarding the subject, does the same
with regard to the predicate. And, although such errors
are very obvious when pointed out, as, indeed, is the
case with nearly all logical fallacies, they may very
easily impose upon us when our minds are not fully
awake, that is, when attention is not active and con-
sciously on guard. Of the other methods of conversion
perhaps contraposition is most likely to be a source of
error. We have already ( 27) given the rules for ob-
taining the contrapositive of any proposition. Some
practice in working examples will assist students in
perceiving what is the logical contrapositive to any
proposition, and in detecting fallacies.
(2) Amphiboly, or amphibology (afi<f>i/3o\a\ consists
in misconception arising from the ambiguous gram-
matical construction of a proposition. A sentence may
have two opposite meanings, but one may be more
natural and prominent than the other. A deception
may be practised by leading a person to accept the
meaning more strongly suggested, while the significance
intended is the very opposite, as, e.g., ' I hope that you
the enemy will slay.' In Shakespeare's Henry VI., we
have an instance of amphiboly in the prophecy of the
spirit, that "the Duke yet lives that Henry shall
depose."
(3) The Fallacy of Accent is a misconception due to
the accent or emphasis being placed upon the wrong
words in a sentence. It may, therefore, be regarded
as a rhetorical, rather than as a logical fallacy. Jevons's
45- FORMAL FALLACIES 157
examples of this fallacy may be quoted in part. " A
ludicrous instance is liable to occur in reading Chapter
XIII. of the First Book of Kings, verse 27, where it is
said of the prophet, ' And he spake to his sons, saying,
Saddle me the ass. And they saddled him' The italics
indicate that the word him was supplied by the trans-
lators of the authorized version, but it may suggest a
very different meaning. The commandment, 'Thou,
shalt not bear false witness against thy neighbour,' may
be made by a slight emphasis of the voice on the last
word to imply that we are at liberty to bear false
witness against other persons. Mr. De Morgan who
remarks this also points out that the erroneous quoting
of an author, by unfairly separating a word from its
context, or italicizing words which were not intended to
be italicized, gives rise to cases of this fallacy." 1 Jevons
is also authority for the statement that Jeremy Bentham
was so much afraid of being led astray by this fallacy
that he employed a person to read to him whose voice
and manner of reading were particularly monotonous.
45. Formal Fallacies. We shall follow our table,
and deal with mistakes of Reasoning under the two
headings of Formal Fallacies, and Material Fallacies.
Formal fallacies arise from violations of the rules of the
syllogism. The breaches of these rules have been
already pointed out, and illustrated in our discussion of
the various forms of syllogistic argument. The analysis
of arguments, with a view to the detection of such
fallacies, where any exist, is a very important exercise,
1 Jevons, Lessons in Logic, p. 1 74,
158 FALLACIES OF DEDUCTIVE REASONING
and affords valuable mental discipline. It seems only
necessary here to add a remark regarding the first
fallacy on our list, that of Four Terms, or Quaternio
Terminorum, as it is usually called by logicians.
The first canon of the categorical syllogism states
that 'a syllogism must contain three and only three
terms.' This rule would of course be violated by such
an argument as,
Frenchmen are Europeans,
Englishmen are Anglo-Saxons,
Therefore Englishmen are Europeans.
It is so obvious that this example does not contain
a real inference that no one would be likely to be mis-
led by the pretence of argument which it contains. In
some cases, however, a term may be used in two senses,
although the words by which it is expressed are the
same. The following example may be given :
Every good law should be obeyed,
The law of gravitation is a good law,
Therefore the law of gravitation should be obeyed.
Here we have really four terms. The word 'law,' in
the first proposition, means a command given or enact-
ment made by some persons in authority. A 'good
law' in this sense then means a just law, or one which
has beneficial results. But in the second proposition
it signifies a statement of the uniform way in which
phenomena behave under certain conditions. A ' good
law' from this point of view would imply a correct
statement of these uniformities. It is interesting to
note that this example may also be regarded as an
46. MATERIAL FALLACIES 159
instance of Equivocation, and classified as a case of an
ambiguous middle term. It is often possible to classify
a fallacy under more than a single head.
There are, however, cases where an argument may
seem at first sight to have four terms, but where the
defect is only verbal. The matter must, of course, be
determined by reference to the meaning of terms and
not merely to the verbal form of expression. It is ideas
or concepts, and not a form of words, which are really
operative in reasoning.
46. Material Fallacies. What are called material
fallacies do not result from the violation of any specific
logical rules. They are usually said to exist, not in the
form, but in the matter of the argument. Consequently,
it is sometimes argued, the detection and description of
them do not properly belong to logic at all. We have
found, however, that all these fallacies have their
source in Equivocation and Presumption. They thus
violate two of the fundamental principles of logical
argument. For all logical reasoning presupposes that
the terms employed shall be clearly defined, and used
throughout the argument with a fixed and definite
signification. And, secondly, logic requires that the
conclusion shall not be assumed, but derived strictly
from the premises. The violation of these principles
is, therefore, a proper matter of concern to the logician.
We shall treat first of the fallacies of Equivocation.
(A) The fallacies of Equivocation have been enumer-
ated as Ambiguous Middle Term, Composition, Division,
and Accident. These all result from a lack of clearness
160 FALLACIES OF DEDUCTIVE REASONING
and definiteness in the terms employed. We shall deal
with them briefly in order.
(1) The phrase, Ambiguous Middle Term, describes
the first fallacy of this group. It is obvious that the
middle term cannot form a proper standard of com-
parison if its meaning is uncertain or shifting. A
standard of measure must be fixed and definite. One
illustration of this fallacy will be sufficient :
Partisans are not to be trusted,
Democrats are partisans,
Therefore Democrats are not to be trusted.
The middle term, 'partisan,' is evidently used in two
senses in this argument. In the first premise it signifies
persons who are deeply or personally interested in some
measure ; and in the latter it simply denotes the
members of a political party. When an argument is
long, and is not arranged in syllogistic form, this fallacy
is much more difficult of detection than in the simple
example which has been given. It is of the utmost
importance, then, to insist on realizing clearly in con-
sciousness the ideas for which each term stands, and not
to content ourselves with following the words.
(2) The fallacy of Composition arises when we affirm
something to be true of a whole, which holds true only
of one or more of its parts when taken separately or
distributively. Sometimes the error is due to confusion
between the distributive and collective signification of
' all,' as in the following example :
All the angles of a triangle are less than two right angles,
A, B, and C are all the angles of this triangle,
Therefore A, B, and C are less than two right angles.
46. MATERIAL FALLACIES l6l
It is, of course, obvious that ' all the angles of a
triangle' in the major premise signifies each and every
angle when taken by itself, and that the same words in
the minor premise signify all the angles collectively.
What is true of all the parts taken separately, is not
necessarily true of the whole. We cannot say that
because no one member of a jury is very wise or very
fair-minded, that the jury as a whole are not likely to
bring in a just verdict. The members may mutually
correct and supplement each other, so that the finding
of the jury as a whole will be much fairer and wiser
than the judgment of any single individual composing
it. Another instance of this fallacy which is often
quoted is that by which protective duties are sometimes
supported :
The manufacturers of woollens are benefited by the duty on
woollen goods ; the manufacturers of cotton by the duty on cotton ;
the farmer by the duties on wool and grain ; and so on for all the
other producing classes ; therefore, if all the products of the country
were protected by an import duty, all the producing classes would
be benefited thereby.
But, because each class would be benefited by an import
tax upon some particular product, it does not necessarily
follow that the community as a whole would be benefited
if all products were thus protected. For, obviously, the
advantages which any class would obtain might be more
than offset by the increased price of the things which
they would have to buy. On the other hand, it would
be necessary to take into consideration the fact that an
increase in the prosperity of one class indirectly brings
profit to all the other members of the same society.
1 62 FALLACIES OF DEDUCTIVE REASONING
We cannot regard a whole as simply a sum of parts,
but must consider also the way in which the parts act
and react upon each other.
(3) The fallacy of Division is the converse of Com-
position. It consists in assuming that what is true of
the whole is also true of the parts taken separately.
Some term, which is used in the major premise collec-
tively, is employed in a distributive sense in the minor
premise and conclusion. The following example will
illustrate this :
All the angles of a triangle are equal to two right angles,
A is an angle of a triangle,
Therefore A is equal to two right angles.
To argue that, because some measure benefits the
country as a whole, it must therefore benefit every
section of the country, would be another instance of
this fallacy. Again, we may often find examples of
both Division and Composition in the practice so com-
mon in debate of ' taking to pieces ' the arguments by
which any theory or proposed course of action is justi-
fied. A person would be guilty of Division if he should
argue that, because a complex theory is not completely
proved, none of the arguments by which it is supported
have any value. It is, however, perhaps more common
to fall into the fallacy of Composition in combating the
arguments of an opponent. Some measure, for example,
is proposed to which a person finds himself in opposi-
tion. It is usually easy to analyze the different argu-
ments which have been advanced in support of the
measure, and to show that no single one of these taken
46. MATERIAL FALLACIES 163
by itself is sufficient to justify the change. The con-
clusion may then be drawn with a fine show of logic
that all the reasons advanced have been insufficient.
This, of course, is to neglect the cumulative effect of
the arguments ; it is to assume that what is true of
'all,' taken distributively, is also true of 'all' when
taken in conjunction.
(4) It is often difficult to distinguish the various forms
of the fallacy of Accident from Composition and Divi-
sion. We have seen that the latter rest upon a confu-
sion between whole and part ; or, as we have already
expressed it, on an equivocation between the distributive
and collective use of terms. The fallacies of Accident
are also due to Equivocation. But in this case the con-
fusion is between essential properties and accidents,
between what is true of a thing in its real nature, as
expressed by its logical definition, and what is true of it
only under some peculiar or accidental circumstance.
There are two forms of this argument which are
usually recognized : (a) The Direct or Simple Fallacy
of Accident, which consists in arguing that what is true
of a thing generally is also true of it under some acci-
dental or peculiar circumstance. The old logicians
expressed this in the formula, a dicto simpliciter ad
dictum secundum quid. The second form is (b) the
Converse Fallacy of Accident, which consists in arguing
that what is true of a thing under some condition or
accident, can be asserted of it simply, or in its essential
nature. The formula for this is, a dicto secundum quid
ad dictum simpliciter.
It would be an illustration of the direct fallacy to
164 FALLACIES OF DEDUCTIVE REASONING
reason, that because man is a rational being, there-
fore a drunken man or an angry man will be guided by
reason. Similarly, we should commit this fallacy if
we were to argue that because beefsteak is wholesome
food, it would be good for a person suffering with fever
or dyspepsia; or to conclude from the principle that
it is right to relieve the suffering of others, that we
ought to give money to beggars.
It would be a case of the converse fallacy to argue,
that because spirituous liquors are of value in certain
cases of disease, they must therefore be beneficial to a
person who is well. We should also be guilty of the
same fallacy if we should conclude that it is right to
deceive others, from the fact that it is sometimes neces-
sary to keep the truth from a person who is sick, or to
deceive an enemy in time of war.
The fallacies of Accident, like all the fallacies of
Equivocation, are largely the result of a loose and care-
less use of language. By qualifying our terms so as
to state the exact circumstances involved, they may
easily be detected and avoided.
,(^) Fallacies of Presumption. The fallacies of this
group are the result of presumption or assumption on
the part of the person making the argument. It is pos-
sible (i) to assume the point to be proved, either in
the premises of an argument, or in a question (Petitio
Principii, and Complex Question); or (2) to assume
without warrant that a certain conclusion follows from
premises which have been stated (Non Sequitur)\ or
(3) that the conclusion obtained proves the point at
issue (Irrelevant Conclusion).
46. MATERIAL FALLACIES 165
(i) Petitio Principii, or 'Begging the Question,' is a
form of argument which assumes the conclusion to be
proved. This may be done in either of two ways,
(i) We may postulate the fact which we wish to prove,
or its equivalent under another name. Thus, for ex-
ample, we might argue that an act is morally wrong
because it is opposed to sound ethical principles. 'The
soul is immortal because it is a simple and indecom-
posable substance/ may be regarded as another ex-
ample of this assumption. But (2) the question may
be begged by making a general assumption covering
the particular point in dispute. Thus, if the advisa-
bility of legislation regulating the hours of labor in a
mine or factory were under discussion, the question-
begging proposition, 'all legislation which interferes
with the right of free contract is bad,' might be pro-
pounded as a settlement of the whole question.
A special form of this fallacy results when each of
two propositions is used in turn to prove the truth of
the other. This is known as 'reasoning in a circle,'
or circulus in probando. This method of reasoning is
often adopted when the premise, which has been em-
ployed to prove the first conclusion, is challenged. ' I
should not do this act, because it is wrong.' ' But how
do you know that the act is wrong ? ' ' Why, because
I know that I should not do it.'
It is always necessary, then, to see that the conclu-
sion has not been assumed in the premises. But, since
the conclusion always follows from the premises, we
may say in one sense that the conclusion is always thus
assumed. It is, therefore, easy to charge an opponent
1 66 FALLACIES OF DEDUCTIVE REASONING
unjustly with begging the question. De Morgan in his
work on Fallacies, says : " There is an opponent fallacy
to the Petitio Principii which, I suspect, is of more
frequent occurrence : it is the habit of many, to treat
an advanced proposition as a begging of the question
the moment they see that, if established, it would es-
tablish the question." All argument must, of course,
start from premises to which both parties assent. But
candour and fairness forbid us to charge an opponent
with Petitio because the results of his premises are
unwelcome. It was Charles Lamb who humorously
remarked that he would not grant that two and two
are four until he knew what use was to be made of
the admission.
(2) The Complex Question is an interrogative form of
Petitio, It is not really a simple interrogation, but is
founded upon an assumption. Examples may be found
in popular pleasantries, such as, ' Have you given up
your drinking habits ? ' ' Do the people in your part of
the country still carry revolvers ? ' Disjunctive questions,
too, always contain an assumption of this kind : 'Is this
an oak or an ash ? ' ' Does he live in Boston or
New York ? ' The ' leading questions ' which lawyers
frequently use in examining witnesses, but which are
always objected to by the opposing counsel, are usually
of this character. Further instances may perhaps be
found in the demand for explanation of facts which are
either false, or not fully substantiated ; as, e.g. ' Why
does a fish when dead weigh more than when alive ?-'
' What is the explanation of mind-reading ? '
(3) The Irrelevant Conclusion, or Ignoratio Elenchi,
^ Ot/YlX
46. MATERIAL FALLACIES l6/
consists in substituting for the conclusion to be proved
some other proposition more or less nearly related to it
This fallacy may be the result of an involuntary con-
fusion on the part of the person employing it, or it may
be consciously adopted as a controversial stratagem to
deceive an opponent or an audience. When used in
this latter way, it is usually intended to conceal the
weakness of a position by diverting attention from the
real point at issue. This is, indeed, a favourite device
of those who have to support a weak case. A counsel
for the defence in a law-suit is said to have handed
to the barrister presenting the case the brief marked,
' No case ; abuse the plaintiff's attorney.' To answer
a charge or accusation by declaring that the person
bringing the charge is guilty of as bad, or even worse,
things, what is sometimes called the tu quoque form
of argument is also an example of this fallacy.
Apart from such wilful perversions or confusions,
many unintentional instances of this fallacy occur. In
controversial writing, it is very natural to assume that
a proposition which has some points of connection with
the conclusion to be established, is 'essentially the
same thing,' or ' practically the same, as the thesis
maintained.' Thus one might take the fact that a great
many people are not regular church-goers, as a proof
of the proposition that religion and morality are dying
out in the country. Many of the arguments brought
against scientific and philosophical theories belong to
this class. Mill cites the arguments which have been
urged against the Malthusian doctrine of population,
and Berkeley's theory of matter. We may quote the
1 68 FALLACIES OF DEDUCTIVE REASONING
passage referring to the former: " Malthus has been
supposed to be refuted if it could be shown that in
some countries or ages population has been nearly
stationary, as if he had asserted that population always
increases in a given ratio, or had not expressly declared
that it increases only, in so far as it is not restrained by
prudence, or kept down by disease. Or, perhaps, a
collection of facts is produced to prove that in some one
country with a dense population the people are better
off than they are in another country with a thin one, or
that the people have become better off and more
numerous at the same time ; as if the assertion were
that a dense population could not possibly be well off." l
There are several cases or forms of Irrelevant Con-
clusion to which special names have been given, and
which it is important to consider separately. When
an argument bears upon the real point at issue, it is
called argumentum ad rem. But, on the other hand,
there are the following special ways of obscuring the
issue : argumentum ad hominem, argumentum ad popti-
lum, argumentum ad ignorantiam, and argumentum ad
verecundiam.
The argumentum ad hominem is an appeal to the
character, principles, or former profession of the person
against whom it is directed. It has reference to a
person or persons, not to the real matter under discus-
sion. In order to confuse an opponent, and discredit
him with the audience, one may show that his character
is bad, or that the views which he is now maintaining
1 Logic, Bk. V. Ch. VII. 3.
46. MATERIAL FALLACIES 169
are inconsistent with his former professions and practice.
Or the argument may be used with the hope of persuad-
ing the opponent himself. We then try to convince
him that the position which he maintains is inconsistent
with some other view which he has previously pro-
fessed, or with the principles of some sect or party
which he has approved. Or we may appeal to his in-
terests by showing him that the action proposed will
affect injuriously some cause in which he is concerned,
or will benefit some rival sect or party. In all of these
cases the real point at issue is, of course, evaded.
The argumentum ad populum is an argument ad-
dressed to the feelings, passions, and prejudices of
people rather than an unbiassed discussion addressed to
the intellect.
The argumentum ad ignorantiam is an attempt to
gain support for some position by dwelling upon the
impossibility of proving the opposite. Thus we cannot
prove affirmatively that spirits do not revisit the earth,
or send messages to former friends through 'mediums/
Now it is not unusual to find ignorance on this subject
advanced as a positive ground of conviction. The
argument seems to be :
It is not impossible that this is so,
What is not impossible is possible,
Therefore it is possible that this is so.
The fallacy arises when we confuse what is only ab-
stractly possible i.e., what we cannot prove to be
impossible with what is really possible, i.e., with what
we have some positive grounds for believing in, though
those grounds are not sufficient to produce conviction.
I/O FALLACIES OF DEDUCTIVE REASONING
The argumentum ad verecundiam is an appeal to the
reverence which most people feel for a great name.
This method of reasoning attempts to settle a question
by referring to the opinion of some acknowledged
authority, without any consideration of the arguments
which are advanced for or against the position. It is, of
course, right to attach much importance to the views of
great men, but we must not suppose that their opinion
amounts to proof, or forbids us to consider the matter
for ourselves.
There is, however, a more common, though still less
justifiable, form of the argument from authority. A
man who is distinguished for his knowledge and attain-
ments in some particular field, is often quoted as an
authority upon questions with which he has no special
acquaintance. The prestige of a great name is thus
irrelevantly invoked when no significance properly
attaches to it Thus, for example, a successful general
is supposed to speak with authority upon problems of
statescraft, and the opinions of prominent clergymen
are quoted regarding the latest scientific theories.
(4) The fallacy of non sequitur, or the fallacy of the
consequent, occurs when the conclusion does not really
follow from the premises by which it is supposed to be
supported. The following example may serve as an
illustration :
Pennsylvania contains rich coal and iron mines,
Pennsylvania has no sea-coast,
Therefore the battle of Gettysburg was fought in that state.
This argument, of course, is thoroughly inconsequent,
46. MATERIAL FALLACIES I /I
and would deceive no one. But when the conclusion
repeats some words or phrases from the premises, we
are likely, when not paying close attention, to be im-
posed upon by the mere form of the argument. We
notice the premises, and remark that the person using
the argument advances boldly through ' therefore ' to his
conclusion. And if this conclusion appears to be related
to the premises, and sounds reasonable, the argument is
likely to be accepted. The following example will illus-
trate this :
Every one desires happiness, and virtuous people are happy,
Therefore every one desires to be virtuous.
What is known as the False Cause (non causa pro
causa ; post hoc ergo propter hoc) is the inductive fallacy
corresponding to the non sequitur. In this we assume
that one thing is the cause of another merely because we
have known them to happen together a number of times.
The causal relation is assumed without any analysis or
examination, on the ground of some chance coincidence.
Thus a change in the weather may be attributed to the
moon, or the prosperity of the country to its laws re-
quiring Sunday observance (cf. pp. 255 f.).
References
J. H. Hyslop, The Elements of Logic, Chs. XVII. and XVIII.
J. S. Mill, Logic, Bk. V.
A. Sidgwick, Fallacies [Int. Scient. Series].
PART II. INDUCTIVE METHODS
CHAPTER XIII
THE PROBLEM OF INDUCTION. OBSERVATION AND
EXPLANATION
47. The Problem of Induction. In Part I. we have
outlined the general nature of the syllogism, and have
shown what conditions must be fulfilled in order to
derive valid conclusions from given premises. But the
syllogism does not represent completely all of our ways of
thinking. We do not always find premises which every
one accepts ready to our hand. The propositions which
serve as the premises of syllogisms are themselves the
result of the activity of thought. It requires thinking
to arrive at such simple propositions as, 'all men are
mortal,' 'water is composed of hydrogen and oxygen.'
Facts of this kind are of course learned through expe-
rience, but they none the less require thought for their
discovery. Sense-perception without thought could give
us only a chaos of unordered impressions which would
have no meaning and no significance. It is important,
then, to understand how our intelligence proceeds to
discover the real nature of things, and the laws accord-
ing to which they operate. Thinking is the means by
which we interpret nature, and to show how this is to
172
47- THE PROBLEM OF INDUCTION 1/3
be accomplished was the purpose of Bacon's Novum Or-
ganum. The problem is the discovery of the real nature
of things, and their relations with one another. The
assumption of all knowledge, as we have already seen
( 9, cf. also 79, 80), is that there is a permanent con-
stitution of things which secures uniform ways of acting.
The procedure by means of which intelligence discovers
the permanent laws of things is usually known as In-
duction. We shall have to study this kind of thinking
in this and the following chapters. The general prob-
lem may perhaps be stated in this way : What are the
methods which inductive thinking employs, in order to
pass from the chaotic and unordered form in which the
senses present our experience, to a perception of the
order and law in things that is required by real know-
ledge or science ?
Before we attempt to answer this question, however,
there are several remarks to be made which will, I
hope, throw further light upon the nature of our under-
taking. In the first place, it is to be noticed that we
have spoken in the preceding paragraph of the methods
of inductive thinking. Now, as we shall show more
fully in 88, there is no essential difference between
the results of an inductive and a deductive inference.
The purpose of an inference is always_jthe same :
namely, to exhibitTTHelrelation and connection of par-
ticular facts or_events_in virtue of some universal law
or principle. In deductive thinking, sucE a law is
known, or provisionally assumed as known, and the
problem is to show its application to the facts with
which we are dealing. In induction, on the other hand,
1/4 THE PROBLEM OF INDUCTION
the starting-point must be the particular facts, and the
task which thought has to perform is to discover the
general law of their connection. Both deduction and
induction play an important part in the work of building
up knowledge. But the various sciences must start
with particular facts learned through experience. The
mind has not before experience any store of general
principles or innate truths which might serve as the
starting-point of knowledge (cf. 76). It must fall
back, therefore, upon the particular facts and events
learned through perception. This 'elementary know-
ledge,' as has been already pointed out, does not pass
over in a ready-made form into the mind, but is itself
the result of thinking or judging. However, before
any one deliberately and consciously undertakes to dis-
cover new truth, to understand the world, he is already
in possession of a store of such perceptive judgments.
These constitute the beginnings of knowledge, and
serve as the starting-point for scientific explanation.
The knowledge of laws and general principles comes
later, and is derived from a study of the particular facts.
It is clear, then, that the procedure of all the sciences
must be inductive, at least in the beginning. The various
sciences are occupied, each in its particular field, with
an attempt to reduce to order and unity facts, which at
first sight appear to be lawless and disconnected. And
it is true to say that in this undertaking the general
procedure is inductive. But it will also appear that in
performing this task thought does not always proceed
in strictly inductive fashion. Our thought uses every
means which will help it to its desired end. It is often
47- THE PROBLEM OF INDUCTION 175
able, after pushing its inquiries a little way, to discover
some general principle, or to guess what the law of
connection must be. When this is possible, it is found
profitable to proceed deductively, and to show what re-
sults necessarily follow from the truth of such a general
law. Of course, it is always essential to verify results
obtained in this deductive way, by comparing them with
the actual facts. But in general, the. best results are
obtained when induction and deduction go hand in
hand. We shall expect to find, then, that the so-called
inductive methods sometimes include steps which are
really deductive in nature.
It is to be noticed, further, that in dealing with the nature of the
inductive methods, we are not laying down rules which thought must
follow. We are not attempting, that is, to prescribe to thinking its
mode of procedure. To do so would be quite futile. It is impos-
sible, as we have already seen ( 3), for logic to lay down any
a priori rules. Its task is rather to point out the methods by which
success has been already won in the various fields of knowledge.
Logic does not attempt to invent any methods of scientific proced-
ure, but it undertakes to describe the road by which truth has
already been gained. The scientific inquirer is interested pri-
marily in the results of his thinking : he is usually not interested in
tracing the various steps through which his thought has passed, and
the methods employed in reaching the goal. Oftentimes he would
be unable to give any such description even if he tried to do so.
Logic, however, takes the procedure of the thinking process for its
subject-matter. It undertakes to make thought conscious of its
own nature, of the goal at which it aims, and the methods which
are employed in the attainment of this goal. The comparative
value of these methods, too, must be decided by the actual charac-
ter of the results which they have yielded. One method is to be
regarded as better than another when it gives us knowledge which
Js universally acknowledged to be more complete and satisfactory
1/6 THE PROBLEM OF INDUCTION
than that afforded by the other. For logical methods, like every,
thing else, must be known and judged by their fruits.
Again, it must be remembered that complete scien-
tific explanation, which we found to be the type of per-
fect knowledge, is not attained at a single stroke.
Scientific inquiry may have various purposes. It is
often limited to an attempt to gain a knowledge of the
quantitative relations of things, or of the way in which
they are connected as antecedents and consequents.
In some cases, too, the conclusions reached are only
more or less probable, and require further confirmation
through the use of other methods. It follows, then,
that the various scientific methods which we shall have
to describe are not to be regarded as self-sufficient and
independent ways of reaching truth, but rather as
mutually helpful and complementary. For example, the
work done by thought in dealing with the quantitative
aspect of things, and the conclusions which it reaches
through analogical inference, are necessary steps in the
progress toward complete and satisfactory explanations
of the nature of things. We shall find it necessary, there-
fore, to keep in mind in our investigation this relation
of the various methods to one another. For our purpose,
we may perhaps classify the various scientific methods
as those of Observation and Explanation, the latter in-
cluding Analogy and Complete Scientific Explanation.
48. Observation. We may include under this
heading, Simple Enumeration, Statistical Methods, and
Methods of determining Causal Connection. Before
describing these processes in detail, however, it is neces-
48. OBSERVATION 1 77
sary to make clear what is implied in the nature of scien-
tific observation, and what are the results aimed at by the
methods which it employs. It is customary to say that
Observation has to determine the nature and order of the
particular facts presented by our experience, and that
after this has been done, there still remains the task of
furnishing the theory, or Explanation of the facts. This
distinction, though not absolute, affords a convenient
principle of division in treating of the inductive methods.
We may say that it is observation which enables us to
discover the nature of particular facts, and to determine
the order of their connection. Accurate observation is
thus a first and necessary step in the work of reducing
our experience to systematic form. We have already
seen how emphatically and eloquently this doctrine was
proclaimed by Bacon in the Novum Organnm.
It is important, however, to remember that scientific
observation itself involves intellectual activity. To
observe at least in the sense in which the word is
used in scientific procedure requires something more
than the passive reception of impressions of sense in
the order in which they come to us. Without some
activity on the part of mind, it would be impossible to
obtain even the imperfect and fragmentary knowledge
of everyday life. But accurate observation is one of
the means which science employs to render this know-
ledge more complete and satisfactory ; and when obser-
vation thus becomes an exact and conscious instrument,
it involves, to even a greater extent than in ordinary
life, intellectual activities like judgment and inference.
It is because this is true, because scientific observation
N
1/8 THE PROBLEM OF INDUCTION
demands the constant exercise of thought, in selecting
and comparing the various elements in the material
with which it deals, that it affords such excellent intel-
lectual discipline. The observational sciences do not
merely train the sense-organs ; the discipline which
they afford is mental as well as physiological, and it
is, of course, true that mental training can only be
gained through the exercise of mental activity.
It is quite true that it is of the utmost importance to distinguish
between a fact, and further inferences from the fact. As will be
pointed out in the chapter on Inductive Fallacies, errors very fre-
quently arise from confusing facts and inferences. The point which
is emphasized in the previous paragraph, however, is that it requires
a certain amount of thinking in order to get a fact at all. Facts do
not pass over ready-made into the mind. Simply to stare at things
does not give us knowledge ; unless our mind reacts, judges, thinks,
we are not a bit the wiser for staring. To observe well, it is neces-
sary to be more or less definitely conscious of what one is looking
for, to direct one's attention towards some particular field or object ;
and to do this implies selection among the multitude of impressions
and objects of which we are conscious. Moreover, scientific obser-
vation requires analysis and discrimination. It is not unusual, in
text-books on logic, to symbolize the various facts learned through
observation by means of letters, <z, b, c, etc., and to take it for granted
that they are given in our experience as distinct and separate phe-
nomena; but, as we have just seen, judgments of analysis and
discrimination are necessary to separate out the so-called ' phenom-
ena' from the mass or tangle of experience in which they were
originally given. Again, to determine the nature of a fact through
observation, it is essential to note carefully how it differs from
other facts with which it is likely to be confused, and also, to some
extent, what relations and resemblances it has. But such knowledge
presupposes that thought has already been at work in forming judg-
ments of comparison.
48. OBSERVATION 179
It may seem strange at first sight that the determina-
tion of the causal order and connection of phenomena
should be regarded as belonging to Observation rather
than to Explanation. To discover the causes of things
is, indeed, a very essential step in the process of expla-
nation ; but, as will appear more fully hereafter, the
distinction between observation and explanation is not
an absolute one. The process of knowledge is essen-
tially the same from beginning to end. The determina-
tion of the nature and order of phenomena is a long
step towards rendering them comprehensible. If the
distinction between observation and explanation as
methods of scientific procedure is to be made, it seems
right to assign to observation the task of determining
what phenomena are invariably conjoined as antecedents
and consequents. Experience presents to us a variety
of objects simultaneously or in rapid succession, but
in many cases such conjunction is merely temporary
and accidental. The problem which scientific obser-
vation has here to determine is the discovery of what
particular phenomena are necessarily connected, what are
the real antecedents and consequents in the case. ' The
sun was very hot this morning, and a picnic party went
on the lake, and this afternoon there is a severe thunder-
storm.' These events (and many others) are conjoined
temporally. Is there also a real connection between
any of them, or is their concurrence merely accidental ?
This is the question which must be answered by the
methods of determining causal connection. Of course
merely passive observation will not suffice to obtain an
answer. The relation of antecedent and consequent is
180 THE PROBLEM OF INDUCTION
not given, but has to be made out by the help of analysis
and inference. But, since the point to be determined
has reference to the nature and order of a set of facts
which can be observed, the methods employed may well
be included under Observation.
A distinction is sometimes made between observa-
tion and experiment. In observation, it is said, the
mind simply finds its results presented to it in nature,
while in experiment the answer to a question is obtained
by actively controlling and arranging the circumstances
at will. There are, no doubt, some grounds for this dis-
tinction, though it is not true that the mind is passive
in the one case, and active in the other. Even in ob-
servation, as we have seen, knowledge always arises
through active analysis and comparison of the impres-
sions received through sense. The difference is rather
this : In observing, where experiment is impossible, one
must wait for events to occur, and must take them in
the order in which .they are presented in the natural
series. But, where experiment is employed, we have
control of the ' conditions, and can produce the phe-
nomena to be investigated in any order, and as often
as we choose. In experiment, as Bacon says, we can
put definite questions to nature, and compel her to
answer. This is, of course, an immense advantage.
In some of the sciences, however geology and as-
tronomy for example it is not possible thus to con-
trol the conditions : one must wait and observe the
results of nature's experiments. Physics and chemis-
try are the experimental sciences par excellence ; and,
in general, we may say that a science always makes
48. OBSERVATION l8l
more rapid progress when it is found possible to call
experiment to the aid of observation. It is not possible
to conceive how physics and chemistry could have
reached their present state of perfection without the
assistance of experiment. Indeed, the almost total
neglect of experiment by the Greek and mediaeval
scholars must be regarded as one of the chief reasons
why the physical sciences made so little progress dur-
ing those centuries. Dr. Fowler states in the following
passage some of the main advantages to be derived
from experiment:
"To be able to vary the circumstances as we choose, to produce
the phenomenon under investigation in the precise degree which is
most convenient to us, and as frequently as we wish, to combine it
with other phenomena or to isolate it altogether, are such obvious
advantages that it is not necessary to insist upon them. Without
the aid of artificial experiment it would have been impossible, for
instance, to ascertain the laws of falling bodies. To disprove the
old theory that bodies fall in times inversely proportioned to their
weight, it was necessary to try the experiment ; to be able to affirm
with certainty that all bodies, if moving in a non-resisting medium,
would fall to the earth through equal vertical spaces in equal times,
it was essential to possess the means of removing altogether the
resisting medium by some such contrivance as that of the air-pump.
. . . Even when observation alone reveals to us a fact of nature,
experiment is often necessary in order to give precision to our
knowledge. That the metals are fusible, and that some are fusible
at a lower temperature than others, is a fact which we can conceive
to have been obtruded upon man's observation, but the precise
temperature at which each metal begins to change the solid for the
liquid condition could be learned only by artificial experiment." l
It is important, then, to recognize the services which
1 Fowler, Inductive Logic, p. 41 f.
1 82 THE PROBLEM OF INDUCTION
experiment renders in helping us to understand the
facts with which the various sciences deal. But it is not
necessary to distinguish experiment from observation as
if it were a separate and independent mode of investiga-
tion. We should rather say that observation, in the
sense in which we have used the word, employs experi-
ment wherever practicable as an indispensable auxiliary.
The methods of observation, then, which have still to be
described, will in many cases call for the employment of
experiments. Indeed, it will be seen that some of these
are essentially methods of experimentation.
49. Explanation. We have already seen that the
distinction between observation and explanation is not
an absolute one. The task which thought has to per-
form the task which is undertaken by science is to
reduce the isolated and chaotic experiences of ordinary
life to order and system. And it is important to remem-
ber that all the various methods employed contribute
directly towards that result. It has, however, seemed
possible to divide this undertaking into two main divis-
ions. Observation, it was said, seeks to discover the
exact nature of the facts to be dealt with, and also to
determine the ways in which they are necessarily and
invariably connected. But, when this has been accom-
plished, we have not by any means reached an end of
the matter. The desire for knowledge is not satisfied
with a mere statement of facts, or with the information
that certain phenomena always occur in a fixed order
as antecedents and consequents. Complete knowledge
demands an explanation of the facts as thus determined
49- EXPLANATION 183
by the methods of observation. ' Why,' we ask, ' should a
always precede b ? ' ' Why should dew be deposited under
such and such conditions, or water rise thirty-two feet in
a pump ? ' Science, we feel, should do more than de-
scribe the facts ; it should offer an explanation of
them as well. To explain events, however, is to furnish
reasons for them. The scientist is not content to know
merely that such and such phenomena exist, and occur
in conjunction with each other, but he attempts to dis-
cover why this is so. His knowledge is not confined to
the 'what,' but includes the 'why.' It is, of course, true
that a large part of scientific work is occupied with an
attempt to determine precisely and accurately the nature
of facts. Until the facts are thus scientifically deter-
mined attempts at explanation are usually quite futile.
But after this has been accomplished, it is still necessary
to show reasons why the phenomena with which we are
dealing have the precise character which they are found
to possess, and why they should occur in the invariable
order in which they are observed. Explanation, in other
words, completes the knowledge obtained through ob-
servation. It does further intellectual work on the
results given by the latter process. Explanation, itself,
has various degrees of completeness ; it may be more or
less satisfactory. When we come to treat Analogy, for
example, we shall find that it affords a kind of expla-
nation, though not one of an entirely satisfactory
type. In general, however, we may say that explana-
tion goes beyond the particular facts, and seizes upon
general principles or laws to which the facts are re-
ferred. And it is only when one knows the general law
1 84 THE PROBLEM OF INDUCTION
or principle involved in the case, that one can be said
really to understand the particular facts.
It is usually said that where we know merely the nature of phe-
nomena, and their connection, without being able to explain these
facts, our knowledge is empirical. Thus, I may know that an ex-
plosion follows the contact of a lighted match with gunpowder, or
that a storm follows when there is a circle around the moon, without
being able to explain in any way why these facts are connected.
On the other hand, if we can connect events by showing the gen-
eral principle involved, we say that our knowledge is really scientific.
It is important to notice, however, that empirical knowledge is simply
in a less advanced stage than the scientific knowledge which has suc-
ceeded in gaining an insight into the general law. Empirical know-
ledge leaves a problem which intelligence has still to solve. It is, of
course, true that a large part of every one's knowledge is empirical in
character. We all know many things which we cannot explain. In
all the sciences, too, phenomena are met with which seem to defy all
attempts at explanation. Indeed, some of the sciences can scarcely
be said to have passed the empirical stage. The science of medi-
cine, for example, has hardly yet reached any knowledge of general
principles. The physician knows, that is, as a result of actual ex-
periment, that such and such drugs produce such and such effects.
But he knows almost nothing of the means by which this result is
achieved, and is therefore unable to go beyond the fact itself. In
this respect, he is very little better off than the ordinary man, who
knows that if he eats certain kinds of food he will be ill, or if he
drinks strong liquors in excess he will become intoxicated.
CHAPTER
METHODS OF OBSERVATION. ENUMERATION AND STA-
TISTICS
50. Enumeration or Simple Counting. We shall
begin the account of the scientific methods with Enu-
meration. To count the objects which we observe,
and to distinguish and number their parts, is one of
the first and most essential operations of thought. It is
of course true that qualitative distinctions precede quan-
titative. The child learns to distinguish things by some
qualitative mark, such as 'black' or 'hot,' before he is
able to count them (cf. 82). But we may say, never-
theless, that the qualities of things are known, in a
general way at least, before scientific procedure begins.
The determination of quantity, on the other hand, seems
to demand a more conscious effort on the part of the
mind. We learn, that is, to distinguish the general
qualities of things without effort, but, in order to obtain
quantitative knowledge, it is necessary to set ourselves
deliberately to work. We may, therefore, take Enumer-
ation, or Simple Counting, which is perhaps the easiest
kind of quantitative determination, as our starting-point
in dealing with the Inductive Methods.
A considerable step in advance, in the task of re-
ducing the world of our experience to order and unity,
is taken when we begin to count, i.e., to group together
185
1 86 ENUMERATION AND STATISTICS
things of the same kind, and to register their number.
Thus Enumeration is, to some extent, also a process of
classification. What is counted is always a collective
whole, the units of which are either all of the same kind,
or else belong to a limited number of different classes.
Thus one might determine by Enumeration the number
of sheep in a flock, taking each individual as belonging
to the same general class, ' sheep ' ; or the analysis might
be pushed further so as to give as a result the number
of white and of black sheep separately. The purpose
for which the enumeration is undertaken always deter-
mines the length to which the process of analysis and
distinction is carried. For example, if the object of a
census enumeration were simply to determine the num-
ber of inhabitants in a country, it would not be neces-
sary to make any distinctions, but each person would
count as one. But where, as is often the case, the
aim is not simply to count the sum-total, but also to de-
termine the relative numbers belonging to various
classes, analysis has to be pushed further. In such
cases, we might count the number belonging to each
sex, the native-born, and those of foreign birth, those
below, and those above any given age, etc.
