PEACTICAL LOGIC;
OR, THE
AET OF THINKING.
BY
D. S. GREGORY, D.D..
PRESIDENT OF LAKE FOREST UNIVERSITY.
Of THE
UNIVERSITY
or
NEW YORK AND PHILADELPHIA
HINDS, NOBLE & ELDREDGE
WFFITT
J^AX
Entered, according to Act of Congress, in the year 1881, by
ELDREDGE & BROTHER,
In the Office of the Librarian of Congress, at Washington.
PREFACE.
"VTEXT to right and noble living, which is the highest thing
•U* to which man may aspire, may be placed the right think-
ing which is essential to such living. Logic, as the Science
of the Laws of Thought, is very widely studied, in the higher
schools, as an aid to the pupil in thinking ; yet it is the set-
tled conviction of many of the best educators that this Sci-
ence, as it is ordinarily presented, does very little toward
training to think or preparing for thinking. In short, there
seems to be a growing feeling that it rather serves, in case
of the average mind, to cram the memory and paralyze the
thinking powers. The author of this volume shares to some
extent in this conviction and feeling; hence the present
attempt to construct a Practical Logic, by the use of which
intelligent teachers may train inquiring minds to correct
thinking.
The only way to learn to think is by thinking; the only
way of training a pupil to think is by making him practise
thinking. Assuming the correctness of this principle, Logi-
cal Praxis is made the prominent and essential feature of
the work. Each principle of thought is turned into a Rule,
iii
215264
IV PREFACE.
and then made part of the mental property and power of the
student by abundant exercises.
The best training in thinking must be intelligent and sys-
tematic. Accordingly the foundation for this is laid by a
comprehensive and systematic presentation of the forms and
laws of thinking. The processes of formation and unfolding,
of involution and evolution, are presented in succession. Be-
ginning with the simplest process of observation, the praxis
is carried, by successive stages, up to the highest and most
complex processes of constructive thinking, and the mind
capable of such work trained intelligently and systematically
to clear, distinct, connected, continuous, and constructive
thought.
To the various writers on the subject of Logic, the author
would acknowledge his indebtedness, and especially to Ueber-
weg, Hamilton, Thomson, Whately, Mill, Jevons, Atwater,
McCosh, Davis, Bowen, and Day.
To teachers he would suggest that Part I. may be used
in the earlier stages of training, and the remaining parts
reserved for a later stage. In the use of the text-book
the teacher will ordinarily do his best work for his pupil by
drawing largely on his own resources for material for praxis.
Each locality, school-room, branch of study, and experience
will suggest innumerable topics of fresh and living interest,
which may be profitably substituted for those given in the
text-book.
D. S. GREGORY.
LAKE FOREST UNIVERSITY, 1
LAKE FOREST, ILL., August, 1881. )
1
INTRODUCTION.
PAGE
I.— NATURE OF LOGIC 9
TOPIC 1. — OBJECT-MATTER OP LOGIC 10
TOPIC 2. — PRACTICAL AIM OP LOGIC .... 13
TOPIC 3. — PRINCIPLES OR LAWS OF THOUGHT . . .17
II.— DIVISIONS OF LOGIC 22
PART I.
The Logic of Conception or the Term.
CHAPTER I.
THE FORMATION OF CONCEPTIONS . . 25
SECTION I.— OBSERVATION 26
TOPIC 1. — THE PREDICABLES OR THINGS KNOWABLE . 27
TOPIC 2. — OBSERVATION OF THINGS PREDICABLE . . 30
SECTION II. — CONCEPTION PROPER 34
TOPIC 1. — PROCESS OP CONCEPT-FORMING . . . .34
TOPIC 2. — PRODUCT OP CONCEPT-FORMING. . . .38
SECTION III.— CLASSIFICATION 41
TOPIC 1. — PROCESS OP CLASSIFICATION . . . .41
TOPIC 2. — EESULTS OP CLASSIFICATION .... 44
SECTION IY. — DENOMINATION OR NAMING . . .49
TOPIC 1. — PROCESS OF NAMING 49
TOPIC 2. — PRODUCTS OF NAMING 52
1* v
VI CONTENTS.
CHAPTER II.
PACK
THE UNFOLDING OF CONCEPTIONS . . 56
SECTION I.— LOGICAL PARTITION 57
TOPIC 1. — FORMS OP LOGICAL PARTITION . . . .59
TOPIC 2— RULES OP LOGICAL PARTITION . . . .60
SECTION II. — LOGICAL DIVISION 64
TOPIC 1. — FORMS OF LOGICAL DIVISION . . . .65
TOPIC 2.— RULES OP LOGICAL DIVISION . . . .68
SECTION III.— LOGICAL DEFINITION 75
TOPIC 1.— KINDS OP DEFINITION 75
TOPIC 2.— RULES OF LOGICAL DEFINITION , 81
PART II.
The Logic of Judgment or the Proposition.
CHAPTER I.
THE FORMATION OF JUDGMENTS OR PROP-
OSITIONS 93
SECTION I.— PROCESS or JUDGMENT-FORMING . . 93
TOPIC 1. — THE ELEMENTS OP JUDGMENT . . . .93
TOPIC 2. — VERIFICATION OR PROOF OF JUDGMENTS . . 98
SECTION II. — PRODUCTS OF JUDGMENT .... no
TOPIC 1. — QUALITY OF JUDGMENTS Ill
TOPIC 2. — QUANTITY OF JUDGMENTS 112
TOPIC 3. — RELATION OF JUDGMENTS 116
TOPIC 4. — GRAMMATICAL COMBINATION OF JUDGMENTS . 118
CHAPTER II.
THE UNFOLDING OF JUDGMENTS. . . 121
SECTION I.— DEVELOPMENT OF CONTAINED JUDG-
MENTS 121
SECTION II. — DEVELOPMENT OF IMPLIED JUDGMENTS 123
TOPIC 1. — SIMPLER FORMS OP IMPLICATION . . . 123
TOPIC 2. — OBVERSION . . 123
CONTENTS. vii
PAGE
SECTION III. — DEVELOPMENT OF INFERRED JUDG-
MENTS 125
TOPIC 1. — INFERRED JUDGMENTS BY ADDITIONS . . 126
TOPIC 2. — INFERRED JUDGMENTS BY DISJUNCTION . . 126
TOPIC 3. — INFERRED JUDGMENTS BY CONVERSION . . 126
TOPIC 4. — INFERRED JUDGMENTS BY OPPOSITION . 128
PART III.
The Logic of Reasoning or the Syllogism.
CHAPTER I.
THE FORMATION OF REASONING OR MEDI-
ATE INFERENCES . . . .135
SECTION I. — PROCESS OF REASONING IN GENERAL . 135
TOPIC 1. — FORMS OF REASONING 135
TOPIC 2. — ELEMENTS OF REASONING 137
TOPIC 3. — FINDING AND VERIFYING ARGUMENTS . . 139
SECTION II.— DEDUCTIVE REASONING . . . .139
TOPIC 1. — PROCESS OF VERIFYING THE ARGUMENT IN DE-
DUCTION 139
TOPIC 2. — PRODUCTS OF DEDUCTIVE REASONING . . 141
SECTION III.— INDUCTIVE REASONING .... 147
TOPIC 1. — VERIFYING CAUSE IN INDUCTION . . . 147
TOPIC 2. — PRODUCTS OF INDUCTIVE REASONING . . 157
CHAPTER II.
THE UNFOLDING OF REASONING OR THE
SYLLOGISM 162
SECTION I. — THE CATEGORICAL SYLLOGISM UNFOLDED 162
TOPIC 1.— POSSIBLE FORMS OR FIGURE AND MOOD . . 162
TOPIC 2. — TESTING OF VALID FORMS 164
TOPIC 3.— COMPLEX AND ABNORMAL FORMS . . . 179
SECTION II.— THE HYPOTHETICAL SYLLOGISM UN-
FOLDED 185
TOPIC 1. — CONDITIONAL OR CONJUNCTIVE SYLLOGISM . 185
Vlll CONTENTS.
PAGE
TOPIC 2. — DISJUNCTIVE SYLLOGISM 188
TOPIC 3. — DlLEMMATIC SYLLOGISM 189
SECTION III.— CONSPECTUS OF FALLACIES . . .191
TOPIC 1. — FALLACIES IN INDUCTION 191
TOPIC 2.— FALLACIES IN DEDUCTION . . 192
PART IV.
The Logic of Construction or the System.
CHAPTER I.
THE FORMATION OF CONSTRUCTION OR
SYSTEM ..... 200
SECTION I.— SCIENTIFIC CONSTRUCTION . . . .200
TOPIC 1. — PROCESS OF FORMING AND VERIFYING SCIEN-
TIFIC SYSTEM 200
TOPIC 2. — PRODUCTS OF SCIENTIFIC CONSTRUCTION . . 202
SECTION II.— PRACTICAL CONSTRUCTION . . .206
TOPIC 1. — PROCESS OF FORMING AND VERIFYING PRAC-
TICAL SYSTEM 206
TOPIC 2. — PRODUCTS OF PRACTICAL CONSTRUCTION . . 207
CHAPTER II.
THE UNFOLDING AND TESTING OF SYSTEMS. 207
SECTION I.— ASCERTAINING THE ELEMENTS. . . 208
TOPIC 1. — THE WHOLE AND ITS PRINCIPLE . . . 208
TOPIC 2. — THE ARTICULATION OR KELATION OF THE PARTS 209
TOPIC 3. — THE RELATION TO THE OBJECTIVE REALITY . 209
SECTION II.— TESTING OF SYSTEMS 210
TOPIC 1. — DIRECTIONS FOR TESTING 210
TOPIC 2.— EXAMPLES ILLUSTRATIVE , .211
INDEX 213
PRACTICAL LOGIC,
INTRODUCTION.