It will be noticed that the process of enumeration
takes account of each individual instance. And the
judgment which sums up the process puts the result in
a numerical form. ' There are twenty-five thousand
inhabitants in this town, five thousand of whom are of
foreign birth.' In cases where the examination of par-
ticular instances has been exhaustive, the result may be
stated in the form of a universal proposition. Thus,
50. ENUMERATION OR SIMPLE COUNTING 1 87
after examining the calendar of each of the months
separately, we might say : ' All of the months contain
less than thirty-two days.' Or, after measuring each
individual in a company, the assertion might be made :
'No one in this company is more than six feet tall.'
Cases of this kind, where a general assertion is made
after an examination of all the individuals concerned,
are termed by Jevons, instances of Perfect Induction.
11 An Induction, that is an act of Inductive reasoning, is
called Perfect, when all the possible cases or instances
to which the conclusion can refer, have been examined
and enumerated in the premises." l On the other hand,
where, as usually happens, it is impossible to examine
all the cases, the inductive process is regarded as Im-
perfect by the same writer, and the conclusion expressed
in the general law as only probable. The assertion
that all the months of the year contain less than thirty-
two days, is derived from Perfect Induction, and is ab-
solutely certain, but the proposition that 'all men are
mortal,' is derived from Imperfect Induction, and there
is no certainty, but only a probability that all future
cases will agree with those which we have already
experienced.
This distinction, however, seems to be founded on a
mistaken view of the nature of inductive reasoning. It
assumes that it is the business of induction to count
instances. When the examination and enumeration is
exhaustive, the results can, of course, be summed up in
a general proposition which is absolutely certain. But
1 Jevons, Elementary Lessons in Logic, pp. 212-213.
)8S ENUMERATION AND STATISTICS
where the counting is incomplete, where all the possible
cases cannot be examined, the conclusion is regarded
as uncertain. Now, this could be accepted as an ac-
count of induction, only if it were maintained that this
process aims merely at a summation of particular in-
stances. We have already seen, however, that the real
object of inductive inference is to discover the general
law or principle which runs through and connects a
number of particular instances. It is, of course, true
that we shall be more likely to obtain a correct insight
into the nature of the law from an examination of a
large number of cases than from that of a small number.
But the discovery of the principle, and not the number
of instances, is the main point. If the purpose of the
induction, the discovery of the universal principle, can
be adequately attained, one case is as good as a hun-
dred (cf. 88).
The truth seems rather to be that enumeration is merely the
beginning, rather than the end of the inductive process. It gives
us important information regarding particular instances and indi-
viduals. But in itself it is not sufficient to bring to light the gen-
eral law that explains why the particular objects enumerated are
connected together, or act as they do. Enumeration plays a part
as a method of observation, but it affords no real explanation of
the particular facts with which it deals. Even where all the pos-
sible cases are examined, it cannot rightly be called Perfect In-
duction, for the goal of Induction is explanation by means of a
general principle. The requirements of inductive science are not
completely fulfilled, for example, when an examination of Mercury,
Venus, Mars, and all the other known planets yields the proposi-
tion : ' All the planets revolve around the sun in elliptical orbits.'
The 'all' in this proposition denotes simply an aggregate of indi-
viduals. It is merely an expression of fact. The reasons necessary
51. STATISTICS AND STATISTICAL METHODS 189
to explain the fact are not reached by enumeration ; in order to ob-
tain them it is necessary that further work shall be done by think-
ing, and that the process of induction shall be carried further.
The conclusion which we reach, then, is that no
process of enumeration has any claim to the title of
Perfect Induction. Enumeration is the beginning,
rather than the end of the inductive procedure.
Nevertheless, it is exceedingly useful as a preliminary
step and preparation for scientific explanation. The
number of stamens and pistils which a plant contains,
or the number of tympanic bones possessed by an ani-
mal, is often of the greatest service in classification.
And classification, although it is by no means the end
of scientific investigation, is in many of the sciences a
most essential and important step towards it. The task
of explaining the infinite variety of natural objects
would be a hopeless one, if it were not possible to
discover similarities of structure, in virtue of which
things can be grouped together in classes. To this,
enumeration in a very great degree contributes.
51. Statistics and Statistical Methods. Statistical
methods depend upon enumeration. They aim at mak-
ing the process of counting as exact and precise as pos-
sible. Modern science has come to understand that its
first task must be to become acquainted, as completely
as possible, with the nature of the facts presented to it
by experience. And, for this purpose, the careful classi-
fication and precise enumeration of particulars afforded
by statistics, is often of the greatest importance. " The
extent to which the statistical method prevails, and
ENUMERATION AND STATISTICS
everything is counted," says Professor Sigwart, "is
another instance of the fundamental difference between
ancient and modern science." l It would, of course, be
impossible to enter here into a full description of the
methods employed by statistical science. The method-
ology of every science must be learned by actual prac-
tice within the particular field. What we are interested
in from a logical point of view is the purpose which sta-
tistical investigation seeks to fulfil, and the part which
it plays in rendering our knowledge exact and syste-
matic.
We notice, in the first place, that the class of facts
to which statistics are applied has two main character-
istics : the subject dealt with is always complex, and
capable of division into a number of individual parts or
units ; and, secondly, it is also of such a nature that
the underlying law or principle of the phenomena to be
investigated cannot be directly discovered. Thus, we
employ statistics to determine the death-rate of any
country or community, or the ratio between the num-
ber of male and of female births. It is clear that it is
impossible to make use of experiment when we are deal-
ing with facts of this kind, because the conditions are not
under our control. If it were possible, for example, to
determine exhaustively the general laws according to
which the various meteorological changes are coordinated
with their conditions, we should not trouble ourselves to
count and register the separate instances of changes in
the weather. Nor, if we knew exactly the general condi-
1 Logic (Eng. trans.), Vol. I., p. 286.
5L STATISTICS AND STATISTICAL METHODS 19 1
tions under which any given human organism in contact
with its environment would cease to exist, should we
count the individual cases of death. " In proportion as
we are unable to reduce the particular event to rules and
laws, the numeration of particular objects becomes the
only means of obtaining comprehensive propositions
about that which is, for our knowledge, fortuitous ; as
soon as the laws are found, statistical numeration ceases
to be of interest. There was some interest in counting
how many eclipses of the moon and sun took place year
by year, so long as they occurred unexpectedly and in-
explicably ; since the rule has been found according to
which they occur, and can be calculated for centuries
past and to come, that interest has vanished. But we
still count how many thunder-storms and hail-storms
occur at a given place, or within a given district, how
many persons die, and how many bushels of fruit a
given area produces, because we are not in a position to
calculate these events from their conditions." 1
In cases like those mentioned above, where we are
as yet unable to determine the general laws which are
at work, we call to our aid statistical enumeration.
There are two main advantages to be derived from the
employment of this method. In the first place, it con-
tributes directly towards a clear and comprehensive
grasp of the facts. Instead of the vague impression de-
rived from ordinary observation, statistics enable us to
state definitely the proportion of fine and rainy days
during the year. Statistical enumeration is thus one
1 Sigwart, Logic (Eng. trans.), Vol. II., p. 483.
1 92 ENUMERATION AND STATISTICS
of the most important means of rendering observation ex-
act and trustworthy, and of summing up its results in a
convenient and readily intelligible form. It is of the
utmost importance when dealing with complex groups of
phenomena, to have a clear and comprehensive view of
the facts of the case. Thus, when trying to understand
the nature of society, it is necessary to determine accu-
rately by means of statistics, such facts as the number
of male and of female births, the death-rate, the pro-
portion of marriages, the age of marriage, etc. But,
in the second place, statistics often serve to reveal
quantitative correspondences or uniformities between
two groups of phenomena, and thus suggest that some
causal connection exists between them. It is found,
for example, that the number of births in any given
country varies inversely as the price of food during the
previous year. Now this fact at once suggests the ex-
istence of certain physiological and psychological laws
which may serve to bring these facts into causal rela-
tion. In many cases, such correspondences serve only
to confirm our expectation of the presence of a causal
law, which is based on other grounds. Thus we should
naturally expect that there would be a relatively greater
number of cases of fever in a town which had an insuf-
ficient water supply, or an antiquated system of sewer-
age, than in a town where these matters were properly
provided for; and statistics might bear out our conclu-
sions. In general, however, it may be said that causal
laws are suggested, not by corresponding uniformities,
but by corresponding variations, as shown by the sta-
tistics of different sets of facts. So long as the death-
5L STATISTICS AND STATISTICAL METHODS 193
rate, for example, shows a constant ratio to the pop-
ulation, no causal inference is suggested ; but if the
annual number of deaths increases or decreases consid-
erably, we are led to look for some variation from the
normal in some coincident group of phenomena. And
if it is found that the variation in the death-rate has
been accompanied by unusually favourable or unfavoura-
ble conditions of weather, the presence or absence of
epidemics, or any similar circumstances, there will be at
least a presumption that a causal relation exists between
these two sets of events. From a certain likeness
or quantitative resemblance between the variations of
two distinct classes of phenomena, we are led to the
hypothesis of their causal connection.
Statistical enumeration is frequently employed to determine the
average of a large number of instances of a particular kind. This is
obtained by dividing the sum of the given numbers by the number
of individuals of which account is taken. In this way a general
average is reached which does not necessarily correspond exactly
with the character of any individual of the group. It represents a
purely imaginary conception, which omits individual differences and
presents in an abbreviated form the general character of a whole
class or group. In this way, by the determination of the average, it
becomes easier to compare complex groups with one another. Thus,
when the average height of Frenchmen and Englishmen has been
determined, comparison is at once made possible. For the mean
or average of a number of individuals, or set of instances, however,
we can infer nothing regarding the character of any particular indi-
vidual, or of any particular instance. What is determined by the
method of averages is the general nature of the group, as represented
by the average or typical individual. But this method does not en-
able us to infer anything regarding the character of any member of
the group, A, or B. When exact statistics are obtainable, however,
o
194 ENUMERATION AND STATISTICS
it is possible to show what the probabilities are in reference to any
particular case, so long as the peculiar circumstances which belong
to each instance are not considered, and each case is reckoned simply
as one unit of the group. This is, of course, the principle employed
by the method of mathematical probabilities. It will be sufficient
here to indicate the general method of procedure in such cases.
52. The Calculation of Chances. There is, of course,
no such thing as 'chance/ regarded as a power which
controls and governs events. When we speak of some-
thing happening ' by chance,' or of some occurrence as
'probable,' we are expressing merely a deficiency in our
own knowledge. " There is no doubt in lightning as
to the point it shall strike ; in the greatest storm there
is nothing capricious ; not a grain of sand lies upon the
beach but infinite knowledge would account for its lying
there ; and the course of every falling leaf is guided by
the same principles of mechanics as rule the motions of
the heavenly bodies." 1 To assert that anything hap-
pens by chance, then, is simply to confess our ignorance
of the causes which are operative.
It is clear that we are in this position regarding many
of the ordinary events which belong to the future. Be-
cause of my ignorance of the causes at work, I can only
say, ' It may rain to-morrow.' It is impossible to tell
upon which side a penny will fall at any particular
throw, or what card may be drawn from a pack. But in
cases like these, we have to accept, for lack of anything
better, a numerical statement of the chances for any
particular event. Thus we know that, since there
1 Jevons, The Principles o/Scitnce, Vol. I., p. **},
52. THE CALCULATION OF CHANCES 195
are only two sides upon which a penny can fall, the
chances of throwing heads in any trial is |. Similarly,
there are four chances out of fifty-two of drawing an
ace from a pack of cards. The chance of obtaining
an ace by any draw is therefore ^V = iV These figures
express the mathematical chances. Experience of a
limited number of instances may, however, sometimes
appear to show a lack of harmony between the mathe-
matical and the actual chances. But in proportion as
the number of trials is increased, the result is found to
approximate more and more nearly to the mathematical
expectation. In twenty throws of a penny or a die, we
should not be surprised to find that the result differed
from the fraction expressing the mathematical chances.
But this discrepancy would tend to disappear as the
number of cases was increased. Jevons illustrated this
by actual trial, using a number of coins at a time. Out
of a total of 20,480 throws, he obtained a result of 10,353
heads. On the result of the experiment he remarks :
" The coincidence with theory is pretty close, but con-
sidering the large number of throws there is some
reason to suspect a tendency in favor of heads." 1
Apart from the simple and somewhat artificial cases
where we are concerned with coins and dice, etc., it is
impossible to determine with mathematical precision the
chances for or against any event. In cases where the
whole series of possibilities does not lie before us, we
have to base our calculations for the future on what
is known regarding the frequency with which the events
1 Jevons, loc. cit. Vol. I., p. 230.
196 ENUMERATION AND STATISTICS
under consideration have occurred in the past. Now
the results of the last paragraph make it clear that it is
of the utmost importance that the statistics, which are
taken as the basis, shall be as full and comprehensive
as possible. It is evident, for example, that serious
errors would be likely to arise, if the death-rate for a
single year, or for a single county or town, were taken
as typical of the country as a whole. To render sta-
tistics trustworthy, they must be extended over a consid-
erable period of time, and over a large extent of country,
so as to eliminate the accidents due to a particular time
or to a particular locality.
When this has been done, however, and statistics have been ob-
tained that have a right to be regarded as really typical, the chances
in any individual instance can be readily shown. Thus we find that
out of one thousand children born, about two hundred and fifty die
before the age of six years. The chances, then, at birth, that any
child will reach this age, are T 7 <,%% or f . Again, it is found that
only about two persons in one thousand live to be ninety years old.
So that the probability of any child living to this age would be ex-
pressed by the fraction -^^ or -5^. This is essentially the princi-
ple upon which life insurance companies proceed. Their business is
conducted on the assumption that there will be an approximately
constant death-rate, though they cannot foretell what particular indi-
viduals are to die in any year. It thus becomes possible to calculate
what losses from death may be expected each year. Suppose that
it is found that the annual death-rate among men of a certain age
throughout the country is twenty out of every thousand. If each
man's life were insured for $1000, the loss to the company from
this source would be $20,000. To compensate for this loss, the
company would be obliged to demand an annual payment of $20
from each of the one thousand individuals in the class. Of course,
the actual computations upon which insurance is based in concrete
52. THE CALCULATION OF CHANCES 197
cases are vastly more complex than this, and many other consider-
ations arise of which account has to be taken. But the general
principle involved is, that by taking a sufficiently large number of
cases, chance can be almost eliminated. We can have no means
of determining whether any healthy individual will or will not die
before the end of the year. There would be a very serious risk,
amounting practically to gambling, in insuring his life alone. But
the transaction, as we have seen, is no longer a mere speculation
when a large number of individuals are concerned ; for the actual
loss can be accurately foretold and provided for.
References
C Sigwart, Logic, 101, 102.
J. G. Hibben, Inductive Logic, Ch. XV.
L. T. Hobhouse, The Theory of Knowledge, Pt. II. Ch. XI.
J. S. Mill, Logic, Bk. III. Ch. XVIII.
B. Bosanquet, Logic, Vol. I., pp. I28ff.
CHAPTER XV
METHODS OF OBSERVATION
Determination of Causal Relation,
53. Mill's Experimental Methods. So far, we have
been dealing with the methods employed in discovering
the nature of particular things. We have been con-
sidering how our knowledge of the qualities and quanti-
ties of objects may be made as exact and complete as
possible, but almost nothing has yet been said regard-
ing the connection of things. Our experience, however,
is not made up of isolated facts and events. We can
scarcely be said to know at all, until we become aware
that certain parts of our experience are united, like the
links of a chain, one part involving another. And, as
has been already frequently pointed out, the growth of
knowledge is constantly bringing to light new connec-
tions between facts that were previously taken to be
independent of each other. Of these principles of
connection, the most universal and important is that
of cause and effect. Thus we say that everything
which happens has its cause, and is in turn followed
by its effect. What rule, or rules, can now be given
which will enable one to discover what is the cause or
the effect of an event in any particular case ?
Before we proceed to the answer of this question, however, it is
necessary to explain briefly what is meant in science by the relation
198
53- MILL'S EXPERIMENTAL METHODS 199
of cause and effect. As the terms are used in modern scientific
investigation, a cause of any phenomenon is that which necessarily
and invariably precedes it ; and an effect is what follows, in the
same uniform way, some event which has gone before (cf. 84).
To determine the causal relation between phenomena, then, is to
discover what events or circumstances always accompany each
other as antecedent and consequent. Now, as will appear when
we come to describe the methods actually employed, it is very often
impossible to do this by means of direct observation. Reasoning
and experiment have oftentimes to be summoned to the aid of
observation in distinguishing between events which are merely
accidentally conjoined, and those which are necessarily connected
as cause and effects. But, as has been already shown ( 48, 49),
there is no hard and fast distinction to be made between methods
of observation and methods of explanation. To discover the in-
variable antecedent of a phenomenon is at least the beginning of
explanation. Thus B is explained to some extent when I am able
to point to A as its invariable antecedent. Nevertheless, since this
connection of A and B is itself a fact which may be observed, its
discovery may, I think, be fairly said to belong to observation rather
than to explanation. Explanation, in its complete form, carries one
beyond the mere fact of connection to its reas.oris. At the stage
we have now reached, however, the problem is to show what other
phenomenon, or group of phenomena, is necessarily and uniformly
connected with a given event or circumstance.
The methods by which such a law of connection may
be established were first formulated by Mill in his Logic.
He stated, in general terms, the principles which were
already in use in scientific procedure. Mill gives five
separate canons, but, as he himself recognizes, there
are but two main principles involved. "The simplest
aftd most obvious modes of singling out from among
the circumstances which precede or follow a phenome-
non, those with which it is really connected by an
200 CAUSAL DETERMINATION
invariable law are two in number : One is by com-
paring together different instances in which the phe-
nomenon occurs. The other is by comparing together
instances in which the phenomenon does occur with
instances in other respects similar in which it does not.
These two methods may be respectively denominated
the Method of Agreement, and the Method of Differ-
ence." 1 Of the other three methods mentioned by
Mill, one the Joint Method of Agreement and Dif-
ference is, as the name implies, a direct combination
of the first two, while the Method of Residues and the
Method of Concomitant Variations are corollaries from
the same principles. We shall now proceed to state
and illustrate these canons.
54. The Method of Agreement. The principle upon
which this method proceeds is stated in the following
way by Mill : "If two or more instances of the phenome-
non under investigation have only one circumstance in
common, the circumstances in which alone all the in-
stances agree is the cause (or effect} of the given phenome-
non." The purpose of this rule, it will be remembered,
is to help us to determine what particular facts in our
experience are connected as causes and effects. If the
problem is to find the cause of some phenomenon, the
canon may be illustrated in the following way. Let
P 1 , P 2 , P 3 represent different instances of a phenome-
non, P, whose cause is to be ascertained. And suppose
that we are able to analyze,
1 Mill, Logic, Bk. III. Ch. VIII. $ 1
54- THE METHOD OF AGREEMENT 2OI
the antecedents of P 1 into abed ;
the antecedents of P 2 into gfcm ;
the antecedents of P 3 into klnc.
Now it is clear that c is the sole circumstance in which
the antecedents of all these instances of P agree. We
should be justified in concluding, therefore, according to
this method, that c is probably the cause of the phe-
nomenon under investigation, P. We may, then, adopt
Jevons's formula for discovering the cause of any given
phenomenon by this method : "The sole invariable ante-
cedent of a phenomenon is probably its cause"
If, now, we wished to discover the effect of some-
thing which happens, it would be necessary to deter-
mine, by observing a number of instances, what common
circumstance can be found among the events which
follow it.
If Q 1 were followed \>y fghk,
and Q 2 were followed by Irngc,
and Q 3 were followed by grst,
we should be able to say that Q and g were connected
as cause and effect. The rule might then be expressed :
The sole invariable consequent of a phenomenon is prob'
ably its effect.
When antecedents and consequents are thus repre-
sented schematically by means of letters, it is easy to
perceive at once the common circumstance in a number
of instances. But the facts and events of the real world
are not separated off from each other in this way. The
common circumstance in which a number of instances
agree has to be separated out by analysis from the varia-
202 CAUSAL DETERMINATION
ble elements which form part of the different antecedents
and consequents. In order to discover the common
characteristic, it is necessary that we should be able
to analyze a complex phenomenon into its constituent
parts, and should also be able to recognize the common
element as common, though it may appear in wholly
different circumstances. This will become evident by
considering a number df concrete cases in which this
method may be employed.
If a number of cases of typhoid fever were to appear
at about the same time in a community, one would nat-
urally wish to explain this phenomenon by tracing it to
its cause ; and to do this one would try to discover
some circumstance which was the common antecedent
of all the cases. The water supply might first be ex-
amined. But if it were found that this were derived
from entirely different sources in the different cases, we
should probably conclude that the explanation must be
sought elsewhere. Suppose that as a result of careful
analysis it was discovered that all the individuals pros-
trated with the fever had eaten oysters bought at the
same market. If this were the only common circum-
stance discoverable after careful investigation, we should
conclude that probably the oysters were the cause of
the fever. The process of analysis could be pushed
still further, if one wished, in order to determine more
exactly the precise source of the infection ; e.g., it might
be found, as a result of further inquiry, that the water
in which the oysters were kept was vitiated by a sewer.
Another example of the method of agreement which
is often quoted by logicians may be given. One would
54- THE METHOD OF AGREEMENT 203
naturally suppose that the colours and lines of mother-of-
pearl were due to the chemical or physical character of
the substance itself. Sir David Brewster, however,
happened to take an impression of a piece of mother-
of-pearl in beeswax and resin, and was surprised to see
the colours reproduced upon its surface. He then took
a number of other impressions in balsam, gum-arabic,
lead, etc., and found the iridescent colours repeated in
every case. In this way he proved that the colours were
caused by the form of the substance, and not by its
chemical qualities or physical composition. The dif-
ferent substances, wax, balsam, lead, etc., in which the
phenomenon of colour appeared, had nothing in common
except the form. This, therefore, according to the
method of agreement, was properly regarded as the
cause of the phenomenon to be explained.
An example of the application of this method to the
discovery of the effect of a phenomenon may now be
given. Let us suppose that the problem is to determine
the effect of some proposed legislation. It is necessary,
of course, to refer to other instances where this legisla-
tion has been put in force. Let us suppose that in one
case what followed the enactment of the law under con-
sideration was falling off of revenue, increase of immi-
gration, good crops, etc., and in a second, revival of
ship-building, rainy weather, and increase of immigra-
tion ; and that in other instances where still other
conditions prevailed, the number of immigrants still
continued to increase. Since this latter circumstance is
the only one which follows invariably upon the enact-
ment of the law, we are justified in concluding, after a
204 CAUSAL DETERMINATION
certain number of observations, that it is necessarily
connected with the law as its result. It is important
to note that the conclusions reached by this method
are greatly strengthened by increasing the number of
observations, and by taking instances as dissimilar in
character as possible.
The method of Agreement by itself, however, is not able to
afford us certainty in every case. We have spoken of the cause as
'the invariable antecedent,' and of the effect as 'the invariable con-
sequent.' So long, then, as we are dealing with events which fol-
low each other, there is no difficulty in perceiving which is cause,
and which effect. But we are often called upon to investigate the
relation between phenomena that are more permanent in character.
And it is then not at all easy to determine by means of the method
of Agreement which is cause and which is effect. Poverty and in-
temperance, for example, are found conjoined so frequently as to
make it evident, apart from other considerations, that some causal
relation exists between them. It might be maintained with appar-
ently equal show of reason, that the former is the cause, or the effect,
of the latter. Again, is one to say that ignorance is the cause or the
effect of moral degradation? There seems to be no method of de-
termining which is antecedent and which consequent. As a matter
of fact, it is probably true in such cases that the phenomena act
and react upon each other: that each term, in other words, is at
once both cause and effect.
There is still another circumstance which renders uncertain the
results of the method of Agreement. We have proceeded on the
assumption that the given phenomenon is always produced by
the same cause ; and, on the other hand, that the effects of different
causes are always different. But this is not so ; heat, for example,
may be caused by combustion, or by friction, or electricity. The
fact that an effect may be produced by any one of several causes, is
what is meant by the phrase 'Plurality of Causes.' Again, neither
the cause nor the effect need be composed of a simple phenomenon,
55- THE METHOD OF DIFFERENCE
or single circumstance, as has been supposed. Indeed, so far as
observation can show, antecedents and consequents usually seem to
consist of complex sets of circumstances. The difficulty with the
method of Agreement is that it does not push the process of analysis
far enough to enable us to establish completely a law of causal rela-
tion. The fact of Agreement between phenomena often serves, how-
ever, to suggest a law of connection. This law has afterwards to be
tested by the other methods, especially by the method of Difference.
55. Th Method of Difference. According to the
method of Agreement, we cotnpare a number of diverse
instances, in all of which a given phenomenon occurs,
and endeavour to discover some circumstance which is
invariably present. The method of Difference, on the
other hand, compares an instance in which a phenome-
non occurs with another as nearly similar to it as possi-
ble, in which it does not occur. Its canon is expressed
by Mill as follows : " If an instance in which the phe-
nomenon under investigation occurs, and an instance in
which it does not occur, have every circumstance in
common save one, that one occurring only in the former ;
the circumstance in which alone the two instances differ
is the effect or the cause or an indispensable part of
the cause, of the phenomenon" It will perhaps make
the matter clearer to say : ' whatever alone is present
in a case when the phenomenon to be investigated
occurs, and absent in another when that phenomenon
does not occur, other circumstances remaining the
same, is causally connected with that phenomenon.'
That is, by means of this method we compare two
instances which differ only in the fact that the phe-
nomenon in which we are interested, is present in the
2O6 CAUSAL DETERMINATION
one, and absent in the other. If now the two cases are
represented in this way,
PHK conjoined with alg,
and HK conjoined with Ig,
we conclude at once that P is causally connected with a.
Almost any instance in which experiment is em-
ployed will serve to illustrate this method. If a bell is
rung in a jar containing air, the sound will of course be
heard at any ordinary distance. But after having re-
moved the air by means of an air-pump, let the bell be
again struck. It will now be found that the sound is no
longer heard. When the two cases are compared, it is
at once evident that the only difference in the antece-
dents is the presence of the air in the one case, and its
absence in the other. When the air was present, the
sound was heard ; when it was absent, the sound was
not heard. We conclude, therefore, that the perception
of sound is causally connected with the presence of
atmospheric air. Again, we can prove that the so-called
'taste ' of different objects depends upon smell, by tast-
ing, say, an orange, and after a little time has elapsed,
tasting it a second time while holding the nose. It
will be found in this latter case that instead of the
familiar 'orange taste,' one senses merely 'acid,' or
'sweet.' The only difference in the two trials being
that in the former the organ of smell, which was ex-
cluded in the latter, was operative, the so-called 'orange
taste ' is proved to be due to smell rather than to taste
proper.
An essential requirement of the method of Difference
55- THE METHOD OF DIFFERENCE 207
is that only one circumstance shall be varied at a time.
The object of the method is to isolate the various con-
ditions which go to make up a complex phenomenon,
in order that we may mark the effect of the presence
or absence of each one individually. Now, in observing
what goes on in nature, we rarely find changes in
which but a single element has varied. If we find that
to-day is cooler than yesterday, we may be inclined to
refer the change to the thunder-storm of last night.
But rain also accompanied the thunder-storm, and the
direction of the wind has changed. So that it is im-
possible in such cases to apply the method of difference.
To employ this method successfully, observation usually
must be supplemented by experiment. In performing
experiments, we determine what conditions are to be
operative, and arrange the apparatus so as to carry out
our purpose. Having thus control of the conditions, we
are able to vary them at pleasure. In this way, experi-
ment becomes an instrument by means of which analysis
can be carried further than is possible for unaided ob-
servation. It enables us to separate things which are
usually conjoined, and to observe the result of each when
taken by itself. In employing experiment, however, the
greatest care must always be taken to introduce only
one new condition at a time, or at least only one new
circumstance which can in any way influence the result.
It often happens, too, as Jevons points out, that the
experimenter is not aware of all the conditions which
are operative when his investigations are made. " Some
substance may be present, or some power may be in
action which escapes the most vigilant examination
2O8 CAUSAL DETERMINATION
Not being aware of its existence, we are of course
unable to take proper measures to exclude it, and thus
determine the share which it may have in the results of
our experiments." 1 For this reason, it is always neces-
sary that experiments should be repeated by different
persons, and so far as possible under varying conditions.
I quote two examples from the work of Jevons to which
reference has just been made.
" One of the most extraordinary instances of an erroneous opinion
due to overlooking interfering agents is that concerning the increase
of rainfall near the earth's surface. More than a century ago it was
observed that rain gauges placed upon church steeples, house-tops,
and other elevated places, gave considerably less rain than if they
were on the ground, and it has very recently been shown that the
variation is most rapid in the close neighborhood of the ground.
All kinds of theories have been started to explain this phenomenon ;
but I have attempted to show that it is simply due to the interfer-
ence of wind which deflects more or less rain from all the gauges
which are at all exposed to it.
" The great magnetic power of iron renders it a constant source of
disturbance in all magnetic experiments. In building a magnetic
observatory great care must be taken that no iron is employed in
the construction, and that no masses of iron are near at hand. In
some cases, magnetic observations have been seriously disturbed by
the existence of masses of iron in the neighborhood. In Faraday's
experiments upon feebly magnetic or diamagnetic substances, he
took the greatest precautions against the presence of any disturbing
substance in the copper wire, wax, paper, and other articles used in
suspending the test objects. It was his invariable custom to try the
effect of the magnet upon the apparatus in the absence of the object
of experiment, and without this preliminary trial no confidence
could be placed in the results." 2
1 Jevons, Principles of Science, Vol. II. p. 37.
2 Jevons, op. cit. pp. 40, 41.
CHAPTER XVI
METHODS OF OBSERVATION
Determination of Causal Relation (continued')
56. The Joint Method of Agreement and Difference.
When it is not possible to obtain experimental proof
directly, recourse is often had to what Mill has called
the joint method of Agreement and Difference. This
writer has given the following expression of the canon :
"If two or more instances in which the phenomenon
sccurs have only one circumstance in common, while
two or more instances in which it does not occur have
nothing in common save the absence of that circum-
stance, the circumstance in which alone the two sets
of instances differ is the effect, or the cause, or an
indispensable part of the cause, of the phenomenon"
This method, as the name implies, is a combination
of the two already described. We may perhaps sim-
plify Mill's canon somewhat by putting the matter in
the following way : A number of diverse instances hav-
ing been examined, if it is found that there is a single
circumstance invariably present when the phenomenon
under investigation is present, and invariably absent
when the latter is absent, this circumstance is causally
connected ivith that phenomenon. By the help of this
method, the weakness which has already been noticed
in the method of Agreement is overcome. We first
p 309
2IO CAUSAL DETERMINATION
compare different instances in which the phenomenon
occurs. If these are found to agree in only a single
circumstance, we conclude, according to the canon
of Agreement, that this circumstance is probably con-
nected causally with the phenomenon in which we are
interested. But the proof is not yet complete. To
really prove the connection, we must show that where-
ever this circumstance is absent, there the phenome-
non is also absent.
As an illustration of this method, we may take the
case where one is trying to decide whether some stimu-
lant like coffee or tobacco is injurious to him or not. If a
person invariably found himself troubled with insomnia
or nervousness after smoking, and if this seemed to him
the only circumstance in his mode of life common to all
these occasions, he might suspect that this was the cause.
That is, the coincidence or agreement between the habit
and ill-health would suggest a causal relation. But as yet,
the relation would be only suggested, not proved. The
method of Agreement, as we have already seen, only
gives us probable conclusions. Here, however, we have
the conditions under our control, and can resort to ex-
periment and the method of Difference, in order to verify
or disprove the suggestion. If after having given up
smoking for a reasonable length of time, a man found
that the disagreeable symptoms still continued, he would
conclude that his suspicion was unfounded. But if it
were found that his insomnia and nervousness had dis-
appeared during his period of abstinence, and if the
sole circumstance common to all these days and nights
of exemption was the absence of smoking, he would be
57- THE METHOD OF CONCOMITANT VARIATIONS 211
forced to admit, however reluctant he might be to do so,
that the troublesome physiological derangements were
probably connected with the smoking habit.
57. The Method of Concomitant Variations. The
methods of Agreement and Difference are employed,
as we have seen, to determine what events are necessa-
rily connected as causes and effects. By examining a
considerable number of instances, and by comparing
the cases in which the phenomenon of interest to us
occurs, with cases in which it does not occur, we seek
to rule out all accidental and unessential conjunctions.
But as yet nothing has been said of quantitative rela-
tions. The discovery of a quantitative agreement or cor-
respondence between two phenomena, or two groups of
phenomena, often enables us to detect a causal relation
between them (cf. pp. 192-193). Moreover, science does
not rest satisfied with the mere discovery and description
of changes, and the order in which they occur. We may
almost say that science does not exist until the quanti-
tative aspects of phenomena are taken into account
until things are weighed and measured. The physicist
does not think his work finished when he has proved
that sound is produced by atmospheric vibrations. He
carries on his analysis until he can discover the qttanti-
tative relations between the amplitude and velocity of
the vibrations, and the loudness and pitch of the result-
ing tone. And the psychologist is not satisfied with the
general statement that certain sensations are causally
connected with certain kinds of stimulus ; but he seeks
to discover, whenever possible, the exact quantitative
relation between sensation and stimulus. In short, the
212 CAUSAL DETERMINATION
most important feature, the very essence, one may say,
of modern scientific investigation, is the establishment
of quantitative relations.
Looking at two things from the standpoint of quan-
tity, then, we say that when their variations keep pace
with each other, they are in some way causally con-
nected. The following is Mill's statement of the canon :
" Whatever phenomenon varies in any manner whenever
another phenomenon varies in a particular manner, is
either a caiise or an effect of that phenomenon, or is con-
nected with it through some fact of causation." The
illustrations of this law given by Jevons are so excellent
that we cannot do better than adopt them :
"The illustrations of this law are infinitely numerous. Thus
Mr. Joule, of Manchester, conclusively proved that friction is a cause
of heat by expending exact quantities of force by rubbing one sub-
stance against another, and showed that the heat produced was
exactly greater or less in proportion as the force was greater or less.
We can apply the method to many cases which had previously been
treated by the simple method of difference ; thus instead of striking
a bell in a complete vacuum, we can strike it with a very little air in
the receiver of the air-pump, and we then hear a very faint sound
which increases or decreases every time we increase or diminish the
density of the air. This experiment conclusively satisfies any per-
son that air is the cause of the transmission of sound.
" It is this method which often .enables us to detect the material
connection which exists between two bodies. For a long time it
had been doubtful whether the red flames seen in total eclipses of
the sun belonged to the sun or moon ; but during the last eclipse of
the sun. it was noticed that the flames moved with the sun, and were
gradually covered and uncovered by the moon at successive instants
of the eclipse. No one could doubt thenceforth that they belonged
to the sun.
58. THE METHOD OF RESIDUES 2 1 3
" Whenever, again, phenomena go through Periodic Changes, alter-
nately increasing and decreasing, we should seek for other phe-
nomena which go through changes in exactly the same periods, and
these will probably be a connection of cause and effect. It is thus
that the tides are proved to be due to the attraction of the moon and
sun, because the periods of high and low, spring and neap tides,
succeed each other in intervals corresponding to the apparent revo-
lutions of those bodies round the earth. The fact that the moon
revolves upon its own axis in exactly the same period that it revolves
round the earth, so that for unknown ages past the same side of the
moon has always been turned toward the earth, is a most perfect
case of concomitant variations, conclusively proving that the earth's
attraction governs the motions of the moon on its own axis.
" The most extraordinary case of variations, however, consists in
the connection which has of late years been shown to exist between
the Aurora Borealis, magnetic storms, and the spots on the sun.
It has only in the last thirty or forty years become known that the
magnetic compass is subject at intervals to very slight, but curious
movements ; and that, at the same time, there are usually natural
currents of electricity produced in telegraph wires, so as to interfere
with the transmission of messages. These disturbances are known
as magnetic storms, and are often observed to occur when a fine dis-
play of the Northern or Southern Lights is taking place in some
part of the earth. Observations during many years have shown
that these storms come to their worst at the end of every eleven
years. . . . Close observations of the sun during thirty or forty years
have shown that the size and number of the dark spots, which
are gigantic storms going on upon the sun's surface, increase and
decrease exactly at the same periods of time as the magnetic storms
upon the earth's surface. No one can doubt, then, that these strange
phenomena are connected together, though the mode of the con-
nection is quite unknown. . . . This is a most remarkable and
extensive case of concomitant variations." 1
58. The Method of Residues. We have said that
1 Jevons, Lessons in Logic, pp. 249-251.
214 CAUSAL DETERMINATION
modern science employs measurement whenever possi-
ble, in order to determine exactly the quantitative rela-
tions of phenomena. Groups of facts whose connections
are at first not perceived, or at best but vaguely appre-
hended, are brought into close relations with each other
by the establishment of definite quantitative relations.
The knowledge that electricity possesses energy, for
example, is very vague and incomplete when compared
with the definite equations which the physicist can fur-
nish between the electrical current generated under cer-
tain definite conditions, and the amount of work which
it is capable of performing. But the discovery of quan-
titative relations not only renders our knowledge more
perfect and complete, it also enables us in some cases to
detect laws of connection which would not otherwise be
observed. We have already seen how the perception of
corresponding changes in the quantities of phenomena
has led to the discovery of causal laws by means of the
method of Concomitant Variations. The method of
Residues, which we now have to discuss, is also a method
of quantitative determination.
In general, this method calls attention to any remain-
der or residue which is left over after other portions of
a complex phenomenon have been explained. There are
two results of this method which may be discussed sep-
arately.
(a) The application of this method to a complex
phenomenon which is the result of several causes,
often enables us to determine what part each of these
causes plays in the determination of the whole fact
under consideration. Mill's fifth canon seems to apply
58. THE METHOD OF RESIDUES
to this case. It is as follows : Subduct from any phe-
nomenon such part as is known by previous inductions to
be the effect of certain antecedents, and the residue of the
phenomenon is the effect of the remaining antecedents.
Thus, if it is known that the complex phenomenon
BAG is the result of bac, and if it is further known
that a is the cause of A, and b of B, it follows, of course,
by subtraction that the residue still unexplained, C, is
caused by c, the remaining antecedent.
Of course the application of this method in concrete cases does
not usually resolve itself into such a simple process of subtraction.
It requires work ' previous inductions,' as Mill says to deter-
mine what are the whole number of antecedents in any case, as well
as to isolate the various antecedents so as to determine exactly what
part of the effect is to be ascribed to each one. This may be illus-
trated by an example : after my student's lamp has been lighted two
hours, I find the thermometer has risen from 65 to 70 Fahr. The
phenomenon to be explained then is the additional 5 of heat.
There is no fire, and it seems that the increase in temperature must
be due to the lamp, and the heat given off from my body during
this period. Suppose that the lamp is burned for the same length
of time while the room is unoccupied, all other conditions remaining
the same, and that the thermometer shows an increase of 4 in the
temperature. By subtraction we could conclude that the heat given
off by the body on the former occasion was the cause of the additional
degree of temperature.
To carry the process of analysis a step further. Let us suppose
that a half pint of oil, which is composed of hydrogen and carbon,
has been consumed. We could determine, by measuring the heat
produced by the oxidation of the exact amount of carbon contained in
one half a pint of oil, what quantity of heat is due to the combustion
of the carbon contained in the oil, and, by subtraction, what must be
ascribed to the burning of the hydrogen. 1
1 This is, of course, not strictly correct. For it leaves out of account the
heat generated by the chemical combination of the carbon and hydrogen.
It may therefore serve to illustrate a case where the method of Residues
breaks down.
2l6 CAUSAL DETERMINATION
(&} The second case in which this method may be
applied is where there is an unexplained remainder or
residue left over after the result of all the known causes
has been calculated. Mill does not distinguish between
such instances and the method of simple subtraction
discussed above. Since, however, the cause must ex-
plain the whole of the effect, the method of residues
enjoins us to continue the search for explanation.