I. THE NATURE OF LOGIC.
What is Logic? — This question has been variously
answered. Whately says it may be considered as " the
Science and also as the Art of Reasoning." Hamilton de-
fines it as " the Science of the formal and necessary Laws
of Thought as Thought." Dr. Watts called his work, " The
Art of Thinking." According to his view, " Logic is the
art of directing the reason aright in acquiring the knowl-
edge of things, for the instruction both of ourselves and
others."
Without stopping to discuss these definitions, which would be un-
intelligible to the ordinary student at the outset, it is clear that these
different authors must either be defining different things, or defining
the same thing from different points of view, or defining different
things from different points of view. "Reasoning" and "thought"
are different things, the former being only one form of the latter.
The points of view of science and art are different, the one being
theoretical, the other practical.
Definition. — As treated in the present work, Logic is the
Q
10 PRACTICAL LOGIC.
Practical Science of the Principles or Laws which govern
the various forms of correct Thinking or Thought.
This definition will be best explained by considering the
following Topics :
Topic I —The Object-Matter of Logic,
Topic II— The Practical Aim of Logic,
Topic III— The Principles or Laws of Thinking or Thought,
Topic First. — The Object-Matter of Logic is found in
the Forms of Thinking or Thought.
1. What is Thinking or Thought ?
(1.) In a loose sense, any operation of the human soul is
sometimes spoken of as thought. The man knows, feels and
purposes or wills; any act of knowing, feeling, or willing
may, in this loose sense, be called thinking. The term is
evidently not used in this loose sense in the definition of
Logic.
(2.) In a stricter sense, thinking or thought is confined
to the operations of the intellect or power of knowing.
In popular phrase, it is any act of the head as distinguished
from the heart and will of the man. In this sense, "think-
ing " is synonymous with " knowing."
The main office of the human intellect is to know, i. e., first, to
apprehend objects in themselves and their phenomena or attributes ;
and secondly, to apprehend objects or their phenomena in their con-
nections or relations. The first of these forms may be termed simple
apprehension, or intuition, or simple knowledge ; the second, thought-
knowledge, or thought. Logic has to do with thought-knowledge, or
thought.
To state the same thing in another and fuller form, the cognitive
power or intellect of man performs its entire office of knowing in
four different ways ; in other words, it has four different faculties :
1st. The intellect acquires the fundamental facts of knowledge of
things material and spiritual by the senses and consciousness ; and
has, therefore, a simple cognitive faculty. Its office is to gather the
material for the use of the higher faculties of thought.
THE NATURE OF LOGIC. 11
2d. The intellect keeps the acquired knowledge in such shape as to
be able to reproduce it for use at any time when it may be needed by
the higher faculties ; and has, therefore, a conservative faculty or
memory.
These two faculties furnish knowledge and keep it at command for use,
and their operations are often spoken of, in a loose sense, as thought ;
but, using thought in the strict sense, it is often truly said of one who
uses these two powers with great ease, " He never had a thought in
his life. He is a mere man of memory.''
3d. The intellect compares the knowledges acquired and conserved,
and connects them into conceptions, judgments, and arguments ; and
has, therefore, a comparative, or elaborative, faculty.
4th. The intellect groups in systems, according to the law of the
true, the beautiful, or the good, the knowledges acquired by the simple
cognitive faculty, kept and reproduced by the conservative faculty,
and connected in thought by the comparative faculty ; and has, there-
fore, a system-making, or constructive, faculty. This is also discursive.
The term " thinking" or " thought " is often applied to all four forms
of intellectual action. This is evidently not the sense in which it is
used in the definition of Logic.
(3.) Thought or thinking, strictly speaking, is the opera-
tion or product of the operation of the third and fourth fac-
ulties only, i. e., of the comparative and constructive facul-
ties only. These faculties are the thought faculties ; their
operation is thinking ; and the product of their operation is
thought. Ordinarily, the word thought is used for any or
all three : the faculty, its exercise, its product. These fac-
ulties are also called discursive, since they proceed from
simple knowledges to new results founded upon them.
2. What are the Forms of Thinking or Thought ?
The forms of thinking or thought are the forms in which
the discursive or thought faculties act, or the products of
that action.
(1.) As thinking is embodied in language, the most common forms
of thought may be learned by an examination of thought expressed
in language. Take the following example : Light is opposed to dark-
ness ; feathers are light ; therefore, feathers are opposed to darkness.
12 PRACTICAL LOGIC.
This is in the form of a syllogism. A syllogism embodies an argu-
ment, or process of reasoning. In it two propositions are compared
and a conclusion reached which is expressed in a third proposition.
This is thought as reasoning.
These three propositions are verbal expressions of judgments, in
which the mind compares and connects two terms. This is thought
as judgment.
Each of the terms in these propositions is a thought, and must be
understood, as is shown by the example given, if any correct think-
ing is to be done. This is thought as conception.
When a series of terms, propositions, arguments, etc., is grouped
together to make a larger whole of thought, the result is thought as
system.
(2.) Or looking at the subject from the thought side, instead of
from the language side, the same result is reached.
The comparative faculty acts in three ways : a. By comparing the
objects or knowledges, given by the simple cognitive faculty and re-
tained by the conservative faculty, and connecting them by resembling
attributes or marks, thus forming notions or concepts, classes and
general terms. This is thought as conception, b. By comparing
concepts or general terms and connecting them by agreement or dis-
agreement, resulting in judgments and propositions. This is thought
as judgment, c. By comparing judgments or propositions and connect-
ing them by the principle of reason and consequent, resulting in argu-
ments including syllogisms. This is thought as reasoning.
The constructive faculty also acts in three ways : a. Grouping by
the Law of the True, or in the form of scientific construction, result-
ing in scientific systems, b. Grouping by the Law of the Beautiful,
or in the form of artistic or aesthetic construction, resulting in artistic,
or aesthetic, systems, including all art productions, c. Grouping by
the Law of the Good, or in the form of practical construction, result-
ing in practical systems, including inventions, plans of conduct, etc.
It will at once be seen that the second of these forms of construc-
tion falls within the sphere of ^Esthetics, leaving only the first and
third in the sphere of Logic.
The distinct Forms of Thought with which Logic deals
are, therefore, as follows :
Conception, embodied in the general term ;
Judgment, embodied in the proposition ;
THE NATURE OF LOGIC.
13
Reasoning1, embodied in the argument ;
Construction, embodied in system, scientific and prac-
tical.
The facts concerning the workings of the Human Soul may be tabu-
lated so as to present their relations to the eye.
THE HUMAN SOUL,
or Man, the Conscious
Subject,
Man, by the COGNI-
TIVE POWER,
KNOWS, and, therefore, has a Cog-
nitive Power, or Intellect ;
FEELS, and, therefore, has an Emo-
tive Power, or Sensibility ;
WILLS, and, therefore, has a power
of Endeavor, or Conative Pow-
er, or Will.
ACQUIRES knowledges by the Simple
Cognitive Faculty ;
KEEPS knowledges by the Conserv-
ative Faculty, or Memory ;
COMPARES knowledges, or works out
their Relations by the Comparative
Faculty ;
CONSTRUCTS knowledges into Systems
by the Constructive Faculty.
s ~
9 ^
' •*
I
1 5-
COMPARES, by
the Compara-
tive Faculty,
MAN, by the
DISCURSIVE •
Faculties,
CONSTRUCTS, by
the Construct-
ive Faculty,
Simple knowledges, in Con-
ception ;
Conceptions, in Judgment ;
Judgments, in Reasoning.
The True, in Scientific Sys-
tem;
The Beautiful, in .Esthetic
System ;
The Good, in Practical Sys-
tem.
Topic Second. — The Practical Aim of Logic is to train to
Correct Thinking or Thought.
Logic, as here treated, is a practical science, aiming to
lead the thinker to a systematic knowledge of the laws of
2
1 PRACTICAL LOGIC.
thought, in order to find in these the rules by which to
train to skill in right thinking-.
1. What is Practical Science or Art?
A science is a complete and systematic presentation of the facts and
principles in any sphere of knowledge, in accordance with truth.
Hamilton draws from Aristotle the distinction between Philosophy
" Theoretical " and " Practical." " Theoretical, called likewise specu-
lative and contemplative, philosophy has for its highest end mere
truth or knowledge. Practical philosophy, on the other hand, has
truth or knowledge only as its proximate end, — this end being subor-
dinate to the ulterior end of some practical action." Notwithstanding
Hamilton's objections to the expressions, they are in common use, and
will doubtless continue in use. "Science" and "Art" are also often
used to express substantially the same distinction.
The sciences and arts are both systematic forms of human knowl-
edge. The aim of a science is to give systematic knowledge of some-
thing ; that of an art, to give skill in doing something. The one calls
for the study of scientific principles ; the other for the intelligent appli-
cation to practice of rules based upon these principles. A science pre-
sents truths to be grasped ; an art, exercises to be performed.
Practical Science, or Art, as it is sometimes called, is a
form of science in which the systematic knowledge of the
subject treated is subordinate to the training to skill in
some activity.
2. How far is Logic Theoretical and how far Practical ?
Logic is a theoretical science, or science proper, so far
as it aims to give a systematic view of the laws of thought ;
it is a practical science, or art, so far as it subordinates
this to its aim to train to skill in applying the laws of
thought in avoiding error and arriving at truth. From the
scientific side, Logic should present in systematic shape the
laws which govern the various forms of thought, or the laws
by which the mind must be governed when it thinks cor-
rectly, i. e., when it conceives, judges, reasons, systematizes
correctly. From the practical side, Logic should turn these
THE NATURE OF LOGIC. 15
laws into rules and train the mind to think correctly and
efficiently, by training it to use these rules of thought intel-
ligently and skilfully. It should, if it is to be of the most
service, train the thinker at once to accuracy of thought in
reaching truth and avoiding error, and to power in using
the thought-faculties, — in other words, it should train both
to skill and power. In accordance with this view, Pro-
fessor Bain remarks, that although " Logic, no doubt, has a
certain theoretic aspect, ... its chief aim must ever be
practical. Had the subject not been wanted as an aid to
the search of truth, it would never have been called into
existence."
3. Logic aims at Correct Thinking, or at Truth.
Logic is defined, in the " Port Eoyal Logic," as " the
science of the operations of the understanding in the pur-
suit of truth." Logic aims at correct thinking. Such
thinking is, from one point of view, thinking that is done
in accordance with the laws of thought which are treated
in works on Logic. From another point of view it is think-
ing which, by conformity to the laws of thought, arrives at
truth.
(1.) Truth. — In order to understand the meaning of these statements
concerning truth, there is need of considering : the nature and crite-
rion of truth ; the modes of arriving at truth ; the degrees of assur-
ance in the grasp of truth.
a. The Nature and Criterion of Truth.
According to Hamilton, truth is " the correspondence or agreement
of a cognition with its object." Or, including both thought and state-
ment, truth is the agreement of a thought or statement with the reality
which the thought or statement concerns. Error is the opposite, or
the want of harmony between a thought or statement and its object.
The criterion, or test of truth, arises out of its nature as thus stated.
Does it correspond with the reality ? " Man is mortal." " The sun
shines." " Madagascar is inhabited." " The earth is spherical." In
deciding whether these statements are true, the question to be asked
of each is, Does it agree with fact or reality f
16 PRACTICAL LOGIC.
b. Modes of Arriving at Truth.
The truth in any given case is arrived at in one or other of two
ways :
First, by the use of one's own powers intuitive or discursive. These
give knowledge in the narrower sense. The intuitive powers furnish
immediate knowledge, or a priori knowledge : (a.) By external or sense
perception, of matter and its phenomena ; (6.) By internal perception
or self-consciousness, of spirit and its operations ; (c.) By intuition
proper, of the self-evident and necessary notions and principles which
underlie and condition all human experience. The discursive powers
furnish mediate or a posteriori knowledge by the processes of thought,
conception, judgment, reasoning, and construction.
Secondly, by acceptance of the statements of others. These give
belief in the narrow and strict sense, or the acceptance of truth on the
ground of testimony. Most of man's knowledge in the wide sense,
and that the most valuable part of it, is derived from this source.
The witnesses gain their knowledge either : (a.) By the use of their
intuitive powers, which lays the foundation for testimony proper; or,
(6.) By the use of their discursive or thought powers, which lays the
foundation for authority.
o. Degrees in the Assurance of Truth.
The mind does not lay hold of all its knowledge with the same de-
gree of certainty. Distinction is made between belief, opinion, proba-
ble truth, certain truth.
Certainty is the consciousness of the necessity of agreement between
a thought and its object, in whichever of the above ways that thought
may be reached. It absolutely excludes the admission of any opposite
supposition. Where this is not the case, doubt and uncertainty arise.
Considered with reference to the degree of certainty, there appear,
at the two extremes :
Knowledge, in the strictest sense, where the consciousness of neces-
sity is absolute, or certainty perfect ;
Opinion, or the admission of something where the evidence is not
such as to necessitate a perfect certainty.
Probability appears in the approximation of the imperfect certainty
of opinion to the perfect certainty of knowledge.
Belief is used in various loose senses, but the distinction given above
will, it is thought, commend itself as the fundamental sense. Belief
is the acceptance of truth on the ground of testimony, including testi-
mony proper and authority.
THE NATURE OF LOGIC. 17
(2.) Truth by Thought. — The aim of Logic is to arrive at truth
through the powers of thinking or thought. The grasp of the truth
reached will evidently depend upon the kind of truth and the accu-
racy of the thinking. Correct thinking will give a more or less cer-
tain grasp of the truth reached as the result of it. In mathematical
and intuitive truth the result reached is absolutely certain. In other
regions of thought the results of thought are more or less probable.
These varying degrees of certainty may be illustrated by examples.
It is certain that two and two cannot but make four ; that things
which are equal to the same thing are equal to each other ; that every
event must have a cause. It is probable that the first day of January,
1900, will be cold. It is extremely probable that the sun will rise
to-morrow. It is probable that a young man of good capacity, char-
acter, and habits will succeed in business. It is the opinion of certain
astronomers that the moon is uninhabited. It is the belief of most
intelligent men that the earth is about 93,000,000 miles from the sun.
Topic Third.— The Principles or Laws of Thinking or
Thought.
Logic deals with the principles or laws which govern
thought.
Every rational human activity proceeds according to definite laws,
known or unknown. The highest degree of intelligence and efficiency
in any such activity requires that the laws be known and correctly
made use of in directing the activity. This is true of the various
forms of thought ; they have their laws which govern their action.
There are laws of conception, laws of judgment, laws of reasoning,
laws of construction. Logic should enable the thinker to ascertain
and apply these laws, and thus aid him in correct thinking and save
him from incorrect thinking. It is likewise true that the highest
degree of intelligence and efficiency in thinking requires a thorough
knowledge of the laws of thought and a correct use of them in guid-
ing the exercise of thought. Practical Logic should aim to give the
thinker the most thorough knowledge of the laws and the greatest
efficiency in using them in thinking.
Besides the special laws which govern the various forms
of thought, there are certain general laws, certain axioms
or fundamental laws and certain postulates with which
Logic sets out. The special laws will be unfolded in con-
2* B
18 PRACTICAL LOGIC.
nection with the treatment of the various forms of thought ;
at the outset must be presented the fundamental laws and
postulates.
1, The Fundamental Laws of Thought.
Logic, like other sciences, has certain fundamental prin-
ciples upon which the more special laws rest. These are
usually reduced to four :
The Law of Identity, or Affirmation ;
The Law of Contradiction, or Negation ;
The Law of Excluded Middle, or Exclusion ;
The Law of Reason and Consequent, or Sufficient Reason.
(1.) The Law of Identity, or Affirmation.
The Law of Identity may be stated as follows : Every-
thing is identical with itself, or is what it is, and we may
affirm this of it. This has been formulated : A is A ; or
A = A. Whatever is, is.
The identity may be : a. Absolute, or that of total sameness of a
thing or thought with all its parts ; or, 6. Relative, or that of partial
sameness of a thing or thought with each or some of its parts. The
logical concept or notion expressed by the general term, man, is made
up of the following elements : being, material, organized, animated,
rational, terrestrial. Man is, therefore, totally identical with all these
elements ; so that it may be correctly affirmed that man is material,
organized, animated, rational, terrestrial being. Man is partially iden-
tical with any of these elements ; so that it may be correctly affirmed
that man is material ; man is organized, etc.
The Law of Identity gives the logical right to affirm such
total or partial identity in all cases where it exists. It is
at the basis of all consistent affirmative thinking, — of all
positive conceptions, logical definitions, affirmative judg-
ments, and categorical arguments.
(2.) The Law of Contradiction, Negation, or, as Ham-
ilton terms it, Non-contradiction, may be stated as fol-
THE NATURE OF LOGIC. 19
lows : Everything is not what it is not, and we may affirm
this of it. Or, conflicting attributes cannot co-exist in and
may not be affirmed of the same object. This has been
formulated : A is n't not -A. Nothing can both be and
not be.
The logical concepts expressed in the following pairs of general
terms are contradictories : black and not-black ; round and not-round ;
good and wicked ; finite and infinite. We are logically excluded from
affirming the co-existence of these mutually contradictory thoughts or
things. A thing cannot be black and not-black at the same time and
in the same sense. A door cannot be open and shut (not-open) at the
same time and in the same sense. Black-white, round-square, good-
wickedness, finite-infinitude, combine mutual contradictories, and are,
therefore, logically excluded from correct thought by this law.
The law of non-contradiction is the complement of that
of identity. Its importance arises from the fact that it
is at the basis of all logical negation and distinction in
thought, — of all negative conceptions and judgments.
(3.) The Law of Excluded Middle, or Exclusion, may be
stated as follows : Of two contradictories one must be true
and the other false. If one is affirmed, the other is thereby
denied. One excludes the other, and hence there can be
no medium affirmation between the two. This axiom has
been formulated : A either is or is not. A either is or is
not B. Everything must either be or not be.
E. g., An intra-mercurial planet, Vulcan, exists or does not. The
moon either is inhabited or it is not. Bacon either was Shakespeare
or he was not. The two propositions, Vulcan exists, Vulcan does not
exist, are first tested by the Laws of Identity and Contradiction. If
by the Law of Identity it is true that Vulcan exists, then, by the
Law of Exclusion, the proposition, Vulcan does not exist, must be
false. If by the Law of Contradiction it be true that Vulcan does
not exist, then, by the Law of Exclusion, the proposition, Vulcan
exists, must be false.
The importance of the Principle of Exclusion arises from
20 PRACTICAL LOGIC.
its being the foundation of all disjunctive judgments, i. «.,
" of judgments in which a plurality of judgments are con-
tained, and which stand to each other in such a reciprocal
relation that the affirmation of one is the denial of the
other."
(4.) The Law of Reason and Consequent, or Sufficient
Reason. — The Law is stated as follows: All continuous
thought must be rationally connected. The Law has been
formulated : Infer nothing without a ground or reason. The
starting-point in continuous thinking is the affirmation of
some knowledge by which the mind is necessitated to affirm
or posit something else. This starting-point is called the
logical reason, ground, or antecedent, or, as Hamilton sug-
gests, condition; that something else which the mind is
necessitated to affirm or posit is called the logical conse-
quent, or the conditioned ; the relation between the reason
and consequent is called the logical connection or consequence.