When any part of a complex phenomenon is still un-
explained by the causes which have been assigned, a
further cause for this remainder must be sought. If, for
example, it were found by actual measurement that the
heat produced by the lamp, and by the body of the
occupant, were not sufficient to account for the change
in temperature of the room, it would be necessary to
seek for some further cause to account for this unex-
plained remainder.
This method can scarcely be said to be more than
a demand for complete and precise explanation. The
attempt, however, to account for unexplained resi-
dues has led to many extremely important discoveries
in science. Residual phenomena are often so obscure,
and appear so uninteresting and unimportant to the
ordinary mind, that they are passed over without ex-
planation. It usually requires the eye of a scientific
genius to see the importance of things which appear
trivial and unessential. With Darwin, facts which might
appear to an ordinary observer mere unimportant ex-
ceptions, were made the object of special attention, and
often served as starting-points for his investigations.
Francis Darwin, speaking of his father, says : " There
was one quality of mind which seemed to be of special
58. THE METHOD OF RESIDUES 2 1/
and extreme advantage in leading him to make discover.
ies. It was the power of never letting exceptions pass
unnoticed. ... A point apparently slight and uncon-
nected with his present work is passed over by many
a man almost unconsciously, with some half-considered
explanation, which is really no explanation. It was just
these things that he seized upon to make a start from." l
Among the many important discoveries which have resulted from
the investigation of some obscure and seemingly unimportant fact,
we may mention that of ozone. It had been observed for a long
time that the passage of electric sparks through the air is accom-
panied by a peculiar odour. This odour was also found near
electrical machines, and was known as the ' electrical smell.' No
one seemed to have attached any importance to it or to have attempted
to explain it in any way, until Friedrich Schb'nbein, a professor of
chemistry at Basel, turned his attention to the subject. The result
of his investigations was the discovery of ozone, the peculiar modifi-
cation of oxygen, which was the cause of the odour.
Another very striking example of the application of this method
is afforded by the history of the discovery of the planet Neptune.
In 1781 a new planet was discovered moving outside all the other
planets by Sir William Herschel. This was the planet Uranus,
When its orbit came to be calculated, it was found that it did not
move as it might be expected to do according to the theory of gravi-
tation. That is, the attraction of the sun and the known planets did
not account for the path it took : it moved outwards into space
further than it ought to have done. It was evident that either some
mistake must have been made in the observation of the astronomers,
or some unknown body must be dragging it out of its course. No
traces of any such planet could be perceived, and the problem
remained unsolved. In 1843, a student of St. John's College,
Cambridge, named Adams, undertook to work out the movements
of Uranus, to discover, if possible, the position of the body which
1 Life and Letters of Charles Darwin, Vol. I. p. 125.
2l8 CAUSAL DETERMINATION
was pulling it out of what would otherwise be its proper path, the
attractions exercised by the sun and the planets in their different
positions, and to show what effect they would have in determining
the orbit of Uranus. Whenever the planet was deflected outwards,
it was necessary to show where the body was situated which was
thus influencing it. In 1845 ne was a l e to send a paper to the
astronomer royal at Greenwich, informing him in what quarter of the
heavens the new planet should be observed. When the discovery
was afterwards made, it was proved that his calculations were almost
exactly correct. A failure on the part of the astronomer royal to
cooperate by looking through his telescope for the planet gave the
prior right of discovery to a Frenchman named Leverrier. The
latter worked out his calculations in the same way as Adams, and
obtained almost exactly the same results. He sent these results to
Professor Galle of the Berlin University on the 23d September,
1846, asking him to look in the part of the heavens which he
indicated. That same evening, by following out the directions, the
planet was discovered in almost the exact spot predicted. 1
The history of this discovery illustrates as well several methods
and processes which we have not yet discussed, such as the forma-
tion and verification of hypotheses. It is also interesting as showing
how reason is able in certain conditions to anticipate perception.
The relations and forces of the heavenly bodies had been so per-
fectly formulated in the law of gravitation that these two investi-
gators, working in their studies, were able to predict not only the
presence but the exact position of a planet which up to that time had
never been observed.
In connection with Chapters XV. and XVI., the student is ad-
vised to read Mill, Logic, Bk. III. Chs. VIII. and IX.
1 Cf. Clerke, A Popular History of Astronomy during the Nineteenth
Century, pp. 96 ff. ; Buckley, A Short History of Natural Science, pp.
302 ff.
CHAPTER XVII
METHODS OF EXPLANATION
Incomplete Explanation. Analogy
59. Explanation by Analogy. We have now passed
from the field of observation to that of explanation.
Scientific observation, aided by experiment, as we have
seen, has to determine the exact nature of the facts of
experience, and the order in which those facts are con-
nected. Explanation, on the other hand, undertakes to
furnish reasons why the facts are as we- find them to be.
But, as has already been pointed out ( 48, 49), no hard
and fast line can be drawn between the determination
of the nature and connection of facts, and their explana-
tion. The task which our thought is called upon to
perform is to transform obscurely known and isolated
facts into an orderly and consistent system of know-
ledge. And, to accomplish this, it is necessary, in the
first place, that the facts shall be thoroughly analyzed
and carefully examined ; and, secondly, that they shall
be grouped together according to some general principle
or principles which shall make clear and intelligible the
relations in which they stand to each other.
To explain, then, is just to show that some fact or
group of facts is related to some other fact or group with ,
which we are acquainted. So far as the methods we have
219
22O ANALOGY
discussed enable us to establish connections between
events, they may fairly claim to be methods of explana-
tion. Nevertheless, although the difference between
these methods and those of explanation proper is one of
degree rather than of essential nature, it is important to
keep it in mind. The canons which were stated in the
last two chapters what Mill named the experimental
methods are rules for determining the order and
succession of particular facts. The problem before us
in those chapters was to determine what particular
phenomena of our experience are essentially and neces-
sarily connected as antecedents and consequents. And
for this purpose active observation, aided by experi-
ment, suffices. It is, of course, true that these observa-
tions and experiments furnish the starting-point for
explanation. But they constitute a more or less distinct
step in the work of systematization which is carried on by
thought. The method of Difference, for instance, enables
us to say that hot water will break thick glasses when
poured into them, but will not injure thin ones. ' So
much for the fact,' we say, ' but the explanation is still
wanting.' We must try to make the fact intelligible by
going outside of it, and showing that this behaviour on
the part of the glasses is simply a case or illustration of
what we already know of the properties of bodies when
heated. Again, the method of Concomitant variations,
as we have seen from Jevons's example, has led us to
believe in some causal connection between electrical
storms, sun-spots, and the Aurora Borealis. In this
instance, knowledge has not been able to advance
beyond the fact to its explanation. No satisfactory
59- EXPLANATION BY ANALOGY 221
theory has yet been established to account for the
undoubted fact that these phenomena are in some way
causally connected.
In discussing methods of Explanation, we deal first
with Analogy. The principle of Analogy is resem-
blance. The phenomenon to be explained is connected
with some more familiar occurrence through some
perceived or imagined likeness between the two cases.
In the early stages of the history of the race, everything
was explained on the analogy of human actions (cf. 84).
All natural events, that is, were supposed to be produced
by superhuman agents, who were, however, endowed
with essentially the same qualities as man. In the
thunder, the men of a primitive age heard the voice of a
god. An eclipse of the sun or moon was interpreted as
a divine sign or warning. When the sea became tem-
pestuous and lashed its shores, they believed that the
sea-god was angry. In every case, they interpreted
these mysterious happenings of nature by referring
them to causes similar in character to those which they
best understood the motives and volitions of them-
selves and their fellows.
The principle of analogy is employed in the same
way in modern times. It is true that we no longer
think that natural events are directly caused by the
action of some spiritual agent more or less like our
selves. But, when we endeavour to show that the phe-
nomena which we are interested to explain are similar
in important respects to some group of facts with whose
mode of operation we are familiar, we proceed by anal-
ogy. On the basis of this similarity, we argue that the
222 ANALOGY
phenomena with which we are dealing probably have
the same properties, or operate in the same way, or are
governed by the same laws, as the better-known facts
which they resemble. The formula of analogy may
be stated in this way : Two things resemble each
other in one or more respects, they are therefore of
the same general type or character; therefore a cer-
tain proposition which is true of the one is probably
true of the other. The following example of analogy
has been frequently used as an illustration :
" We may observe a very great similitude between this earth
which we inhabit, and the other planets, Saturn. Jupiter, Mars,
Venus, and Mercury. They all revolve round the sun, as the earth
does, although at different distances and in different periods. They
borrow all their light from the sun, as the earth does. Several of
them are known to revolve around their axes like the earth, and by
that means must have a like succession of day and night. Some of
them have moons that serve to give them lignt in the absence of the
sun, as our moon does to us. They are all in their motions subject
to the same law of gravitation as the earth is. From all this simili-
tude, it is not unreasonable to think that those planets may, like our
earth, be the habitation of various orders of living creatures." l
The word 'analogy ' at the present time is somewhat loosely used
for any mark of similarity or resemblance which enables us to rea-
son from one thing to another. " The original word avaXoyia,
as employed by Aristotle, corresponds to the word Proportion in
Arithmetic ; it signifies an equality of ratios, ICTOT^S Aoywv : two
compared with four is analogous to four compared with eight.
There is something of the same meaning in the technical use of the
word in physiology, where it is used to signify similarity of function as
distinguished from similarity of structure, which is called homology ;
thus the tail of a whale is analogous to the tail of a fish, inasmuch
1 Reid, Intellectual Powers of Man, Essay I. Chap. III.
6o. ANALOGY AS SUGGESTIVE OF HYPOTHESES 223
as it is similarly used for motion, but is homologous with the hind-
legs of a quadruped. A man's arms are homologous with a horse's
fore legs, but they are not analogous, inasmuch as they are not used
for progression." 1
Apart from these technical uses, what is known as
analogical reasoning may, perhaps, be best defined as
an argument from similar instances. In analogy, we do
not stop to work out a law of connection between
phenomena by comparing a number of cases, or by
using any of the ordinary inductive canons. But
finding a striking resemblance between some circum-
stance quality, arrangement, function, etc. in the
phenomena to be explained, and some phenomena with
which we are already acquainted, we used the latter as
a basis for conclusions about the former. Analogy is
thus an argument from examples or instances, its value
depending upon the real identity in some important
aspect of the cases compared. When, however, our
thought is able to extend to a new case, or set of
cases, some general law or principle with whose opera-
tion it is already acquainted in other instances, we have
passed beyond analogy to complete explanation. In
the former case, we argue from the resemblance of
instances ; in the latter, the thread which binds the
new instance with the old is the identity of a general
principle.
60. Analogy as Suggestive of Explanatory Hypothe-
ses. We have shown above that analogical reasoning
1 Minto, Logic Inductive and Deductive, p. 367.
224 ANALOGY
depends on the resemblance which exists between indi
vidual cases or instances, and that it is not guided by
any general law or principle. In the next section, how-
ever, we propose to show in more detail wherein it falls
short, and why, taken by itself, it can only be regarded
as incomplete explanation. Here we have to notice the
important part which it plays in suggesting laws and
principles. Although analogy ' sticks in the particular
instances,' it leads the mind on to general laws and
explanatory theories. It is thus of the greatest impor-
tance as a necessary stage on the way to complete
explanation.
When we are able to discover some general resem-
blance between a group of phenomena which we are in-
terested to explain, and another group whose principle of
operation we already understand, our thought strives to
extend the known principle and to bring the new facts
under it. The unknown or unexplained facts are thus
brought under a known law. It is of course true that
the application of the law to a new set of facts broadens
our conception of its scope, and often requires us to state
it in a more adequate way. Thus the analogy which
Newton perceived between the heavenly bodies falling
through space and the falling of the apple towards the
ground, led to the formulation in exact mathematical
terms of the universal law of gravitation. Our know-
ledge of the various functions of plants digestion, re-
production, etc. has been obtained by ascribing to the
various organs of the plant, purposes analogous to those
which are fulfilled by the parts of animal bodies. And,
in turn, the study of plant physiology has thrown light
60. ANALOGY AS SUGGESTIVE OF HYPOTHESES 225
upon animal physiology, and enlarged and modified many
of its theories.
An extremely interesting instance of the part which analogy
plays in suggesting possible explanations, is found in the account
of the discovery of the principle of Natural Selection given by Dar-
win in his Autobiography. In 1837 Darwin opened a note-book
for the purpose of recording all facts in any way connected with the
variation of species in nature and under domestication. He first
investigated the variations of plants and animals which are produced
under domestication, by printed enquiries, by conversation with
skilful breeders, and by extensive reading. " I soon found," he says,
" that selection was the keystone of man's success in making useful
races of plants and animals." When useful or pleasing varieties
of plants or animals occur, the gardener or breeder preserves them,
and their peculiar qualities are transmitted to their offspring. And,
in a number of generations, these qualities become more pronounced
through accumulation. The differences between varieties of the
same species of domesticated animals varieties which areas differ-
ent, for example, as the mastiff and Skye terrier are due to the
selective agency of man. But is there anything analogous takes
place on an indefinitely larger scale in nature ? If so, what is it
which plays the part of the gardener or breeder, and preserves cer-
tain varieties?
When Darwin had reached this point in his investigations, and
had come to appreciate what selection could do, he happened to
read Malthus's book, On Population. The purpose of this book
was to dispel the optimistic ideas of some of the writers of the
eighteenth century who looked for the speedy realization of social
well-being and happiness. Such an ideal is impossible of fulfilment,
said Malthus, because of the inevitable tendency of population to
increase faster than the supply of food. Human beings increase in
a geometrical ratio ; the means of subsistence, at best, only by an
arithmetical ratio. The population will thus constantly tend to
exceed the limit of the food supply, and will be kept in check only
by starvation. A constant struggle for food is the lot, then, to
Q
226 ANALOGY
which each individual is doomed in virtue of this law. Darwin's
observations of the rate at which plants and animals tend to repro-
duce their kind, led him at once to extend Malthus's principle to
the whole of nature. The fecundity of natural beings leads to a
struggle for existence, not merely among men, but throughout the
whole organic world. And if there is a struggle, we have natural
selection or the survival of the fittest. Darwin saw "that natural
selection was the inevitable result of the rapid increase of all organic
beings." It is not difficult to see that this discovery was the result
of Darwin's wonderful power of perceiving analogies between differ-
ent classes of facts. His genius led him to recognize first the re-
semblance of the variations of species in nature, to the more familiar
variations which go on among domesticated plants and animals.
And, secondly, he perceived that the competition for the means of
subsistence, which the pressure of population imposes upon the mem-
bers of the human race, is simply one phase of ' the struggle for
existence,' which is going on everywhere throughout the organic
world.
6 1. The Incompleteness of Analogical Reasoning.
The most striking feature of analogical arguments is
found in the fact that they yield only probable conclu-
sions. And the reason for this is not far to seek. For,
as has been already shown, analogy is a method of
reasoning from one particular case to another on the
basis of some imagined or perceived similarity between
the two cases. Complete logical demonstration, or cer-
tainty, however, is attained only when the new fact or
group of facts is really and essentially united by means
of some general principle with what is already known.
But it must not be forgotten that ' probability ' is not
a fixed quantity. An argument from analogy may have
any degree of value, from zero almost up to the limit
of complete logical certainty. To fully explain or
6i. INCOMPLETENESS OF ANALOGICAL REASONING 22/
demonstrate any fact, we are obliged, I think, to go
beyond analogy, and to verify its conclusions by a
method which has still to be described. It is evident,
nevertheless, that the value of an analogical argument
will depend upon the nature of the resemblance which
is taken as the basis of inference. In general, it is
true that the greater the resemblance between the two
cases, the more certainly can we reason from one to the
other. This is not to say, however, that the value of
the conclusion is in direct proportion to the number
of points of resemblance which can be discovered. For
example, we might reason : These two men are of the
same height, of the same age, live in the same house,
come from the same town ; the one man stands well
in his classes, therefore the other probably does so also.
If the number of points of resemblance were the essen-
tial thing, the argument ought to possess some weight,
but it is clear that it has none. The difficulty is that
none of the resemblances mentioned are fundamental,
or in any way essential to the real nature of the things
compared. If we knew that the two men were similar
in character, this one characteristic would be worth
more, as a basis for the conclusion, than all the circum-
stances which we have mentioned combined.
It is true, then, as Mr. Bosanquet remarks, that in
analogical reasoning we must weigh the points of re-
semblance rather than count them. 1 Other things
being equal, the more points of resemblance we can
make out the better; but if these are to contribute at
1 Logic, Vol. II., p. 99.
228 ANALOGY
all to the certainty of the conclusion, they must rep-
resent some deep-lying characteristic of the things
compared. In general, it must be said that it is only
experience which can inform us what resemblances are
fundamental, and what merely external. Systematic
knowledge in any field enables us to separate the essen-
tial from the accidental. And, what is perhaps a corol-
lary from this, it must not be forgotten that the value
of an inference from analogy depends largely upon the
amount of intellectual insight possessed by the mind
which makes it. The ordinary mind, at least in its
undisciplined and untutored condition, regards all things
as of equal importance. It is therefore led away by
the strongest stimulus by striking external and acci-
dental resemblances. On the other hand, a scientific
genius whose mind is well stored with facts, and who
is gifted in addition with imagination, is able to pene-
trate beneath the surface and to apprehend the real or
fundamental resemblance. His imagination enables
him to see beyond the chaos of the particular facts,
and to detect the underlying principle by means of
which these facts can be connected and systema-
tized.
Analogy thus becomes deepened until it passes from
the stage of a mere argument from particular to par-
ticular, to the perception of a general law which includes
the individual instance. But no such direct insight can
claim the title of knowledge, until it is tried and tested
by the facts. The guesses of scientific men unfortu-
nately often prove mistaken. It is always necessary
that fancy shall be confronted with facts. Even Dar-
6i. INCOMPLETENESS OF ANALOGICAL REASONING 22Q
win's magnificent analogical inference was nothing
more than a hypothesis, as he himself well under-
stood, until its power of explaining the facts of organic
life was demonstrated. We have now to explain in
the next chapter the methods by which such guesses
are tested.
References
J. S. Mill, Logic, Bk. III. Ch. XX.
A. Bain, Logic, Part Second, Induction, pp. 140-148.
J. G. Hibben, Inductive Logic, Ch. XIV.
B. Bosanquet, Logic, Vol. II. Ch. III.
" " The Essentials of Logic, pp. 155-158.
W. Minto, Logic Inductive and Deductive, pp. 367-373.
CHAPTER XVIII
METHODS OF EXPLANATION. THE USE OF HYPOTHESES
62. Reasoning from an Hypothesis. An hypothesis
is a guess or supposition made to explain some fact or
group of facts. We have seen in the last chapter how
the mind is led on by the perception of analogies to
formulate a general law or principle of explanation for
phenomena which were not previously understood. But
even when guided by analogy, a guess or hypothesis is
only the beginning of explanation. A mere hypothesis
or supposition must be tried by its capacity to explain
facts, and in this way either verified or disproved.
4 Theory ' is another word that is often used as equiva-
lent to hypothesis. Strictly speaking, however, it is
more correct to use the term ' hypothesis ' for the un-
verified, or only partially verified guess, and to reserve
' theory ' for the hypothesis that has been more com-
pletely demonstrated. This distinction, however, is not
usually maintained, and even in scientific writings the
terms ' theory ' and ' hypothesis ' are used interchangea-
bly. Nevertheless, it is necessary to distinguish in some
way the 'mere hypothesis,' or supposition, which is
quite as likely to be false as true, from the hypothesis
which has been established by proof.
It is well to remember that it is not only in solving
scientific problems that we employ hypotheses. In our
230
62. REASONING FROM AN HYPOTHESIS 231
ordinary experience, we are constantly trying to imagine
the most likely explanation of facts which we perceive
through the senses. If, for example, one should find on
returning to one's room that a pane of glass had been
broken, one would straightway set about finding some
explanation of this occurrence. One might perhaps
first imagine that a stone or something of the kind had
been thrown against it. Acting on this supposition, one
would look for the stone in the room. If it were found
there, the hypothesis would be confirmed ; if no traces of
it could be discovered, and if, moreover, on examination
the glass proved to be shattered in a way that would
probably not result from the projection of a stone
against it, our first hypothesis would have to be aban-
doned. We should then make another guess perhaps
that the outside blind had been violently closed by the
wind and again examine the facts to see if they gave
any support to this supposition. We are constantly
making hypotheses of this character to explain phe-
nomena which we meet with in everyday experience.
If we find a stream swollen, we conclude that it must
have rained in some part of the country drained by
the stream. If a man has typhoid fever, we are pretty
sure to guess that he has been drinking impure water.
We no sooner perceive something unusual or striking
than we begin .to guess out, as it were, its explanation.
The formation of hypotheses, then, is simply the mind's
response to the demand for explanation.
It is worth noticing that it is only unusual or striking events, or
those in which they have some practical concern, which attract the
attention.of the majority of mankind, and lead them to form explana-
232 THE USE OF HYPOTHESES
.ory hypotheses. What is familiar, or of no practical importance,
does not usually awaken curiosity. Indeed, in a great many cases,
such phenomena are not observed at all. But the great scientist is
distinguished, one may say, by his intellectual curiosity. He tries
to understand phenomena which the ordinary mind neglects, and
simply takes for granted. He has questions in his mind with regard
to familiar things which he wishes to have answered, guesses which
he is desirous of having proved or disproved. We have found it
convenient, in the preceding chapters, to separate the description of
the processes of determining the nature of facts, from the account
of the methods of explanation. But it must by no means be sup-
posed that the nature of facts is discovered quite independently of
the influence of hypotheses or theories. Unless the mind has
some question to answer, or theory to test, it is impossible to see
any significance in an experiment. In other words, every ex-
periment must have a purpose, and the purpose is to get some
information that will help us to answer a question which we bring
with us to the investigation.
In the actual process of acquiring knowledge, then,
observation and theorizing go hand in hand. Unless we
go to nature with something in our mind, we are not
likely to learn much. As a rule, we see only what we
look for. Francis Darwin says of his father : " He
often said that no one could be a good observer unless
he were an active theorizer. This brings me back to
what I said about his instinct for arresting exceptions:
It were as though he were charged with theorizing
power ready to flow into any channel on the slightest
disturbance, so that no fact, however small, could avoid
releasing a stream of theory, and thus the fact became
magnified into importance. In this way it naturally
happened that many untenable theories occurred to him,
but fortunately his richness of imagination was equalled
62. REASONING FROM AN HYPOTHESIS 233
by his power of judging and condemning the thoughts
which occurred to him. He was just to his theories and
did not condemn them unheard ; and so it happened
that he was willing to test what would seem to most
people not at all worth testing. These rather wild trials
he called 'fool's experiments,' and enjoyed exceedingly.
As an example, I may mention, that finding the cotyle-
dons of Biophytum to be highly sensitive to vibrations
of the table, he fancied that they might perceive the
vibrations of sound, and therefore made me play my
bassoon close to a plant." l
A good example of how essential theories are for an
observer, and how blind he may be to what he is not
looking for, is found in the work from which we have
just quoted. In the brief autobiography contained in
the first volume, Darwin tells of a geological trip through
Wales which he took while a student at Cambridge, in
company with Sedgwick, the professor of geology. It
must be remembered that this was before Agassiz had
come forward with his theory of a glacial period in the
world's history. Darwin writes : " We spent many
hours in Cwm Idwal, examining all the rocks with su-
preme care, as Sedgwick was anxious to find fossils in
them ; but neither of us saw a trace of the wonderful
glacial phenomena all around us ; we did not notice the
plainly scored rocks, the perched boulders, the lateral
and terminal moraines. Yet these phenomena are so
conspicuous that, as I declared in a paper published
many years afterward in the Philosophical Magazine, a
l Life and Letters of Charles Darwin, Vol. I., p. 126.
234 THE USE OF HYPOTHESES
house burnt down by fire did not tell its story more
plainly than did this valley. If it had been filled by a
glacier, the phenomena would have been less distinct
than they now are." l
63. Formation of Hypotheses. We are now ready to
consider a little more closely the formation of hypothe-
ses or theories. In the first place, it is to be noticed
that hypotheses are not received from without through
sense-perception, but are made by the mind. They are
the creations of the imagination. A good theorizer, like
a poet, is in a certain sense born, not made. The man
to whom ' nothing ever occurs,' whose intellectual pro-
cesses are never lit up with a spark of imagination, is
unlikely to make any important discoveries. It has
been by a flash of scientific genius, by imaginative in-
sight which we may almost call inspiration, that great
scientific theories have been discovered. Not even a
scientific genius, however, can afford to neglect the
facts. But, guided by accurate observation, the scien-
tific imagination tries to invent some law or principle
which will serve to connect and explain facts. Tyndall
has an essay on " The Scientific Use of the Imagina-
tion," from which we may quote a short passage.
" With accurate experiment and observation to work
upon, imagination becomes the architect of physical
theory. Newton's passage from a falling apple to a
falling moon was an act of the prepared imagination.
. . . Out of the facts of chemistry the constructive
1 Life and Letters of Charles Darwin, Vol. I., p. 49.
63. FORMATION OF HYPOTHESES 235
imagination of Dalton formed the atomic theory. Davy
was richly endowed with the imaginative faculty, while
with Faraday its exercise was incessant, preceding,
accompanying, and guiding all his experiments. His
strength and fertility as a discoverer are to be referred
in great part to the stimulus of the imagination. Scien-
tific men fight shy of the word because of its ultra-
scientific connotations ; but the fact is, that without the
exercise of this power, our knowledge of nature would
be a mere tabulation of coexistences and sequences." 1
In speaking of hypotheses as ' guesses,' or 'creations of the im-
agination, 1 their dependence upon facts must not be forgotten. It is
only when the phenomena to be explained have been carefully ob-
served that our guesses at their explanation are likely to be of value.
It is well known that a considerable amount of knowledge is usually
required to ask an intelligent question. And in the same way, the
mind must be well stored with facts, in order to render our hypo-
thetical explanations worthy of consideration. Indeed, observation
of facts, and the formation of theories go hand in hand, and naturally
assist each other. We have already spoken of the lack of theory
which makes us blind to facts which seem to lie directly before us.
But we have perhaps not yet emphasized sufficiently the dependence
of theories upon the facts of observation. The process of explanation
may be described as a fitting together of the facts given by observa-
tion, with the explanatory theories which the mind originates. The
theory with which we start enables us to ask questions, and leads us
to scrutinize the phenomena which are to be explained ; while the
latter react upon the theory, and cause it to undergo constant modifi-
cation. The account of Darwin's discovery of the principle of ; the
survival of the fittest ' is a good illustration of an hypothesis con-
structed by a constant dependence upon the facts during every step
of its progress.
1 Fragments of Science, p. 104.
236 THE USE OF HYPOTHESES
We have already referred to the way in which analogy
leads the mind on to general principles of explanation
( 60). Analogy is a method of inferring that what is
true of one object is probably true of others which
resemble it. But the ordinary mind sees resemblances
only when they are very obvious and striking. The man
of scientific insight, on the other hand, like the poet, pene-
trates more deeply into the nature of things, and is able
to discover analogies and resemblances to which the
ordinary man is blind. Who but a genius like Newton
would have thought of connecting the fall of an apple
with the fall of the heavenly bodies through space ? The
history of science shows that great discoveries are
made by means of imaginative insight, but it also
teaches that mere imagination without dependence
upon known facts is frequently a source of much mis-
chief. Mere theories without facts are not only empty,
but often stand in the way of true knowledge. The
fruitful exercise of the imagination, if we may judge
from the way in which great discoveries have been made,
always takes place in closest connection with what ob-
servation and experiment reveal regarding the nature
of phenomena. If the imagination is to have power to
discover any truth, it must constantly ' touch earth,'
and be guided in its course by the nature of facts which
are already known.
In framing hypotheses, then, the imagination is
constantly prompted by analogies with processes which
are more or less familiar. The hypothesis, then, is not
created by the imagination 'out of nothing.' It is rather
an extension or development of a known law, than an
absolute creation.
64. THE PROOF OF AN HYPOTHESIS 237
64. The Proof of an Hypothesis. We have discussed
the way in which hypotheses are formed, but as yet have
said nothing regarding the means of determining their
truth and falsity. But to form hypotheses is usually
easy, to verify them is often exceedingly difficult. The
scientific worker constantly finds that theories which he
has formed are without foundation, and must therefore
be discarded. It is not only essential that a scientific
investigator shall possess a mind fertile in ideas ; he
must also love truth more than any theory, no matter
how interesting or attractive it may appear. In behalf
of truth, every theory must be subjected to the most
thorough and searching tests possible ; if it is not borne
out by the facts, it must be at once discarded. What
now is the general method of procedure in testing an
hypothesis ? Two steps or stages may be distinguished
in this process : (i) We assume that the hypothesis is
true, and proceed to show what are the necessary results
which follow from it. In doing so we proceed deduc-
tively ; that is, assuming the truth of the hypothesis,
we reason out what consequences it must have. (2) The
conclusions thus reached are compared with the actual
facts, as given to us directly in perception, or as deter-
mined by experiment. If these are found to agree, the
hypothesis is regarded as true ; if they do not agree, it
must be discarded or modified.
This procedure may become clearer by considering
some concrete examples. If we were to come on the
campus some morning and find that several branches
had been broken from one of the trees, we should
naturally try to explain this circumstance by making
238 THE USE OF HYPOTHESES
some hypothesis. Perhaps the first thing which would
occur to us would be that there had been a violent wind-
storm. The hypothesis having been made, the next step
would be to look around to see if it could be verified.
' If there has been a cyclone,' we might argue, ' there
should be other signs of its presence ; we should find
broken twigs and blown leaves lying about, and all the
trees should present a storm-tossed appearance.' If
observation showed that these things were actually
present, we would consider our hypothesis so far con-
firmed. But if not, our first guess would be disproved,
and it would be necessary to look about for another
explanation.
An excellent illustration of the way in which an hypothesis
becomes more and more completely demonstrated, is found in the
history of the experiments by which it was proved that the atmos-
phere has weight. Galileo noticed that water will rise in a pump only
about 33 feet. He could not find out, however, why it was that the
water should stop at this point. After his death, his friend and pupil
Torricelli took up the problem, and asked himself : Why does the
water rise at all ? It then occurred to him that air must weigh some-
thing, and that it might be this weight on the surface of the water
which forced the water up the pump when there was no air pressing
it down. Now, if this were so, he reasoned, the weight of the air
ought to lift mercury, which is fourteen times heavier than water, to
one-fourteenth of the height. So he took some mercury, and filling
a tube about 34 inches long, turned it upside down into a basin of
mercury which was open, and therefore under the pressure of the
atmosphere. The mercury began to settle in the tube, and finally
rested at a height of 30 inches. Torricelli had thus invented the
barometer, an instrument which would measure the weight of the
atmosphere. It was afterwards suggested by the famous French
writer, Pascal, that at the top of a high mountain, where there is less
64. THE PROOF OF AN HYPOTHESIS 239
air pressing downwards, the column of mercury should fall consid-
erably if the atmosphere were really what caused the water and the
mercury to rise. When this experiment was made by carrying the
barometer to the top of a mountain called the Puy de Dome, the mer-
cury fell nearly three inches. Still further confirmation of Torri-
celli's theory was afforded by the discoveries of Otto Guericke of
Magdeburg. In 1650 Guericke invented the air-pump. The first use
which he made of his new invention was to show that the atmos-
phere is pressing down upon us heavily and equally in all directions.
He fitted closely together two metal hemispheres and exhausted the
air between them by means of his pump. It was found that the
pressure of the atmosphere was so great that it took a great force to
separate the hemispheres. 1
To establish a scientific theory, then, there are neces-
sary not only a ready imagination, but also patience and
perseverance in the careful deduction of the conse-
quences of the theory, and in the comparison of the
results thus obtained with the actual facts. Scientific
work also demands the utmost candor and openness of
mind on the part of those who engage in it. One must
be willing to abandon any theory as soon as it is found
to disagree with the facts. And this is by no means an
easy thing to do. When one has a theory which suffices
for nearly all the facts, there is always a temptation to
cling to it, and to neglect or explain away any trouble-
some or contradictory facts. There is no doubt that
the scientific explanations which have become accepted
and established were not the ideas which first happened
to occur to the men with whose names they are associ-
ated. When Newton first attempted to work out the
verification of the gravitation hypothesis, he used the
1 Cf. Buckley, Short History of Natural Science, pp. 114-121.
\
240 THE USE OF HYPOTHESES
most accurate measurements he could obtain regarding
the size of the earth. But in calculating on this basis
the pull of the earth on the moon, and the consequent
deflection of the moon from the straight line, his results
came out wrong. That is, the moon moved more slowly
than it ought to do according to his theory. The differ-
ence was not great, but Newton could not overlook this
lack of agreement with the observed facts. He put the
whole matter aside ; and it was only when he heard
sixteen years later that Picart had discovered, from new
and more accurate measurements, that the earth was
larger than had been supposed, that he repeated his
calculations, and found his hypothesis verified.
Although it very frequently turns out, both in every-
day matters and in scientific work, that our hypotheses
are disproved, the negative answers thus obtained are
not without value. For we are often able at once to
limit the number of possible hypotheses. In a field
where we already possess some systematic knowledge, it
is often possible to say : The explanation of this group
of phenomena must be either a or b or c. If, then, one
is able to show that neither a nor b will afford the
required explanation, these negative conclusions will
lead directly to the establishment of c.
65. Requirements of a Good Hypothesis. Various
conditions or requisites of a good hypothesis are laid
down by writers on logic. The three laws which are
most frequently stated are as follows: (i) That the
hypothesis shall be conceivable and not absurd. (2)
That it shall be of such a character that deductions
65. REQUIREMENTS OF A GOOD HYPOTHESIS 241
can be made from it (3) That it shall not contradict
any of the known laws of nature.
It does not seem to me that the first law is of much
value. It is largely individual taste or education which
leads us to pronounce certain theories ' absurd ' or ' in-
conceivable.' Thus, for a long time, it seemed incon-
ceivable that the earth should be round, and should
revolve on its own axis ; and less than a generation
ago the theory of evolution, as propounded by Darwin,
seemed to many persons utterly ' absurd.' Nor can the
third law always be applied as a test of an hypothesis,
for many great discoveries seemed, at the time when
they were announced, to contradict known laws of nat-
ure. The difficulty is that no one is able to affirm,
unconditionally, that a law of nature forbids us to
make this or that hypothesis. Of course, we feel that
a theory is very probably false which is at variance with
the law of gravity, or with that of the conservation
of energy, or any of the laws which we regard as es-
tablished beyond a reasonable doubt. But, although
the chances are always very greatly against any theory
which runs counter to what are regarded as well-estab-
lished laws, there is yet always a possibility that it may
be true. There is no law of nature so certain as to be
infallible. Even those laws which appear to be beyond
the possibility of doubt, may require to be modified or
supplemented. We may find that, practically, it is not
wise to trouble ourselves with theories which undertake
to overthrow the law of gravitation, or to disprove other
fundamental laws of the physical world. But theo-
retically, at least, there is always a chance in cases
242 THE USE OF HYPOTHESES
such as we have been supposing the chance is almost
infinitely small that the new theory may be right, and
the old one wrong. The practical objection to admit-
ting the claims of this canon is the difficulty in apply-
ing it fairly. The phrase, ' contrary to the laws of
nature,' like 'inconceivable,' and 'absurd,' is likely to be
used to condemn any theory with which one disagrees.
In this way, it is evident that the very point is begged
which is really at issue.
Of these three canons, therefore, the second appears to
state the only condition which is essential to an hypothe-
sis. An hypothesis, if it is to be of any value, must be
capable of being proved or refuted. But, unless its
consequences can be shown by way of deduction, it
is impossible to know whether it agrees, or does not
agree, with the facts which it is supposed to explain.
An hypothesis from which nothing can be deduced,
then, is of no value whatever. It always remains at
the stage of mere possibility, and without any real
connection with fact. It is a mere guess which has
no significance whatever, for it is entirely incapable
either of proof or of disproof.
In general, it is possible to deduce the consequences of a theory
only when the principle employed is analogous, in mode of opera-
tion, to something with which we are familiar. Thus, for example,
it is because the ether is conceived as resembling other material
bodies in important respects that it can be used as a principle of
explanation. It is assumed to be elastic and capable of receiving
and transmitting vibrations, and as spread out like other material
bodies in space. In virtue of these similarities to other material
substances, it is possible to deduce the consequences which such
a substance as ether would imply, and to compare them with the
65. REQUIREMENTS OF A GOOD HYPOTHESIS 243
actual facts. But if one should make the assumption that certain
phenomena are due to some agency totally unlike anything of which
we have any experience, a disembodied spirit, or ghost, for example,
it would be impossible either to prove or to disprove the assertion.
For knowing nothing whatever of the way in which spirits act, one
could not say whether the phenomena to be explained, table-rap-
ping, planchette-writing, etc., were or were not consistent with a
spirit's nature and habits.
Another example of a barren hypothesis from which no conclu-
sions can be drawn, is afforded by the ' catastrophe ' or ' convulsion '
theory in geology, which was first combatted by Lyell, in his Prin-
ciples of Geology, published in 1830. " People had so long held the
belief that our earth had only existed a few thousand years, that
when geologists began to find a great number of strange plants and
animals buried in the earth's crust, immense thicknesses of rock
laid down by water, and whole mountain masses which must have
been poured out by volcanoes, they could not believe that this had
been done gradually, and only in parts "of the world at a time, as the
Nile and the Ganges are now carrying down earth to the sea, and
Vesuvius, Etna, and Hecla are pouring out lava a few feet thick
every year. They still imagined that in past ages there must have
been mighty convulsions from time to time, vast floods swallowing
up plants and animals several times since the world was made, vio-
lent earthquakes and outbursts from volcanoes shaking the whole
of Europe, forcing up mountains, and breaking open valleys. It
seemed to them that in those times when the face of the earth was
carved out into mountains and valleys, table-lands and deserts, and
when the rocks were broken, tilted up, and bent, things must have
been very different from what they are now. And so they made
imaginary pictures of how nature had worked, instead of reasoning
from what they could see happening around them." 1
The convulsions, or catastrophes, which were thus assumed to take
place were regarded as the result of strange incalculable forces
whose mode of operation could never be exactly determined.
1 Buckley, Short History of Natural Science, pp. 441-442.
244 THE USE OF HYPOTHESES
*nstead of these mysterious agencies, Lyell assumed that causes
similar to those with which we are now acquainted had been
acting uniformly for long ages. The nature of the causes at work
being known, it became possible to calculate the nature of the effects,
and thus to reduce the facts of geology to order and system. As
we have already shown, hypotheses which are to prove really service-
able are formed by extending some known principle through analogy
to a new class of facts. The assumption of mysterious agencies
and principles whose mode of operation is unlike anything which is
known to us, does not aid in the extension of knowledge.
References
W. S. Jevons, Elementary Lessons on Logic, Ch. XXX.
" " The Principles of Science, Ch. XXIII.
C. Sigwart, Logic, 83.
B. Bosanquet, Logic, Vol. II., pp. 155-167.
CHAPTER XIX
FALLACIES OF INDUCTION
66. The Source of Fallacy. It is necessary at the
close of our discussion of the inductive methods, to say
something regarding the errors to which we are most
subject in this kind of thinking. We have seen that
knowledge is the result of the mind's own activity, and
that it grows in completeness through a persistent effort
to keep distinct things which are different, and to con-
nect phenomena which belong together. Truth, in other
words, is gained by intellectual activity. And, on the
other hand, we fall into error, and are led away by false
arguments as a result of mental indolence. Thinking is
hard work, and there is always a tendency to avoid it. As
a matter of fact, we all think much less frequently than
we suppose. Usually, we are content to follow familiar
associations, and to repeat current phrases, without doing
any real intellectual work. The difficulty is that we can
get along comfortably without thinking for the most
part more comfortably, perhaps, than when we do
think. Then, again, the mind is less directly under con-
trol of the will than the body. One may force himself
to sit down at his desk and open a book ; but it is more
difficult to compel oneself to think.
The only way in which we can be saved from becom-
ing ' intellectual dead-beats,' is by the formation of good
245
246 FALLACIES OF INDUCTION
mental habits. It requires eternal vigilance and unceas-
ing strenuousness to prevent our degeneration into mere
associative machines. What the logical doctrine of fal-
lacies can do is to put us on our guard against this ten-
dency. It enumerates and calls attention to some of
the commonest and most dangerous results of slovenly
thinking, in the hope that the student may learn to
avoid these errors. Some of the fallacies of which we
shall treat in this chapter, apply equally to deductive
or syllogistic reasoning, and have been already treated
in Chapter XL We shall, however, enumerate them
here again for the sake of completeness. It is conve-
nient to discuss the various fallacies under the following
heads :
(1) Fallacies due to the careless use of Language.
(2) Errors of Observation.
(3) Mistakes in Reasoning.
(4) Fallacies due to Individual Prepossessions.
67. Fallacies due to the Careless Use of Language.
The careless and unreflective use of words is a very fre-
quent source of error. Words are the signs or symbols
of ideas; but the natural sluggishness of the mind leads
often to a substitution of the word for the idea. " Men
imagine that their reason governs words, whilst, in fact,
words react upon the understanding ; and this has ren-
dered philosophy and the sciences sophistical and inac-
tive." 1 It is much easier to deal with counters than
1 Bacon, Novum Organum, Aph. LIX.
67. THE CARELESS USE OF LANGUAGE 247
with realities. Since we must use words to express our
thoughts, it is almost impossible to prevent them from
becoming our masters. The dangers from the use of
words has been well represented by Locke, from whom
I quote the following passage :
" Men 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 con-
tinue 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 inconsistency in men's words when they come to reason con-
cerning 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 numerous collections of ideas not regu-
larly and permanently united in nature, their bare sounds are often
only thought on, or at least very obscure and uncertain notions
annexed to them. Men take the words they find in use among their
neighbours ; and, that they may not seem ignorant what they stand
for, use them confidently, without much troubling their heads about
a certain fixed meaning ; whereby, besides the ease of it, they obtain
this advantage : That, as in such discourses they seldom are in the
right, so they are as seldom to be convinced that they are in the
wrong ; it being all one to go about to draw men out of their mis-
takes who have no settled notions, as to dispossess a vagrant of his
habitation who has no settled abode." 1
(i) In treating of the misuse of words, we mention,
in the first place, errors arising from the use of a word
1 Essay Concerning Human Understanding, Bk. III. Ch. X.
248 FALLACIES OF INDUCTION
or phrase in more than one sense. This is usually
called the fallacy of Equivocation. In some cases, the
equivocation may be mere wilful quibbling on the part
of the person propounding the argument, as in the
following example of Jevons :
All criminal actions ought to be punished by law,
Prosecutions for theft are criminal actions,
Therefore prosecutions for theft ought to be punished by law.
Examples of this kind do not mislead any one ; but in
some instances the change of meaning in words may
not be perceived, even by the person who employs the
argument. For example, one might reason :
It is right to do good to others,
To assist A in obtaining office is to do him good,
Therefore it is right to assist him in this way.
Here the phrase which is used equivocally is, 'to do
good,' as will at once be perceived.
(2) Another frequent source of error in the use of
words is found in what has been excellently named
the Question-begging Epithet. As is well known, there
is much in a name. Epithets like 'class-legislation,'
' compromise measure/ ' a dangerous and immoral doc-
trine,' are terms freely used to describe the measures
or views of opponents. And, as it is always easier to
adopt a current phrase, than to examine the facts and
draw our own conclusions, it is not surprising that the
name settles the whole matter in the minds of so many
people. Of course, the epithet employed may beg the
question in favour of the subject it is used to describe,
as well as against it. Politicians well understand the
67. THE CARELESS USE OF LANGUAGE 249
importance of adopting an impressive and sonorous
election cry to represent the plank of their party. Thus,
party cries like ' honest money,' ' prohibition and prosper-
ity,' ' the people's cause,' etc., are essentially question-
begging epithets. Even words like 'liberty,' 'justice,'
and 'patriotism,' are frequently used in such a way as
to bring them under the class of fallacies which we
have here described. Under this heading, also, may be
grouped ' cant ' words and phrases. When we accuse
a person of using cant, we always imply that he is
more or less consciously insincere, that he is profess-
ing opinions and sentiments which he does not really
possess. Any insincere expression which is made pri-
marily for the sake of effect may be rightly termed
cant It is not even necessary that the speaker should
be fully conscious of his insincerity. A man may easily
deceive himself, and, as he repeats familiar words and
phrases, imagine himself to be overflowing with patriot-
ism, or with sympathy for others, or with religious
feelings.
(3) Figurative language is another frequent source of
error. Of the various figures of speech, perhaps meta-
phors are the most misleading. The imagery aroused
by metaphorical language is usually so strong as to make
us forget the difference between the real subject under
consideration, and the matter which has been used to
illustrate it. Thus in discussing problems of mind, it
is very common to employ metaphors drawn from the
physical sciences. For example, we read in works on
psychology and ethics of ' the struggle of ideas/ of ' the
balancing and equilibration of motives,' of ' action in
250 FALLACIES OF INDUCTION
the direction of the strongest motive/ etc. Another
illustration, which has been often quoted, is Carlyle's
argument against representative government founded
on the analogy between the ruler of a state and the
captain of a ship. The captain, he says, could never
bring the ship to port if it were necessary for him
to call the crew together, and get a vote every time
he wished to change the course. The real differences
between the relation of a captain to his crew, and the
executive officers in a state to the citizens, is lost sight
of by the metaphor. Metaphorical reasoning is simply
a case of analogy, the imperfections and dangers of
which have been already pointed out. It is, however,
one of the errors which it is most difficult to avoid. A
hidden metaphor lurks unsuspected in many of the
words in common use. We may thus appreciate the
force of Heine's humorous petition : " May Heaven
deliver us from the Evil One, and from metaphors." l
68. Errors of Observation. Sometimes insufficient
observation is the result of a previously conceived the-
ory ; sometimes it may be due to inattention, to the
difficulties of the case, or to lack of the proper instru-
ments and aids to observation. We have already had
occasion to refer to the influence of a theory on obser-
vation (cf. 62). As a rule, we see only those instances
which are favourable to the theory or belief which we
already possess. It requires a special effort of attention
to take account of negative instances, and to discover the
1 Quoted by Minto, Logic, p. 373.
68. ERRORS OF OBSERVATION 251
falsity involved in some long-standing belief. Indeed, it
perhaps requires quite as much mental alertness to over-
throw an old theory, as to establish a new one. This
tendency of the mind to seize upon affirmative instances,
and to neglect the evidence afforded by negative cases,
is well set forth by Bacon in the following passage :
" The human understanding, when any proposition has been once
laid down (either from general admission and belief, or from the
pleasure it affords), forces everything else to add fresh support and
confirmation ; and although most cogent and abundant instances
may exist to the contrary, yet either does not observe or despises
them, or gets rid of and rejects them by some distinction, with
violent and injurious prejudice, rather than sacrifice the authority of
its first conclusions. It was well answered by him who was shown
in a temple the votive tablets suspended by such as had escaped the
peril of shipwreck, and was pressed as to whether he would then
recognize the power of the gods ; ' But where are the portraits of
those who have perished in spite of their vows? ' All superstition is
much the same, whether it be that of astrology, dreams, omens,
retributive judgment, or the like, in all of which the deluded ob-
servers observe events which are fulfilled, but neglect and pass over
their failure, though it be much more common. But this evil insin-
uates itself still more craftily in philosophy and the sciences, in
which a settled maxim vitiates and governs every other circumstance,
though the latter be much more worthy of confidence. Besides,
even in the absence of that eagerness and want of thought (which
we have mentioned), it is the peculiar and perpetual error of the
human understanding to be more moved and excited by affirmatives
than negatives, whereas it ought duly and regularly to be impartial ;
nay, in establishing any true axiom the negative instance is the most
powerful." *
The nature of this fallacy has been so well illustrated
*Novum Organum, Bk. I. Aph. XLVI.
2$2 FALLACIES OF INDUCTION
by the quotation which has just been given, that we may
pass on at once to speak of other cases of insufficient
observation. Our discussion of the processes of reason-
ing have made it clear how necessary it is to observe
carefully and attentively. The majority of the false
theories which have appeared in science and in philoso-
phy, as well as those of common life, have arisen from
lack of observation. The doctrine of innate ideas, and
the theory that combustion was a process of giving off
phlogiston a substance supposed to be contained in
certain bodies may be given as examples. In some
seaside communities, there is a belief that living beings,
botH. human and animal, never die at flood tide. 'They
always go out with the ebb,' it is said. Again, there is
a general belief, which was shared by such an eminent
scientist as Herschel, that the full moon in rising pos-
sesses some power of dispersing the clouds. Careful
observations made at the Greenwich observatory have,
however, shown conclusively that the moon has no such
power as that supposed. 1
Another circumstance to be considered in this con-
nection is the inaccuracy and fallibility of ordinary
memory. Every one must have noticed how rarely two
persons agree completely in the report which they give
of a conversation which they have heard, or of events
which they have experienced. This is due in part to
diversity of interest : each person remembers those cir-
cumstances in which for any reason he is most strongly
interested. But, in addition, it is largely the result of
1 Cf. Jevons, Principles of Science, Ch. XVIII.
68. ERRORS OF OBSERVATION 253
the inevitable tendency of the mind to confuse what is
actually observed, with inferences made from its obser-
vations. The inability to distinguish between what is
really perceived, and what is inferred, is most strongly
marked in uneducated persons, who are not on their
guard against this fallacy. An uneducated person is cer-
tain to relate, not what he actually saw or heard, but the
impression which the events experienced made upon
him. He therefore mixes up the facts perceived, with
his own conclusions drawn from them, and with state-
ments of his own feelings in the circumstances. A
lawyer who has to cross-examine a witness is usually
well aware of this tendency, and takes advantage of it
to discredit the testimony. The experienced physician
knows how worthless is the description of symptoms
given by the ordinary patient, or by sympathetic friends,
or by an inexperienced nurse. The more one's sympa-
thies and interests are aroused in such a case, the more
difficult it is to limit oneself to an exact statement of
actual occurrences.
But this tendency is not confined to persons deficient
in knowledge and ordinary culture. It usually requires
special training to make one a good observer in any
particular field. It is by no means so easy as it may
appear to describe exactly what one has seen in an
experiment. If we know, or think that we know,
the explanation of the fact, there is an almost inevita-
ble tendency to substitute this interpretation for the
account of what has been actually observed. Recent
psychological investigation, aided by exact experimental
methods, has done much to disentangle the data of
254 FALLACIES OF INDUCTION
perception from inferences regarding these data. As
every one knows who has practised psychological intro-
spection, it is only with the utmost difficulty, and after
long training, that one can distinguish the actual psy-
chological process present to consciousness, from the
associative and logical elements which are bound up
with them in our ordinary experience. The following
passage from Mill deals with this question :
" The universality of the confusion between perceptions and the
inferences drawn from them, and the rarity of the power to discrimi-
nate the one from the other, ceases to surprise us when we consider
that in the far greater number of instances the actual perceptions of
our senses are of no importance or interest to us except as marks
from which we infer something beyond them. It is not the colour
and superficial extension perceived by the eye that are important to
us, but the object of which these visible appearances testify the
presence ; and where the sensation itself is indifferent, as it gener-
ally is, -we have no motive to attend particularly to it, but acquire a
habit of passing it over without distinct consciousness, and going on
at once to the inference. So that to know what the sensation ac-
tually was is a study in itself, to which painters, for example, have
to train themselves by long-continued study and application. In
things further removed from the dominion of the outward senses,
no one who has not had great experience in psychological analysis
is competent to break this intense association ; and when such ana-
lytic habits do not exist in the requisite degree, it is hardly possible
to mention any of the habitual judgments of mankind, from the
being of God and the immortality of the soul down to the multi-
plication table, which are not, or have not been, considered as mat-
ter of direct intuition." a
69. Mistakes in Reasoning. The problem of the
inductive processes of reasoning is to ascertain what
* Logic, Bk. V. Ch. IV. 5.
69. MISTAKES IN REASONING 255
facts are necessarily and essentially connected, and to
explain this connection. Now, in order to distinguish
between chance conjunctions of phenomena, and real
causal connections, careful and extensive observation,
aided whenever possible by experiment, must be em-
ployed. In short, to establish a real law of connection
between phenomena, it is necessary to use one or more
of the inductive methods described in Chapters XIV.
and XV. But to do this implies, in many cases, long
processes of analysis ; the performance of intellectual
work, which ordinary minds, at least, have the tendency
to shirk whenever possible. It is much easier to allow
associations to control our thoughts, and to assume that
events which happen together in our experience a num-
ber of times are causally connected. We are led to
such a conclusion by a natural psychological tendency,
without taking any thought about the matter, while
logical analysis and discrimination require a distinct
conscious effort.
The general name used to describe fallacies which
are due to this particular form of mental sluggishness
is post hoc, ergo propter hoc. Two events occur in close
conjunction with each other, and it is then assumed
without further investigation that they are related to
each other as cause and effect. Many popular supersti-
tions, are examples of this fallacy. Some project begun
on Friday turns out disastrously, and it is inferred that
some causal relation existed between the fate of the
enterprise, and the day on which it was begun. Or
thirteen persons sit down to dinner together, and some
one dies before the year is out. It is to be noticed that
256 FALLACIES OF INDUCTION
such beliefs are supported by the tendency, to which
we referred in the last section, to observe only the
instances in which the supposed effect follows, and to
neglect the negative cases, or cases of failure. ' Fortune
favours fools," we exclaim when we hear of any piece
of good luck happening to any one not noted for his
wisdom. But we fail to take account of the more
usual fate of the weak-minded. The belief that the
full moon in rising disperses the clouds, which was also
quoted earlier, is a good example of post hoc, propter hoc.
In fact, all the fallacies treated in this chapter, except
those due to language, might quite properly be included
under this heading.
A special case of this fallacy, to which attention may
be called separately, arises from hasty generalization, or
generalization on an insufficient basis of fact. There
is a constant tendency on the part of the mind to seek
general conclusions, to express all its knowledge in the
form of general statements. But, although it is the
aim of science to express the truth regarding the nature
of the world in the form of general laws, it is not allow-
able to hurry on to such principles without first making
our observation of the facts as complete as possible.
Thus it is not unusual to hear a traveller declare, on
the basis of a very limited experience, that ' the hotels
of some city or country are thoroughly bad.' The
generalizations which are so frequently made regarding
the peculiar characteristics of Americans, or English-
men, or Frenchmen are usually of the same sort. Con-
clusions regarding the effect of moral and political
conditions, too, are often drawn from observations in
70. FALLACIES DUE TO INDIVIDUAL PREPOSSESSIONS 257
a limited field. Even scientific books are not always
free from this error. In a recently published psycho-
logical study of the first year of the life of a child,
by the mother, it was explained why a baby always
sucks its thumb rather than its fingers. The explana-
tion was that the thumb, being on the outside and pro-
jecting outwards, got oftenest into the baby's mouth,
and so the habit was formed. The point is, that the
mother assumed what she had observed in her own
child to be true universally. Other parents, however,
declare that their babies never put the thumb into the
mouth, but always the fingers or the whole hand.
70. Fallacies due to Individual Prepossessions.
Bacon named this class of fallacy " The Idols of the
Cave." Each individual, as he represents the matter,
is shut up in his own cave or den ; that is, he judges
of things from his own individual point of view. In
the first place, one's inclinations and passions, likes
and dislikes, pervert one's judgment. It is exceed-
ingly difficult, as we all know, to be fair to a person
we dislike, or to refrain from judging too leniently
the shortcomings of those to whom we are warmly
attached. Again, it is not easy to put oneself in
the position of an impartial spectator when one's
interests are at stake. " The understanding of men,"
says Bacon, "resembles not a dry light, but admits
some tincture of the passions and will." Further-
more, each individual has a certain personal bias as a
result of his natural disposition and previous training.
Thus it is almost impossible for an individual to free
s
258 FALLACIES OF INDUCTION
himself from national prejudices, or from the standpoint
of the political party, or the church in which he was
brought up. Or, if a person does give up his old views,
he not infrequently is carried to the opposite extreme,
and can see no good in what he formerly believed.
Even education and the pursuit of special lines of
investigation may beget prejudices in favour of particular
subjects. When a man has been engaged exclusively for
a long time in a particular field, employing a particular
set of conceptions, it is almost inevitable that he should
look at everything with which he has to do in the same
light. The mathematician's view of the world is almost
sure to be different from that of the historian, or that
of the student of aesthetics. It is very difficult for the
physicist to conceive of any natural process except in
terms of molecules and vibrations. It is inevitable that
each man should be blinded to some extent by his own
presuppositions. But to recognize one's limitations in
this respect, is to pass, to some extent at least, beyond
them.
Moreover, each age, as well as each individual, may be regarded
as governed largely by current presuppositions and prejudices.
Throughout the Middle Ages, theological doctrines and opinions
controlled almost absolutely the opinions and beliefs of mankind.
This influence, doubtless, still .makes itself felt, but people are now
pretty generally awake to the dangers from this source. On the
other hand, it is more difficult to realize at the present time that
it is not impossible for prejudices and prepossessions to grow out
of scientific work. The success of modern scientific methods
has sometimes led investigators to despise and belittle the work of
those who do not carry on their investigations in laboratories, or do
not weigh and measure everything. But conceptions and method!
70. FALLACIES DUE TO INDIVIDUAL PREPOSSESSIONS 259
which prove useful in one science cannot always be employed profit-
ably in another. A conception, or mode of regarding things, which
has proved serviceable in one field is almost certain to dominate a
whole age, and to be used as an almost universal principle of ex-
planation. The eighteenth century, for example, was greatly under
the influence of mechanical ideas. Newton's discovery made it pos-
sible to regard the world as a great machine, the parts of which
were all fitted together according to the laws of mechanics. This
view led to such a vast extension of knowledge in the realm of
physics and astronomy, that the conceptions upon which it is based
were applied in every possible field to psychology, to ethics, to
political science. The world itself, as well as religious creeds and
political and social institutions, were supposed to have been de-
liberately made and fashioned by some agent. Again,, in these later
years of the nineteenth century we are dominated by the idea of
evolution. The biological notion of an organism which grows or
develops has been applied in every possible field. We speak, for
example, of the world as an organism rather than as a machine, of the
state and of society as organic. And the same conception has been
found useful in explaining the nature of human intelligence. It is
easy for us to realize the limitations and insufficiency of the notion
of mechanism as employed by the thinkers of the eighteenth century.
But it is not improbable that the twentieth century may be able to
see more clearly than we are able to do, the weaknesses and limita-
tions of the conception which has proved so fruitful in this genera-
tion.
References
Bacon, No-vum Organum, Aph. XXXVIII-LXVIII.
Locke, Essay Concerning Human Understanding, Bk. III. Chs.
X. and XI.
J. S. Mill, Logic, Book V.
A. Bain, Logic, Pt. II. Induction, Bk. VI.
J. Fowler, Inductive Logic, Ch. VI.
J. G. Hibben, Inductive Logic, Ch. XVII.
A. Sidgwick, Fallacies [Int. Scient. Series].
PART III. THE NATURE OF
THOUGHT
CHAPTER XX
JUDGMENT AS THE ELEMENTARY PROCESS OF THOUGH!
71. Thinking the Process by which Knowledge grows
or develops. Logic was defined ( i) as the science of
thinking, and we have seen that the business of thought
is to furnish the mind with truth or knowledge. Under
what general conception, now, shall we bring thinking,
and what method shall we adopt to aid us in its investi-
gation ? It is at once clear that thinking, the conscious
process by which knowledge is built up, does not re-
semble mechanical processes like pressure, or attraction
and repulsion. It is more nearly related to something
which has life, like a plant or an animal, and which
grows or develops from within, in accordance with the
laws of its own nature. Thinking must be regarded
rather as a living, than as a dead thing, though it is
necessary also to remember that it is conscious as well
as living.
When the thinking process is regarded in this way,
moreover, a method of procedure at once suggests itself.
In these days we have become familiar with the notion
of evolution or development, and the application of this
260
;i. THE PROCESS OF THINKING 26 1
notion has proved of the greatest service to science, and
particularly to those sciences which deal with the phe-
nomena of life. What is characteristic of this manner of
regarding things is the fact that it does not consider the
various phenomena with which it deals as fixed, un-
changeable things, each with a ready-made nature of its
own. But each thing is simply a stage of a process, a
step on the way to something else. And the relations
of the various phenomena to each other, their connec-
tion and unity as parts of the one process, come out
more clearly when viewed in this way. In other words,
by taking a survey of the genesis and growth of things,
we gain a truer idea of their nature and relations than
would be possible in any other way. The past history
of any phenomenon, the story of how it came to be
what it is, is of the greatest possible service in throwing
light upon its real nature. Now, one cannot doubt
that this conception will also prove serviceable in the
study of logic. That is to say, it will assist us in gain-
ing a clearer idea of the nature of thinking, to conceive
it as a conscious function, or mode of acting, which un-
folds or develops in accordance with the general laws of
organic evolution. And this process may be supposed
to go on both in the individual, as his thought develops
and his knowledge expands, and in the race, as shown
by its history. By adopting this notion, we may hope
to show also that there is no fundamental difference
in kind between the various intellectual operations.
Judgment and Inference, for example, will appear as
stages in the one intellectual process, and the relation
between Induction and Deduction will become evident
262 JUDGMENT AS THE ELEMENTARY PROCESS
72. The Law of Evolution and its Application to Logic.
The most striking characteristic of any organism at a
low stage of development is its almost complete lack of
structure. An amoeba, for example, can scarcely be
said to have any structure ; it is composed of protoplasm
which is almost homogeneous, or of the same character
throughout. When we compare an amoeba, however,
with an animal much higher in the scale of life, e.g.,
a vertebrate, a great difference is at once evident.
Instead of the simple, homogeneous protoplasm, the
organism is composed of parts which are unlike or hete-
rogeneous, such as bones, muscles, tendons, nerves,
blood-vessels, etc. In Mr. Spencer's language, there
has been a change from a state of homogeneity, to
one of heterogeneity. The process of evolution from
the lower organism to the higher has brought with
it a differentiation of structure. That is, in the amoeba
there are no special organs of sight, or hearing, or
digestion, but all of these acts seem to be performed
by any part of the organism indifferently. In the
vertebrate, on the other hand, there is division of
labour, and a separate organ for each of these func-
tions. One may also notice that the same change is
observable when the acts or functions, performed by a
lower organism are compared with those of a higher.
The life of the amoeba seems to be limited almost en-
tirely to assimilation and reproduction ; while, when we
advance from the lower animals to the higher, and from
the higher animals to man, there is an ever-increas-
ing complexity and diversity in the character of
the actions performed. We thus see how the process
72. THE LAW OF EVOLUTION 263
of evolution involves differentiation both of structure
and of function, in passing from the homogeneous
to the heterogeneous.
But differentiation, or increase in diversity, is only
one side of the process of evolution. As we pass from
a lower to a higher stage, the various parts of an or-
ganism are seen to become more essential to each other.
If certain plants or low animal organisms are divided
into several parts, each part will go on living. Its con-
nection with the other parts does not seem to have been
at all necessary to it. But when we are dealing with
higher forms of life, each part is seen to have its own
particular function, and to be essential to the other
parts, and to the organism as a whole. In other words,
the parts now become members, and the whole is not
simply an aggregation of parts or pieces, but is consti-
tuted by the necessary relation of the members to each
other. The more highly evolved the whole with which
we are dealing, the more closely connected and essential
to each other are the various parts seen to be. It be-
comes increasingly true that if one member suffers, all
the other members suffer along with it.
Evolution, then, not only exhibits a constant process
of differentiation, and a constant increase in the diver-
sity of parts and organs, but there goes along with this
what might be called a process of unification, whereby
the parts are brought into ever closer and more essen-
tial relation to one another. In this way, a real or or-
ganic whole, as opposed to a mere aggregate, is formed.
This is what Mr. Spencer calls the process of integra-
tion ; and it accompanies, as we have seen, what the
same writer calls differentiation.
' 264 JUDGMENT AS THE ELEMENTARY PROCESS
The application of this general law of evolution to
the development of the thinking process is not diffi-
cult. We shall expect to find that thinking, in its
first beginnings, both in the individual and in the race,
will be much less complex than at a higher stage.
That is, the earliest or simplest thinking tends to take
things in a lump, without making any distinctions.
The infant, for example, does not distinguish one
person from another, or perhaps does not distinguish
even the parts of its own body from surrounding ob-
jects. Now, it is clear that intellectual development,
growth in knowledge, must in the first place involve
differentiation. What is complex must be analyzed or
separated into its various parts. Things which are
different must be distinguished, and clearly marked
off from each other. The development of thought
implies then, as one of its moments, discrimina-
tion or analysis what we previously called differen-
tiation.
The other moment of the law of evolution, integration,
also finds a place in the development of thought, and
goes hand in hand with the former. The child and the
uneducated man not only often fail to make distinctions
where these really exist, but the parts of their know-
ledge are fragmentary, and have little or no relation to
one another. The various pieces of their knowledge
are like the parts of the amoeba they may be in-
creased or diminished without themselves undergoing
any change. But in order to pass from a lower to a
higher intellectual point of view, to become better
educated, in a word, it is necessary to see the way in
72. THE LAW OF EVOLUTION 265
which the various pieces of our knowledge are con-
nected and depend upon one another. It is not enough
to analyze and keep separate things which are distinct,
but it is also necessary to understand how the various
parts of our knowledge are so related as to be essential
to one another. In other words, we may say that it is
characteristic of our intelligence to endeavour to put
things together so as to form a whole, or system of
interconnected parts. And the more completely it is
able to do this (provided that the process of differentia-
tion has also made a corresponding advance), the higher
is the stage of development which has been attained.
The ideal of knowledge, or of complete intellectual
development, would be to understand the oneness and
relation of everything which exists, even of all those
things which seem now to be entirely different in kind.
A knowledge of any one fact would then carry with it a
knowledge of every other fact. Or, rather, our know-
ledge would be so completely unified, that each part
would show the nature of the whole or system to
which it belongs ; just as a leaf of a plant, or the tooth
of an animal, is sufficient to tell the naturalist of the
wholes to which they belong.
This, of course, will always remain an ideal ; but it is
in this direction that thinking actually develops. It is
a step in advance to discover the reasons for any fact
which one previously knew as a mere fact. But, to
discover the reasons for a fact, is to bring it into con-
nection with other facts, to see them no longer as
isolated and independent, but as belonging together
to one group or system of facts. And the further
266 JUDGMENT AS THE ELEMENTARY PROCESS
the process of explanation goes on, the more completely
is our knowledge unified and related.
There is, however, another fact implied in the very
nature of evolution, of which logic, as well as the other
sciences, may take advantage. We have assumed that
the more complete and difficult kinds of thinking have
grown or developed from simpler types of the same
process, and not from something different in kind. It
will therefore follow, that the essential characteristics of
the thinking process may be discovered in its simplest
and most elementary form. It is found that all the
essential functions of the fully developed organism are
discharged by the primitive cell. And because it is
easier to study what is simple than what is complex,
the cell is taken as the starting-point in biology. Simi-
larly, there will be an advantage in beginning with the
simplest and most elementary forms of thinking. What
is found true of these simple types of thought, may be
assumed to be essential to the thinking process as such.
73. Judgment as the Starting-point. What, then,
is the simplest form of thinking ? What shall we take
as a starting-point, which will correspond to the cell in
biology, or the elementary process in psychology ? To
answer this question, it is not necessary first to decide
where in the scale of animal life that which we are en-
titled to call thinking actually begins. We shall not be
obliged to discuss the much-debated question, whether
or not dogs think. Wherever thinking may be found,
it is essentially an activity of the mind. When it is
present, that is, there is always work done, something
73- JUDGMENT AS THE STARTING-POINT 267
interpreted or put together, and a conclusion reached.
One may perhaps say that thinking is simply the way
in which the mind puts two and two together and sees
what the result is. It implies that the mind has waked
up to the significance of things, and has interpreted
them for itself. Suppose that one were sitting in one's
room very much engaged with some study, or wrapt up
in an interesting book, and suppose that at the same
time the sound of a drum fell upon one's ears. Now,
the sound sensations might be present to consciousness
without calling forth any reaction on the part of the
mind. That is, we might be so intent on our book that
we should not wake up, as we have been saying, to the
meaning or significance of the drum-taps ; or perhaps
not even to the fact that they were drum-taps at all.
But if the mind did react upon the sound sensations,
it would try to interpret them, or put them together so
as to give them a meaning. As a result, some conclu-
sion would be reached, as, for example, 'the drum is
beating ' ; or sufficient intellectual work may have been
done to give as a conclusion, ' that is the Salvation Army
marching up the street.' In any case, it is of the great-
est importance to notice that the conclusion does not
come into our minds from without, but that it is the
product of the mind's own activity, as has been de-
scribed. It is not true, in other words, that knowledge
passes into our minds through the senses ; it is only
when the mind wakes up to the meaning of sensations,
and is able to put them together and interpret them,
that it gains any knowledge.
Now, the simplest form of such an act of thought is
268 JUDGMENT AS THE ELEMENTARY PROCESS
called a judgment. Judgment, we may say, is a single
intellectual act of the kind we have described ; and its
conclusion is expressed by means of a Proposition ; as,
for example, 'the grass is green,' 'the band is playing.'
In accordance with general usage, however, we may use
the term 'Judgment' for both the act itself and its
result. And the word ' Proposition ' will then denote
the external expression in speech or writing of the
product of an act of judgment.
In our investigation of the nature of thought, then,
we must begin with Judgment. There are three things
which we shall have to do : (i) to endeavour to discover
the fundamental characteristics of this simple type of
thinking ; (2) to show the various forms which it as-
sumes, or to describe the different kinds of Judgment ;
and (3) to trace the process by which Judgment ex-
pands into the more complete logical form of Inference.
Before any of these questions are considered, however,
it is necessary to meet a very serious objection to our
whole procedure of beginning with Judgment as the
elementary process of thinking.
74. Concepts and Judgments. In the last section,
we endeavoured to show that Judgment is the elemen-
tary process of thought, and that with it all knowledge
begins. This view, however, may seem to be contra-
dicted by the treatment of Judgment usually found in
logical text-books. Judgment, it is said, is expressed
by a proposition ; and a proposition is made up of three
parts, subject, predicate, and copula. Thus in the prop-
osition, 'iron is a metal,' 'iron ' is the subject, 'a metal'
74- CONCEPTS AND JUDGMENTS 269
the predicate, and the two terms are joined or united by
means of the copula 'is.' A Judgment is therefore
defined as an act of joining together, or, in negative
judgments, of separating, two concepts or ideas. If
this account be accepted, it follows that the ideas of
which the judgment is composed (iron and metal, in
the example given above) are pieces of knowledge
which precede the judgment itself. And the act by
which these logical ideas (or, as they are usually called,
concepts) are formed must also be earlier and more
fundamental than the act of judging. It is therefore
held that logic should begin with concepts, which are
the elements out of which judgments are compounded,
and that the first logical act consists in the conception
or simple apprehension of the ideas or concepts (cf. n).
It is necessary to examine this position very care-
fully. What is maintained is that a process of forming
concepts, or logical ideas, presumably quite distinct
from the activity of judgment, necessarily precedes the
latter. Before it is possible to judge that 'iron is a
metal,' for instance, one must have gained, by means of
Conception or Apprehension, the ideas denoted by the
subject and predicate of this proposition. Judgments,
that is, are made or compounded out of something
different from themselves.
It may be well to begin the defence of our own
position by noting what_ is undoubtedly true in what
has just been stated. In making a judgment like 'iron
is a metal,' it is, of course, necessary to have the con-
cept 'iron,' and the concept 'metal.' But what is
implied in having a concept of anything ? Let us
2/0 JUDGMENT AS THE ELEMENTARY PROCESS
suppose that a person is making the above-mentioned
judgment for the first time that is, really drawing a
conclusion for himself, and not merely repeating words.
He would begin, we may say, with the concept 'iron.'
But if this concept is more than a mere word, if it
really means anything, it must have been formed by a
number of judgments. The concept 'iron,' if it has
any significance for the person using it, means a defi-
nite way of judging about some substance that it is
hard, malleable, tough, etc. The greater the number
of judgments which the concept represents, the more
meaning or significance it has; apart from the judg-
ment, it is a mere word, and not a thought at all.
To admit, then, that in judging we always start from
some concept, does not imply that there is a different
form of intellectual activity prior to judgment, which
furnishes the latter with ready-made material for its
use. But, as we have seen, in ordinary judgments like
the example with which we have been dealing, the new
judgment is a further expansion or development of a
previous set of judgments which are represented by the
concept. The concept, then, stands for the series of
judgments which have already been made. Language
comes to the aid of thought, and makes it possible to
gather up such a set of judgments and represent them
by a single expression often by a single word. Every
word that is the name of some logical concept repre-
sents intellectual work the activity of judgment in
its formation. In learning our own language, we
inherit the word without doing the work. But it must
never be forgotten that the word in itself is not the
74- CONCEPTS AND JUDGMENTS 2/1
concept. To make the thought our own, to gain the
real concept, it is necessary to draw out or realize to
ourselves the actual set of judgments for which the
word is but the shorthand expression.
The view which regards the judgment as a compound
of two parts subject and predicate rests upon the
substitution of words for thoughts. It analyzes the
proposition (the verbal or written expression of
the judgment), instead of the judgment itself. In
the proposition, the parts do exist independently of
each other. The subject usually stands first, and is
followed by the predicate. But there is no such order
of parts in a judgment. When one judges, 'it is rain-
ing,' or, 'that is a drum,' the piece of knowledge is one
and indivisible. And the act by which this knowledge
is gained, is not an external process of joining one part
to another, but is an intellectual reaction by which we
recognize that something, not previously understood,
has a certain meaning or significance.
Again, it is only when concepts are identified with
the words which make up the parts of the proposition,
that they can be regarded as ready-made existences,
which are quite independent of their connection in a
judgment. The terms, 'iron,' and 'metal,' are separable
parts of the proposition and exist independently of their
connection with it. The conclusion has been therefore
drawn that concepts had a like independence of judg-
ments, but might enter into the latter and form a part
of them without affecting their own nature in any way.
But, as we have already seen, the concept has no
meaning apart from the series of judgments which it
2/2 JUDGMENT AS THE ELEMENTARY PROCESS
represents. And, as thinking goes on, as new judg-
ments are made, its nature is constantly changing. In
short, concepts are not dead things, but living thoughts
which are in constant process of development.
The objection, then, which urges that conception is a
logical process, which is prior to judgment, turns out
when rightly understood to be no objection at all. For,
in the light of what has been already said, it only
amounts to this : In making new judgments regarding
anything, we must set out from what we already know
of it, as represented by the judgments already made.
That is, the starting-point for a new judgment is the con-
cept or series of judgments which represents the present
state of our knowledge. The progress of knowledge
is not from the unknown to the known, but from a state
of partial and incomplete knowledge to one of greater
perfection. Thus the judgment 'gold is malleable'
(supposing it to be a real judgment made for the first
time), adds to, or develops further, our existing know-
ledge of gold, as represented by a series of judgments
previously made regarding it.
It may be urged, however, that not every judgment can grow out
of previous judgments in this way. For, if we go back far enough,
we must reach some judgment which is absolutely first, and which
presupposes no antecedent judgment. This is like the paradox
regarding the origin of life. If all judgments are derived from an-
tecedent judgments, how was it possible for the first one to arise?
It will, perhaps, be sufficient answer to deny the existence of the
paradox. Consciousness must be regarded as having from the first
the form of a judgment. No matter how far one goes back in the
history of consciousness, one will always find, so long as conscious-
ness is present at all, some reaction, however feeble, upon the
74- CONCEPTS AND JUDGMENTS 2/3
content, and something like knowledge resulting. Even the
consciousness of the newly born infant, reacts, or vaguely judges,
in this way. These primitive judgments are, of course, very weak
and confused, but they serve as starting-points in the process of
intellectual development. Growth in knowledge is simply the
process by means of which these vague and inarticulate judgments
are developed and transformed into a completer and more coherent
experience.
References
W. S. Jevons, Elementary Lessons in Logic, pp. 9-16.
F. H. Bradley, The Principles of Logic, Bk. I. Ch. I.
B. Bosanquet, Logic, Vol. I. Ch. I. 1-6.
H. Lotze, Logic (Eng. trans.), Vol. I., pp. 13-61.
C. Sigwart, Logic, 40-42.
L. T. Hobhouse, The Theory of Knowledge, Pt. I. Chs. I. and II.
CHAPTER XXI
THE MAIN CHARACTERISTICS OF JUDGMENT
75. The Universality of Judgments. We have now
to examine the nature of Judgment a little more closely
than we have done hitherto. And, in the first place,
we note that all judgments claim universality. There
are, however, several kinds of universality, and more
than one sense in which a judgment may be said to be
universal. We speak of a universal judgment (more
properly of a universal proposition), when the subject is
a general term, or is qualified by some such word as
'all,' or 'the whole.' And we distinguish from it the
particular judgment, where the subject is only the part
of some whole, and is usually preceded by ' some,' or by
other partitive words. But here we have no such dis-
tinction in mind ; we are speaking of the universality
which belongs to the very nature of Judgment as such,
and which is shared in by judgments of every kind.
When we say that judgments are universal, in the
sense in which the word is now used, we mean that the
conclusions which they reach claim to be true for every
one. No matter what the subject and the predicate
may be, a judgment, e.g., ' man is mortal,' comes forward
as a fact for all minds. We have shown in the last
chapter that it is by judging, or putting things together
for itself, that the human mind gains knowledge. Now,
274
75- THE UNIVERSALITY OF JUDGMENTS 2/5
the assumption upon which this process is based is
that the result thus reached knowledge is not some-
thing merely individual and momentary in character.
When I judge that 'two and two are four,' or that 'iron
has magnetic properties,' the judgment is not merely a
statement of what is going on in my individual con-
sciousness ; but it claims to express something which is
true for other persons as well as for me. It professes
to deal with facts which are true, and in a sense inde-
pendent of any individual mind. The judgments by
which such conclusions are reached are universal, then,
in the sense of being true for every one and at all times.
The word 'objective' has essentially the same meaning.
Although each man reaches truth only by actually judg-
ing for himself, yet truth is objective, out there beyond
his individual or ' subjective ' thought, shared in by all
rational beings. The assumption upon which all argu-
ment proceeds is that there is such a standard, and that
if people can be made to think they will arrive at it.
Thought is objective, or, in other words, has in itself
its own standard of truth.
The only alternative to this position is scepticism, or pure in-
dividualism. If Judgment is not universal in the sense that it
reaches propositions which are true for everybody, it is of course im-
possible to find any standard of truth at all. The judgments of any
individual in that case would simply have reference to what seems
true to him at the moment, but could not be taken to represent any
fixed, or permanent truth. Indeed, if one regards Judgment as deal-
ing merely with particular processes in an individual mind, the
ordinary meanings of truth and falsehood are completely lost, and it
becomes necessary to give a new definition of the words. This was
the position of the Sophists at the time of Socrates (cf. 5). Each
2/6 THE MAIN CHARACTERISTICS OF JUDGMENT
individual man was declared to be the measure of what is true and
false, as well as of what is good and bad. There is thus no other
standard of truth or value than the momentary judgment (or ca-
price) of the individual. This is, in a way, the reductio ad
absurdum of scepticism.
The common nature of truth, as something in which all can
share, presupposes, then, a common mode of thinking or judging on
the part of all rational beings. And it is this universal type or form
of knowing with which logic deals. The question as to whose
thought is investigated, or in what individual mind the thought takes
place, is in itself of no importance. The consciousness of a savage
differs very greatly from that of an educated man ; it is much less
complex and less highly developed. But yet, in spite of the enor-
mous differences, there exists in both an intelligence, or way of
thinking, which shows the same essential character, and operates
according to the same fundamental laws.