Reason and consequent involve not only cause and effect, but every
case where an antecedent compels the mind to affirm something else,
as logically following it. It includes the relations of whole to part,
cause to effect, substance to attribute, etc., with the reversed relations
of part to whole, effect to cause, attribute to substance, etc.
The axiom, as presented by Hamilton, takes a positive and a nega-
tive form.
(a.) Positive Form. — "When a reason is explicitly or implicitly
given, then there must exist a consequent ; and, vice versa, when a
consequent is given, there must also exist a reason." The presence of
a tree as a whole always implies the presence of any or all of its parts,
— roots, trunk, branches. The presence of any attribute, as intelli-
gence, always implies the presence of the substance of which it is an
attribute, — mind.
(b.) Negative Form. — Where there is no reason, there can be no
consequent (either implicitly or explicitly). Where there is no con-
sequent, there can be no reason. The absence of mind involves the
absence of memory as an attribute of mind. The absence of will
implies the absence of moral accountability, of which it is an attribute.
THE NATURE OF LOGIC. 21
The logical significance and value of the Law of Keason
and Consequent lies in this, " that, in virtue of it, thought
is constituted into a series of acts all indissolubly con-
nected; each necessarily inferring the other." Without it,
continuous and connected thought or reasoning would be
impossible.
2. The Postulates of Logic.
There are certain fundamental postulates, or practical
propositions, assumed at the outset of the treatment of
Logic. The two here emphasized respect the reality of
truth, and the requirement of full, explicit statement.
(1.) The First Postulate, — There is such a thing as truth,
which can be ascertained, and on which all minds, acting
in accordance with the laws of thought, must agree.
Without this assumption there can be no starting-point
for thought, and no goal for the activity of the thought-
power. No two minds could otherwise have any common
basis from which to start together or on which to come to-
gether in thinking or discussion.
(2.) The Second Postulate. — This, as stated by Hamilton,
is, " to be allowed to state explicitly in language all that is
implicitly contained in thought." Logic deals ultimately
with thought, and it has to do with language only as ex-
pressing thought. It is, therefore, proper to ask, in connec-
tion with any term, proposition, or argument, " What is the
thought in this?" or, in other words, "What is the full
and exact meaning of this?" and to state in full this
meaning. Abridged forms are to be completed, rhetorical
forms to be translated into plain language, and expressions
changed, if need be (provided the thought be preserved),
until the thought is brought out naked and entire. Mill
states this postulate as follows : " Logic postulates to be
allowed to assert the same meaning in any words which will
22 PRACTICAL LOO 1C.
express it ; we require the liberty of exchanging a propo-
sition for any other that is equipollent (that is, having equal
power and reach) with it."
II. THE DIVISIONS OF LOGIC.
WHAT are the Divisions under which Logic should be
presented ? This question has been variously answered.
The answer should, in any case, depend upon the point of
view and object of the work.
The most common division is, perhaps, into Pure Logic
and Applied Logic. Hamilton divides it into Pure and
Modified. Regarded as a Practical Science, it is, perhaps,
better to base its divisions on the various Forms of Thought.
1. Distinction of Pure and Applied Logic. — The logical
writers who follow the common division find it necessary to
define and distinguish Pure and Applied Logic, or Theo-
retical and Practical Logic. As these terms will constantly
be met with in the works on Logic, a brief explanation of
them will here be given.
(1.) Pure Logic is the Science of the Necessary and
Formal Laws of Thought as Thought. It treats of the
necessary laws of thought, in the strict sense of discursive
thought, as they are in themselves, whatever may be the
object-matter to which they are applied. In this sense
Logic is a science of abstractions, like pure mathematics or
metaphysics. As furnishing the principles implied in and
underlying the construction of all other Sciences, it has also
been called " the science of sciences."
(2.) Applied Logic treats of the application of the prin-
ciples, or laws of thought, unfolded in Pure Logic, to the
investigation of truth. It assists in ascertaining and fol-
THE DIVISIONS OF LOGIC.
23
lowing right processes of thought and in avoiding wrong
processes.
This division is the same as the distinction of the School-
men, of Logica Docens and Logica Utens ; of the Wolfian
School in Germany into Theoretical and Practical ; also, as
General and Special, Abstract and Concrete.
The following Outline presents the common Divisions of
Logic from this point of view :
LOGIC, the Science
of the Laws of Dis-
cursive Thought,
comprises —
I. THEORETICAL, or
PUEE, LOGIC, or
the Science of
these Laws
themselves,
eluding —
m
in-
II. PEACTICAL, or
APPLIED, LOGIC,
including —
1. Laws of Conception.
2. Laws of Judgment.
3. Laws of Eeasoning.
1. The Doctrine of Fal-
lacies, or the modes
of avoiding incor-
rect thinking.
2. Method, or the right
modes of ascertain-
ing truth.
2. Distinction of Pure and Modified Logic, — Sir William
Hamilton divides Logic into Pure and Modified : confining
attention to Abstract or General Logic.
(1.) Pure Logic, in the Hamiltonian sense, " considers
Thought Proper simply and in itself, and apart from the
various circumstances by which it may be affected in its
actual application. But human thought, it is evident, is
not exerted except by men and individual men." It is,
therefore, variously modified by individual peculiarities,
original and acquired, and by the circumstances of the
thinker. Hence arises —
(2.) Modified Logic, which considers "the conditions to
which thought is subject, arising from the empirical circum-
24 PRACTICAL LOGIC.
stances, external and internal, under which exclusively it
is the will of our Creator that man should manifest his fac-
ulty of thinking."
For Hamilton's Divisions, see Hamilton's "Logic," page
49.
3. Divisions based on the Forms of Thought. — In treat-
ing Logic as a Practical Science, it is more convenient and
satisfactory, if not more logical, to base the divisions on the
various Forms of Thought, — Conception, Judgment, Rea-
soning, and System. It is more convenient and satisfac-
tory, since by this method, first, the learning of the princi-
ples will go hand in hand with their use ; secondly, the
scientific view will be kept in strict subordination to the
practical end aimed at. It is more logical, since in this
way it is believed that, first, the subjects of Fallacies and
of Method will fall into their natural places, in connection
with the presentation of the laws of correct thinking ;
secondly, the whole subject will take such shape as is best
to train to skill and power in right thinking and in testing
the products of thought.
According to this view, Logic will be treated under four
Divisions :
PART FIRST. Logic of Conception, or of the Term.
PART SECOND. Logic of Judgment, or of the Proposition.
PART THIRD. Logic of Reasoning, or of the Syllogism.
PART FOURTH. Logic of Construction, or of the System.
PART I.
THE LOGIC OF CONCEPTION OR THE TERM.
THE aim of the Logic of Conception is to train the mind
to skill in dealing with the first and fundamental Form of
Thought.
Definition. — Conception is that form of thought in which
we compare various acquired knowledges and connect them
by resembling marks or attributes, thus forming Concepts,
Classes, and General Terms.
This definition suggests, as a first subject for treatment,
the formation of conceptions. The every-day practical
necessity for studying and logically testing the work of
thinkers, as embodied in their scientific, philosophic, and
literary productions, suggests, as a second subject, the un-
folding1 of conceptions. The Logic of Conception will,
therefore, be treated in two Chapters.
CHAPTER I.
THE FORMATION OP CONCEPTIONS.
WORKS on Logic are usually mainly confined to the work
of unfolding thought ; but as the process of forming con-
ceptions furnishes the key to their unfolding, it will be first
3 25
26 PRACTICAL LOGIC.
considered. The definition of conception suggests the four
elements of the process, to be treated in as many Sections :
First, the gathering of the materials for conception, i.e.,
the knowledges or objects of thought. This is the work of
Observation.
Second, the placing of these materials side by side,
noting the resembling parts, marks, or attributes, and
gathering these into thoughts, called concepts. This is
Conception proper.
Third, the gathering of the objects, to which these con-
cepts or bundles of common attributes apply, into classes.
This is Classification.
Fourth, the embodying of both concepts and classes in
names, or general terms. This is Denomination.
The skilful thinker will need to have command of the laws of these
four elements of Conception : Observation, Conception proper, Classi-
fication, and Denomination. The last three will be seen in their
formation to involve comparison as an essential element. In the
treatment of the three in the First Chapter, both the process and
product will be considered. The unfolding of the products of the
three — the concept proper, the class, and the term — by Partition,
Division, and Definition, will be the work of the Second Chapter.
Section I.— Observation.
Strictly speaking, Observation is a condition rather than
an element of conception. It must always precede the
proper work of conception, since, without careful examina-
tion of the objects or facts about which the work of think-
ing is done, no material would be furnished in fit shape for
the use of thought in its first form.
Definition. — Observation is the mental process by which
we gain a minute and comprehensive knowledge of objects
and their make-up.
The Instruments of Observation are the Senses and Consciousness.
In gaining a knowledge of the external or material world, the ob«
THE FORMATION OF CONCEPTIONS. 27
server must make use of his five senses. This is observation in the
narrow sense. In gaining a knowledge of the facts of the inner
world, or world of mind, he must make use of consciousness, or inter-
nal perception. This is sometimes known as reflection, or introspec-
tion, and, with observation by the senses, makes up observation in
the wide sense.
Topic First. The Predicables, or Things Knowable or
Nameable. — The first thing in order to observe well for the
purpose of correct thinking is to know the kinds of things
that may be known, or what the observer may expect to
find. This will furnish him with the clew needed to make
his observation exact and complete in gathering his material
for thinking.
From another point of view, the kinds of things know-
able or nameable are called the categories (from a Greek
word meaning to predicate), or the predicates (from the
Latin, meaning to assert), or the predicables, since they
sum up what may be predicated or asserted of anything.
It should manifestly be the aim of every intelligent man to acquire
the power to know as much as possible of what may be known and
named.
1. The Predicables. — Starting with being, or thing, as
the conception including all things in the universe, a simple
classification may be made which will be of practical value
to the observer. Being always appears as substance having
properties or attributes. Properties may be divided into
four kinds, reducible to three :
1st, Properties of quality, or those which constitute any-
thing what it is.
2d. Properties of action, or those which manifest the
active and passive powers of any being.
3d. Properties of condition, or those which express the
connections of beings with space and time.
4th. Properties of relation, or those which express the
connections of beings with other beings.
28 PRACTICAL LOGIC.
The properties or attributes of condition and relation
are sometimes known together as properties of relation in the
wide sense, and the scheme thus reduced to three kinds of
properties.
Substance and property and the kindred terms need to
be carefully distinguished.
1. Substance is used in two kindred meanings: first, as being, in
contrast to and independent of its properties, as that which exists
absolutely and of itself, absolute being; second, "as conjoined with
the attributes " and furnishing their basis, that which stands under
and supports the attributes, the thing back of all phenomena " which
is and abides." In the latter and more common meaning, substance is
divided into matter and spirit, or that which is extended and that
which thinks. Subject is used in the more recent philosophy, es-
pecially German, to denote the spirit, " the basis of the various mental
phenomena." Conscious subject means the thinker or the mind itself.
Object is a term for that about which the knowing subject is conver-
sant. Subjective is applied to that which belongs to or proceeds from
the conscious subject; objective, to that which belongs to 01 proceeds
from the object known.
2. Various properties — called, also, attributes, qualities, parts, marks,
characteristics, phenomena, etc. — are the materials to be gathered, in
connection with substance, for conception. These terms are often used
in a loose sense as synonymes. The first three — property, attribute,
quality — are the most important, from the point of view of logic, and
need to be carefully distinguished ; the others sufficiently explain
themselves. Property may be regarded as the widest of the three
terms, and as including whatever belongs to or pertains to any object
of knowledge. Quality, etymologically, is that which makes anything
what it is, and may, therefore, be properly regarded as including the
essential properties, called, in the Scheme given, properties of quality.
With Aristotle and Descartes, attributes are real properties, essential
and inherent. They may be restricted to properties of quality, or
extended so as to include properties of action.
Properties may be distinguished as intrinsic and extrinsic. The
intrinsic properties of any object of knowledge are those which are
inherent in the object itself. In the Categories the properties of quality
and action may be regarded as intrinsic. Intrinsic properties may
be looked upon as including what are sometimes called peculiar prop~
THE FORMATION OF CONCEPTIONS. 29
erties and inseparable accidents. The extrinsic properties of any
object are those which arise from its connection with something exter-
nal rather than from its own nature. They include the properties of
condition and relation.
Properties are also distinguished as essential and non-essential. An
essential property is one of those which make any object, class, or
species what it is, as, in man, the faculties of sense and intelligence ;
in body, the dimensions of length, breadth, and thickness. An essen-
tial property might appropriately be called a quality, in the strict
etymological sense. The essential properties of any object, or those
which make it what it is, are known as its essence or (in the old Logic)
its definition. Non-essential properties are those which do not belong
to the essence of an object. Essential properties are substantially the
same as intrinsic, and non-espential as extrinsic. The former may be
looked upon as embracing properties of quality and of action ; the
latter, properties of condition and relation.
Note.— Logicians have, from the earliest times, made use of the distinctions
of peculiar property (often called simply property) and of accidental property,
or accident. A peculiar property has been defined to be one which is common
to the whole of a class of objects, but is not necessary to mark off that class
from other classes. " Capable of speaking correctly " is said to be a peculiar
property of man, not embraced in the definition or essence of man, " rational
animal." " It is, however," as Thomson has shown, " a part of the essence,
for rational implies it. In like manner, all the properties seem to be implicitly
contained in every perfect definition. No criterion can be given for distin-
guishing between the essence and the inseparable accompaniment of the
essence ; and a larger acquaintance with the nature of things makes it evident
that, what one science regards as a property, another must consider as essen-
tial, and that there is no one paramount quality which is absolutely essential
and can never be degraded to the rank of a property."
An accidental property, or accident, is one which may indifferently belong
or not belong to the objects of any class without affecting their essence. The
birthplace of a man and the clothes he wears are accidents which have no
necessary effect upon his manhood. Accidents are separable or inseparable.
A separable accident is one that can be changed, as the clothes of a man, his
position, and many other circumstances. An inseparable accident is one that
can never be changed, although it may have no necessary connection with
essential properties, as the birthplace of a man, his height, etc. Thomson has,
however, shown that it is often difficult, if not impossible, to distinguish acci-
dent from essential property. Writing in England, he says: " It is an accident
to the people of this country that they were born in it ; because we might con-
ceive them to have been born elsewhere ; but then it has modified their nature
or essence, and we understand by Englishman not merely one who was born
within the four seas, but a man of particular feelings, views, and privileges,
which are parts of his very nature. Here accident and genus or property seem
to become confused."
3*
30 PRACTICAL LOGIC,
It is, therefore, proposed to abandon these distinctions as at least unneces-
sary for logical purposes.
The Scheme of Predicables, therefore, becomes :
f Substance,
BEING, j Properties, or
Modes of
Substance,
Quality, I Intringic and Essential
Action, J
Condition, ^
Relation,
Extrinsic and Non-essential.
The old Aristotelian logicians looked upon all existing things as
being divided by nature into ten classes or categories. These, accord-
ing to Aristotle, are: substance, quantity, quality, relation, place,
time, posture, possession, action, passion. A thing that can be known
or named comes under one or other of these categories. As will be
seen at a later stage in the study of Logic, the categories will not
stand the test of the laws of accurate division.
It will readily be seen that these categories of Aristotle may all be
placed under one or other of the categories of the simpler scheme pre-
viously given.
2. Use of the Predicables. — The accurate and intelligent
observer must consciously or unconsciously make use of
some such scheme in order to make his observations intelli-
gent and complete ; otherwise he will never know when he
has learned the most important facts in any given case, nor
when he has learned all the main facts.
The scheme will decide the general questions to be asked
when attention is called to any object of knowledge.
1st. What is it in its substance— spiritual or material ? This will bring out
what is included under Aristotle's category of substance.
2d. What are its properties of quality ? This will embrace Aristotle's cate-
gory of quality.
3d. What are its properties of action? This will embrace Aristotle's catego-
ries of action and passion.
4th. What are its properties of condition ? This will take in Aristotle's cate-
gories of time, place, Quantity, and posture.
5th. What are its properties of relation? This will include Aristotle's cate-
gories of relation and possession.
Topic Second. Observation of Things Predicable. — The
practical work of observation lies at the foundation of cor-
THE FORMATION OF CONCEPTIONS. 31
rect thinking, since such thinking must depend upon first
ascertaining the exact facts about which it is to be done.
The tendency is to careless and superficial observation. Per-
haps more errors in science arise from want of proper obser-
vation of facts than from any other source. Hence the neces-
sity of securing, in the earlier stages of training, the careful
study and diligent practice of the processes and rules of
exact observation.
I. Processes and Products of Observation in General.
Whately styles the operation of the mind, in contem-
plating any object, simple apprehension. It is often called
intuition, or immediate knowledge. The result of this
operation may be called the simple notion. This notion
may take various forms, from that of the vaguest percept
to that of the complete, concrete thing.
In beginning the work of observation we apprehend ob-
jects, whether material or mental, with various properties
or parts. We perceive a tree with its trunk, branches, and
leaves, with their forms, colors, qualities, etc. We thus
gain what is called a percept of the tree. We may subse-
quently give special attention to any particular part or
property of the tree, as its height, or color, or firmness of
texture. This is called abstraction, or the drawing away
of a part or property from the concrete whole. The result
is an abstract, or abstract notion, of these parts or attri-
butes, of height, color, etc. The most important element in
accurate observation is mental analysis, in which the atten-
tion is voluntarily turned to particular parts or properties
of any object of knowledge. This process of mental sepa-
ration is continued until many constituent parts of the
object are brought out. In examining material objects,
these parts may evidently be regarded either as spacial
parts or as attribute parts. The first point of view leads
to what is called physical partition, the second to mental
analysis proper.
32 PRACTICAL LOGIC.
Physical partition is the simplest form of mental analysis. The
analysis of tree into roots, trunk, branches, leaves, brings out the
spacial parts. Such partition is of special service in the earlier stages
of mental training.
Praxis. — Name in an orderly manner the parts of the following
objects: 1. A peach. 2. A piano. 3. A ship. 4. A book. 5. A house.
6. A landscape. 7. A mountain view. 8. A telephone. 9. A telescope.
10. A locomotive.
Mental analysis proper, the more important form of observation,
deals with attributes rather than with spacial parts. It belongs to a
more advanced stage of mental training. Water may thus be ana-
lyzed in thought into the separate properties named weight, liquid-
ity, transparency, refracting power, solvent power. A dime may be
analyzed into the attributes or parts, material substance, heavy,
round, small, white, coin.
Note.— It will be obvious that chemical analysis, involving intricate proc-
esses of thought, belongs to a different range of mental activity. It would
bring out of water its chemical components, oxygen and hydrogen, and out
of a gold dollar its chemical components, gold and the alloy of silver and
copper.
The result of the careful application of these processes
of abstraction and mental analysis is the notion of the com-
plete concrete object, or thing1, which, according to Horn
Tooke, is the same as think, a thing being what one thing-
eth or thinketh.