76. The Necessity of Judgment. The second char-
acteristic which we note as belonging to Judgment is
necessity. By this we mean that when a person judges,
he is not free to reach this or that conclusion at will.
As an intellectual being, he feels bound to judge in a
certain way. This is sometimes expressed by saying
that we cannot believe what we choose, we must believe
what we can.
In many of the ordinary judgments of everyday life,
which are made without any clear consciousness of their
grounds, logical necessity is implicitly present as an im-
mediate feeling of certainty. In cases of this kind, we
simply identify ourselves with the judgment, and feel
that it is impossible that it can be false. But, of course,
no judgment can claim to be necessary in its own right.
Its necessity comes from its connection with other facts
76. THE NECESSITY OF JUDGMENT
which are known to be true. Or, in logical terms,
we may say that it comes from reasons or premises
which support it. And one should always be ready
to show the grounds or reasons upon which one's
feeling of necessity rests. But in ordinary life, as we
have seen, it is not unusual to regard a conclusion as
necessary, without clearly realizing the nature of the
reasons by which it is supported. An uneducated man
is rarely able to go back and discover the reasons for
his belief in any statement of which he is convinced.
If you question his assertion, he feels that you are
reflecting upon his veracity, and consequently grows
angry. In the feeling of immediate necessity or con-
viction, he identifies himself with the judgment, and
does not see that the criticism is not directed against
the latter, but against the grounds by which it is sup-
ported.
In this distinction between necessity that is merely
felt, and the necessity that is conscious of its own
grounds, we see the direction in which judgment must
develop. In the evolution of thought, we must become
conscious of the grounds upon which our judgments
are made. That is, the simple judgment, which seems
to stand in isolation, must expand so as to unite with
itself its reasons. By itself, it is only a fragment of a
more complete and widely embracing thought. The
feeling of necessity is an evidence of its dependence and
connection, though this dependence and connection upon
other facts may not be clearly understood. But what
is implicit must be made explicit ; the necessity which
is merely felt to belong to the simple judgment must
2/8 THE MAIN CHARACTERISTICS OF JUDGMENT
be justified, by showing the grounds or reasons upon
which it rests. And, for this purpose, the simple judg-
ment must expand so as to include the reasons which
are necessary to support it. In other words, it must
develop into an inference. As a matter of fact, the
same form of words as used by different persons, or by
the same person at different times, may express either
a judgment or an inference. Thus, 'the price of wheat
rose after the war began,' might express either a simple
historical fact, which is accepted from experience or from
hearsay, or it might, in the mouth of a person acquainted
with the laws of supply and demand, be the necessary
conclusion of a number of premises. Again, a child
might read that, ' the travellers found great difficulty in
breathing when they reached the top of the mountain,'
accepting this as a simple statement of fact. If he were
to read this same statement some years later, however,
he would probably connect it at once with other facts re-
garding the nature of the atmosphere, and the action of
gravity, and so perceive at once its inferential necessity.
According to the view which has just been stated, necessity is not
a property which belongs to any judgment in itself, but something
which arises through its dependence upon other judgments. In
other words, necessity is always mediate, not immediate. This
view, however, differs from a theory that was once generally received,
and has some adherents, even at the present time, especially among
thinkers who belong to the Scottish or 'common-sense 1 school. In
dealing with the facts of experience, we always explain one fact by
referring it to a second, and that second by showing its dependence
upon some third fact, and so on. Thus the movement of the piston-
rod in an engine is explained by the pressure of steam, and this is
due to the expansive power of heat, and heat is caused by combus-
77- JUDGMENT BOTH ANALYTIC AND SYNTHETIC 279
tion of fuel, etc. We are thus pushed back in our explanations from
one fact or principle to another, without ever reaching anything
that does not require in its turn to be explained.
Now, it is said that this process cannot go on forever ; for if it
did there could be no final or complete knowledge ; the whole
system would be left hanging in the air. There must, therefore,
it is argued, be some ultimate facts which furnish the support for
the world of our experience, some principle or principles which are
themselves necessary and do not require any proof. That is, there
must be certain propositions which are immediately necessary, and
which serve as final explanation for everything else. Now, it is
clear that such propositibns must be entirely different in character
from the ordinary facts of experience, since their necessity belongs
to their own nature, and is not derived from any other source. It
had to be supposed, therefore, that they stood upon a different
plane, and were not derived from experience. To explain the su-
perior kind of certainty which they were assumed to possess, it was
supposed that they were present in the mind at birth, or were innate.
They have also been called necessary truths, a priori truths, and
fundamental first principles, in order to emphasize their supposed
distinction from facts which are derived from experience.
77. Judgment involves both Analysis and Synthesis.
The business of our thought is to understand the ways
in which the various parts of the real world are related.
And a judgment, as we have already seen, is just a
single act of thought, one step in the process of
understanding the world. Now we ask : How does
Judgment accomplish its task? Does it proceed by
analysis, showing the parts of which things are com-
posed, or does it employ synthesis in order to show
how various parts combine in such a way as to form
a whole ? Or is it possible for both these processes to
be united in one and the same act of judgment?
280 THE MAIN CHARACTERISTICS OF JUDGMENT
Suppose that one actually makes the judgment for
oneself (and does not merely repeat the words), ' the
rose has pinnate leaves.' What has taken place ? We
notice, firstly, that a new property of the rose has been
brought to light; a distinction, or mark, has been dis-
covered in the content 'rose,' which was not seen to
belong to it before the judgment was made. So far,
then, the process is one of analysis, of discovering the
parts or distinctions of something which is at first taken,
as it were, in a lump. And this is a most essential ele-
ment in all thinking. In order to know, it is absolutely
necessary that the differences between the parts of
things should be clearly apprehended, that we should
not confuse things which are unlike, or fail to make
proper distinctions. If we examine a number of in-
stances where a real judgment is made, we shall find
that this moment of analysis, or discrimination, is always
present. Sometimes, indeed, analysis may not seem to
be the main purpose of the judgment ; but if one looks
closely, one will always find in a judgment that elements
which are unlike are held apart or discriminated.
Let us look again at the same judgment, 'the rose
has pinnate leaves.' It is not difficult to see that the
discovery of something new in itself is only one part of
what the judgment has accomplished. The judgment
also affirms the union of this new discovery with the
properties of what we call the rose. It is, therefore,
from this point of view, an act of synthesis. It asserts
that the prickly branches, fragrant flowers, feather-like
leaves, and other distinctions, are united in the one
content which we call the rose. It does not stop with
77- JUDGMENT BOTH ANALYTIC AND SYNTHETIC 281
the mere assertion, 'there is a mark or distinction,' but
it affirms that it is a mark of something, i.e., that it is
united with other marks or properties to form a con-
crete whole. In other words, we may say that every
judgment affirms the imity of the different parts, or
aspects, of a thing ; and this is, of course, synthesis.
From this point of view, then, Judgment can be defined
as a process of synthesis, just as we denned it above as
one of analysis.
But how, it may be asked, is it possible for a judg-
ment to be both analytic and synthetic ? Are not these
processes directly opposed to each other? There can
be no doubt that this is the case when we are dealing
with material things : pulling things to pieces is the
opposite of putting them together. When we are
doing the one we cannot also be doing the other. But
there is no such opposition between these processes
when they go on in our minds. An illustration may
make this clear. Suppose that one is trying to under-
stand some piece of mechanism, say a watch ; in order
to be able to see how it goes, or judge correctly regard-
ing it, two things are necessary. First, one must notice
all the parts of which it is composed the wheels of
various sizes, springs, pins, etc. But, in the second
place, one would not understand the watch until one
saw how all the parts were united, how one part fits
into another, and all combine together into one whole.
We do not mean that these are two steps which take
place in succession ; as a matter of fact, the detection
of the various parts, and the perception of their connec-
tion, go hand in hand. In the process of understanding
282 THE MAIN CHARACTERISTICS OF JUDGMENT
the watch, we have both taken it to pieces and put it
together again at one and the same time. Not really,
of course, but in our thought. In the world of material
things, as we have said, only one of these processes
could go on at a time ; but in every act of thinking,
in every judgment, analysis and synthesis go hand in
hand, and one has no meaning except with reference to
the other.
Although every judgment contains, as we have
seen, the two moments of analysis and synthesis, these
are not always equally prominent. The main purpose
of the judgment usually falls on one side or the other.
In a judgment like, 'water can be divided into hydro-
gen and oxygen,' the main emphasis seems to be on
the parts, and the assertion that these elements are
parts of a whole, though present, is only implied. But
when one asserts, ' these springs and wheels together
make up a watch,' it is the nature of the whole upon
which the emphasis is laid, and the separation or dis-
crimination of the parts, is, as it were, secondary. It is
not difficult to see, however, that the two moments of
Judgment are present in both of these cases. The dif-
ference consists in the fact that at one time analysis,
and at the other synthesis, is made the main purpose.
It was at one time supposed that analytic and
synthetic judgments were entirely different in kind
from each other. An analytic judgment, it was said,
is one in which the predicate is obtained by analyzing,
or bringing to light, what is contained in the subject.
Thus the judgment, 'all material bodies fill space,' is
analytic ; for the predicate (space-filling) is contained in
77- JUDGMENT BOTH ANALYTIC AND SYNTHETIC 283
the very notion, or idea, of a material body. All that
is necessary in order to obtain the judgment is to com-
prehend the meaning of the subject. An analytic judg-
ment, then, adds nothing to our knowledge. It merely
enables us to bring to light and express what is con-
tained in the ideas we already possess. A synthetic
proposition, on the contrary, was defined as one in which
the predicate was not already contained in the subject,
but which added a new element or idea to it. ' This body
weighs ten pounds,' for example, is a synthetic propo-
sition, for one cannot obtain the predicate by analyzing
the subject. The predicate adds a new fact which
must have been derived from experience.
This view is of course fundamentally different from the account
of Judgment which we have just given. The absolute distinction
between analytic and synthetic judgments, like the theory that
thought begins with concepts, arises, I think, from a substitu-
tion of the spoken or written proposition for the judgment itself.
In the proposition the subject seems to be the starting-point. We
have a word or term which appears to be independent and capa-
ble of standing alone. The question is, then, where shall we find
the predicate ? For example, in the proposition, 'iron is an ele-
ment,' the subject stands first, and the predicate comes later. It
seems possible then to say that we have first the subject ' iron,' and
then join on to it the predicate ' element,' which has been obtained
either by analyzing the subject, or from some previous experience.
But the proposition, as a collection of words, must not be substituted
for the act of judgment. Judgment, as we have already seen, is a
single act of intelligence, which at once discriminates and brings
into relation different aspects of the whole with which it is dealing.
A mere subject by itself has not any intelligible meaning. If one
hears the word ' iron,' for example, the word may call up certain
mental images ; but by itself it is not a complete thought or fact in
284 THE MAIN CHARACTERISTICS OF JUDGMENT
which we can rest. ' Well, what of it? ' we say. The mind at once
goes on to form some judgment like, 'this is iron, 1 or ' iron is heavy.'
We cannot think a term without thinking something of it. In short,
although the words which form the subject of a proposition are
relatively independent, and can be used without the words which
make up the predicate, in a judgment, on the other hand, a subject
is only a subject through its relation to a predicate. The propo-
sition may be divided into parts, but the judgment is a single
thought-activity, and cannot be divided (cf. 74).
78. Judgment as Constructing a System of Knowledge.
In this section we have not to take account of any new
characteristic of Judgment, but rather to emphasize
the part it plays in building up knowledge. As we
have seen, Judgment works both analytically and syn-
thetically : it discovers new parts and distinctions, and
at the same time brings the parts into relation and thus
builds up a whole. That is the law according to which
thinking develops, and is just what we called differen-
tiation and integration in a previous section ( 72).
It is necessary here, however, to dwell upon the fact
that each judgment may be regarded as a step in the
process of building up a system of knowledge. The
emphatic word here is ' system,' and we must be per-
fectly clear about its meaning. A system is a whole
which is composed of various parts. But it is not the
same thing as an aggregate or heap. In an aggregate
or heap, no essential relation exists between the units
of which it is composed. In a heap of grain, or pile of
stones, one may take away any part without the other
parts being at all affected thereby. But in a system,
each part has a fixed and necessary relation to the whole
78. CONSTRUCTING A SYSTEM OF KNOWLEDGE 285
and to all the other parts. For this reason we may say
that a building, or a piece of mechanism, is a system.
Each stone in the building, each wheel in the watch,
plays a part, and is essential to the whole. In things
which are the result of growth, the essential relations in
which the parts stand is even more clearly evident.
The various parts of a plant or an animal have each their
own function, but at the same time they are so neces-
sary to each other that an injury to one is an injury to
all. We express this relation in the case of living things
by saying that the parts are organic to each other. And,
in the same way, it is not unusual to speak of society as
an organism, in order to express the fact that the vari-
ous individuals of which it is composed are not inde-
pendent units, but stand in necessary relations to one
another, and are all mutually helpful or hurtful.
We have said that Judgment constructs a system of
knowledge. This implies, then, that it is not merely
a process of adding one fact to another, as we might
add one stone to another to form a heap. No ! Judg-
ment combines the new facts with which it deals, with
what is already known, in such a way as to give to
each its own proper place. Different facts are not
only brought together, but they are arranged, related,
systematized. No fact is allowed to stand by itself, but
has to take its place as a member of a larger system
of facts, and receive its value from this connection. Of
course, a single judgment is not sufficient to bring a
large number of facts into relation in this way. But each
judgment contributes something to this end, and brings
some new fact into relation to what is already known.
286 THE MAIN CHARACTERISTICS OF JUDGMENT
In a simple judgment like, 'that was the twelve o'clock
whistle,' the constructive or systematizing work accom-
plished is evident. The auditory sensation, which in
itself, as a mere wandering sound, was not a piece of
knowledge at all, is interpreted in such a way as to find
a place in the system of experience. One may appreciate
what part the judgment really plays by remembering how
the sound appeared before one was able to judge. There
may have been at first a moment of bewilderment
' What does this mean ? ' one asks. In the next moment
the judgment is made: 'It is the twelve o'clock whistle.'
That is, our thinking has constructed a meaning for it,
and brought it into relation with the rest of our know-
ledge.
(i) Every new experience is thus brought into relation with the
facts which we already know, and is tested by them. It has to find its
place in the system of knowledge to join itself to what is already
known. If this is impossible, if what claims to be a fact is entirely
opposed to what we already know on the same subject, it is usually
declared to be false. Thus, we would refuse to believe that some
person whom we know well and respect was guilty of theft ; for it
would be impossible to connect such conduct with what we already
know of his character. And, similarly, we find it impossible to
believe, even although we have the evidence of our senses, that the
conjurer has actually performed what he professes ; for to do so
would often be to reverse entirely our conception of natural laws. It
must not be forgotten, however, that the existing system of know-
ledge, which seems to serve as the standard and test of new facts, is
itself undergoing constant modification through the influence of
these facts. As new experiences are brought into connection with
the existing body of our knowledge, there is a constant rearrange-
ment and readjustment of the latter going on. Usually this adjust-
ment is slight, and takes place almost imperceptibly. But, in some
78. CONSTRUCTING A SYSTEM OF KNOWLEDGE 287
cases, a single fact may be so significant as completely to transform
what seemed to be the accumulated knowledge of years. The
experiment which Galileo made by dropping balls of different
weight from the tower of Pisa, made it impossible to hold any longer
the old theory which seemed as certain as anything well could be
that the velocity with which bodies fall is proportional to their
weight. Again, if theft were actually proved against the man we
respect, that single fact might be sufficient to force us to give up
everything which we supposed that we knew about his character.
(2) We have said that judgment is the process by which know-
ledge grows into a system. It is by judging or thinking that we
attempt to bring the various parts of our experience into relation
with one another. The degree to which this has been done is the
measure of our intellectual development. The knowledge of the
uneducated and unthinking man, like that of the child, is largely
composed of unrelated fragments. It is an aggregation, not a
system of facts. The facts which go to make it up may quite well
be contradictory, but this contradiction is not seen because no
attempt is made to unite them. There is, of course, no human
experience which is entirely systematic, or which has been com-
pletely unified. Even those who have thought most deeply find it
impossible to fit together exactly knowledge gained from different
fields, and from different sciences. The facts of one science, for
example, may seem to stand by themselves, and not to have any
relation to the facts derived from another science. Or there may
appear to be a conflict between the results of physical sciences,
and the truths of moral philosophy and religion. But the ideal
always remains that truth is one and indivisible, and that it must
be possible ultimately to harmonize all facts in one all-embracing
system of judgment.
References
B. Bosanquet, The Essentials of Logic, Lecture II.
" " Logic, Vol. I., pp. 97-103.
C. Sigwart, Logic, 18.
CHAPTER XXII
THE LAWS OF THOUGHT
79. The Law of Identity. We found ( 73) that
Judgment is the simplest form of thinking. And, in
the last chapter, we were engaged in studying its main
characteristics, and becoming acquainted with its mode
of operation. The essential nature of the thinking
process, therefore, has already been stated, though we
have not traced the mode of its development, nor shown
its application to the various problems of experience. In
nearly all books dealing with logic, however, one finds a
statement of three fundamental laws of thought which
differ greatly, in form at least, from what we have so
far learned regarding the nature of Judgment. These
laws are so well known by name, and yet so ambiguous
in their mode of statement, that it seems well to try to
decide what meaning to apply to them. It will also be
interesting to note their relation to the discussion of
Judgment already given. They are usually regarded as
axioms, or propositions which require no proof, rather
than as descriptive of the nature of thought. In this
sense, they are supposed to be the foundation of all
logic, since they are presupposed in all thinking.
The first of these laws, or axiomatic principles, is that
of Identity. Whatever is, is ; everything remains iden-
tical with itself ; A is A. These are some of the forms
in which the law is usually stated. In all argument, we
288
79- THE LAW OF IDENTITY 289
assume at least that each thing possesses a permanent
character, and does not pass now into this, now into
that. If any knowledge is to be possible at all, the
character of things must remain fixed. Socrates is
always to be Socrates, and iron, iron. Every one as-
sumes as much as this, though he may not himself be
conscious of it (cf. 9).
Another interpretation of this principle was, how-
ever, offered by Boole and Jevons, who developed what
is known as the Equational, or Symbolic logic. Accord-
ing .to these writers, the law of Identity expresses
the fundamental nature of Judgment. That is to say,
every judgment is the expression of an identity between
the subject and the predicate. The judgment, 'New
York is the largest city in America,' is simply a case of
a is a. It expresses the fact, that is, that New York
and the largest city in America are identical. ' Iron is
a metal,' is another example of the same principle. It
may be written : iron = metal. And, since the copula
may often be ambiguous, it will be better to discard it
in working out arguments, and adopt, in its place, the
sign of equality.
Judgment, then, is simply an equation, and may be
written as such. Further, the conclusion of a series of
logical premises may be obtained by a process similar
to that employed in working algebraical equations.
That is, we can substitute for any term in a judgment,
its equivalent, or the value which it has in another
judgment. This method Jevons calls ' the substitution
of similars,' which he maintains is the fundamental
principle of all reasoning.
2QO THE LAWS OF THOUGHT
If, now, we employ letters to symbolize the terms of
the propositions, it is claimed that we can work out
any argument by the equational method. Take the
argument,
All metals are elements,
Iron is a metal,
Therefore iron is an element.
Now represent metal by M ; iron by I ; and element by
E. Then the argument in equational form will be,
M = E (i)
I = M (2)
and by the substitution in (i) of the value of M in (2)
we get I = E, the required conclusion.
Or, we may illustrate this method by a somewhat
more complex example which is also taken from Jevons :
' Common salt is sodium chloride, which is a substance
that crystallizes in cubical form ; but what crystallizes
in cubical form does not possess the power of double
refraction.' The conclusion of this argument may be
found by letting A = Common Salt, B = Sodium Chlo-
ride, C = something which crystallizes in cubical form,
and D = something which possesses the power of double
refraction. The negative of any of these terms will be
expressed by the corresponding small letters. The argu-
ment may now be expressed :
A = B (i)
B = C (2)
C = d ....... (3)
By substitution of the value of C in (2) we get,
B = d (4)
And substituting here the value of B in (i),
A = d
79- THE LAW OF IDENTITY 29 1
Giving to these symbols their meanings, we get the
result ' common salt does not possess the power of
double refraction,' which is the conclusion of the argu-
ment.
Of course, in simple arguments like those we have
been examining, there is nothing gained by the use
of symbols, and the representation of arguments in
this form. But when the various terms employed are
much longer and more complex, simplification may be
attained in this way. Various other symbols have also
been used to express the relation of the various terms
to each other, and a symbolic logic has been developed
which follows very closely the procedure of algebra.
The examples given may, however, serve as illustrations
of this method. 1
It is, however, as a theory of the meaning of Judg-
ment that we are interested in this mode of interpreting
the law of Identity. We have seen that it works fairly
well in practice, and therefore cannot be wholly false.
But there are certain forms of reasoning in which it will
not work. We cannot get the conclusion by the equa
tional method in an example like the following : ' B is
greater than A, C is greater than B, therefore C is still
greater than A.'
This practical objection being left out of account, we
have to ask whether an equation represents fairly the
nature of Judgment. Does a judgment express merely
1 The clearest statement of the aims and methods of the Equational
Logic may perhaps be obtained from Jevons, The Principles of Science,
Introduction. Cf. also G. Boole, An Investigation of the Laws of 7 hought.
London, 1854.
292 THE LAWS OF THOUGHT
the identity of subject and predicate ? And if so, what
kind of identity is referred to ? In mathematical rea-
soning, the sign of equality expresses the identity of
quantitative units. When one says, 2 + 3 = 5, the
meaning is that the number of units on each side of
the equation is identical. And, similarly, the assertion
that a parallelogram = 2 triangles with the same base
and of the same altitude as itself, expresses the fact that,
in the two cases, the number of units of area, square
feet, square yards, etc. is the same. In mathematics, the
equation declares that the quantitative relations of its
two sides are identical. It does not assert that the two
things compared the triangle and one half the par-
allelogram, for example have the same qualities, or
are exactly the same in all respects. Now, if we ex-
tend the use of the sign of equality, it must take on
a new meaning. It is clear that in a judgment like
'iron = metal,' there is no reference at all to quantita-
tive relations. We are not asserting that the number
of units in the two terms is identical. What, then, does
the sign of equality express in such a case?
The answer is not difficult, say those who hold this
theory. The sign of equality in such cases expresses
absolute identity ; the entire and complete sameness of
subject and predicate. The proposition, ' mammals =
vertebrates/ asserts that mammals and vertebrates are
one and the same thing. But that statement in its
present form is not true : the class mammal does not
completely correspond with the class vertebrate. To
make it exact, say those who uphold the equational
form, one must qualify or limit the predicate and write
79- THE LAW OF IDENTITY 293
the proposition, ' mammals = some vertebrates.' But,
even so, we may urge, the form of the judgment is still
defective. In the first place, it does not correspond to
the model a = a. For one side, ' mammal,' is clearly
marked off, while the other is indefinite and vague.
And, secondly, just because of its vagueness, it is not
a satisfactory piece of knowledge. To obviate these
objections, one must go further and write, mammals =
mammalian vertebrates. At last the judgment seems
to correspond to the type, a = a. But a new difficulty
arises. Has not the judgment lost all its original mean-
ing and become a mere tautology ? There seems to be
no escape from the following dilemma : either there is
some difference between subject and predicate, and the
judgment is therefore not in the form a = a, or the judg-
ment is tautologous and expresses nothing. The view
of the equational logic that Judgment affirms the entire
identity of subject and predicate refutes itself. The
form a = a cannot be regarded as the type to which all
judgments conform.
But there must be some kind of identity between the
parts of a judgment. In one sense, we do seem to
declare that the subject and predicate are identical
when we say, 'iron is a metal.' As we have seen, how-
ever, if these terms are merely identical and nothing
more, the judgment loses all meaning. We are forced
to the conclusion that every judgment affirms both
identity and difference, or that there is identity running
through and underlying the diversity. But is not this
a paradoxical statement ? When we affirm identity,
does not this imply the absence of all difference? If
294 THE LAWS OF THOUGHT
a is a, how can it at the same time be something differ-
ent from itself ?
And yet this is just what every judgment which has
any meaning affirms. 'Iron is fusible.' 'This table is
made of oak.' 'The sword is rusty with age.' In all
these judgments there is an assertion of the unity of
different properties or parts in one whole. A is B, and
yet does not cease to be A, is rather the type of judg-
ment than a is merely or abstractly a. It is worth
noticing that this view of the matter corresponds with
the account of Judgment already given. We saw
that Judgment constructs a system of knowledge by
showing that various things, which seem at first unre-
lated, are yet connected by an underlying unity. Know-
ledge is always the synthesis or union of different parts
or different properties in a common identity. And
each judgment, as an element of knowledge, displays
the same essential structure which belongs to knowledge
as a whole. It involves, as was shown in ( 77), both
analysis and synthesis, and declares the oneness or
identity of a number of properties or parts, without at
the same time losing sight of their distinctness.
Let us now sum up our discussion of the law of Iden-
tity. When rightly understood, as we have seen, it does
not affirm that a can only be bare a, that the subject
and predicate are absolutely identical. It is a law of
thought, and expresses the fact that Judgment brings
together differences ; i.e., different things and qualities,
and shows that they are parts of one whole or unity.
It reveals the underlying unity or identity which is
present in the midst of variety. This law also states
8o. THE LAW OF CONTRADICTION 295
another characteristic of Judgment which we have
already emphasized. This is what we have called the
universality of Judgment ( 75). It is to judgments, and
not to concepts or terms, as has sometimes been sup-
posed, that the law of Identity properly applies. What
it affirms in this connection is simply that Judgment
claims to be true, and hence is identical at all times
and for all persons. It cannot be true for you and
false for me that, 'iron is a metal.' Truth is not a
matter of individual taste, but every judgment which
is true has a permanent character or identity belonging
to it.
80. The Law of Contradiction. The law of Contra-
diction is the second of the so-called laws of thought.
It is usually stated as follows : It is impossible for the
same thing both to be a, and not to be a ; or, a is not
not-a. It is evident that this law states in a negative
form the same characteristics of thought as the law of
identity. Indeed, it was in this form that the principle
was first laid down by Aristotle. " It is impossible,"
he says, "that the same predicate can both belong and
not belong to the same subject at the same time, and
in the same sense." l We cannot assert in the same
sense that Socrates is both wise, and not wise. Truth
is not, as the Sophists supposed, a matter of taste or
convenience, but must be consistent with itself. If a
judgment affirms that 'iron is a metal,' it at the same
1 Metaphysics, Bk. III. Ch. IV. See also the remaining chapters of
the same book for Aristotle's demonstration that all thought presupposes
such a principle.
296 THE LAWS OF THOUGHT
time excludes the assertion that it is not a metal.
There is a fixity and permanence about judgments
which prevents them from changing into anything else.
And it is just this permanence which we have already
called the universality of Judgment, which the law of
Contradiction expresses in a negative form.
The law of Contradiction has, however, sometimes
been interpreted in such a way as to make it equivalent
to the assertion of abstract or bare identity which we
found in the Equational logic. That is, the statement
that it is impossible for any judgment to unite a and
not-a may be taken to mean that it is impossible to
assert the unity of a and anything different from a.
But, as we have seen, this is exactly what we do in
every judgment which is more than a tautology. The
law, then, does not forbid the union of differences in
one judgment, but of contradictories, or of what would
destroy the integrity of the judgment and render it
unmeaning. If the law is to hold true of Judgment,
not-a must not be taken as equivalent to anything which
is different from a, but as signifying what is opposed, or
contradictory to a.
It is not by any means easy to decide what things are merely
different, and therefore compatible with each other, and what con-
tradictory or opposed. Logic can give no rule which may be applied
in every case. If experience shows that two things, or two proper-
ties, are at any time united, we say that they are merely different
from each other ; if they have never been found in conjunction and
we are not able to conceive how their union could take place, we
call them opposites or contradictories. It io worth noticing, too,
that no terms are in themselves contradictory, except those which
are in the form a and not-a, wise and not-wise. But they become
8i. THE LAW OF EXCLUDED MIDDLE 297
contradictory and exclude each other when they claim to occupy
the same place in some particular system of facts. Thus ' maple '
and ' oak ' denote trees of a different variety, which are, however, so
little opposed that they may exist side by side. If both these terms
were applied to the same tree, however, they would become con-
tradictory. By claiming to stand in the same relations, these
terms become rivals, as it were, and exclude each other. But a
knowledge of the particular facts involved is always necessary
in order to determine whether or not two assertions are really
incompatible.
8 1. The Law of Excluded Middle. The third law is
a corollary from what has just been said in the last sec-
tion. There is no middle ground, it declares, between
contradictories. A is either b or not-b. To affirm the
one is to deny the other. When we have real contra-
dictories, i.e., when not-b is not merely something
different from b, but something which excludes it,
every judgment is double-edged, and both affirms and
denies at the same time. To deny that the throw of a
penny has given heads, is to assert that it has fallen
tails. As we have seen, however, logic affords no rules
of deciding when things do thus stand in the relation
of mutual opposition. The law of Excluded Middle
states only that where this relation does exist, every
proposition has a double value, and both affirms and
denies at the same time. It requires special know-
ledge of the particular facts in each case to enable
us to decide what things are thus opposed to one
another. There is no logical law by means of which
things may be divided into two opposing groups or
classes.
298 THE LAWS OF THOUGHT
It is important to notice that all of the judgments
which we use in everyday life are to some extent double-
edged. That is, they contain, besides what is directly
affirmed, some implication or counter statement. For
example, to say, 'that object is red,' is implicitly to deny
that it is blue, or any other colour. The statement, 'A
never looks at a book,' carries with it the implication
that A is not very intelligent. In almost any field
where we have any systematic knowledge, we can limit
pretty definitely the number of possibilities a must
be either b, or c, or d. In such cases, to affirm that a is
b, is of course to deny implicitly c and d ; and con-
versely, the denial of any one possibility, as c, enables
one to assert that a is b or d. In ordinary conversa-
tion, misunderstandings and misconceptions frequently
arise because neither party is fully aware of all the pos-
sible cases and the relation between them. It is very
difficult, however, to make a statement which will have
no counter implications. If one says, 'this railway sys-
tem does not employ steam power,' the proposition
seems to justify the question: 'Does it then use elec-
tricity or compressed air ? ' We should feel that it was
a mere quibble if the person who made the statement
should reply: 'I did not say that it employed any kind
of power.' 'There are some small errors in this paper,'
would ordinarily be taken to imply the counter propo-
sition, 'the paper contains no serious errors.' It is
clear that it is only when one's knowledge becomes
systematic, i.e., when one knows the relations in
which all the facts in the field under consideration
stand to each other, that one can be fully aware
8i. THE LAW OF EXCLUDED MIDDLE 299
^f what is really implied in each assertion or denial
irf. 41, 78). '
References
F. H. Bradley, The Principles of Logic, pp. 131-154, 343-360.
B. Bosanquet, Logic, Vol, II., pp. 207-212.
W. S. Jevons, Elementary Lessons in Logic, Ch. XIV.
" " " The Principles of Science, Introduction.
G. T. Ladd, The Philosophy of Knowledge, Ch. IX.
C. Sigwart, Logic, 23-25.
J. Watson, " The Metaphysic of Aristotle," Philos, Review, Vol
VII., pp. 113-134-
CHAPTER XXIII .
TYPES OF JUDGMENT
82. Judgments of Quality. We have hitherto been
considering the nature of Judgment in general, and
have learned something regarding its main character-
istics. It is now necessary to examine briefly some of
the more important forms or types of Judgment. We
shall begin with very simple and elementary ways of
judging, and afterwards consider some of the more
complex types. In this way, we shall see the nature
and structure of Judgment illustrated at different levels
of thought. And we also hope to show that there are
no arbitrary divisions in the process of thinking, that
the lower forms of Judgment gradually develop into the
higher in accordance with the general law of evolution.
It is, of course, impossible to carry out at present this
plan in detail, for that would be to give a complete his-
tory of the development of thought. It will be neces-
sary for us to take long steps, and content ourselves
with a general view of the relation of the various stages
in the development of Judgment.
The first efforts of intelligence to understand the
world take the form of judgments of Quality. At a low
stage of mental development, it is the simple qualities
of things which force themselves on attention. The
young child, for example, takes notice of only the
300
82. JUDGMENTS OF QUALITY 301
most striking qualities of things. His judgments are
very vague and indefinite, and take account only of
some prominent quality of things. That is, there is no
discrimination of the various parts and relations of the
objects, but the judgments express merely a general
impression based upon some striking quality. Thus it
has often been noticed that the child calls every man
'papa,' and any light, of whatever size, the moon. A
little boy, known to the author, used to call Sisters
of Charity, crows, on account of the colour of their
dresses. The objects as he apprehended them were
simply black, and nothing more. His intelligence
rested in the qualitative total impression ; the vari-
ous parts, with their quantitative relations, which he
afterwards learned to know and distinguish, did not
at that time exist for him.
It is perhaps impossible to find in the experience of
an adult any judgments which deal entirely with simple
qualities, and which take no account of the numbers, and
even to some extent of the relations, of the parts. But
we can find examples of judgment where the qualitative
aspect is much the most prominent where indeed the
quantitative and more complex relations are scarcely
noticed at all. ' This is green,' ' that is a strange odour,'
'there is something a long way off.' all these seem to
be judgments of quality or general impression, and to
involve scarcely any other element. It is, too, the
easiest kind of judgment to make, the judgment which
involves least mental effort, and which notices only
the most evident, and, as it may be seen, the most
superficial, aspect of things. It is evident that such
302 TYPES OF JUDGMENT
judgments belong to a lower stage of thinking, than
those which imply analysis and perception of quantita-
tive relations. Compare, for example, 'this is very
large/ with, 'this object is made up of roots, trunk,
branches, and leaves ' ; or 'this is green,' with, 'this leaf
is divided into two parts by a rib running through the
centre.' The first judgment in each pair obviously
involves much less intellectual work than the latter.
The judgment of simple quality is, as we have seen, the
starting-point of thought. It is with this kind of
thinking that the knowledge of the child begins. And,
before the savage learns to count, i.e., to distinguish
and enumerate the parts of the objects with which he
deals, his judgments must necessarily belong to this
same type.
It must never be forgotten, however, that simple
judgments of quality are really judgments; i.e., are not
given to the mind from any external source, but are the
products of its own activity. A judgment, as we have
already pointed out ( 73), implies a reaction on the
part of the mind on what is presented to consciousness
through the senses. It distinguishes and puts together
the material which sense presents in such a way as to
perceive its significance what it really amounts to
as a piece of knowledge. This act of interpretative
intelligence has gone, however, but a little way in the
type of judgment with which we are dealing. But even
in a vague qualitative judgment like, 'there is something
black,' the essential characteristics of Judgment can be
already distinguished. For it presupposes at least some
analysis or discrimination of the black object from the
8a. JUDGMENTS OF QUALITY 303
rest of the environment, and of the black colour from
other colours. And the judgment, 'something is black,'
has made at the same time a beginning in constructing
this vague something into a system of qualities, or into a
thing that is known. The other qualities and relations
are as yet wrapped up in the indefiniteness of the 'some-
thing.' In spite of its indefiniteness, however, the latter
plays the part of a permanent centre or identity. It is
the whole from which the quality of blackness has been
separated out, and to which it is again attached.
Our thought, however, is not satisfied with a know-
ledge of the general qualities of things, but pushes
farther its work of analysis and construction. In this
way, it begins to distinguish the various parts of objects,
and to compare one with another. We not only judge
that ' the grass is green,' but go further and say ' this
piece is dark green, and that light green.' The indefinite
judgment, 'this cane is heavy,' is no longer satisfactory,
and is replaced by, 'this end of the cane is much
heavier than that.' And when this stage is reached,
judgments of Quality are already passing into the next
higher type, judgments of Quantity. For the moment
of comparison, which is already contained in these
judgments, is the basis of counting, measuring, and all
quantitative determination. In advancing from the
simple apprehension of quality, to take note of, and
compare, the degree or intensity which the same quality
manifests in different instances, intelligence has entered
upon a path which leads directly to judgments of
quantity. To distinguish parts, to regard things as
degrees or instances of a common quality, is at once
304 TYPES OF JUDGMENT
to suggest the quantitative process of counting and
measurement.
83. Judgments of Quantity. It is very difficult, as
we have seen, to draw a hard and fast line between
quality and quantity. Indefinite judgments of general
impression which do not imply any comparison, seem
always to be qualitative rather than quantitative in
character. This is true, I think, of judgments like,
'this object is very large,' 'there was a great flock of
sheep in the field.' In such cases, the interest does not
seem to be quantitative at all ; i.e., there is no effort
made to determine how many units or parts there are in
the whole about which the judgment is made. But the
general impression of size or number is apprehended
and judged of at the same level of intelligence, and in
the same vague way, as the simple qualities with which
we dealt in the last section. It is by means of such
a general qualitative impression that the savage who
cannot count beyond five, is able to distinguish between
six and some larger number. And we must suppose
that the shepherd's dog does not learn that some of the
sheep are missing by any process of counting. We
must suppose that the general qualitative impression
made by the smaller flock is different from that made by
the larger, and that there has been no real counting or
estimation of number in the case.
But quantitative judgments proper belong to a higher
stage of intelligence than do those which have just
been described. Indefinite judgments, like 'this is very
large,' or, ' there are a great many stars in that group/
83. JUDGMENTS OF QUANTITY 305
are not satisfactory pieces of knowledge. We accord-
ingly set ourselves to get more exact information about
the parts which compose the wholes. The first step
in this process leads to Judgments of Enumeration. If
the whole which is analyzed is composed of homogene-
ous parts, the judgments of enumeration take the form
of simple counting. 'There are one, two, three, . . .
twenty men in this company.' Where the parts are
not of the same kind, however, a separate name may
have to be given to each. ' This plant is composed of
root, stalk, leaves, and flower.'
But exact quantitative knowledge requires us to do
more than enumerate the parts of which a whole is
composed. We must go on and weigh or measure
them. There is of course no essential difference be-
tween weighing and measuring, so that we may call
all judgments which express the result of this process
Judgments of Measure. It is worth noting that judg-
ments of this class are not so simple and direct as may
appear at first sight. When we measure, we express
the relation of the parts with which we are dealing to
some common unit or standard. The judgment, 'this
tower is 200 feet high,' means that if the tower is com-
pared with a foot-rule, it will be found to contain it
200 times. It really, then, involves a proportion, and
might be expressed :- tower : foot-rule = 200 : i.
The point which it is important to notice is that all
measurement is the result of comparison. In the first
place, some unit is more or less arbitrarily selected.
Then the judgment states simply the relation between
this unit and the object measured : one is contained in
x
306 TYPES OF JUDGMENT
the other once, or twice, or ten times. The quantita-
tive determination thus obtained, then, is merely rela-
tive. That is, it does not belong absolutely, and in its
own right to the object measured, but indicates the
relation of that object to something else.
For this reason, it may seem that quantitative rela-
tions tell us nothing regarding the real nature of
objects, and that to discover what the latter are in
themselves, we shall have to return to the point of view
of quality. But we have seen that simple judgments of
quality yield a very unsatisfactory kind of knowledge.
Moreover, we should find on examination that even
qualities always imply a reference to each other, and
are no more absolute than quantities.
In order to obtain more satisfactory knowledge re-
garding things, we shall have to go forward to a higher
type of judgment, rather than backward to quality.
But the importance of quantitative determination for
exact knowledge must not be overlooked. By means
of measurement, things are reduced to common terms,
as it were, and thus a basis of comparison is afforded
where it would otherwise be impossible. To reduce
everything to such a common measure is the business
of the physico-mathematical sciences. Everything has
a quantitative value, and can be expressed mathemati-
cally in terms of some unit or standard, as, for exam-
ple, the unit of heat, or of pressure, or the electrical
unit. It was this tendency to count and measure and
weigh things which established the body of exact know-
ledge which we call science. And in almost every field,
.knowledge increases greatly, both in extent and exact-
84. JUDGMENTS OF CAUSAL CONNECTION 307
ness, as soon as it is found possible to reduce all phe-
nomena to a common measure, and to express their
relations by means of mathematical formulas.