Praxis. — Analyze and describe in an orderly way the following
objects : 1. A diamond. 2. A gold dollar. 3. A painting. 4. A piece
of wood. 5. A flower. 6. A rose. 7. A forest. 8. A sunset at sea.
9. A church service. 10. An act of memory.
II. Exact or Scientific Observation and its Rules.
The general and superficial observation thus far consid-
ered, however well it may serve the purposes of common
life, is insufficient for the purposes of accurate thinking.
Scientific observation must be made accurate and exact by
intelligent conformity to certain rules, and must be made
complete by careful use of the scheme of things knowable.
1. The Rules of Observation, which need to be grasped
and practised in order to reach the best results, are three.
THE FORMATION OF CONCEPTIONS. 33
They are substantially Hamilton's Laws of Integrity, Par-
cimony, and Harmony.
Rule 1st. Observe all the essential facts, parts, or proper-
ties in any given case.
Rule 2d. Admit no fact, part, or property that does not
belong to the case in hand.
Rule 3d. Avoid all delusive mixtures of inference with
the facts of observation.
Rule 1st is needed to guard against the common fault of incomplete
observation. Through the careless use of the powers, or the holding
of some false theory, or the blinding influence of prejudice, men are
liable not to see all the facts. The honest observer should see to it
that none of these things stand in the way of completeness or integ-
rity of observation. Rule 2d is intended to guard against the danger
of receiving as facts things that are not such, and of receiving as facts
of the region under observation things which belong to some other
sphere of facts. This danger arises in the same way as the preceding.
Rule 3d is to guard against the introduction of unsound or irrelevant
inferences among the facts of observation. The sources of this danger
are the same as the preceding. Here is the fruitful source of much of
the scientific and philosophic error in all ages.
2. Scientific Observation, in order to the best results,
while conforming to these rules, must make intelligent use
of the categories. The observer must make use of the
questions, already given in connection with the scheme, in
order to bring out the facts of all kinds.
The character of this observation will appear more fully in the later
stages of the study of Logic. The mode of using the scheme may
here be cursorily illustrated, and the main things in the process sug-
gested, by the observation of a white-oak tree in the school-yard or
campus. Question first will bring out the fact of material substance
or constitution. Question second will give the facts of extension, of
organization, of life, and of unity of structure and plan in the tree,
the facts of cupule-bearing and half-covered fruit, and the other facts
peculiar to the white-oak. Question third will furnish the facts of
growth, of resisting violence, of counteracting pressure, etc. Question
fourth will lead to the facts concerning the height, size, shape, habitat,
C
34 PRACTICAL LOGIC.
etc., of the tree, and those concerning its time of planting, length of
life, periods of growth, etc. Question fifth will direct to the facts con-
cerning the position of the tree with reference to the school-building,
to other trees and objects on the grounds, to other trees belonging to
the class, oak, to the industrial arts in which its wood is used, etc.
Praxis. — Observe systematically and describe carefully the following
objects: 1. An inkstand upon the writing-desk. 2. A clock upon the
mantel-piece. 3. A student's lamp upon the table. 4. A Worcester's
Dictionary in the library-case. 5. A stove in the room. 6. A ship at
sea. 7. Jupiter as the evening star. 8. The centre-table in the library.
9. The feeling of home-sickness in the student. 10. The contemplation
of Church's Niagara.
Note.— The teacher will do well to use as an adjunct some such work as the
little Manual, published by Eldredge & Brother, entitled " The Cultivation of
the Senses." This will prepare the way for the application of the right princi-
ples to the more difficult work of introspection and analysis of mental objects.
Section II,— Conception Proper,
Conception proper is the first essential element in the
first Form of Thought. The work of Observation makes
ready the material for it; Conception proper begins the
work of comparing that material, arriving at the thought-
connections, and gathering up and combining the results in
a thought.
Topic First.— The Process of Concept-Forming.
Definition. — Conception proper is the mental process of
fixing upon resembling parts, marks, or properties of objects,
and grasping them singly or together as attribute thoughts
or concepts.
This element of conception always involves a comparison of two or
more objects of knowledge, and has more or less direct reference to
the process of classification by similar properties. The concept may,
indeed, be said to be formed for the purpose of being used to classify
objects, and this gives it its chief value. There is need, therefore, of
considering two things : first, the gathering of similars by comparison ;
second, the grasping of similars in thought by conception.
THE FORMATION OF CONCEPTIONS. 35
I. The Gathering of Similars by Comparison.
Comparison in the formation of concepts proper begins
with the work of fixing upon similar properties. Observ-
ing objects side by side, we note and affirm differences and
resemblances, and then fix upon and abstract the resem-
blances or properties common to the objects.
1. The simplest connecting act in thought is in finding
a single point of resemblance, and withdrawing, or abstract-
ing, this from the points of difference.
E.g., water has materiality, weight, liquidity, refracting power,
solvent power, transparency, etc. A dime has materiality, weight,
whiteness, hardness, malleability, roundness, smallness, the stamp of
a coin, etc. Air has materiality, fluidity, elasticity, invisibility, etc.
Examining these three objects side by side, they are all found to have
in common materiality. They resemble each other in this point, or, in
other words, this is a characteristic common to them all.
2. A more important connecting act in this first stage of
thought is that of finding and seizing upon several or all
the points of similarity in the objects compared.
It will readily be seen that the same objects may be ob-
served from different points of view. A gold or silver coin
may be observed as a substance having essential attributes
of its own, or as a piece of money used in the work of com-
mercial exchange. The observer should first fix upon his
point of view, and then seek the resemblances from that
point of view.
Considered as a substance, a sovereign is material, of yellow color,
extremely malleable, of circular shape, nineteen times heavier than
water, etc. As a piece of money it is of the metal gold, of compara-
tively high value, being worth five dollars, of the kind which is the
standard of values in most countries, a coin, etc. Considered as a
substance, a silver dollar is material, of white color, moderately mal-
leable, of circular shape, ten times heavier than water, etc. As a
piece of money it is a coin, fashioned of the metal silver, of moderately
high value, being worth one hundred cents, etc. Treating the gold
and silver coins as substances merely, they resemble each other in
36 PRACTICAL LOGIC.
being material, having color, being malleable, having circular shape,
being of high specific gravity, etc. These are the resembling or
common properties or parts. Treating them as pieces of money, they
resemble each other in being coins, composed of metal shaped into
circular form and valuable for the purposes of exchange.
3. The most important connecting act in this stage of
thought is that of finding and fixing upon the essential
points of similarity in the objects compared. Scientific
thinking, as will be seen further on, must fix mainly upon
the essential points of resemblance, rather than upon the
non-essential.
Praxis. — State, concerning the properties of the following objects,
whether they are intrinsic or extrinsic ; whether essential or non-
essential; whether properties of quality, action, condition, or relation :
1. Of George Washington, — born in Virginia in 1732, studied mathe-
matics under a private instructor, tall, wise, just, brave, president, led
the armies of his country, the friend of Hamilton, the father of his
country, died in 1799. 2. Of Great Britain, — populous, fertile, insu-
lar, powerful, manufacturing, agricultural, commercial, philanthropic,
missionary, kingdom, colonizing, literary, modern, small, nation.
Compare the following objects, fixing upon some resembling prop-
erty, and stating to what class of properties it belongs : 1. Snow, light,
chalk, lime. 2. Book, parchment roll, Kosetta stone, paper manu-
script. 3. Oak-tree, rose, elephant, man. 4. Memory, argument, fence,
watch, world.
Compare the following objects, fixing upon the resembling proper-
ties, and stating to what class they belong : 1. Wood, coke, charcoal,
bituminous coal. 2. Plumbago, charcoal, diamond. 3. Star, student's
lamp, sun. 4. Tree, carriage, watch, poem. 5. Poem, painting, statue,
anthem, temple. 6. Triangle, polygon, dodecahedron, globe.
Note.— The teacher may, with great profit to the student, devote much time
to the processes of Observation and Comparison. They lie at the very basis of
correct thinking, so that their importance cannot well be over-estimated.
II. The Grasping of Similars by Conception,
The work of observation and comparison up to the pres-
ent point has only brought out common attributes without
fixing them in a thought binding them together into logical
THE FORMATION OF CONCEPTIONS. 37
unity. The attributes of the sovereign as money are named
each by itself. The work of conception brings together
all these attributes into one thought, which, as being the
product of conception, is called a concept, or attribute-
thought. This concept, which is named sovereign (in accord-
ance with the laws of naming to be considered under Section
Fourth) embraces in itself the characteristics — coin, fash-
ioned of the metal gold, of comparatively high value, being
worth five dollars, of the kind which is the standard of
values in most countries, etc.
The value of the product of thought reached by the
process of grasping together properties will depend upon
the method and principles followed.
1. It is obvious that any of the kinds of properties
already considered may be fixed upon and embodied in the
concept or attribute-thought, and that this may be done in
various ways.
a. A single property of any kind may be fixed upon, in which case
the result may be looked upon as a simple concept, although the
mental act is one of simple grasping, and not of grasping together.
b. The properties of any particular object may be grasped together,
without special attention to other objects, or to the principle of simi-
larity. This may also be regarded as an unapplied concept, which
may be applied later to similar objects in the work of classification.
c. The similar properties of various objects may be grasped together,
keeping in view the principle of similarity. This is the concept in the
strictest sense.
2. The Rules which must govern concept-forming, if the
best results are to be reached, may be reduced to two.
Rule 1st. — In order to the best thought, essential prop-
erties should be grasped in preference to others.