It is a great step in advance to be able to compare things as
quantities, and to express their relations in terms of number. But
judgments of quantity are not entirely satisfactory ; they are, as has
already been noticed, merely relative in character. Moreover, from
a quantitative point of view, each thing is equivalent to the sum of
its parts. When the parts have been enumerated and measured,
the value of the whole is obtained by addition. But it is scarcely
ever possible to represent adequately the nature of a whole in this
way. So long as we are dealing with a piece of inorganic matter,
the method of regarding the sum of the parts as equivalent to the
thing, generally gives good results and leads to no difficulty. But it
is quite different when the whole in question belongs to something
which has life and consciousness. In such cases, we have what has
already been called an organic whole ( 78). Now, it is clear that
the principle of quantity, which can only add and subtract, is in-
sufficient to represent completely the nature of an object of this kind.
It has no means of representing the individuality or real whole,
which rather constitutes the parts, than is constituted by them.
That is, to understand such objects, we shall have to take a new
point of view, and begin with the whole rather than with the parts.
From the point of view of quantity, the nature of the whole is dis-
covered by adding together the parts ; while in order to understand
objects which possess an individuality of their own, there seems to
be a central principle to which the parts are subordinated, and in
relation to which alone they can be understood. The type of judg-
ments which deal with such objects we shall have to discuss in
85.
84. Judgments of Causal Connection. Another class
of judgments used in building up knowledge, may be
called judgments of Causal Connection. They under-
take to show how the various changes which go on in
308 TYPES OF JUDGMENT
things are connected causally with other things or
events. This type of judgment leading as it does
beyond the particular object, to a knowledge of the ways
in which objects are connected seems to belong to-a
higher stage of mental development than those which
merely take note of quality and quantity. This does
not mean that we never look for causes, until the quali-
ties and quantities of things have been discovered. Nor
is it true that any causal judgment, however vague and
unsatisfactory, is higher than any judgment of quality
or quantity whatsoever. But, in the beginnings of know-
ledge, one may say, thought does not travel outside the
particular object to show the connections of the latter
with anything else. And beginning in this way, it
seizes first upon quality and quantity which seem to be-
long to things in themselves. We have seen, however,
that as a matter of fact judgments of quantity involve
comparison, and so a reference of one thing to another,
though that reference is not usually made consciously
or explicitly. But, when we judge that one thing is
causally connected with another, the external reference
has become explicit, and is the very essence of the judg-
ment.
The word ' cause ' has been used in a great many
senses, and its various meanings have given rise to a
great deal of discussion. That every event must have
a cause, was formerly regarded as an innate truth, or a
priori proposition. We have seen, however, that we do
not come into the world with any ready-made stock of
knowledge. All knowledge, we have often repeated, is
the result of the mind's own judging activity. The so-
84. JUDGMENTS OF CAUSAL CONNECTION 309
called law of causation (every event must have a cause)
must therefore express the fact that thought does con-
nect things as causes and effects. Intelligence is not
satisfied to take things in isolation ; it tries to gain an
insight into the ways in which they are connected, to
discover what one has to do with another. And this is
just the characteristic of thought which was emphasized
in 78. Judgment, it was there said, is a process of
constructing a system, of showing how the various parts
of knowledge fit into one another, and are mutually de-
pendent upon one another. The tendency of thought
to connect things causally, then, is the same as its ten-
dency towards a system, which has now become more
explicit and conscious of itself in this type of judgment
than it was in quality and quantity.
It will be interesting to note some of the most impor-
tant changes which take place in the principle of causal
explanation at different stages in the development of
knowledge. The child and the savage regard all
changes and events which take place in the natural
world, as due to the agency of living beings. These
beings are represented as more or less similar to men,
and as endowed with human passions and emotions.
Thus we say that the earliest kind of explanation is es-
sentially anthropomorphic. This word is derived from
avdptoTTos, a man, and pop^ij, shape or form, and hence
is used to describe the way of representing either a
spiritual being, as for example, the Deity, or natural
forces like fire, wind, etc., in human form. It is proba-
bly true that at a very early stage in the development
of both the individual and the race, every object is
3IO TYPES OF JUDGMENT
supposed to have life. Or, perhaps, it would be truer to
say that the young child (and the same would be true
for the savage on a low plane of intelligence) has not
yet made the distinction between animate and inani-
mate objects, but vaguely regards everything as like
himself. This stage is usually known as animism,
because each object is supposed to be endowed with
a spirit, or anima.
Gradually, however, the distinction between animate
and inanimate objects becomes clear. Accordingly,
we find that at a somewhat more advanced stage the
mode of explanation takes a different form, though
it is still anthropomorphic. Physical objects are no
longer regarded as living, but the changes in them
are supposed to be due to the action of spirits, who
are outside of the objects, but who use them to ac-
complish their purposes. These invisible spiritual
agents, to whom all natural events are referred, have
been variously named. It is clear, however, that the
gods of mythology belong here, as well as the fairies,
elfs, ghosts, and witches of the popular folk stories.
It was a great advance when a Greek thinker, named
Thales, came to the conclusion that it does not in
any way explain natural events to refer them to the
action of the gods. For, in the first place, to say that
the gods cause this or that event, is to state some-
thing which we have no means of proving. And even
if the assertion were true, it would not really explain
anything. For it would not enable us to understand
how the changes in question came about. It would
tell nothing whatever regarding the actual steps in the
84. JUDGMENTS OF CAUSAL CONNECTION 3 1 1
process itself. Thales saw this, and tried to give a
natural explanation of the world, and all that goes on
in it. He tried to build up a real system of know-
ledge by attempting to show how everything which has
happened in the world has been connected with some
natural cause. We know very little about the actual
explanation of the world which Thales gave, except that
he tried to derive everything from water. It is on ac-
count of the method which he adopted, rather than of
what he actually performed, that he is regarded as the
founder of science. Thales first showed, one may say,
that knowledge means an insight into the ways in which
the actual phenomena of the world are connected. We
cannot unite into a system things so different in kind
as spirits and natural phenomena. Or we may say that
real explanation demands that there shall be some like-
ness, or ground of similarity, between the cause and the
effect. An event which happens in the world of objects,
must be explained by showing its connection with some
other event, of a similar character, which precedes it.
The development of this conception of scientific ex-
planation also influenced still further the notion of
causality. We have seen that in the beginnings of
knowledge every event was supposed to be due to the
action of some living agent, or spiritual being. Even
after this mythological mode of explanation is dis-
carded, and natural causes put in the place of spirits,
it is still difficult to rid oneself entirely of the old an-
thropomorphism. The popular mind still tends to
regard the cause as an agent which produces the effect,
through some power or efficiency which it possesses. It
312 TYPES OF JUDGMENT
is not necessary to raise the question at present whetbef
there are any grounds for this belief. To discuss this
problem would carry us beyond logic into metaphysics.
What we wish to notice is that science has gradually
abandoned the notion that the cause does something to
the effect. That, as we have seen, is a remnant of the
old prescientific idea, and a notion which does not aid
at all in explaining our knowledge. It is the business
of science to show how the things and events which
make up our experience are necessarily connected with
one another. Science has to discover what things in-
variably go along with one another, and necessarily pre-
suppose one another. And, when it is found that some
particular thing or event, A, invariably precedes another
particular occurrence, B, the former is regarded as the
cause, and the latter as the effect. In order to elimi-
nate as far as possible the notion of agency or effi-
ciency which attaches to the word cause, the terms
'antecedent' and 'consequent' are often used to in-
dicate this relation. For science, the cause is not an
active agent, but the invariable antecedent of something
else which simply follows it. The cause does not explain
the effect by assigning an agent which brings the latter
about through its personal efforts ; but it explains,
because it reveals another necessary step in the process,
and gives us a new fact which joins on or can be con-
nected with the one from which we start.
We conclude then that the cause of any event is its
invariable and necessary antecedent. In another part of
this book (Chs. XV., XVI.), it is shown what tests it is
necessary to apply in order to determine whether two
84. JUDGMENTS OF CAUSAL CONNECTION 313
phenomena are merely accidentally conjoined, or whether
the connection is essential and real. It is necessary now
to take one more step in tracing the various ways in
which the idea of causality has been used. As a re-
sult of a famous scientific discovery, which was made
about the middle of the present century, a new element
has been added to the notion of cause in its application
to physical phenomena. The law of the Conservation
of Energy states that the amount of energy, or power of
doing work, possessed by any set of bodies, remains con-
stant. Any change in a material body is the result of
a transformation of energy from one form to another.
The same is true of the world as a whole : the total
amount of energy which it contains remains constant.
All changes which take place in the physical universe
motion into heat, or electricity into motion are sim-
ply different forms, or manifestations, of the one world-
energy.
As a result of this law, the effect always represents
the same amount of energy, or power of doing work,
as the cause. Since no energy is ever lost, the one
must be equal to the other. And, as a matter of fact,
the quantitative equivalence of many of the various forms
of energy has been proved by actual measurement. In
working out this law, for example, Joule showed that
"the energy stored up in the I Ib. weight which had been
pulled up 772 feet was gradually transformed, as soon as
the weight was released, into an amount of heat capable
of raising the temperature of a pound of water i
Fahr. ; while Him showed, on the other hand, that ex-
actly this amount of heat would, if it could be turned
314 TYPES OF JUDGMENT
back again into energy, raise the I Ib. weight to the
height of 772 feet at which it stood before." 1
The new element which this law adds to the idea of
cause as a necessary and invariable antecedent, is that of
the quantitative identity of cause and effect. Taking the
phenomena which are connected in this way to repre-
sent simply certain quantities of energy, we say that the
one is equivalent to the other. The energy which the
cause represents has been transformed without loss, and
reappears in the effect. If what seems to be the total
effect is not equal to the cause, part of the energy of
the latter must have been transformed into something
else. No energy can have been lost.
It becomes, therefore, the task of the physical sci-
ences to show that this relation of quantitative identity
exists between phenomena which are causally connected.
The ideal of physical science, is to prove that two phe
nomena are connected as cause and effect, by showing
that both represent the same quantity of energy. For
this purpose, measurement and calculation are neces-
sary. The physical sciences, as was pointed out in the
last section, deal largely with judgments of quantity,
and devote themselves to showing by measurement that
the same amount of energy persists through the various
changes which phenomena undergo. In establishing
causal connections, the physical sciences find it necessary
to use the principles of measurement and calculation.
It will be evident, from what has been already stated, that this
relation of cause and effect should apply to all phenomena whose
1 Buckley, Short History of Natural Science, p. 339.
85. JUDGMENTS OF INDIVIDUALITY 3 1 5
energy Is capable of being measured and represented in quantitative
terms. As a matter of fact, however, the law has been proved only
in physics and chemistry. From the very nature of the case, it is
extremely difficult to measure exactly the relations of cause and effect
in the sciences which deal with organic life. But even in those
sciences, the law of the Conservation of Energy is assumed to hold
true. For example, the amount of energy which a plant contains, is
assumed to be exactly the same as that represented by the various
elements or forces water, sunlight, mineral substances, etc.
which were instrumental in composing it. In the same way, we
suppose that the same relation holds of the changes which go on
in the brain, though we are, of course, unable to prove this by
actual measurement.
It is difficult, however, to see how this law can have any applica-
tion to mental phenomena. We can indeed measure the intensity
and duration of sensations. But neither feelings nor complex pro-
cesses of mind seem to be capable of measurement. Moreover, it is
never possible to measure the energy, or power of doing work, which
states of consciousness possess, and to equate one with another in
this respect. And this being so, the law of the Conservation of
Energy cannot, of course, apply to psychical causes and effects. In
the mental sciences, then, we cannot claim that the notion of Cau-
sality contains the element of quantitative identity between cause
and effect which has been found to exist in the physical sciences. 1
85. Judgments of Individuality. By Judgments of
Individuality, we mean judgments which regard some
complex object as a real whole with a definite nature of
its own. We have already had occasion ( 78) to dis-
tinguish a mere aggregate or sum of parts, like a heap
of stones, from a true whole which possesses a certain
character and individuality of its own. It is the former
point of view from which judgments of quantity and
1 Cf. Wundt, Ethik (ist ed.) pp. 398 f.; Sigwart, Logic, 97*, 7.
316 TYPES OF JUDGMENT
of causal connection regard objects. For these types of
judgments are concerned wholly with the parts the
former to measure, and the latter to show their causal
connection. It requires a new form of judgment to
represent adequately the nature of a complex object
which possesses individuality. This form gives expres-
sion to the organic unity and wholeness of things, and
emphasizes the way in which the parts cooperate for a
common purpose or end. Thus we regard the parts of
a plant as a unity cooperating in a common purpose,
and a man as a conscious system of ends.
(i) We have seen that judgments of causal connection relate phe-
nomena as causes and effects. A change in an object is explained
by showing that some other change or event invariably precedes it.
But this change, in its turn, demands explanation, and has to be
accounted for by the discovery of a new cause. This type of judg-
ment shows that one phenomenon is connected with a second, and
a second with a third, and so on indefinitely. The view of the
world which it presents is that of a never-ending series of causes
and effects. It is never possible to find a cause which is not itself
the effect of something else. No phenomenon possesses any inde-
pendence of its own, but is simply a link in a series, or a piece of
a whole that is never completed.
In the last section, it was stated that causal judgments connect
one part of our knowledge with another, and, in this way, aid in
uniting the parts of our experience in a systematic way. Now it
is undoubtedly true that it would be impossible to have any real
knowledge of anything as a whole, or an individual, without know-
ing the way in which the parts are related, and mutually depend
upon each other. In that sense, judgments of causal relation are
indispensable to a knowledge of a true whole. But this form of
judgment itself resolutely goes on connecting part with part one
phenomenon with another and refuses to regard any group of
parts as possessed of an independent character or individuality
85. JUDGMENTS OF INDIVIDUALITY 317
From this point of view, everything is externally determined ; its
cause, or principle of explanation, lies outside of it in something
else. The mark of individuality, on the other hand, is the power
of origination, or self-determination.
(2) Psychology, one may say, adopts the standpoint of Causal
Connection ; Ethics, that of Individuality. The former science re-
gards mind as a sum of mental processes, and undertakes to show
how its various parts are connected. Every state of consciousness
is supposed to be determined by something external to itself some
antecedent mental state, or some bodily process. The interest, as
was previously said, is centred in the parts, and it is very rarely that
the psychologist stops to look at the mind as a whole. Ethics, on
the other hand, has to begin with the individual. It does not regard
mind as a thing or substance (that is the naive point of view against
which psychology rightly warns us), but as a self-conscious system
of ideas, purposes, and feelings, which possesses the power of initia-
ting action, and of determining itself. Ethics can adopt all that psy-
chology has to tell regarding the mechanism of the mental processes.
Indeed, without a systematic and detailed account of the nature and
laws of mental life it could have no adequate conception of mind
as a whole : the judgment of Individuality must use the results of
judgments of Causal Connection. What it really does, is to trans-
form the sum of mental processes into a system which has a real
unity of its own. For it is only when a person is regarded as a
self-conscious and self-acting individual, that he can be supposed
capable of conduct to which the terms ' moral ' and ' immoral ' can
properly be applied.
References
Hegel, Logic, Pt. II., The Doctrine of Essence (Wallace's trans.,
2d ed.), pp. 206-286.
B. Bosanquet, Logic, Vol. I. Chs. II.-V.
J. S. Mill, Logic, Bk. III. Ch. V.
C. Sigwart, Logic, 73.
CHAPTER XXIV
THE NATURE OF INFERENCE. INDUCTION AND
DEDUCTION
86. Judgment and Inference. It must not be for-
gotten that our object in these chapters is to obtain as
definite a conception as possible regarding the nature of
thought. To attain this end, we agreed ( 73) that
it would be advantageous to begin with the simplest or
most elementary form of thinking. That form we found
to be Judgment. We have now endeavoured to show
what Judgment is, and what part it plays in building up
knowledge. And, in the last chapter, we have attempted
to see some of the steps in the evolution of Judgment,
as it passes from simple judgments of Quality to judg-
ments of Individuality. This account being completed,
it remains now to discuss the nature of reasoning or
Inference.
We shall probably get the clearest idea of the nature
of Inference by regarding it as a completely developed
judgment. As thinking develops from the form of sim-
ple judgment to that of Inference, it displays progressive
differentiation and integration. In accordance with this
law, we can say (i)that Inference is more complex than
Judgment. The latter process, in its simplest form, can
scarcely be said to have any parts : it represents a single
act or pulsation of intelligence. Inference, on the other
318
86. JUDGMENT AND INFERENCE 319
hand, seems to imply steps or stages in thinking a
passage of the mind from one fact to another. More-
over, (2) Inference differs from Judgment in exhibiting
the grounds upon which its statement rests. The sim-
ple judgment makes a declaration on the basis of sense-
perception, as, for example, 'the mail-train has just gone
down ' ; ' it rained yesterday.' Each of these statements
stands alone, as it were ; it does not attempt to gain
support by pointing out the connection with other facts.
To infer, however, is just to show the necessary con-
nection of facts that from the presence or absence
of certain things, the presence or absence of certain
other things necessarily follows. It is not necessary
for Inference that the conclusion reached should be a
fact which was not hitherto known. We often do reach
new truths by reasoning from necessary connections.
Thus we might infer that the mail-train has just gone
down, from the fact that this train is always on time,
and that it is now five minutes past the hour. Or, we
might prove, to a person who doubted the correctness of
our memory, that it rained yesterday, by pointing to
other facts with which rain is necessarily connected.
We might point to the muddy condition of the roads,
the swollen streams, or, perhaps, might remind the per-
son who questions the statement, that it was yesterday
that A was out driving, and came home soaking. In
this way, one tries to exhibit the necessity of the fact
under consideration ; and to do this is to infer.
In the actual process of knowledge, we more fre-
quently go from a fact to its reasons, than in the oppo-
site direction. The intelligence begins by accepting all
320 THE NATURE OF INFERENCE
the connections as true and universal which it meets
with in ordinary experience, or which are suggested to
it in any way. It does not trouble itself at all about
the grounds of its judgments, and thus the insufficient
basis on which many of these stand is at first not evi-
dent. The child, for example, believes everything which
it is told by its mother or nurse, or it may be, all the
pleasant things which it imagines. Very often, too, the
judgments of older persons are determined by their own
wishes. The French peasant, girl was sure that it was
impossible for the Germans to take Paris. Another
principle upon which both children and adults quite
unconsciously proceed, is that the future must always
resemble the past. The child assumes that the order
of events each day will be the same, that there will
always be games after dinner, and visitors in the after-
noon, because that has happened a number of times in
the past. And one may have no better reason for
believing that the sun will rise to-morrow, than the fact
that it rose yesterday and to-day.
In these early, unreflective judgments, the ground or
principle upon which they are based is, of course, not
conscious at all. Each judgment is accepted by itself,
and no questions are raised as to how it is known. But
the development of intelligence may be regarded as a
process of becoming conscious of the reasons which
show the falsity of certain of our beliefs, and the neces-
sity of others. The original judgment is not in reality
so isolated and unrelated as it appeared ; it contains
implicitly its own reasons. But the validity of its pro-
cedure cannot be made manifest, until the reasons
86. JUDGMENT AND INFERENCE 321
for the statement made by the judgment are brought
to light. In the development of knowledge, the judg-
ment must expand so as to show the reasons which it
necessarily presupposes. In itself, it is only a fragment
of the complete statement, and it tries to complete itself
by making clear the nature of the whole which it in-
volves. It is not until the implicit reasons which every
judgment contains are thus brought to consciousness,
that it can be either proved or disproved. Taking the
mere judgment by itself, it is only possible to place
one man's assertion against another's denial. But proof
or disproof of a proposition implies that reasons are
given for or against it. If its connection with some
fact, or set of facts, known to be true, becomes evident
on reflection, the felt necessity which the judgment
possesses ( 76), is transformed into logical necessity.
But, if no such connection can be found, or, if the
judgment in question is seen to presuppose propositions
which are themselves false, we must, of course, cease to
regard it as valid.
When a judgment develops so as to become conscious of its
reasons, it has already taken on the form of Inference. And, as
we have already seen, this is the usual procedure of knowledge.
We begin by believing without reason, or we assume that certain
things are true, and try to find reasons for our belief. The conclu-
sion, which is, of course, logically last, is usually first for us, and we
set out from it to find the grounds, or the premises.
This way, however, of proceeding from conclusion to
premises, or from a judgment to its reasons, implies
that the mind is already aware of the distinction be-
tween false knowledge and true, and therefore that the
Y
322 THE NATURE OF INFERENCE
work of criticising and testing knowledge has already
begun. The criticism of knowledge is probably forced
upon the mind at first by the practical consequences of
false judgments. So long as false judgments lead to
no unpleasant results, they are likely to pass unnoticed,
without any question being raised regarding the grounds
by means of which they are supported. The child usu-
ally believes all that he is told, until he discovers that
his credulity is making him a laughing-stock, or has led
to the loss of some pleasure which he values. Sooner
or later he learns that the ground upon which he has
been unconsciously proceeding somebody told me
is insufficient. In the same way, the natural tendency
to regard all connections which we happen to find ex-
isting between events as universal and necessary, be-
comes more critical and discriminating. The child soon
learns that the events of one day do not necessarily
follow in the order of the day before, and that it is not
always rainy on Fridays, and fine on Sundays. But, in
order to discriminate between what is true and what is
false, he is obliged to go beyond the facts themselves,
and to become more or less clearly aware of the grounds
assumed in each type of judgment. He is forced to
include in the judgment the reasons by which it is sup-
ported. And, in this way, the distinction between valid
and invalid principles of connection is gradually learned.
Through experience, which is more or less dearly
bought, we learn that we cannot depend upon hear-
say, and also that many of the most obvious connec-
tions between events are not essential, and have no
claim to be regarded as universal laws. It becomes
86. JUDGMENT AND INFERENCE 323
evident that it is necessary, in order to reach true
principles of connection, to take a wider survey of the
facts, and to push the process of analysis further than
is done by our ordinary judgments of sense-perception.
For example, we may at one time have supposed it to
be a universal law that hot water will break glasses
when poured into them. But as soon as we have ex-
perience of any instance or instances to the contrary,
we see that there is no essential connection between
hot water and broken glasses. It is necessary then to
go behind the obvious facts of the case, in order to dis-
cover what is the real antecedent in the two cases.
The two instances where the glasses break, and where
they do not seem to be the same ; and yet, since
the result is different, there must be a difference which
further analysis will bring to light. It is by penetrat-
ing behind the point of view of ordinary knowledge,
that science endeavours to show how phenomena are
really and essentially connected.
The judgments of ordinary adult life usually involve some con-
sciousness of their grounds, and are therefore so far inferences.
But in many cases of this kind it would be difficult for the individual
to state explicitly the reasons for his judgment. The connection
which he asserts may be guaranteed to his mind by some complex
set of circumstances very difficult to formulate. Or it may rest
upon some general similarity or analogy, which is so obviously in-
sufficient that he hesitates to acknowledge that it is the only ground
he has for judging. Thus one may be vaguely conscious that
one's only reason for liking A is his resemblance to B. It may be
impossible to say exactly in what points A resembles B ; one may
proceed on a vague general similarity. Or one may hesitate to
make clear, even to oneself, that the only reason for disliking A- is
324 THE NATURE OF INFERENCE
because of some external resemblance in name, or dress, or figure
to C, whom one dislikes.
87. The Nature of Inference. We have seen that
it is difficult to draw any hard and fast line between
Judgment and Inference. In general, however, we may
be said to reason when we do not simply accept a fact
on the basis of sense-perception or memory, but show
that it necessarily follows from some other known fact
or facts. Inference, then, requires (i) that certain data
or premises should be accepted as already known ; and
(2) it implies an insight into the necessary connection
of some new fact or set of facts with what we already
know. Thus one is said to infer B, when one sees that
it necessarily follows from some fact which is already
known. It is not necessary for an inference that B
should never have been in consciousness before. As
we have seen in the last section, what we very often do
in inference is to show the reasons or necessity of some
fact which we have previously accepted without know-
ing why. No matter whether we go from premises to
conclusion (from the reasons to the fact), or in the
opposite direction, from the conclusion to the premises,
we are said to infer whenever we find the ground for
the existence of one fact in the nature of another fact.
In the former case, we use words like ' therefore ' and
' consequently,' to indicate the connection ; and when
the reasons are stated last, ' for ' and ' because.' When-
ever these conjunctions are used correctly, an infer-
ence has been made, and it is always useful in following
a course of reasoning to make clear to ourselves pre-
cisely on what grounds it has been made.
87. THE NATURE OF INFERENCE 325
Although Inference seems very simple and very
natural, its procedure is much more puzzling, when
looked at closely, than one would at first imagine. As
we have seen, there is no Inference unless the result
reached is different from the starting-point. But how
are we ever justified in passing from a knowledge of
one fact to another different from it ? How can we
ever pass from the known to the unknown ? The
Greeks, who loved to bring to light the paradoxes
which so often underlie familiar facts, used to discuss
this question. How is it possible for that "which is
unknown external to the mind to pass into the
mind and get itself known ? It was to solve this puz-
zle that Plato propounded the doctrine that all knowing
is remembering. 1 Knowledge, he declares, is not in-
creased by learning that of which we were altogether
ignorant, but by a process of calling to mind or recol-
lecting the knowledge which the soul possessed in a
previous state of existence, but which was forgotten
when it entered upon the conditions of the present life.
It was therefore no longer necessary to suppose, accord-
ing to Plato, that the mind performed the impossible
feat of knowing what is external to itself, or that things
previously unknown pass bodily into our minds, and
thus become known.
Plato was undoubtedly right in protesting against the
popular view that knowledge is received into the mind,
as food is received into the stomach. Knowledge,
as we have frequently seen, comes from within, not
1 This is the theory upon which Wordsworth bases his " Ode on the
Intimations of Immortality."
326 THE NATURE OF INFERENCE
from without. But the apparent paradox of knowledge
may be explained without adopting Plato's poetical
notion of a previous state of existence. We may admit
that the process of inference would be quite inex-
plicable, if it proceeded from one fact, A, to a know-
ledge of a second fact, B, which is totally different from
the former. When we examine cases of inference, how-
ever, we find that there is always a certain amount of
identity between the two ends of the process. The con-
clusion is always different, and yet not entirely different
from the premises. Thus, from the propositions, 'all
metals are elementary substances,' and ' gold is a metal,'
one can infer that gold is an elementary substance.
It is possible to connect ' gold ' and ' elementary.' Here
the identical link what is called in formal logic the
middle term is 'metal.' It is possible to connect gold
and elementary substance, because the former is at the
same time a metal, which in its turn is an element. Of
course, these conceptions gold, metal, element are
not absolutely indentical ; it was pointed out in ( 79)
that propositions cannot be regarded as expressing
mere identity without difference. But we can say that
there is a common thread or element running through
these notions, which furnishes the principle of con-
nection. Where we cannot discover such a common
nature, no inference can be made. Thus, for example,
it would be impossible to draw any conclusion from
the statements that ' it rained yesterday ' and ' gold has
been discovered in Alaska,' because there is no com-
mon element or connecting thread present which would
lead us beyond the premises.
87. THE NATURE OF INFERENCE 327
In formal arguments the middle term, or connecting link, is usu-
ally explicitly stated ; but in the actual process of reasoning things
out, it is frequently necessary to go in search of it. We may notice,
for example, that the fire in a stove burns more slowly when the
damper is shut. In order to understand the fact, we have to find out
some fact which is common to ' closed-damper ' and ' slow-burning,'
some link of identity, as it were, which enables us to pass from the
one to the other. Such a connecting link is afforded, of course, in
this case by the supply of oxygen. Darwin was noted for his keen-
ness in detecting connections which escaped the ordinary eye, as
well as for his skill in giving explanations of them. On one occa-
sion, he observed that in the part of the country where he lived,
clover was abundant in those fields which were situated near villages,
while the outlying fields were almost destitute of it. What now, he
asked himself, is the connecting link between these facts? Some
investigation of the matter convinced him that the two agencies
which produced this result were mice and cats. The field mice
destroy the clover by feeding upon its roots, but the cats go out from
the villages into the fields near by and kill the mice.
We have seen that the passage from one fact to an-
other in inference does not involve a transition to some-
thing wholly different from the starting-point. There is
always some aspect or feature in which the premises are
identical with the conclusion. And it is on the strength
of this identity that a passage can be made from one to
the other. The same fact may be expressed differently
by saying that all inference takes place within a system,
'where the parts are so held together by a common
nature that you can judge from some of them what the
nature of the others must be.' Suppose you were given
the leaf of a plant. If you had some systematic botani-
cal knowledge, it would be possible to infer the species
of plant to which the leaf belonged. That is, from
328 THE NATURE OF INFERENCE
the nature of a part, the nature of the whole to which it
belongs could be determined. The part represents the
whole in some sense contains it implicity. It is said
that the great naturalist Cuvier could determine by ex-
amining a single tooth the nature of the animal to which
it belonged. Let us suppose that the tooth were that of
a ruminant animal. Now a zoologist, who knows the
characteristics of such an animal, could draw various in-
ferences regarding the possessor of the tooth. He could
conclude, for example, that the animal to which it once
belonged must also have had cloven hoofs. A single
piece or part, that is, would enable one who knows the
system or common nature to which all the parts be-
long, to judge what the other parts are like.
The examples just given have referred to the possi-
bility of an inference from one part of an organism to
another. But, as we have already seen, the systematic
connection which here exists between the parts, is more
or less completely present whenever it is possible to
infer at all. Inference pushes further the work of con-
structing a system begun by Judgment ( 78). If each
thing was known by itself, if the parts of our knowledge
did not fall together into systems where each part to
some extent determines the nature of the other parts, no
inference would be possible. It is because the various
pieces of our knowledge are never independent of each
other, but form an organic whole, like the members of a
living organism, that certain facts follow, as we say,
from certain other facts. And it is of course true, that
as our knowledge in any field becomes more completely
organized, it is more possible to use it as a basis for in-
88. INDUCTION AND DEDUCTION 329
ference. The better we are able to put together in a
systematic way the various facts which we have learned
about geology, or astronomy, or the weather, the more
significant each fact becomes. The geologist may be
able to tell from the appearance of the cliffs what has
taken place in a locality thousands of years ago. And,
similarly, for the fisherman, the temperature, direction
of the wind, its rising or falling, etc., are all signs from
which he is able to infer, more or less correctly, the
kind of weather which may be expected. A person
who had no systematic knowledge in either of these
fields, would, however, see nothing in the scarred rocks,
or in the sudden change of the wind ; he might notice
the facts, but would not be able to use them as a basis of
inference.
It is important to notice that what has just been said goes to
confirm our previous statements regarding the increasing degree of
integration which knowledge shows in the course of its development.
The knowledge of the scientist differs from that of the ordinary man,
not only in the greater number of facts which the former contains, but
also, as we have seen, in the degree of integration or coherence
which these facts possess. Inference, then, is simply a deep insight,
based on definite knowledge, into the necessary connection of things.
It is an act of thought which discovers the essential relations be-
tween things which at first sight appear to have no connection with
each other. As has already been said, it is a reasoned judgment ;
i.e., a judgment which has become conscious of the reasons for the
connections which it affirms.
88. Induction and Deduction. It has been already
pointed out that there are two directions in which infer-
ence or reasoning may proceed. We may begin with
certain facts or principles which are already known,
330 THE NATURE OF INFERENCE
or are assumed to be true, and proceed to show that
some result necessarily follows from them. Thus we
might infer that if the draughts of a stove are closed so
that the supply of oxygen is lessened, the fire will burn
slowly ; or from the relative positions and revolutions of
the planets, that an eclipse of the sun will take place on
a specified day and hour. This method of reasoning is
known as Deduction. It proceeds, as we have seen,
from premises to conclusion. In the first part of this
book, this form of reasoning has been treated at some
length and its rules of procedure stated. At present,
we need only notice that in deductive reasoning the par-
ticular case is always brought under some general law
or principle, which is already known or assumed as true.
Socrates is known to be mortal, because as a man he
falls under the general law that all men are mortal ; the
closing of the draughts is a case of lessened supply of
oxygen, and, therefore, in accordance with the general
law, a case of slow burning. A deductive inference
shows what are the results of the application of a gen-
eral law to particular facts or instances. It proceeds
downwards, as it were, from the general law to its con-
sequences.
In Induction, on the contrary, the procedure is just
the opposite of this. We begin with particular
phenomena, and try to discover from them the law
or principle which unites them. Certain facts are
observed to happen together, and the problem is to
find the ground or explanation of this connection.
Inductive inference is thus a process of reading the
general law out of the particular facts. It is an insight
88. INDUCTION AND DEDUCTION 331
into the nature of the whole or system, based upon a
careful examination of the parts. ' Yesterday the smoke
tended to fall to the ground, and it rained in the after-
noon.' These two facts may simply be observed a
number of times without any thought of their con-
nection. But intelligence asks : Why should they
happen in conjunction ? And to answer this question,
we must begin by analyzing the facts in our possession.
When the smoke falls to the ground, the atmosphere
must be lighter than usual ; this is the case when it
contains a great deal of moisture ; but when the
atmosphere is in this condition, it usually tends to
discharge its moisture in the form of rain ; therefore
we have the general law which enables us to show that
the behaviour of the smoke and the rain yesterday were
not only accidentally conjoined, but essentially connected.
Deduction and Induction, then, are both forms of
inference, but the starting-point and mode of procedure
of the one is different from that of the other. Conse-
quently, it is not unusual to speak of them as two kinds
of reasoning which are quite distinct and independent
of each other. It is, however, important to avoid this
popular error, and to remember that the real process of
inference is in each case the same. The essence of
inference, as has been shown, consists in the fact that
it exhibits the manner in which particular facts are
connected together into a system or whole. And this
end is achieved both by Deduction and Induction. In
the former case, the general law of connection what
we may call the nature of the system within which the
particulars fall is known, and we argue from this as
332 THE NATURE OF INFERENCE
to the nature and relations of the various parts which
fall within it. We have the common thread which
unites the various facts in our hand, and following it out
are able to show its application in determining the
nature of events which have not yet come within the
range of our experience. Knowing the law of gravity,
for example, one could infer deductively what momentum
a ball weighing one pound must necessarily have after
falling one hundred feet. It would not be necessary
actually to measure the momentum of the falling body
in this particular case, but it could be shown to be the
necessary result of the general law. What the deductive
inference shows to us, is ,the way in which a general
principle or law of connection runs through a group of
facts, and constitutes them a real or organic whole.
The same insight is reached by inductive inference,
although the starting-point is entirely different. As
we have already seen, induction begins by observing
that certain phenomena are frequently conjoined, and
attempts to discover some law or principle which will
make the fact of their connection intelligible.
It is usual to say that in induction we go from the
particular facts to the general law. The following, how-
ever, would be a more correct form of statement :
Before the inference, we observe that a number of phe-
nomena occur together, but do not know whether this
conjunction is necessary or not ; or, if we assume that
it is necessary, we do not understand why it should be
so. As a result of the inductive inference, we gain an
insight into the necessary connection of the observed
phenomena, and also understand the principle according
88. INDUCTION AND DEDUCTION 333
to which the latter are united. What we really obtain
through an inductive inference is not only a general law,
but also a perception of its concrete application to
particular phenomena. This being so, it is clear that
Induction and Deduction are not two different kinds of
inference. Inference always implies an effort on the
part of the mind to see how phenomena are neces-
sarily connected according to some general principle.
And, in carrying out this purpose, the mind must begin
with the knowledge which it already possesses. When
the general law of connection is known, and the object
is to discover the nature of some particular fact, the
method of procedure is deductive. But, when the
problem by which we are confronted is to read out of
the facts of sense-perception the general law of their
connection, the method of inference which must be
employed is that of induction. But from whatever
point we set out, and whatever may be the immediate
object of the inference, the result is always the same
an insight into the necessary connection of facts accord-
ing to some general principle.
It is not unusual to hear the remark made that
modern science has been built up by the employment
of the inductive method. This must not, however, be
interpreted to mean that deductive inferences are not
also used in the discovery of scientific truth. Science
(which is simply another name for systematic know-
ledge) is the product of thinking, and thought, as we
have seen, is not limited to any one mode of procedure.
Thought aims at extending knowledge, and so long as
it can find any link of connection, or guiding thread, it
334 THE NATURE OF INFERENCE
is not limited to any one direction, or to any fixed mode
of working. It is, of course, to be admitted and
this is what is true in the statement which we have
quoted that general laws cannot be discovered with-
out an examination of particular facts, and that their
validity must always be tested by comparison with the
facts. But as soon as a general law is discovered in
any field, it is always used as a principle from which to
deduce new results. When it is possible to employ
mathematics in the calculation of these results, it is
usually possible to extend our knowledge of the subject
much more rapidly than before. Thus physics and
astronomy owe their rapid development to the applica-
tion of mathematics. It must be remembered, however,
that this presupposes a certain stage of advancement
a certain inductive stage, as it were on the part of
the science. But even in this earlier stage, we are
constantly employing deduction, reasoning out the
results of certain guesses or suggestions to see if they
hold true (cf. 47). Both in ordinary life, and in
scientific procedure, we may see, Induction and Deduc-
tion are constantly employed together.
References
B. Bosanquet, Logic, Vol. II. Ch. I.
F. H. Bradley, The Principles of Logic, pp. 430-468.
W. James, The Principles of Psychology, Vol. II. Ch. XXII.
J. G. Hibben, Inductive Logic, Chs. I. and II.
CHAPTER XXV
RATIONAL AND EMPIRICAL THEORIES
89. The Point of View of Rationalism. In the his-
torical sketch of logic given in Chapter II., it was stated
that there are two rival accounts of the nature of know-
ledge, and the methods by which it is attained (cf. 8).
The first of these theories is known as Rationalism, and
has its best known historical representative in Descartes;
while Empiricism, the opposing theory, is associated with
the names of the great thinkers, Bacon and Locke.
The doctrines of both these schools have been fre-
quently modified, and the contrast between them is
now no longer so pronounced as it was formerly. In
spite of this fact, however, the division has always
represented two schools of thought whose general re-
lations to each other have remained comparatively con-
stant. In general, too, it has been true that English
thinkers have upheld Empiricism, while Rationalism
has had its home on the Continent at first in France,
and later in Holland and Germany.
Rationalism regards mathematics as the type of all
knowledge. Its essential characteristic consists in the
fact that it undertakes to derive all knowledge from
general principles. These principles have sometimes
been regarded as innate (truths which are stamped
upon the mind at birth), or it has been supposed that
335
336 RATIONAL AND EMPIRICAL THEORIES
they are in some way known before experience, and
have a right to the title of a priori propositions ( 76).
Notwithstanding the various forms in which their theo-
ries have been expressed, all rationalistic thinkers agree
in regarding the first principles upon which our know-
ledge is based, as upon a different plane from the facts
of ordinary life. While the latter are known only by
experience, and may be wholly or partially false, the
former are described as principles which are in them-
selves necessary, truths the opposite of which is incon-
ceivable, or sometimes as the axioms presupposed in all
experience. These principles being accepted, the prob-
lem which lay before Rationalism was to show how all
the facts of our experience necessarily follow from
them, just as the various propositions of geometry
follow from the definitions and axioms which are as-
sumed as the starting-point. As a matter of fact, how-
ever, the famous Jewish thinker, Spinoza (1632-1677),
was the only man who ever attempted to carry out
Rationalism in this systematic form. In general, one
may say that rationalistic thinkers have been mainly
interested to show that the facts of the moral and reli-
gious experience are logically derivable from certain
necessary first principles. It was questions like those
regarding the existence of God, the immortality of the
soul, and the freedom of the will, which the rationalists
were anxious to put beyond dispute. And, as a con-
sequence, not nearly the same amount of effort was
devoted to showing how the other facts of experience
could be similarly derived from general principles.
It will be at once clear, from what has been already
90. THE DOCTRINE OF EMPIRICISM 337
said, that the great instrument of knowledge from this
standpoint must be reason. Very little attention is paid
to perception, and the experience which it furnishes is
not regarded as entitled to the name of knowledge.
In order to know, in the true sense of the word, it is
necessary to show the systematic connection of every
fact with some fundamental first principle; and this,
of course, can be done only by the employment of
reasoning. Perception gives us only the bare facts ; it
is reason which enables us to trace the mutual connec-
tions, and derivation of these facts from some general
law. The weakness of the rationalistic position does not
consist in its insistence on the necessity of connecting
the particular facts of experience with general laws or
principles, but in the assumption upon which it pro-
ceeded that these principles could themselves be derived
from some other source than experience. The result
was that the rationalists employed themselves too ex-
clusively in deducing facts from general propositions
which were assumed to be true without sufficient criti-
cism and examination. They saw clearly enough that
mere perception without general principles can never
give us knowledge, but they did not understand that it
is impossible to separate the latter from the former,
and to regard principles as existing in the mind prior
to experience.
90. The Doctrine of Empiricism. Empiricism main-
tains that all knowledge is derived from experience ; and
by experience is understood the separate unconnected
facts with which the mind is furnished in perception.
z
338 RATIONAL AND EMPIRICAL THEORIES
Empiricism refuses to admit that we possess any
store of first principles or general truths which are
native to the mind, or are obtained from any other
source than experience. It is impossible for the mind
to know anything of which it has had no perception.
Moreover, the very fact that perception is made the
standard, of knowledge, led to the belief that the mind
is something essentially passive, upon which ideas are
impressed by external forces. Empiricism regards
knowledge as the sum of the particular facts furnished
to the mind through sense, not as a system which is
the product of the mind's own activity. As a conse-
quence, there results an entirely different theory of
knowledge from that which we have given in this book.
Ideas are supposed to be furnished to the mind by
the channel of the senses, or are compounded from
simpler elements which are supplied in this way. And
when ideas become united by standing in juxtaposition,
or being associated in some other way, the result is a
judgment. In this account, the judging, or interpreting
activity of the mind, which we have made the source
of all knowledge, is wholly omitted. Indeed, one may
say that empirical theories undertake to explain know-
ledge without reference to the mind and its mode of
activity. Although all empirical thinkers do not deny
the existence of the mind, yet none of them wish to go
beyond the particular facts, and to call in its aid as a
principle of explanation.
The same insistence upon particular facts, and
avoidance of general principles, is characteristic of
empirical theories of reasoning. All inference, it is
90. THE DOCTRINE OF EMPIRICISM 339
maintained, is based upon a perception of resem-
blance between individual cases. The general law,
or principle, is nothing in itself but an abbreviated
statement of the manner in which all the instances
act which we have hitherto observed. The clearest
statement of this theory is given by John Stuart
Mill, from whose work on Logic the following pas-
sages are taken : " Now, all which man can observe
are individual cases. From these all general truths
must be drawn, and into these they may again be
resolved; for a general truth is but an aggregate of
particular truths, a comprehensive expression by means
of which an indefinite number of individual facts are
affirmed or denied at once. . . . From instances which
we have observed, we feel warranted in concluding that
what we found true in those instances holds in all simi-
lar ones, past, present, and future, however numerous
they may be. ... When, therefore, we conclude from
the death of John and Thomas, and every other person
we ever heard of in whose case the experiment had
been fairly tried, that the Duke of Wellington is mortal
like the rest, we may indeed pass through the generali-
zation, All men are mortal, as an intermediate stage ;
but it is not in the latter half of the process, the descent
from all men to the Duke of Wellington, that the infer-
ence resides. The inference is finished when we have
asserted that all men are mortal. What remains to be
performed afterwards is merely deciphering our own
notes." 1 In other words, Mill maintains that all in-
ference is based upon the perception of particular
i Mill, Logic, Bk. II. Ch. III. 3.
340 RATIONAL AND EMPIRICAL THEORIES
cases. There is no such a thing as reasoning from
general truths or principles. We may, indeed, arrive
at such general truths by repeated experiences, and
store them up as maxims in our memory ; but they are
not at all necessary for the process of inference, which
may be said to be always inductive in character, since
it sets out from a perception of individual cases. " In-
duction, properly so called, . . . may be denned as a
generalization from experience. It consists in inferring
from some individual instances in which a phenome-
non is observed to occur, that it occurs in all instances
of a certain class ; namely, in all which resemble the
former in what are regarded as the material circum-
stances." 1
This account of the way in which inference proceeds
undoubtedly contains much that is true. Nevertheless,
it is not, I think, an adequate statement of the nature of
inference. What one misses chiefly is some insistence
upon the fact that it is only in virtue of some identical
link, or common element, which is present in all the
individual cases, that one is able to pass from one to
another. On this point we must refer to what was said
in the last chapter ( 87). It will perhaps be possible
to gain a clearer idea of what is true and what is false
in this theory, by considering further Mill's doctrine,
that it is possible to reason from one particular fact to
another, without any reference to general truths.
91. Reasoning from Particulars to Particulars. " Not
only may we reason from particulars to particulars, with-
* Mill, Logic, Bk III. Ch. III. I.
9i. FROM PARTICULARS TO PARTICULARS 341
out passing through generals, but we perpetually do so
reason. All our earliest inferences are of this nature.
From the first dawn of intelligence we draw inferences,
but years elapse before we learn the use of general
language. The child, who, having burned his fingers,
avoids to thrust them again into the fire, has reasoned
or inferred, though he never thought of the general
maxim, Fire burns. He knows from memory that he
has been burned, and on this evidence believes, when
he sees a candle, that if he puts his finger into the flame
of it, he will be burned again. He believes this in any
case which happens to arise, but without looking in
each instance beyond the present case. He is not gen-
eralizing ; he is inferring a particular from particulars.
... It is not only the village matron, who, when called
to a consultation on the case of a neighbour's child, pro-
nounces on the evil and its remedy on the recollection
and authority of what she accounts the similar case of
her Lucy. We all, when we have no definite maxims
to steer by, guide ourselves in the same way." l
The doctrine as thus stated by Mill is the extreme
opposite of Rationalism. Not only are all general
propositions derived from observation of particular in-
stances, but they play no part in the process of infer-
ence proper. All reasoning, according to this account,
is based on the perception of resemblance between
individual cases. No common nature or general prin-
ciple seems necessary to unite the latter into a system.
Nevertheless, it must be confessed that Mill's state-
1 Mill, Logic, Bk. II. Ch. III. 3.
342 RATIONAL AND EMPIRICAL THEORIES
ment affords an excellent account of many of our
ordinary inferences. We may accept it, however, as a
description of fact without committing ourselves to the
theory which it contains. That is, it will still be neces-
sary to ask if inference is not, after all, based on the
perception of some general law or principle, although
it is not always possible to formulate the nature of
the latter. It does not seem to me that the nature of
the inference in the cases cited is completely described
when it is said to be a passage from one particular
case to another which resembles it. For it is necessary
to look further, and to see what is implied in the fact
that one case is perceived to resemble another. When
the child perceives that the bright object before him
resembles something which previously gave him pain,
he has got beyond the merely individual aspect of
things, and is beginning to regard them as types or
instances of a general law. Of course, the child is
not fully conscious of any general principle. He does
not separate the latter from its embodiment in the par-
ticular case, or put it into language even to himself.
But, in order to infer, one must take the individual
case as something more than a mere particular, as this
which is only here and now. In the child's perception
of resemblance between the present object and the one
previously experienced, there is an implicit reference to
a permanent type, or identity which persists through
the two cases. In other words, when one asks what a
perception of resemblance means, one sees that it im-
plies an apprehension on the part of intelligence of
something which is more than merely momentary.
9i. FROM PARTICULARS TO PARTICULARS 343
The same quality or other element which is found in
that object is also found in this. And the inference
proceeds, that ' object was hot, therefore this object
(having the same general nature, or being of the same
type) is also hot. It is, of course, frequently impossible
to formulate clearly the nature of the principle upon
which we proceed, and, in cases like those cited, one may
not be aware that it is present. But, I hope, it will now
be clear that even in such instances the inference is
based upon a permanent nature present in the two cases.
We have already seen that where such an identical link
is not present, it is impossible to pass, by means of in-
ference, from a knowledge of one thing to another. As
mere particulars, two phenomena occurring at different
times are entirely isolated, and have nothing to do
with each other. But as pieces of knowledge, facts
which have been constituted by the interpreting func-
tion of Judgment, they are bound together by a com-
mon principle, the nature of a whole or system. This
principle is, indeed, not anything apart from the facts
connected, or in any way prior to them ; but neverthe-
less something without which it would be impossible to
understand their connection.
The conclusion of the matter, then, is that we never
reason from one bare particular to another particular.
More than that, we may say a fact which is merely
particular something which is only here and now
has no existence in knowledge. For knowledge lays
hold of the universal aspect of things, their permanent
significance. Intelligence sees the universal or typical
nature in what is for sense a fleeting phenomenon. It
344 RATIONAL AND EMPIRICAL THEORIES
is only when the facts of sense are interpreted in this
way, when their real nature is apprehended by thought,-
that they can be said to be known at all. Knowledge
sees the universal in the particular, or reads the partic-
ular as a case of the universal. And when thus inter-
preted, the particular ceases to be a bare particular, and
becomes an individual with a permanent nature of its
own. When one reasons from an individual case, then,
it is the universal or typical nature, not the particular
or momentary existence, upon which the inference pro-
ceeds. If there were any merely particular facts in
knowledge, we could never reason from them. But, as
has been shown, the so-called particular facts, as ele-
ments of knowledge, possess a universal or typical as-
pect in virtue of which alone inference is possible.
92. Reasoning from Individual Cases to a Universal.
- There remains another question which is very closely
related to the points already discussed in this chapter.
We must admit that in inductive inference at least the
starting-point is individual instances, though, as the last
section showed, the latter, as used in reasoning, are
something more than mere particulars. The problem
which meets us, however, is this : How is it ever pos-
sible to get a universal conclusion from individual
instances ? It, of course, frequently happens that we
cannot examine- all the cases. What right then have
we in these circumstances to state our conclusion
generally to assert, for example, that 'all men are
mortal/ or ' all mosses cryptogams ' ?
It is often said that in such cases the general con-
92. FROM PARTICULARS TO A UNIVERSAL 345
elusion is never more than probable, and that its proba-
bility increases directly in proportion to the number of
instances examined. Thus if A and B are conjoined only
once in my experience, it is very improbable that the
connection is a universal and essential one. But if they
are found together ten times, the proposition, 'A is B'
begins to have probability, which is, of course, greatly
increased (without ever becoming more than probable
however), if the conjunction is observed a hundred, or a
thousand times. Now, there can be no doubt that the
frequency of conjunction is, to a certain extent, a prac-
tical test of real or universal connection. Belief, as a
psychological fact, is engendered by frequency of repeti-
tion. But the causes of our belief are here, as in many
cases, quite different from the real or logical grounds.
The fact that two phenomena have occurred together a
hundred times, in itself affords no logical ground for
affirming a universal connection between them, or that
they will be connected the hundred and first time. Of
course, as we have said, psychological belief or expecta-
tion would be engendered by the frequent conjunction ;
but the latter would supply no real or logical grounds.
Practically, we are more certain to be right, if we gen-
eralize on the basis of a large number of observations,
than if we proceed on the authority of a smaller num-
ber. But, as affording logical justification for our pro-
cedure, a hundred instances (if they are merely counted)
are no better than one.
The truth is that a general conclusion does not de-
pend for its logical justification upon the number of
instances observed. Inference is not a matter of count-
346 RATIONAL AND EMPIRICAL THEORIES
ing instances at all, but is an intellectual insight into
the nature of a general law or principle of connection.
The problem of inductive inference is to discover this
principle in the individual case, to penetrate beneath
the surface, and read out of the individual phenome-
non its real meaning or significance. To accomplish
this usually requires an examination of many particu-
lar cases. We have more chances of learning the
secret fully if we take as wide a survey as possible
of the facts. A generalization based upon a small
number of observations is pretty sure to be incorrect
or inaccurate. But though of such great practical im-
portance, the number of instances is logically indiffer-
ent. The essential point is to detect the general law or
principle, and for this purpose one case may conceiva-
bly be as good as a hundred. Inductive inference,
then, is not a process of passing from a certain number
of cases to a general conclusion which always remains
probable because it has no proper justification. But its
real nature consists in the discovery, through the aid of
examples, of a universal law of connection. We have
already shown the part which the constructive imagina-
tion, guided by Analogy, plays in reaching this result
(cf. 60, 63).
It must be admitted that there are many cases where it is impossi-
ble to get beyond the fact that two phenomena are constantly con-
joined in our experience. The grounds which should make this fact
intelligible lie beyond our ken. Under circumstances of this kind,
we are, of course, compelled to act on the presumption that the same
order of events will continue to obtain. We may find that a certain
medicine is followed by certain physiological consequences, without
92. FROM PARTICULARS TO A UNIVERSAL 347
being able to discover anything regarding the way in which the lat-
ter have been produced. And we may confidently predict that the
same results will follow in a new case where the same medicine has
been given. But it must be noticed that this is not the ideal of rea-
soning. Knowledge of the kind we have described is merely em-
pirical, follows a rule of thumb without being able to give any account
of itself. Moreover, even in such cases, it is always assumed that
there is some general principle or law which may yet be discovered,
and which is capable of explaining the facts known empirically.
References
J. S. Mill, Logic, Bk. II.
H. Spencer, Principles of Psychology, 208.
W. James, The Principles of Psychology, Vol. II. Ch. XXVIII.
B. Bosanquet, Logic, Vol. II., pp. 176-179.
QUESTIONS AND EXERCISES
INTRODUCTION
CHAPTER I. The Standpoint and Problem of Logic
1 . What are some of the main characteristics of thought or
thinking ?
2. Explain the use of the verb to think in each of the fol-
lowing sentences : * I do not know, but I think so ; ' 'If you
think the matter over, you will come to the same conclusion.'
3. ' Words and phrases are often repeated without reflection,
and their very familiarity is likely to prevent us from attempting
to understand exactly what ideas they represent.' Give illus-
trations of this fact.
4. What do you mean by a science ? How does ' scientific '
knowledge differ from the knowledge of ordinary life?
5. What is the meaning of the word 'law' in the phrase
' a law of thought ' ? Compare the use of the word in such ex-
pressions as ' laws of nature,' ' the laws of the land."
6. Is it true that Logic and Psychology have the same
subject-matter?
7. Explain carefully how the problem of Logic differs from
that of Psychology.
8. If we parallel Psychology with Morphology, and Logic
with Physiology, what mental science will correspond to
Embryology?
9 Illustrate by means of examples not used in the text the
relation in which science and art, or theory and practice, stand
to each other.
348
QUESTIONS AND EXERCISES 349
10. Criticise the following statement : ' Logic is not only a
science ; it is also an art, for it teaches us to reason correctly.'
11. What part does Introspection play in investigating logi-
cal questions?
12. In what sense may we say that the records of everything
which the human race has accomplished form the material of
Logic?
CHAPTER II. Historical Sketch
1. 'The sciences have arisen in response to the practical
needs of mankind.' Is this statement confirmed by the history
of the origin and development of Logic ?
2. ' Since each individual sees things from his own point of
view, there is therefore nothing really true in itself, or good in
itself.' Give some illustrations of the former part of this state-
ment. What term would you use to describe the theory which
the sentence expresses?
3. Explain what is meant by the statement that Socrates
and Plato found a standard of truth t and of conduct in the
Concept.
4. Why was it not possible for Aristotle to lay down a com-
plete theory of Inductive Reasoning?
5. What is Mill's theory regarding the relation of Induction
and Deduction?
6. Describe the standpoint of Modern Logic.
PART I. THE SYLLOGISMS
CHAPTER III. The Syllogism and its Parts
1. Describe the general purpose and nature of the syllogism.
2. What is the principle upon which syllogistic reasoning
depends? Why is it impossible to reason if this principle is
violated ?
35O QUESTIONS AND EXERCISES
3. Explain the distinction between the formal and real truth
of an argument.
4. Arrange the following sentences as logical propositions,
pointing out the logical Subject and the Predicate in each
case :
(a) Learning taketh away the wildness of men's minds.
() Dissipation wastes health.
(c ) The exposition of a principle indirectly contributes to
its proof.
(d) To me the meanest flower that lives can give thoughts
that do often lie too deep for tears.
(<?) The Alps consist of several parallel ranges.
(/) The travellers had found the city in ruins.
5. Point out the Premises and Conclusion in the following
arguments, and supply any premise which may be wanting :
(a) He is not indifferent to money ; for he is a sensible
man, and no sensible man despises money.
() All human productions are liable to error, and there-
fore all books, being human productions, are liable
to error.
(c) All that glitters is not gold ; for brass glitters.
(</) All bodies which move round the sun are planets;
therefore the earth is a planet.
(<?) Platinum is a metal, and therefore combines with
oxygen.
6. How does Jevons describe Simple Apprehension? Is it
possible to maintain that Apprehension, Judgment, and Rea-
soning are three distinct operations of mind ?
CHAPTER IV. Terms
i. Distinguish in the following list the terms which are
usually (i) Singular, (2) General, and (3) Collective. If any
QUESTIONS AND EXERCISES 351
term may belong to more than one class, explain and illustrate
its various uses :
Niagara Falls, an oak tree, the United States Navy,
gold, a dancing party, Brooklyn Bridge,
chair, the United States, humanity,
a pack of cards, city, the centre of the earth.
2. Explain and illustrate the ambiguity in the use of the
word ' all.'
3. In what two ways are the words Abstract and Concrete
used ? In what sense, if at all, can we say that Psychology and
Logic are ' abstract ' sciences ?
4. Distinguish carefully between Contradictory and Oppo-
site terms.
5. What are Correlative terms? Give at least three ex-
amples.
6. Mention the synonyms for Intension and Extension.
7. Explain the Extensional and Intensional use of the fol-
lowing terms :
metal, chair, man, Caesar, superstition,
justice, student, John Jones, island, emperor.
8. Criticise the statement that ' Extension and Intension
stand in inverse ratio to each other.' What truth does it con-
tain?
9. Invent a series of at least six terms which may be ar-
ranged so as gradually to increase in Extension.
10. What may be said in reply to Mill's contention that
proper names are non-connotative ?
CHAPTER V. Definition and Division
\?. .!< *
1. Why is Definition necessary?
2. What is the distinction between extensive and intensive
definition? What is a verbal definition?
352 QUESTIONS AND EXERCISES
3. In what two ways may we conceive the problem of
Definition?
4. What do you understand by the Socratic Dialectic ? Ex-
plain its purpose and mode of procedure.
5. Explain the terms :
genus, differentia, infima species,
species, summum genus, sui generis.
6. Criticise the following definitions, pointing out what rules,
if any, are violated by them :
(1) Logic is the science of thought.
(2) A power is a force which tends to produce motion.
(3) Tin is a metal lighter than gold.
(4) A gentleman is a man who has no definite means of
support.
(5) The body is the emblem or visible garment of the
soul.
(6) Man is a vertebrate animal.
(7) Thunder-bolts are the winged messengers of the
gods.
(8) A moral man is one who does not lie or steal or live
intemperately.
(9) Cheese is a caseous preparation of milk.
(10) Evolution is to be defined as a continuous change
from indefinite incoherent homogeneity to definite
coherent heterogeneity of structure and function,
through successive differentiations and integra-
tions (Spencer).
(n) Oats is a grain which in England is generally given
to horses, but in Scotland supports the people.
7. Give examples of terms which are indefinable, and ex-
plain why this is the case. What is the distinction between
Description and logical Definition?
QUESTIONS AND EXERCISES 353
8. Define the following terms by giving the genus and dif-
ferentia :
science, republic, psychology, island,
triangle, monarchy, gold standard, import duty.
9. Examine the following Divisions and point out which are
logical and which are not :
(1) Living beings into moral and immoral.
(2) Men into saints and sinners.
(3) Religions into true and false.
(4) Man into civilized and black.
(5) Geometrical figures into rectilinear and non-recti-
linear.
(6) Substances into material and spiritual.
(7) Metals into white, heavy, and precious.
(8) Elementary mental processes into sensations and
affections.
(9) Students into those who are idle, those who are
athletic, and those who are diligent.
(10) Books into scientific and non-scientific.
CHAPTER VI. Propositions
1. What is a proposition? In what sense may a proposition
be said to have parts ?
2. Distinguish between Categorical and Conditional propo-
sitions.
3. What is meant by (a) the Quality, and (b) the Quantity,
of propositions?
4. Arrange the following sentences in the form of logical
propositions, and indicate the Quality and Quantity of each
categorical proposition by the use of the letters A, E, I,
and O:
2A
354 QUESTIONS AND EXERCISES
(1) Brevity has to be sought without sacrificing per-
spicuity.
(2) He that doeth these things is like to a man that
buildeth his house upon a rock.
(3) Socrates declared knowledge to be virtue.
(4) Phosphorus does not dissolve in water.
(5) Nearly all the troops have left the town.
(6) Only ignorant persons hold such opinions.
(7) Few persons are proof against temptation.
(8) Over the mountains poured the barbarian horde.
(9) Except ye repent, ye shall all likewise perish.
(10) Neither gold nor silver is the proper standard of
value.
5. How does formal logic interpret the relation between the
subject and predicate of a categorical proposition? Does this
view do full justice to the signification of propositions?
6. How would you represent by means of circles the propo-
sition, ' gold is the most precious metal ' ?
7. What do you mean by the distribution of terms ? Explain
why negative propositions distribute the predicate, while affir-
mative propositions do not.
8. State precisely what is asserted by Proposition I. What
forms may the diagrams which represent this proposition
assume ?
CHAPTER VII. The Interpretation of Propositions
1. Why is it better to speak of the Interpretation of propo-
sitions than to use the term ' Immediate Inference ' ?
2. What is meant by the Opposition of propositions ?
3. Explain the distinction between Contrary and Contradic-
tory propositions.
4. If proposition O is false, what is known regarding the
truth or falsity of A, E, and I ?
QUESTIONS AND EXERCISES 355
5. What is the simplest proposition which must be estab-
lished in order to disprove the following statements : (a) All
men desire wealth, (b) No man is perfectly happy, (c) Some
knowledge is not of any value, (d) Pain alone is evil. (<?) All
is not lost.
6. Give the contrary (or sub-contrary) , and the contradictory
of: (a) All metals are elements, (b) No coward need apply.
(f) Socrates was the wisest man in Athens, (d) Not all men
are brave. (<?) No man but a traitor would have done this.
(7. Give the Obverse of the following propositions :
(i) All horses are quadrupeds.
(2) Good men are charitable.
(3) None of the captives escaped.
(4) Some of the planets are not larger than the earth.
(5) Some students do not fail in anything.
(6) All English dukes are members of the House of Lords.
(7) No illogical author is truly scientific.
8. Convert in at least one way :
(T) All men are rational.
(2) Some metals are readily fusible.
(3) Perfect happiness is impossible.
(4) None of the captives escaped.
(5) Uneasy lies the head that wears a crown.
(6) Not every man could stand such hardships.
(7) None but the brave deserves the fair.
(8) Phosphorus will not dissolve in alcohol.
(9) Hydrogen is the lightest body known.
, (10) The world is my idea.
9. Convert by contraposition :
(1) All honest men are of this opinion.
(2) Oxygen can be prepared by heating potassium chlo-
rate in a thin glass dusk.
356 QUESTIONS AND EXERCISES
(3) Some of the enemy were not prepared to surrender.
\ (4) Not all who came to scoff remained to pray.
(5) A triangle is a plane figure bounded by three straight
lines.
(6) The return of peace had given fresh confidence to
the government party.
10. Describe the logical relation between each of the four
following propositions :
(1) All substances which are material possess gravity.
(2) No substances which possess gravity are immaterial.
(3) Some substances which are immaterial do not possess
gravity.
(4) Some substances which do not possess gravity are
immaterial. (Jevons.)
11. What is the Obverse of the Converse of, 'None of the
planets shine by their own light ' ?
12. Can we logically conclude that because heat expands
bodies, therefore cold contracts them? (Jevons.)
13. What is the logical relation, if any, between the two
assertions in Proverbs xi. i, 'A false balance is an abomination
to the Lord ; but a just weight is his delight ' ? (Jevons.)
CHAPTER VIII. The Syllogism and its Rules
1. What is the relation of the Proposition and the Syllo-
gism?
2. What is the function of the Middle Term in a Syllogism?
3. How are the major and minor terms, and the major and
minor premises of a Syllogism distinguished?
4. Prove the seventh and eighth canon of the Syllogism,
(a) by means of the previous rules, and () by the use of
circles.
QUESTIONS AND EXERCISES 357
5. Construct an argument to illustrate the fallacy of ambigu-
ous middle term.
6. Arrange the following arguments in the regular logical
order of major premise, minor premise, and conclusion, and
examine them to see whether they conform to the canons of
the Syllogism :
(1) Gold is not a compound substance; for it is a metal,
and none of the metals are compounds.
(2) All national holidays are bank holidays, the bank will
therefore be closed on the fourth of July.
(3) All cruel men are cowards, no college men are
cruel, therefore no college men are cowards.
(4) Some useful metals are becoming rarer. Iron is a
useful metal, and is therefore becoming rarer.
(5) This man shares his money with the poor, but no
thief ever does this, therefore this man is not a
thief.
(6) He who is content with what he has is truly rich.
An envious man is not content with what he has ;
no envious man therefore is truly rich.
7. What does the Figure of an Argument depend upon?
How do you distinguish the four figures?
CHAPTER IX. The Valid Moods and the Reduction of Figures
1. Arrange the following arguments in logical order, and
give the mood and figure in each case :
(i) No P is M, (2) All M is S,
Some S is M, Some M is P,
Therefore some S is not P. Therefore some S is P.
2. Name the premises from which valid conclusions may
be drawn, no account being taken of figures :
358 QUESTIONS AND EXERCISES
AA, EO, IA, IO, II, EE, El, AE, EA, OO.
3. Prove the special canons of the fourth figure.
4. 'The middle term must be distributed once at least.'
In what figures may it be distributed twice? What is the
character of the conclusion when this occurs?
5. Prove generally that when the major term is predicate in
its premise, the minor premise must be affirmative.
6. If the major term be distributed in its premise, but used
undistributively in the conclusion, determine the mood and
figure.
7. Explain why we can obtain only negative conclusions by
means of the second figure and particular conclusions by means
of the third figure.
8. What conclusions do AA, AE, and EA yield in the fourth
figure ? Explain.
9. Is it possible for both major and minor terms to be par-
ticular at the same time in the premises? If so, construct an
argument where this is the case.
10. What do you understand by Reduction? Reduce the
following argument to the first figure :
No fixed stars are planets,
All planets are bright and shining,
Therefore some bright and shining bodies are not fixed stars.
CHAPTER X. Abbreviated and Irregular Arguments
i. Complete the following arguments, determine their mood
and figure, and examine them to see if they violate any of the
rules of the syllogism :
(1) Blessed are the meek, for they shall inherit the
earth.
(2) He must be a strong man, for he was on the crew.
QUESTIONS AND EXERCISES 359
(3) Zoophytes have no flowers ; therefore they are not
plants.
(4) None but material bodies gravitate, therefore air is
a material body.
(5) He has been a politician for years, and is therefore
not to be trusted.
2. Illustrate the difference between the Progressive or
Synthetic, and the Regressive or Analytic methods as em-
ployed in Mathematics and Psychology. May a science
employ both methods at the same time ?
3. Break up the concrete examples of Sorites given on
pages 130, 131, into syllogisms.
4. Show generally why all the premises except the first in
the Aristotelian Sorites must be universal.
5. Prove that in the Goclenian Sorites the first premise
alone can be negative, and the last alone particular.
6. In the examples of arguments given on page 133, is there
any middle term? If not, what serves as the standard of
comparison ?
CHAPTER XL Hypothetical and Disjunctive Arguments
1. What reasons are there for classifying the disjunctive
proposition as conditional ?
2. What are the rules of the hypothetical syllogism ?
3. Is it ever possible to obtain a valid conclusion by deny-
ing the antecedent or affirming the consequent ?
4. Determine which of the following hypothetical arguments
are valid and which invalid ; then express the latter in the
categorical form, pointing out what are the categorical fallacies
which result :
(i) If a man is avaricious, he will be unhappy ; but A is
360 QUESTIONS AND EXERCISES
unhappy, and we may therefore conclude that he is
avaricious.
(2) If A is B, C is D, but A is B, therefore we may
conclude that C is D.
(3) If the door were locked, the horse would not be
stolen ; but the horse is not stolen, therefore the
door must have been locked.
(4) If man were not capable of progress, he would not
differ from the brutes ; but man does differ from
the brutes, therefore he is capable of progress.
(5) If he had studied his lesson, he would have been
able to recite ; but he was able to recite, and there-
fore must have studied his lesson.
(6) If it becomes colder to-night, the pond will be frozen
over; but it will not become colder to-night,
therefore the pond will not be frozen over.
5. What aspects of thinking are emphasized by the cate-
gorical and hypothetical forms of reasoning respectively ?
6. How far may the disjunctive proposition be regarded as
an expression of ignorance, and what is the justification for
the statement that it involves systematic knowledge ?
7. To what fallacy is the disjunctive argument specially
liable?
8. How would you criticise the dilemmatic arguments given
on page 150?
CHAPTER XII. Fallacies of Deductive Reasoning
i." What is the distinction between errors of interpretation
and fallacies in reasoning?
2. Why is the detection of material fallacies a proper subject
of logic?
3. If it is true that all the righteous people are happy, can
QUESTIONS AND EXERCISES 361
we conclude that all unhappy people are unrighteous ? If so,
how do we pass from the first statement to the second?
4. Can we proceed logically from the proposition, ' all good
citizens vote at elections,' to ' all who vote in elections are
good citizens ' ?
5. Does the statement that ' some sciences are useful,' justify
the proposition that ' some useful things are not sciences ' ?
6. Mention the fallacies of Equivocation, and explain what is
common to them all.
7. Explain the terms : Petitio Principii, Circulus inprobando,
Argumentum ad hominem, Argumentum ad populum.
8. Examine the following reasoning: 'The argument from
design must be regarded as without value ; for it has been re-
jected by Spinoza, Kant, Spencer, and Darwin.'
MISCELLANEOUS EXAMPLES
Arrange the following arguments whenever possible in regular
logical order ; determine whether or not they are valid ; give
the mood and figure of the valid categorical arguments ; if any
argument is invalid, point out and name the fallacy involved :
\ i. All virtue is praiseworthy, and charity is a virtue, there-
fore charity is praiseworthy.
2. All colours are physical phenomena ; but no sound is a
a colour, therefore no sound is a physical phenomenon.
3. Some minerals are precious stones, all topazes are pre-
cious stones, therefore some minerals are topazes.
4. Some acts of homicide are laudable, therefore some
cruel things are laudable.
5. If he has found the treasure, he is rich ; but he has not
found it, therefore he is not rich.
6. He must be a Democrat ; for all the Democrats believe
in Free Trade.
362 QUESTIONS AND EXERCISES
7. If only the ignorant despise knowledge, this man cannot
be ignorant, for he praises it. (Edinburgh, 1892.)
8. Whatever is given on the evidence of sense may be taken
as a fact ; the existence of God, therefore, is not a fact, for it is
not evident to sense. (St. Andrews, 1896.)
9. This explosion must have been occasioned by gunpowder ;
for nothing else would have possessed sufficient force.
10. This burglary is the work of a professional ; for an
amateur would not have been half so clever.
n. No stupid person can become President of the United
States ; therefore Mr. Cleveland and Mr. McKinley must both
be men of ability ^
12. Since almost all the organs of the body have some use,
the vermiform appendix must be useful.
13. Every candid man acknowledges merit in a rival, every
learned man does not do so ; therefore learned men are not
candid.
14. Every book is liable to error, every book is a human
production, therefore all human productions are liable to error.
15. Learned men sometimes become mad; but as he is not
learned, there is no danger of his sanity.
1 6. If this candidate used money to secure his election, he
deserved defeat ; but he did not use money in this way, and
therefore did not deserve defeat.
17. All valid syllogisms have three terms ; this syllogism is
therefore valid, for it has three terms.
18. No persons destitute of imagination are true poets;
some persons destitute of imagination are good reasoners ;
therefore some good reasoners are not true poets.
19. Only material bodies gravitate ; ether does not gravitate.
20. In reply to the gentleman's arguments, I need only say
that two years ago he advocated the very measure which he
now opposes.
QUESTIONS AND EXERCISES 363
21. If he claims that he did not steal the goods, why, I ask,
did he hide them as no thief ever fails to do ?
22. If this therefore be absurd in fact and theory, it must
also be absurd in idea, since nothing of which we can form a
clear and distinct idea is impossible. (Hume, Treatise of
Human Nature?)
23. Whatever is produced without a cause is produced by
nothing, or in other words has nothing for its cause. But
nothing can never be a cause. Hence every object has a real
cause of its existence. (Hume, Treatise.}
24. Everything must have a cause ; for if anything wanted
a cause it would produce itself, that is, exist before it existed,
which is impossible. (Hume, Treatise?)
25. If it be true, as Mr. Spencer thinks, that the past
experience of the race has produced innate ideas and feel-
ings, Weismann's denial of Use-inheritance would be refuted.
Certainly, but it is just possible that Mr. Spencer's theory is
not true.
26. Democracy is not a perfect form of government, for
under it there are able men who do not get power; and so
it allows men to get power who are not able.
27. Of university professors, some are zealous investigators,
and some good teachers. A is an excellent teacher, and we
may therefore conclude that he is not a zealous investigator.
28. Seeing that abundance of work is a sure sign of indus-
trial prosperity, it follows that fire and hurricane benefit in-
dustry, because they undoubtedly create work. (St. Andrews,
1895-)
29. I will have no more doctors ; I see that all of those who
have died this winter have had doctors. (St. Andrews, 1896.^
30. If a man is educated, he does not want to work with his
hands; consequently, if education is universal, industry will
cease. (London, 1897.)
364 QUESTIONS AND EXERCISES
31. None but the wise are good, and none but the good are
happy, therefore none but the wise are happy. (Edinburgh,
1897.)
32. Giving advice is useless. For either you advise a man
what he means to do, in which case the advice is superfluous ;
or you advise him what he does not mean to do, and the advice
is ineffectual. (London, 1897.)
33. No pauper has a vote, A B is not a pauper, therefore
he has a vote. (St. Andrews, 1897.)
34. The love of nature is never found either in the stupid
or the immoral man, therefore stupidity and virtue are incom-
patible. (Edinburgh, 1897.)
35. Not all educated persons spell correctly; for one often
finds mistakes in the papers of University students.
36. Free Trade is a great boon to the workingman ; for it
increases trade, and this cheapens articles of ordinary con-
sumption; this gives a greater purchasing power to money,
which is equivalent to a rise in real wages, and any rise in
real wages is a boon to the workingman.
37. If the train is late, I shall miss my appointment ; if it is
not late, I shall not reach the depot in time to go by it, there-
fore, in any case, I shall miss my appointment.
38. He who spareth the rod hateth his child; the parent
who loves his child therefore spareth not the rod.
39. Whatever tends to withdraw the mind from pursuits of
a low nature deserves to be promoted ; classical learning does
this, since it gives us a taste for intellectual enjoyments ; there-
fore it deserves to be promoted.
40. As against the proposition that the formation of public
libraries prevents private individuals from purchasing, and so
decreases the sale of books, a writer urges that whatever
encourages the reading of books encourages the buying of
books. It is a library's purpose to encourage reading, and
QUESTIONS AND EXERCISES 365
hence the net result is rather to increase than to lessen pur-
chases.
41. No reason however can be given why the general hap-
piness is desirable, except that each person, so far as he
believes it to be attainable, desires his own happiness. This,
however, being a fact, we have not only all the proof which
the case admits of, but all which it is possible to require, that
happiness is a good, that each person's happiness is a good to
that person, and the general happiness, therefore, a good to
the aggregate of all persons. (Mill's Utilitarianism.}
42. This man is a Protestant; for he exercises the right of
private judgment.
43. If the orbit of a comet is diminished, either the comet
passes through a resisting medium, or the law of gravitation is
partially suspended. But the second alternative is inadmis-
sible. Hence if the orbit of a comet is diminished, there is
present a resisting medium.
44. How do we know that our intuitive beliefs concerning
the world are invariably true ? Either it must be from experi-
ence establishing the harmony, or an intuitive belief must certify
the correctness. Now experience cannot warrant such har-
mony except in so far as it has been perceived. Still more
futile is it to make one instinctive belief the cause of another.
Thus we cannot know that any intuitive belief is universally
valid. (Bain.)
45. Which of the following are real inferences : (i) 'This
weighs that down, therefore it is heavier'; (2) 'This piece of
marble is larger than that, and therefore is heavier.'
46. The parts of pure space are immovable, which follows
from their inseparability, motion being nothing but change of
distance between any two things ; but this cannot be between
parts that are inseparable, which therefore must be at per-
petual rest one amongst another.
366 QUESTIONS AND EXERCISES
47. If a body moves, it must move either in the place where
it is, or in the place where it is not. But a body cannot move
in the place where it is, nor yet in the place where it is not.
Hence a body cannot move at all.
48. We have no perfect idea of anything but a perception.
A substance is entirely different from a perception. We have
therefore no idea of substance. (Hume.)
49. Every good government promotes the intelligence of the
people, and no despotism does that. (Bain.)
50. He was too impulsive a man not to have committed
many errors. (Bain.)
51. A true philosopher is independent of the caprices of
fortune, for he places his chief happiness in moral and intel-
lectual excellence.
52. Educated among savages, he could not be expected to
know the customs of polite society. (Bain.)
53. No war is long popular ; for every war increases taxa-
tion, and the popularity of anything that touches our pockets
is very short lived.
54. The general object which all laws have, or ought to
have, in common, is to augment the total happiness of the
community ; and therefore, in the first place, to exclude as far
as may be everything that tends to subtract from that happi-
ness : in other words, to exclude mischief. But all punishment
is mischief; all punishment in itself is evil. Upon the princi-
ple of utility, if it ought at all to be admitted, it ought only to
be admitted in as far as it promises to exclude some greater
evil. (Bentham.)
55. Experiments for the purpose of ascertaining the func-
tions of the various organs in animals cause pain, and as we are
not warranted in causing pain to any sentient creature, such
experiments are wrong.
56. Thou shalt not b^ar false witness against thy neighbour.
QUESTIONS AND EXERCISES 367
57. What is the use of all this teaching? Every day you
hear of a fraud or forgery, by some one who might have led
an innocent life, if he had never learned to read and write.
(Edinburgh.)
58. Pious men only are fit to be ministers of religion ; some
men who have not received a college education are pious men,
therefore such men are fitted to be ministers of religion.
59. What fallacy did Columbus commit when he proved
that an egg could stand on end? (Jevons.)
60. No traitor is to be trusted, John is no traitor, and
therefore is to be trusted.
6 1. Against what fallacy does the proverb, 'all that glitters
is not gold,' warn us?
62. Livy describes prodigies in his history, therefore he is
never to be believed.
63. The theory of evolution is true, for it is accepted by
every scientific biologist.
64. The theory of evolution is not true, for it was not ac-
cepted by Agassiz, nor by Gladstone ; moreover, you cannot
accept this doctrine, for it is disclaimed by the authorities of
your church.
65. The advantages which would accrue to the working-
classes are not sufficient to justify Protection, neither are the
advantages which it would bring to the farmers or the manu-
facturers, or to any other class in the community ; Protection
therefore has not enough advantages to justify it.
66. No man should be punished if he is innocent ; this man
should not be punished ; therefore he is innocent.