The loose thinking of common life is characterized by its seizing
upon non-essential properties. In observing an individual man the
separable accident of wearing broadcloth may be observed, abstracted,
and embodied in the concept broadcloth-wearing. Such a concept
brings out nothing essential to man. Scientific thinking, on the other
4
38 PRACTICAL LOGIC.
hand, fixes chiefly upon essential properties, so that it embodies the
very nature of the objects of thought. In observing a man, it fixes
upon the animal and rational properties which make him what he is,
and embodies these in the concept man, or humanity. The products
of scientific thinking will be found of the utmost value in the work
of classifying objects.
Rule 2d. — In order to the best, the only adequate, thought
in this form, all the essential properties should, so far as
possible, be grasped.
It is obvious that any number of abstractions may be drawn from
any object. Strictly speaking, we can never be certain that all the
possible properties have been abstracted. There may always remain
innumerable unobserved or undetected properties. But ordinarily all
the essential properties may be more or less clearly detected and
grasped, and the perfection of the concept as a group of properties
will depend upon the completeness with which it takes in the essence
of the object of thought.
Observing carefully an animal, the properties of organized being, of
life, of sentiency, and of voluntary motion, are fixed upon as essential
properties. These are all embodied in the concept, animal. If but
one of these sets of properties should be embodied, the concept would
be of comparatively little value. Observing some virtuous act, as the
Prophet Daniel's act of praying to the true God notwithstanding the
prohibitory decree of the king, the characteristics, conformity to the
law of right, and intelligent, intentional action, are fixed upon and
embodied in the concept virtue, or virtuousness. If any one of these
essential characteristics is omitted in our conception of virtue, the
thought will be incomplete and of little value scientifically.
Praxis. — Gather up into concepts the similar properties of the fol-
lowing groups of objects, stating the kind of property in each case:
1. A piece of crayon, a chair, a lamp, a book, a tree, a stone. 2. A
man, an eagle, a lion, a serpent. 3. A horse, a tiger, an elephant, a
lap-dog. 4. A cat, a leopard, a hyena. 5. A vulture, a hawk, a
falcon. 6. Love, patience, joy, gratitude. 7. Faith, hope, charity.
8. Cathedral of Milan, Madonna of Raphael, Paradise Lost of Milton.
9. Great Britain, United States, Germany.
Topic Second,— The Product of Concept-Forming.
The product of gathering up the abstracted properties of
THE FORMATION OF CONCEPTIONS. 39
objects in thought is a thought property or group of proper-
ties. It would be appropriately named a notion (from notce,
marks, characteristics), if that word were not used in such
loose and varied senses. Concept proper is, perhaps, the best
name. But whether spoken of as notion, concept proper, or
attribute thought, the essential thing in it is always the
grasping in thought of certain observed properties of objects.
The properties contained in any concept make up its con-
tent. The same thing has also been denoted by internal
quantity, intension, comprehension, depth, marks, etc. The
content of the concept man is made up of animal and
rational properties. The content of triangle is plane figure,
three-sided, rectilineal.
In connection with concepts proper, Logic gives promi-
nence to their reciprocal relations by content. These rela-
tions may be considered from two points of view : first, that
of identity, and, second, that of congruity.
1. Compared by content, concepts proper are distin-
guished as identical and different. They are —
1st. Identical, when they coincide in their marks, or comprise the
same properties. Identity is either absolute or relative. Absolute
identity, or sameness, does not strictly exist between concepts, but rela-
tive identity, or similarity, does exist. The terms of a complete defi-
nition approach most nearly to absolute identity, both comprising the
same marks or properties, e.g., " Body is extended substance."
2d. Different, when they do not comprise the same properties. Dif-
ference is again either absolute or relative.
2. Compared by content, concepts proper are also divided
by logicians into congruent and conflictive.
1st. Congruent notions are such as may be connected in thought
with the same object, as good, wise, powerful, etc.
2d. Conflictive notions are such as may not be connected in thought.
Conflictive opposition is either contradictory or contrary. Immediate
or contradictory opposites are " directly, immediately, and absolutely
repugnant" to each other, as exemplified in yellow, not-yellow ; walk-
ing, not-walking. Of these conflictives there can be two only, and
one of them must be true. In contrary opposition, on the other hand,
PRACTICAL LOGIC.
more than two conflictive characters are possible, as yellow, blue, red,
etc. ; sitting, standing, lying, etc. If one of these be not predicated of
any person, it does not follow that any one other must be. Thus,
though I cannot at once sit and stand, yet I may be neither sitting
nor standing, — I may lie ; but I must either sit or not sit ; I must
either stand or not stand, etc.
These relations of concepts by content may be represented to the
eye by diagram. Squares may be used to represent the sphere or con-
tent of concepts and also the objects of which they may or may not
be predicated. The overlapping parts of the double squares and the
dotted lines indicate the partial coincidence of the properties. The
sign plus (-(-) may indicate congruence, the sign minus ( — ) confliction.
or
1. Identity,
2. Difference,
Absolute, or
Sameness,
Relative, or
Similarity,
Absolute,
Relative,
Humanity and
Rational I and
Animality. ' "• -"-•
Affection
and
Desire.
Common Element = Emotion.
Spirituality
and
Materiality.
Touching in Being.
Science
and
Art.
Common Element = System of Truth.
1. Congruence,
Good,
Wise
Just,
in Moses.
2. Conflic-
tion,
Contradictory
Opposition,
Contrary Op-
position,
Living
and
Not-living. J L —
I with
f Paul.
Red,
Blue,
Green,
and
R
I-
THE FORMATION OF CONCEPTIONS. 41
Praxis. — State and illustrate by diagram the relation by content
of the following concepts: 1. Running, lying. 2. Blue, not-blue.
3. White, black. 4. Money, memory. 5. Learning, virtue. 6. Saint,
sinner. 7. Grace, unmerited favor. 8. Yellow, blue, red. 9. Walk-
ing, standing, sitting, running. 10. Wealth, poverty. 11. Beauty,
virtue. 12. Old, middle-aged, young. 13. Tall, short.
Give five examples of each of the following relations of concepts by
content: 1. Identity absolute. 2. Identity relative. 3. Difference
absolute. 4. Difference relative. 5. Congruence. 6. Contradictory
opposition. 7. Contrary opposition.
Section III,— Classification,
The second essential element of conception, in the wide
sense, may be defined as grasping in one thought, called a
class, all the objects to which the attributes included in
any concept or notion are common. Hence the process is
called classification. From another point of view it may
be defined as extending the application of the content of a
concept or notion to all the objects to which it is applicable.
Hence the process is also called generalization.
A dime has the property of roundness. When we extend the appli-
cation of this property to all bodies that possess it, and so connect
them all with dime into one thought, the result is the class, round
bodies. A dime has the property of whiteness. When we extend the
application of this property in the same manner as before, the result
is the class, white bodies. Making use of both round and white, the
result is the class, round, white bodies. Classifying by the mark,
stamped as coin, the result is the class of coins.
It is thus evident that the work of classification is simply the gen-
eral application of one or more properties of a concept to objects. The
resemblance of properties or attributes furnishes the key to the work.
If bodies had no differences, there would be but one great, monotonous
mass of existing things ; if they had no resemblances, no two could be
brought together into a group, and there would be no possibility of
thought. Classification is possible because objects have both different
and resembling properties.
Topic First— Process of Classification.
Classes may either be considered singly, or in systems
42 PRACTICAL LOGIC.
or combinations. Hence the ordinary distinctions and
rules.
1. In forming single classes, it is obvious that the thinker
may make use of accidental, peculiar, or essential proper-
ties. In order to reach the most valuable scientific results,
classification should keep in view the most important
properties.
Rule. — Classify by essential properties rather than by
non-essential.
Gold might be classified, by the property of color, with yellow
objects ; silver in the same way with white objects. Such a classifica-
tion would, however, be of no scientific value. Taking the resembling
essential properties of the two: (1), they are elements or simple sub-
stances; (2), they possess metallic lustre; (3), they are good con-
ductors of heat and electricity, — they may be classified with other
objects having like properties, as metals. Such classification is of sci-
entific value.
Praxis. — Classify each of the following with like objects by various
non-essential and essential properties : 1. Porter's " Human Intellect."
2. A comet. 3. The north star. 4. The Temple of Solomon. 5. The
Parthenon. 6. The Washington Monument. 7. The Mississippi River.
8. The Mer de Glace. 9. Mount Vesuvius. 10. Victoria of England.
11. Ulysses S. Grant. 12. Jefferson Davis. 13. Moses. 14. Jesus.
2. Objects of knowledge are so related that they may be
arranged in systems of classes. Such classification requires
the application to classes of the process used in forming
single classes, while keeping in view the wider relations of
things. It is a successive classification of classes.
Rule. — Classify the lower classes under higher by fixing
upon properties common to the lower.
Certain figures are classified, by the number and relation of their
straight sides, as triangles, squares, parallelograms, polygons, etc. All
these classes have the common characteristic, being bounded by straight
lines, and may, therefore, be classed as rectilinear figures. Certain other
figures are classified, by the various character of their curved boun-
dary-lines, as circles, ellipses, parabolas, hyperbolas, etc. All these
THE FORMATION OF CONCEPTIONS. 43
classes have the common characteristic, being bounded by curved lines,
and may, therefore, be classed as curvilinear figures. Rectilinear and
curvilinear figures have, as a common characteristic, plane surface,
and may, therefore, be classed as plane figures. Certain other figures
are classed, by the character of their bounding surfaces, as tetrahe-
drons, cubes, parallelepipeds, etc. They are in common bounded by
plane surfaces, and may, therefore, be classed as plane solids. Certain
other figures are classed, by the character of their bounding surfaces,
as spheres, cones, paraboloids, etc. They are in common bounded by
curved surfaces, and may, therefore, be classed as curved solids. Both
plane and curved solids have in common, solidity, and may, therefore,
be classed as solid figures. Plane figures and solid figures have in
common, extension, which is the subject-matter of Geometry, and may,
therefore, all be classed as geometrical figures. The result is a System
of Classes :
Triangles,
Squares,
Rectilinear
Polygons,
Figures.