67. He could not face bullets on the field of battle, and is
therefore a coward.
68. We know that God exists because the Bible tells us so ;
and we know that whatever the Bible affirms must be true
because it is of divine origin.
368 QUESTIONS AND EXERCISES
69. Nations are justified in revolting when badly governed,
for every people has a right to good government. (Edinburgh.)
70. When Croesus was about to make war upon Cyrus, King
of Persia, he consulted the oracle at Delphi, and received for
an answer that, if he should wage war against the Persians, he
would overthrow a mighty empire.
71. England has a gold coinage, and is a very wealthy coun-
try, therefore it may be inferred that other countries having a
gold coinage will be wealthy.
72. Your arguments against the philosophy of Hegel are
of no value ; for you uphold that of Schopenhauer, which is
equally repugnant to common sense.
73. For those who are bent on cultivating their minds by
diligent study, the incitement of academical honours is unnec-
essary ; and it is ineffectual for the idle, and such as are in-
different to mental improvement ; therefore the incitement of
academical honours is either unnecessary or ineffectual.
74. Without order there is no living in public society, be-
cause the want thereof is the mother of confusion, whereupon
division of necessity followeth ; and out of division, destruction.
75. If it is always impossible not to sin, it is always unjust to
punish. Now it is always impossible not to sin, for all that is
predetermined is necessary, and all that is foreseen is pre-
determined, and every event is foreseen. Hence it is always
unjust to punish. (Leibniz, Theodicy?)
76. If a gas is heated, its temperature rises ; if its tempera-
ture rises, its elastic force increases ; if its elastic force increases,
the pressure on the walls of the containing vessel increases ;
therefore if a gas is heated, the pressure on the walls of the
containing vessel increases. (Ray.)
77. The end of human life is either perfection or happi-
ness ; death is the end of human life, therefore death is either
perfection or happiness.
QUESTIONS AND EXERCISES 369
78. If light consisted of material particles, it would possess
momentum ; it cannot consist of material particles, for it does
not possess momentum.
79. This person is very learned, and very sociable, hence it
follows that learning increases sociability.
80. Why advocate socialism? Until men become morally
perfect, it is impossible ; when they have become so, it will be
unnecessary. (Edinburgh.)
8 1. The diameter of the earth is, in round numbers, forty
millions of feet. Consequently the attraction of a sphere of the
same mean density as the earth, but one foot in diameter, will
be TTnnAnnnr P art the attraction of the earth ; that is, TRr ^ T5irTr
of the weight of the body attracted. Consequently, if we should
measure the attraction of such a sphere of lead, and find that
it was just ^TnnrWoT tnat f tne we ight of the body attracted,
we would conclude that the mean density of the earth was
equal to that of lead. But the attraction is actually found to
be nearly twice as great as this ; consequently a leaden sphere
is nearly twice as dense as the average of the matter composing
the earth. (Newcomb, Popular Astronomy?)
82. Mr. C. said that he was certain that the donors gave the
[noperty to the institution with a distinct and unanimous
understanding as to its future use. The directors who acted
for the institution in this transfer must necessarily have had an
understanding, either the same as that of the donors, or differ-
ent. If the understanding of the directors was the same as
that of the donors, then they, the former, were unquestionably
bound to live up to that understanding. If it was different,
then the property was conveyed on a misunderstanding, and
every dictate of honour and fair play would demand the return
of the property.
II
370 QUESTIONS AND EXERCISES
PART II. INDUCTIVE METHODS
CHAPTER XIII. The Problem of Induction
1. Explain why syllogistic logic is not a complete account
of the nature of thinking.
2. In what sense is it possible to lay down the laws of scien-
tific procedure?
3. In solving a complex scientific problem do we usually
employ but a single method ?
4. What can you say regarding the division of inductive
methods into methods of Observation, and methods of Expla-
nation ?
5. Would it be permissible to add Experimental methods as
a third and independent class?
6. What is the distinction between ' empirical ' and ' scien-
tific ' knowledge ?
7. What are the advantages to be derived from experiments
in scientific work ?
CHAPTER XIV. Enumeration and Statistics
1. What is the justification for beginning our account of the
inductive methods with Enumeration?
2. Explain what Jevons regards as 'Perfect' induction.
Has this process any right to the name?
3. For what purpose are statistics employed? To what
classes of phenomena are they applied ?
4. What is meant by a phenomenon?
5. Explain how statistics may suggest causal laws, or confirm
our expectation of them. May statistics also be used to dis-
prove a proposed law of causal connection? Illustrate your
answer.
QUESTIONS AND EXERCISES 3/L
6. Explain what is meant by the ' average/ and show how it
is obtained.
7. How does the procedure of insurance companies differ
from gambling?
CHAPTER XV. Causal Determination
1. What are the two main principles upon which the canons
proposed by Mill are founded ?
2. Give the Canon of the Method of Agreement, and illus-
trate its use.
3. 'I have noticed that A always precedes B, it is there-
fore the cause of B.' Is this good reasoning?
4. What is meant by the ' Plurality of Causes ' ?
5. Under what disadvantages does the Method of Agreement
labour? How is it supplemented?
6. State and illustrate the canon of the Method of Differ-
ence.
7. Why is this method applicable only to the spheres where
experiment can be employed? Would it be safe to depend
upon this method in determining the causes of social or politi-
cal conditions?
CHAPTER XVI. Causal Determination {continued)
1. Where do we employ the Joint Method?
2. What would it be necessary to establish in order to
prove inductively that some change in the tariff laws was
beneficial to the country?
3. ' One of the main characteristics of modern science is its
quantitative nature.' Explain.
4. How does the law of Concomitant Variations assist us in
determining causal relations ?
3/2 QUESTIONS AND EXERCISES
5. In what two ways may the Method of Residues be
applied ?
6. Mention some discoveries to which the investigation of
unexplained residues has led.
CHAPTER XVII. Analogy
1. Why do we include Analogy among the methods of Ex-
planation ?
2. What do you mean by Analogy? What is the principle
upon which it proceeds?
3. How is the word used in mathematical reasoning, and in
physiology ?
4. Into what Figure of the Syllogism does an argument
from Analogy naturally fall? Is the argument formally valid,
and if not, to what syllogistic fallacy does it correspond ?
5. Explain how Analogy may suggest a true law or explana-
tory principle.
6. Why do we speak of Analogy as Incomplete Explanation?
7. If all analogical reasoning yields only probability, is not
one analogy as good as another for purposes of inference ? If
not, upon what does the value of an inference from Analogy
depend ?
CHAPTER XVIII. The Use of Hypotheses
1. How do you distinguish the terms 'theory' and 'hy-
pothesis ' ?
2. What is an hypothesis, and how is it used?
3. Do hypotheses play any part in assisting Observation?
Explain and illustrate.
4. Give some instances in which hypotheses have proved
injurious, and have misled people regarding the nature ol
facts.
QUESTIONS AND EXERCISES 373
5. 'Hypotheses are formed by the imagination working in
dependence upon facts and guided by analogy.' Explain.
6. What are the steps in the proof of an hypothesis?
7. Explain what part is played by Induction and Deduction
respectively in using hypotheses.
8. What canons have been laid down to which a good hy-
pothesis must conform? Why are the first and third of these
rules of little value ?
9. Explain why an unverifiable hypothesis is not worth dis-
cussing.
CHAPTER XIX. Fallacies of Induction
1. What is the source of fallacy? How far is it true that the
study of Logic can protect us from fallacies ?
2. How do you classify Inductive Fallacies?
3. Explain and illustrate the following fallacies : Question-
begging Epithet, Equivocation, Fallacies due to Figurative Lan-
guage.
4. Explain and illustrate the tendency of the mind to neg-
lect negative cases.
5. Is it an easy matter to ' tell just what we saw and heard'
at a particular time ?
6. What do you mean by post hoc ergo propter hoc ? Why
may we take this as the general type of inductive fallacies ?
7. What did Bacon mean by the Idols of the Cave?
8. ' Every age, as well as every individual, has its idols.'
Explain this statement.
MISCELLANEOUS EXAMPLES
Analyze the examples of inductive reasoning given below,
and point out what methods are employed, indicating also
whether or not the conclusion is completely established :
374 QUESTIONS AND EXERCISES
1. In my experience A has been invariably preceded by B,
and we may therefore conclude that it is the cause of it.
2. Scarlet poppies, scarlet verbenas, the scarlet hawthorn,
fd,
and honeysuckle are all odourless, therefore we may conclude
that all scarlet flowers are destitute of odour.
3. What inference, if any, can be drawn from the follow-
ing statement : ' In nine counties, in which the population
is from 100 to 150 per square mile, the births are 296
to 100 marriages ; in sixteen counties, with a population
of 150 to 200 per square mile; the births are 308 to 100
marriages ' ?
4. The great famine in Ireland began in 1845 and reached
its climax in 1848. During this time agrarian crime increased
very rapidly, until, in 1848, it was more than three times as
great as in 1845. After this time it decreased with the return
of better crops, until, in 185 1, it was only 50 per cent more than
it was in 1845. ^ * s evident from this that a close relation
of cause and effect exists between famine and agrarian crime.
(Hyslop.)
5. Sachs maintained, in 1862, that starch is formed by the
decomposition in chlorophyl of carbon-dioxide gas under the
influence of light. He found that when all other conditions
were constant, and light was excluded from a plant, no starch
was formed ; the single circumstance of readmitting light was
accompanied by renewed formation of starch. Further, he
found that if certain portions of the leaves of an illuminated
plant were covered with black paper, no starch was found in
these portions.
6. Jupiter gives out more light than it receives from the sun.
What is the obvious conclusion, and by what method is it
reached ?
7. What methods would you employ in order to test the
truth of the proposition, omne vivum ex vivo ?
QUESTIONS AND EXERCISES 375
8. War is a blessing, not an evil. Show me a nation that
has ever become great without blood-letting.
9. If wages depend upon the ratio between the amount of
labor-seeking employment, and the amount of capital devoted
to its employment, the relative scarcity or abundance of one
factor must mean the relative abundance or scarcity of the
other. Thus capital must be relatively abundant where wages
are high, and relatively scarce where wages are low. Now, as
the capital used in paying wages must largely consist of the
capital-seeking investment, the current rate of interest must be
the measure of its relative abundance or scarcity. So if it be
true that wages depend upon the ratio between the amount of
labor-seeking employment, and the capital devoted to its em-
ployment, then high wages must be accompanied by low inter-
est, and, reversely, low wages must be accompanied by high
interest. This is not the fact but the contrary. (George.)
10. Construct an inductive argument to prove that some
article of food, or some habit, is beneficial or injurious to you,
and analyze your reasoning, showing the methods which you
have employed.
11. Some comets have been observed to have the same
orbits as certain meteoric showers. The hypothesis is suggested
that all meteoric showers may represent the debris of disinte-
grated comets. Biela's comet having been missing for some
time, it was accordingly predicted that when next due it would
be replaced by a meteoric shower. This prediction was verified
by observation.
12. Tyndall found that of twenty-seven sterilized flasks con-
taining infusion of organic matter, and opened in pure Alpine
air, not one showed putrefaction ; while of twenty-three similar
flasks, opened in a hay-loft, only two remained free from putre-
faction after three days. He concluded that putrefaction is
due to floating particles in the air.
376 QUESTIONS AND EXERCISES
13. 'Whether or not a bad theory is better than none,
depends upon circumstances.' Examine this statement, and
point out what are some of the circumstances of which mention
is made.
14. It is said that a general resemblance of the hills near
Ballarat in Australia to the Californian hills where gold had
been found suggested the idea of digging for gold at Ballarat.
(Minto.)
' 15. There are no great nations of antiquity but have fallen
to the hand of time ; and England must join them to complete
the analogy of the ages. Like them she has grown from a
birth-time of weakness and tutelage to a day of manhood and
supremacy ; but she has to face her setting. Everything that
grows must also decay. (Edinburgh, 1893.)
1 6. Goldscheider proved that muscular sensations play no
considerable part in our consciousness of the movements of our
1 limbs, by having his arm suspended in a frame and moved by
an attendant. Under these circumstances, where no work
devolved on his muscles, he found that he could distinguish as
small an angular movement of the arm as when he moved and
supported it himself.
17. Goldscheider also proved that the chief source of move-
ment-consciousness is pressure sensations from the inner sur-
face of the joints, by having his arm held so that the joint
surfaces were pressed more closely together, and finding that
a smaller movement was now perceptible.
1 8. Wages in the United States are higher than in England,
because the former country is a republic and has a protective
tariff.
19. It does not follow that an institution is good because a
country has prospered under it, nor bad because a country in
which it exists is not prosperous. It does not even follow that
institutions to be found in all prosperous countries, and not
QUESTIONS AND EXERCISES 377
to be found in backward countries, are therefore beneficial
For this at various times might confidently have been asserted
of slavery, of polygamy, of aristocracy, of established churches ;
and it may still be asserted of public debts, of private property
in land, of pauperism, and of the existence of distinctly vicious
or criminal classes. (George.)
20. Explain the procedure of the reductio ad absurdum form
of argument.
21. It may be a coincidence merely; but, if so, it is re-
markably strange that while the chloroform has not changed,
while the constitutions of the patients have not changed, where
the use of the inhaler is the rule there are frequent deaths from
chloroform ; whilst in Scotland and Ireland, where the use of
the inhaler is the exception, deaths are proportionally rare.
22. We should think it a sin and shame if a great steamer,
dashing across the ocean, were not brought to a stop at a signal
of distress from the mere smack. . . . And yet a miner is
entombed alive, a painter falls from a scaffold, a brakeman is
crushed in coupling cars, a merchant fails, falls ill and dies, and
organized society leaves widow and child to bitter want or
degrading alms. (George, Protection and Free Traded)
23. Manufacturing countries are always rich countries ;
countries that produce raw material are always poor. There-
fore, if we would be rich, we must have manufactures, and in
order to get them, we must encourage them. : . . But I could
make as good an argument to the little town of Jamaica . . .
in support of a subsidy to a theatre, I could say to them : all
cities have theatres, and the more theatres it has the larger the
city. Look at New York ! . . . Philadelphia ranks next to
New York in the number and size of its theatres, and therefore
comes next to New York in wealth and population. ... I
might then drop into statistics . . . and point to the fact that
when theatrical representations began in this country, its popu-
3/8 QUESTIONS AND EXERCISES
lation did not amount to a million, that it was totally destitute
of railroads, and without a single mile of telegraph wire. Such
has been our progress since theatres were introduced that the
census of 1880 showed we had 50,155,783 people, 90,907 miles
of railroad, and 291,212^ miles of telegraph wires. (George,
Protection and Free Trade.}
24. What methods would you employ to investigate the con-
nection between changes in the barometer and in the weather ?
25. In Sir Humphry Davy's experiments upon the decom-
position of water by galvanism, it was found that, besides
the two components of water, oxygen and hydrogen, an acid
and an alkali were developed at the two opposite poles of the
machine. The insight of Davy conjectured that there might
be some hidden cause of this portion of the effect : the glass
containing the water might suffer partial decomposition, or
some foreign matter might be mingled with the water, and the
acid and alkali be disengaged from it, so that the water would
have no share in their production. ... By the substitution of
gold vessels for glass, without any change in the effect, he at
once determined that the glass was not the cause. Employing
distilled water, he found a marked diminution of the quantity
of acid and alkali evolved ; yet there was enough to show that
the cause, whatever it was, was still in operation. . . . He
now conceived that the perspiration from the hands touching
the instruments might affect the case, as it would contain
common salt, and an acid and an alkali would result from its
decomposition under the agency of electricity. By carefully
avoiding such contact, he reduced the quantity of the products
still further until no more than slight traces of them were per-
ceptible. An experiment determined this : the machine was
put under an exhausted receiver, and when thus secured from
atmospheric influence, it no longer evolved the acid and the
alkali. (Gore, The Art of Scientific Discovery.)
QUESTIONS AND EXERCISES 379
26. Properties known to exist in potassium have been pre-
dicted of and found to exist in rubidium ; for instance, the
carbonates of sodium and potassium are not decomposed by
a red heat, neither are those of rubidium, or caesium. Some
of the statements which are true of chlorine have been found to
be true, in varying degrees, of bromine and iodine. . . . After
I had found the molecular change in antimony electro-deposited
from its chloride, I sought for and discovered it in that de-
posited from its bromide and iodide ; and after having found
magnetic changes in iron by heat, I also found similar ones in
nickel. (Gore, The Art of Scientific Discovery.}
27. What inductive fallacy may David be said to have
committed when he said in his haste that all men are liars?
28. It has been found that linnets when shut up and edu-
cated with singing larks the skylark, woodlark, or titlark
will adhere entirely to the songs of these larks, instead of the
natural song of the linnets. We may infer, therefore, that
birds learn to sing by imitation, and that their songs are no
more innate than language is in man. (Hyslop.)
29. We observe very frequently that very poor handwriting
characterizes the manuscripts of able men, while the best hand-
writing is as frequent with those who do little mental work
when compared with those whose penmanship is poor. We
may, therefore, infer that poor penmanship is caused by the
influence of severe mental labor. (Hyslop.)
30. Galileo describes his invention of the telescope as fol-
lows : This then was my reasoning ; this instrument [of
which he had heard a rumor] must either consist of one glass,
or of more than one ; it cannot be of one alone, because its
figure must be either concave or convex, or comprised within
two parallel superficies, but neither of these shapes alter in the
least the objects seen, although increasing or diminishing them ;
for it is true that the concave glass diminishes, and that the
380 QUESTIONS AND EXERCISES
convex glass increases them ; but both show them very indis-
tinctly, and hence one glass is not sufficient to produce the
effect. Passing on to two glasses, and knowing that the glass
of parallel superficies has no effect at all, I concluded that the
desired result could not possibly follow by adding this one to
the other two. I therefore restricted my experiments to com-
binations of the other two glasses ; and I saw how this brought
me to the result I desired. (Quoted by Gore, The Art of Scien-
tific Discovery?)
31. Darwin was struck by the number of insects caught by
the leaves of the common sun-dew. It soon became evident
to him that " Drosera was excellently adapted for the special
purpose of catching insects." ... As soon as he began to
work on Drosera, and was led to believe that the leaves ab-
sorbed nutritious matter from the insects, he began to reason
by analogy from the well-understood digestive capacity of ani-
mals. . . . Having by analogy established the power of di-
gestion in plants, analogy led him to seek in plants the elements
that do the work of digestion in animals. Bringing together
what was known of plants, he pointed out that the juices of
many plants contain an acid, and so on,e element of a digestive
fluid was at hand ; and that all plants possess the power of
dissolving albuminous or proteid substances, protoplasm, chlo-
rophyl, etc., and that " this must be effected by a solvent, proba-
bly consisting of ferment together with an acid." After writing
the last-quoted sentence, he learned that a ferment which con-
verted albuminous substances into true peptones had been
extracted from the seeds of the vetch. (Cramer, The Method
of Darwin.*)
32. Strongly impressed with the belief that some ' harmonic '
relation must exist among the distances of the several planets
from the sun, and also among the times of their revolution,
Kepler passed a large part of his early life in working out a
QUESTIONS AND EXERCISES 381
series of guesses at this relation, some of which now strike us
as not merely most improbable, but positively ridiculous. His
single-minded devotion to truth, however, led him to abandon
each of these hypotheses in turn so soon as he perceived its
fallacy by submitting it to the test of its conformity to observed
facts. . . . But he was at last rewarded by the discovery of
that relation between the times and the distances of the planet-
ary revolutions, which with the discovery of the ellipticity of the
orbits, and of the passage of the radius vector over equal areas
in equal times has given him immortality as an astronomical
discoverer. But ... he was so far from divining the true
rationale of the planetary revolutions that he was led to the
discovery of the elliptical orbit of Mars by a series of happy
accidents . . . whilst his discovery of the true relations of
times and distances was the fortunate guess which closed a
long series of unfortunate ones, many of which were no less
ingenious.
Now it was by a grand effort of Newton's constructive imagi-
nation, based on his wonderful mastery of geometrical reason-
ing, that, starting with the conception of two forces, one of
them tending to produce continuous uniform motion in a
straight line, the other tending to produce a uniformly acceler-
ated motion towards a fixed point, he was able to show that if
these dynamical assumptions were granted, Kepler's laws, being
consequences of them, must be universally true. And it was
his still greater glory to divine the profound truth that the fall
of the moon towards the earth that is the deflection of her
path from a tangential line to an ellipse is a phenomenon of
the same order as the fall of a stone to the ground. (Gore, The
Art of Scientific Discovery.}
33. After Franklin had investigated the nature of electricity
for some time, he began to consider how many of the effects
of thunder and lightning were the same as those produced by
382 QUESTIONS AND EXERCISES
electricity. Lightning travels in a zig-zag line, and so does an
electric spark ; electricity sets things on fire, so does lightning ;
electricity melts metals, so does lightning. Animals can be
killed by both, and both cause blindness. Pointed bodies
attract the electric spark, and in the same way lightning strikes
spires, and trees, and mountain tops. Is it not likely then that
lightning is nothing more than electricity passing from one
cloud to another, just as an electric spark passes from one sub-
stance to another ? (Buckley, A Short History of Natural
Science?)
34. How did Franklin proceed to verify the hypothesis
stated in the last example ?
35. Galileo discovered by means of his telescope that Jupi-
ter has four moons, instead of one like the earth, and he
regarded this discovery as a confirmation of the Copernican
theory. Explain the nature of the reasoning involved in
reaching this conclusion.
36. That the period of tide should be accidentally the same
as that of the culmination of the moon, that the period of the
highest tide should be accidentally the same as the syzygies, is
possible in abstracto ; but it is in the highest degree improb-
able : the far more probable assumption is, either that the sun
and moon produce the tide, or that their motion is due to the
same grounds as the motion of the tide. (Hibben.)
37. During the retreat of the Ten Thousand a cutting north
wind blew in the faces of the soldiers, sacrifices were offered
to Boreas, and the severity of the wind immediately ceased,
which seemed a proof of the god's causation. (Hibben.)
38. A nectary implies nectar, but Sprengel had come to the
conclusion that orchis morio and orchis maculata, though fur-
nished with nectaries, did not secrete nectar. Darwin examined
the flowers of orchis morio for twenty-three consecutive days,
looking at them after hot sunshine, after rain, and at all hours ;
QUESTIONS AND EXERCISES 383
he kept the spikes in water and examined them at midnight
and early the next morning. He irritated the nectaries with
bristles, and exposed them to irritating vapors. He examined
flowers whose pollinia had been removed, and others which
would probably have them soon removed. But the nectary
was invariably dry.
He was thoroughly convinced, however, that these orchids
require the visits of insects for fertilization, and that insects
visit flowers for the attractions offered in the way of nectar, and
yet that in these orchids the ordinary attraction was absent.
In examining the orchids he was surprised at the degree to
which the inner and outer membranes forming the tube or
spur were separated from each other, also at the delicate nature
of the inner membrane, and the quantity of fluid contained
between the two membranes. He then examined other forms
that do secrete nectar in the ordinary way, and found the mem-
branes closely united, instead of separated by a space. " I was
therefore led to conclude," he says, " that insects penetrate the
lax membrane of the nectaries of the above-named orchids and
suck the copious fluid between the two membranes." He
afterwards learned that at the Cape of Good Hope moths and
butterflies penetrate peaches and plums, and in Queensland a
moth penetrates the rind of the orange. These facts merely
proved his anticipation less anomalous than it had seemed.
(Cramer, The Method of Darwin?)
39. Construct an hypothesis to explain some fact of your
experience, and explain how it may be either verified or over-
thrown.
40. When Darwin began to work on Droscra he was led
to believe that the leaves absorbed nutritious matter from
insects. He then reasoned by analogy from the well-under-
stood digestive capacity of animals. He made preliminary
'crucial' experiments by immersing some leaves of Drosera
384 QUESTIONS AND EXERCISES
in nitrogeneous and others in non-nitrogeneous fluids of the
same density to determine whether the former affected the
leaves differently from the latter. This he found to be the case.
He then experimented with solid animal matter and found
that the leaves are capable of true digestion. Analogy then
led him to seek in plants the elements that do the work of
digestion in animals. He pointed out that the juices of many
plants contain an acid, and so one element of a digestive fluid
was at hand ; and that all plants possess the power of dissolving
albuminous or proteid substance-protoplasm, chlorophyl, and
that this must be effected by a solvent consisting probably
of a ferment together with an acid. Afterwards he learned
that a ferment which converted albuminous substances into
true peptones had been extracted from the seeds of the vetch.
(Cramer, The Method of Darwin, pp. 95-99.)
41. In opposition to the facts stated above, Tischutkin
maintains that the ' digestion ' of insectivorous plants is not
accomplished in the same way as in animals, but is due to
bacteria : that the pepsin is not a secretion of the plant, but
a by-product of the activity of the bacteria. Suppose that this
theory is true, and Darwin's false, what would you say regard-
ing the character of the latter's reasoning ?
PART III. THE NATURE OF THOUGHT
CHAPTER XX. Judgment the Elementary Process
1. What objections are there to speaking of thought as 'a
thing like other things ' ?
2. What is the general law of Evolution? Explain what is
meant by a change from the homogeneous to the heterogene-
ous.
3. What general conclusions are reached by the application
of the law of Evolution to the thought-process ?
QUESTIONS AND EXERCISES 385
4. What do you understand by Judgment? How does a
simple judgment differ from sensation?
5. In what sense may our judgments be said to be the union
of two concepts ?
6. Would the doctrine that in knowing we first have Simple
Apprehension, then as separate intellectual processes, Judgment
and finally Inference, agree with the general evolutionary view
of consciousness ? Explain fully.
CHAPTER XXI. The Characteristics of Judgment
1. What do you understand by the universality of judg-
ments? What is the distinction between the universality of a
judgment and that of a proposition?
2. How would you prove that all judgments are universal?
3. Is any judgment necessary in itself? If not, whence do
judgments derive their necessity?
4. What is the argument by which it has been maintained
that there must be judgments or principles which are in them-
selves necessary?
5. Explain how it is possible for a judgment to be at once
both analytic and synthetic.
6. Explain what is meant by a ' system ' of knowledge.
7. When judgment brings new facts into relation to what
we already know, does the old body of knowledge undergo any
modification ?
CHAPTER XXII. The Laws of. Thought
1. In what sense can we speak of a law of Thought?
2. Explain what is meant by the law of Identity.
3. How has this law been interpreted by Boole and Jevons?
4. What does Jevons mean by the ' substitution of similars,'
and how does he propose to employ this principle?
c
386 QUESTIONS AND EXERCISES
5. What objections are there to employing the sign of
equality to represent the relation between the subject and
predicate of a judgment?
6. Explain how the law of Identity is related to the charac-
teristics of judgment treated in the last chapter.
7. What is the meaning of the law of Contradiction?
8. Explain the use of the law of Excluded Middle.
CHAPTER XXIII. Types of Judgment
1. Why do we begin with judgments of Quality?
2. Explain how we pass in the development of intelligence
from Quality to Quantity.
3. In what sense is it true that judgments of Quantity never
give us the real nature of things, but only their relation to
something else?
4. What is meant by anthropomorphic causes? How are
they distinguished from scientific causes?
5. What new element did the discovery of the law of the
Conservation of Energy introduce in the causal conception as
employed in certain sciences?
6. Why cannot this new extension have any application in
the field of the mental sciences?
7. How does the standpoint of judgments of Individuality
differ from that of judgments of Causality ?
CHAPTER XXIV. Inference
1. How does Inference differ from Judgment? In what
sense may it be said that it is an extension of the latter pro-
cess?
2. Does the passage from Judgment to Inference illustrate
the general law of Logical Evolution? Explain,
a
QUESTIONS AND EXERCISES 387
3. In the development of our knowledge, which usually
comes first, premises or conclusion?
4. How is it possible to pass from the known to the un-
known ?
5. Explain under what circumstances only an Inference is
possible.
6. What is the common element in both Induction and
Deduction? How do they differ?
CHAPTER XXV. Rational and Empirical Theories
1. Who are the great historical representatives respectively
of Rationalism and Empiricism ?
2. Explain the method and procedure of Rationalism.
3. What is the great instrument of knowledge according to
Rationalism ? What according to Empiricism ?
4. State as clearly as you can the various points at issue
between the two schools.
5. Explain Mill's theory that we always reason from one
particular fact to another. How far do you agree with his
conclusions ?
6. Is it true that we obtain a general law by summing up
particulars ?
7. Is there any direct and necessary connection between the
number of instances and the induction of the general law?
8. Criticise Jevon's theory of 'Perfect Induction' as stated
on page 187.
INDEX
Abstract, two Meanings of the Word,
Si-
Accent, the Fallacies of, 156.
Accident, the Fallacy of, 163.
Agreement, the Method of, 200; De-
ficiencies in the Method of, 204.
Amphiboly, the Fallacy of, 156.
Analogy, Explanation by Means of,
219; the Principle of, 221; State-
ment of Law, 222; its Function in
suggesting Hypothesis, 223 ; its Use
by Darwin, 225 ; its Incompleteness
as a Method of Explanation, 226.
Analysis, its Relation to Synthesis, 279.
Anthropomorphism, 309.
Apprehension, Simple, 44.
A priori Truths, 278.
Argumentum, ad rcm, 168 ; ad homi-
nem, 168 ; adpopulum, 169 ; ad igno-
rantiam, 169; ad verecundiam, 170.
Aristotle, Logic of, 22 ; List of Logical
Works, 22 ; his Theory of the Syllo-
gism, 23 ; Importance of Induction
and Deduction in his Logic, 25 ; his
Classification of Fallacies, 152; his
Statement of the Law of Contradic-
tion, 295.
Art, an, its Relation to a Science, 8.
B
Bacon, Logic of, 28 ; his Method, 28 ;
on the Tendency to neglect Negative
Instances, 257 ; his Idols of the Cave,
257-
Bosanquet, his Views of Logic, n, note ;
his Writings on Modern Logic, 17 ;
his Remarks on Analogy, 227.
Bradley, 12.
Cant Words and Phrases, 249.
Causal Connection, Judgments of, 307.
Cause, the Fallacy of the False, 171 ;
the Development of the Principle of,
309.
Causes, the Plurality of, 204.
Chances, the Calculation of, 194.
Circle, Argument in a, 165.
Classification, Principles of, 74 ; Rules
of, 76; of Fallacies, 152, 246; Aris-
totle's, of Fallacies, 152.
Composition, the Fallacy of, 160.
Concepts and Judgments, 268.
Conclusion, the Irrelevant, 168.
Concrete, two Senses of the Word,
Si-
Consequent, Fallacy of the, 170.
Conservation of Energy, the Law of,
and its Influence on the Conception
of Cause, 313.
Contradiction, the Law of, 38, 295.
Conversion, the, of Propositions, 100;
Simple, 101 ; by Limitation, 101 ;
by Contraposition, 102; Errors in,
Darwin, his Power of arresting Ex-
ceptions, 217 ; his Use of Analogy,
225 ; his Employment of Hypotheses,
232.
Deduction, its Relation to Induction,
329.
Definition, the Necessity of, 63 ; Verbal
and Real, 63; Ways of Regarding,
64 ; Socrates' Search for, 65 ; Rules
of, 69.
Descartes, 29, 335.
Dialectic, Socrates' Use of, 65.
Dichotomy, 72.
Difference, Method of, 205.
Differentia, 68.
Dilemma, the simple Constructive, 149 ;
the Complex Constructive, 150; the
Complex Destructive, 150.
389
390
INDEX
Division, Rules for, 76 ; the Fallacy of,
162.
Empiricism, the Doctrine of, 337.
Enthymemes, 41, 126.
Enumeration, as the Starting-point of
Induction, 185; Judgments of, 305.
Episyllogisms and Prosyllogisms, 127.
Equivocation, the Fallacies of, 159.
Ethics, its Standpoint compared with
that of Psychology, 316.
Euler, no.
Evolution, the Law of, 262 ; the Appli-
cation of the Law of, to Thought, 264.
Excluded Middle, the Law of, 72, 297.
Experiment and Observation, 180;
Advantages of employing, 180.
Explanation and Observation, 177 ; the
Problem of, 182.
Extension and Intension of Terms, 55.
Fallacies, Classification of, 152, 246;
Syllogistic, 149 ; Inductive, 245 ; the
Source of, 245; of Interpretation,
154 ; occasioned by Language, 246 ;
of Reasoning, 157, 254 ; of Observa-
tion, 250; Individual, 257.
Figures of the Syllogism, 113; the
Special Canons of the four, 1 17 ; De-
termination of the Valid Moods in,
120; the Perfect, 123 ; the Imperfect,
123 ; Reduction of, 123 ; the Organic
Relation of, 125, note.
Galen, 123.
Generalization, Danger of hasty, 256.
Genus, its Definition, 68.
Guericke, 239.
H
Hegel, Quotation from his Logic, n;
his Influence on the Development of
Logic, 31.
Herschel, J., 30.
Hypothesis, Reasoning from an, 230;
the Employment of, to explain Com-
mon Events, 231 ; Darwin's Use of,
232; the Necessity for an, 233;
Formation of, 234 ; the Function of
Analogy in suggesting, 223, 236 ; the
Proof of, 237; Requirements of a
Good, 240.
I
Identity, the Law of, 38, 288; Je-
vons's Interpretation of the Law of,
289.
Ignoratio Rlenchi, 166.
Imagination, its Part in the Formation
of Theories, 234.
Individuality, Judgments of, 315.
Induction and Deduction, 2, 24, 329;
the Baconian Method of, 28 ; Mill's
Emphasis on, 31; the Problem of,
172; Perfect and Imperfect, 187.
Inference, Mediate and Immediate, 92 ;
the Nature of, 324 ; as distinguished
from Judgment, 318 ; the Paradox
of, 325 ; as a Development of Judg-
ment, 328 ; and Number of Instances,
344. (See also Reasoning.)
Instances, the Value of Numerous, 345.
Intension and Extension of Terms, 55.
Interpretation, of Propositions, 92;
Errors of, 154 ; Judgment a Process
of, 266.
J
James, 7.
Jevons, his Account of Perfect Induc-
tion 187 ; his Calculation of Chances,
195; his Interpretation of the Law
of Identity, 289; his Principle of the
Substitution of Similars, 289.
Judgment, the Starting-point of Know-
ledge, 266; as a Process of Inter-
pretation, 267 ; and Concept, 268 ;
the Universality of, 274 ; the Neces-
sity of, 276; a priori, 279; as involv-
ing both Analysis and Synthesis,
279; as constructing a System of
Knowledge, 284; its Relation to In-
ference, 318.
Judgments, of Quality, 300; of Quan-
tity, 304 ; of Enumeration, 305 ; ol
Measure, 305 ; of Causal Connec-
tion, 307 ; of Individuality, 315.
INDEX
391
Ladd, 7.
Language, Dangers from the Careless
Use of, 6 1 ; Fallacies of, 246 ; Figura-
tive, 249.
Law, of Identity, 38, 288 ; of Contra-
diction, 38, 295 ; of Excluded Mid-
dle, 72, 297; of Conservation of
Energy, 313.
Laws of Thought, 38, 72, 288.
Locke, as the Representative of Em-
piricism, 30, 335 ; on the Careless
Use of Words, 61, 247.
Logic, Definition of, i ; Derivation of
the Word, 3 ; Relation to Psychol-
ogy, 4 ; Comparison with Physiology,
6 ; as a Science and an Art, 8 ; Util-
ity of, 10; Necessity of, 12; the
Materials of, 13 ; of the Sophists, 18 ;
of Socrates, 19; of Aristotle, 22, 32;
of the Schoolmen, 26; of Bacon, 28 ;
Development of Modern, 31 ; the
Equational, 289.
Lyell, his Overthrow of the ' Catas-
trophic ' Theory in Geology, 243.
M
Malthus, his Theories of Population,
168, 225.
Measure, Judgments of, 305.
Mental Operations, proposed Division
of, 43-
Metaphors, Dangers from the Use of,
250.
Method, the Progressive or Synthetic,
128 ; the Regressive or Analytic, 128 ;
the, of Agreement, 200; the, of Dif-
ference, 205 ; the Joint, of Agreement
and Difference, 209 ; the, of Con-
comitant Variations, 211 ; the, of
Residues, 213.
Middle Term, the Function of the, 106 ;
Ambiguous, 160.
Mill, his Importance in the History of
Logic, 30 ; his Experimental Meth-
ods, 198 ; his View of the Nature of
General Principles, 339; his Doc-
trine that all Reasoning is from one
Particular Case to another, 340.
Morphology, compared with Psychol-
ogy, 8.
N
Negative Instances, Tendency to neg-
lect, 251.
Neptune, the Discovery of, 217.
Newton, his Care in testing Theories,
239-
Non sequitur, 170.
O
Observation, and Explanation, 177;
and Experiment, 180; Errors of,
250.
Obversion, the, of Propositions, 98 ;
Errors in, 155.
Opposition, the, of Propositions, 94.
Perception, as involving Judgment,
266 ; Difficulty in distinguishing be-
tween Inference and, 253.
Petitio Principii, 165.
Physiology compared with Logic, 6.
Plato, in the History of Logic, 22 ; and
the Doctrine of Reminiscence, 325.
Post hoc propter hoc, 171, 255.
Predicables, the, 67.
Prejudices, Individual, 257 ; of an Age,
258.
Premises, Definition of, 40.
Presumption, Fallacies of, 164.
Propositions, Categorical, 79; Condi-
tional, 79 ; the Nature of, 78 ; Qual-
ity and Quantity of, 80; Difficul-
ties in classifying, 83; Relation of
Subject and Predicate in, 85; the
Opposition of, 94 ; the Obversion of,
98 ; the Conversion of, 100.
Psychology, its Relation to Logic, 4;
Comparison with Morphology, 6;
Comparison with Ethics, 316.
Quality, of Propositions, 80; Judg-
ments of, 300.
Quantity, of Propositions, 80; Judg-
ments of, 304.
Quaternio Terminorum, 158.
392
INDEX
Question, the Fallacy of the Complex,
166.
Question-Begging Epithet, 248.
R
Rationalism, its Point of View, 335;
the Nature of its Problems, 336 ; its
Neglect of Perception, 337.
Reasoning, the Nature of Syllogistic,
105; Mediate, 92, 107; Immediate,
93 ; Mistakes in, 254 ; Inductive and
Deductive, 329 ; from Particulars to
Particulars, 340 ; from Particulars to
a Universal, 344. (See also Infer-
ence.)
Reduction of the Imperfect Figures,
123.
Residues, the Method of, 213.
Schonbein, his Discovery of Ozone,
217.
Science, as related to Art, 8.
Sigwart, on the Difference between
Ancient and Modern Science, 190;
on the Application of Statistics, 191.
Similars, the Principle of the Substitu-
tion of, 289.
Socrates, his Sense of Ignorance, 4; his
Place in the History of Logic, 20;
his Search for Definitions, 65 ; his
Employment of Dialectic, 66.
Sophists, the Logic of, 19; Socrates'
Refutation of, 20; Plato's Criticism
of their Theory of Knowledge, 22;
their Scepticism, 275.
Sorites, Aristotelian, 131 ; Goclenian,
Species, Definition, 68.
Spinoza, as a Rationalist, 336.
Statistics, 189.
Stout, 7.
Subject, Relation of Predicate and, 85.
Syllogism, the Aristotelian, 23, 32; the
Nature of the, 36; the Principle of
the, 38 ; the Parts of the, 39 ; the
Rules of the, 103 ; the Figures of the,
113 ; the Hypothetical, 136 ; Rules for
the Hypothetical, 137 ; Relation of
Categorical and Hypothetical, 139;
the Disjunctive, 145 ; Fallacies of the
Disjunctive, 148.
Synthesis, its Relation to Analysis, 279.
System, Difference between a, and an
Aggregate, 285.
Thales, 310.
Thought, the Laws of, 38 ; the Nature
of, 260.
Torricelli, 238.
V
Variations, of Statistics, 193; the
Method of Concomitant, 211.
W
Whewell, 15, 30.
Words, the Abuse of, 61, 246.
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