.
etc.
1
Circles,
Plane Figures. •
o
Ellipses,
Curvilinear
8
Parabolas,
Hyperbolas,
etc.
Figures.
Geometrical
<D
Tetrahedrons,
Figures.
3
Cubes,
Plane
1
Parallelepipeds,
Solids.
|
etc.
Solid Figures. J
Spheres,
Cones,
Curved
Paraboloids,
' Solids.
etc.
Such systems are found on the most extensive scale in the classifi-
cation of animals and plants, in Zoology and Botany. Exercises in
forming systems of classes may be drawn from these sciences.
Praxis.— Classify the following collections or masses of objects in
single classes and in systems of classes: 1. The articles in a school-
room. 2. The objects in a school or college campus. 3. The struc-
44 PRACTICAL LOGIC.
tures in New York city. 4. The objects comprised in a farm. 5. The
objects embraced in a Pennsylvania landscape. 6. The objects in the
heavens as revealed by a powerful telescope. 7. The operations of the
human soul. 8. The things seen. 9. The things unseen.
Topic Second. — Results of Classification.
The product of the general application of the concept to
all the objects to which it is common is a thought-group, or
a thought-system, of objects, i.e., a class or a system of
classes.
In the general notion as class, the essential thing is
always the grasping together of individuals. The indi-
viduals contained in any such general notion make up its
extent. The extent has also been denoted by external quan-
tity, extension, breadth, etc.
In connection with the class notion and extent, Logic
gives prominence to two things : first, the relations of gen-
eral notions as classes to one another by extent ; second, the
reciprocal relations of extent and content, or of the class
and the concept proper.
I. Relations of Classes to One Another.
1. Compared by extent, general notions as classes stand
to each other in five mutual relations: exclusion, co-exten-
sion, subordination, co-ordination, and intersection.
1st. Exclusion. — One class excludes another when no part of the
one coincides with any part of the other; e.g., horse and syllogism.
No horse is ever a syllogism, and vice versa.
2d. Co-extension. — One class is co-extensive with another when each
includes exactly the same species ; e. g., living being and organized
being. Using life as including plant life, every living being is an
organized being, and vice versa.
3d. Subordination. — One class is subordinate to another (which is
called the superordinate) when the former is included in the latter as a
part of it ; e. g., dog, horse, under quadruped. Every dog is a quad-
ruped, as is also every horse.
4th. Co-ordination. — Two or more classes are co-ordinate when they
are co-exclusive, yet all immediately comprehended under the same
THE FORMATION OF CONCEPTIONS. 45
higher class ; e. g., dog, horse, while immediately subordinate to the
higher class, quadruped, are co-exclusive and, therefore, co-ordinate.
5th. Intersection. — Two classes intersect each other when each is
partially included in the other ; e. g., rational and animal. Some
rational beings are animals and some are not, and vice versa.
These relations may be symbolized by Euler's circular
notation, in which the extent of classes is represented by
circles, and the relations of classes by the relative positions
of the circles.
fa
§*
1. Exclusion.
Horse, syllogism.
2. Co-extension.
Living being, organized being.
3. Subordination.
Quadruped, horse.
4. Co-ordination.
Quadruped, lion, horse.
5. Intersection.
Rational being, animal.
Starting from Inclusion, other logicians divide the rela-
tions of classes into those of (1), Inclusion, embracing,
(a), Co-extension, and (b), Subordination ; (2), Intersec-
tion ; (3), Exclusion, embracing, (a), Co-ordination, and
(b), Non-co-ordination.
2. Special Relations arising from Classification.
Out of classes and systems of classes arise various logical
distinctions which, as they occur constantly in science and
philosophy, in the writings of the modern as well as ancient
masters, should be understood by the student who expects
to read and think for himself.
46 PRACTICAL LOGIC.
(1.) The simpler forms of classification give rise to the
distinctions of genus, species, differentia, individual.
In any series of higher and lower classes, each higher class is a
genus to those next below it. Those classes next below the genus are
its species. Caucasian, Mongolian, Malaysian, Negro, and American
Indian are species of the genus, man. Or, if European is considered as
a genus, German, Frenchman, Englishman, etc., are the species. Dif-
ferentia, or specific difference, is the characteristic or property, simple
or complex, which distinguishes one species from others under the
same genus. Bed is the differentia of red rose, or that which distin-
guishes it from white, yellow, and other species of the genus, rose. An
individual is one of the single objects of which a species or genus is
always made up. It is only capable of physical or mechanical par-
tition, and can never be a genus. Washington and Napoleon are
individuals.
Note.— Species, in its peculiar use in Natural History, needs to be carefully
distinguished from species in Logic. In Natural History, species means only
"such a class of animals as has, or might have, descended from a single origi-
nal pair, and the varieties of which may permanently interpropagate among
themselves." The sub-species are named varieties. Greyhound, spaniel, ter-
rier, bull-dog, etc., are varieties of the species, dog.
(2.) Systems of classes give rise to the logical distinc-
tions of summum genus, infima species, subaltern genera
and species, proximate genera and species, superordinates,
subordinates, co-ordinates, and disparates.
The highest class in any system of classes is known as summum
genus ; the lowest class, which can never be a genus, as infima species.
The absolute highest genus is being, which includes all the existences
in the universe. In classifying any department of knowledge, it is
usual, however, to assume and start from some relative highest genus.
In Botany, this genus is plant; in Zoology, animal. Subaltern genera,
or sub-classes, are those which are species of a higher genus. Subal-
tern species, or sub-species, are species of some higher species consid-
ered as a genus to those lower than itself. White oak, black oak,
scarlet oak, yellow oak, etc., are subaltern species of oak. Oak is a
species of the genus, mastwort, or cup-bearing trees, and constitutes,
with chestnut, beech, hazel, and hornbeam, the subaltern genera, or
sub-classes, of that class.
This may be illustrated by the following tabular example:
THE FORMATION OF CONCEPTIONS. 47
Designations. Glasses.
Summum Genus. Being or Thing.
Species or Subaltern Genera. Organic (Inorganic).
Intermediate or Sub-Species. Animal (Plant).
Infima Species. Man (Brute).
Individuals. Washington (Other Men).
Genera and species, which are next to each other in order of ascent
or descent in any system of classes, are known as proximate genera
and species, or nearest classes and species ; as animal and man, in the
example just given. The higher genus in relation to a lower is called
the superordinate genus, or next in rank above ; the lower in relation
to the higher, the subordinate, or next in rank below. The species
under any genus are co-ordinates, or of equal rank. This may be
illustrated by the following example :
Assumed Highest Genus, — Cup-bearing Trees.
Species. Oak. Chestnut. Beech. Hazel. Hornbeam.
S f Red, American, American, American, Ironwood,
Spanish, Red, Beaked, Hornbeam,
Dwarf, etc. etc. etc.
etc.
Oak, chestnut, etc., are superordinates with reference to the co-
ordinate species respectively embraced under them. The co-ordinate
species, red, white, etc. ; American, Spanish, etc., are subordinates to
oak and chestnut respectively, and these last to the higher genus, cup-
bearing trees, which embraces also beech, hazel, and hornbeam. Any
one of these co-ordinates, considered in relation to a higher or lower
part in the divisions of any of the other co-ordinates in the system of
classes, is called disparate. Red oak as compared with chestnut is
disparate.
II. Reciprocal Relations of Concepts and Glasses.
The concept and class notions are both very closely con-
nected with one another, and embodied in one word. From
one point of view the word man means the rational and
animal properties which make man what he is. It has,
therefore, content or contained properties. From another
point of view man means all the individuals that have these
48 PRACTICAL LOGIC.
common properties, or all mankind. It has, therefore,
extent or comprehended objects. The Rule expressing the
relation of content and extent is, that as the content in-
creases the extent diminishes, and as the extent increases
the content diminishes.
In other words, the greater the number of properties in a concept,
the less the number of objects that have all these properties in common,
and the greater the number of objects in a class, the less the number
of properties common to them all. This may be illustrated by the
following diagram of concept and class in content and extent :
CONCEPT CONTENT, EXTENT,
and i. e., the properties con- i. e., the objects embraced
CLASS. tained in the concept. in the class.
Body. Extended substance. Stone, Plant, Brute, Man, etc.
Living Body. Body with life. Plant, Brute, Man.
Animal. Body with life and sensation. Brute, Man.
Man | Body with life, sensation, and 1 -^an
i reason. J
Washington, f Body with life> sensation, reason, ) individual.
(. Father of his country. J
From this diagram it is apparent that the concept, body, which has,
as its content, only extended substance, has the greatest extent, em-
bracing stone, plant, brute, man, etc., while the lowest concept, man,
which has, as its content, extended substance with life, sensation, and
reason, has the least extent, embracing only mankind. Washington,
with still broader content, has, as its extent, only an individual.
Being, the concept of least possible content, containing simply exist-
ence, is the absolute highest class, and has the greatest possible extent,
embracing all things material and spiritual.
Praxis. — Give five illustrations of each of the following relations
of classes: 1. Exclusion. 2. Co-extension. 3. Subordination. 4. Co-
ordination. 5. Intersection.
State and illustrate, by diagram and by circular notation, the rela-
tions of the classes: I.Man, horse. 2. Dog, ox, alligator. 3. Book,
manuscript. 4. Magazine, daily paper. 5. Planet, body moving round
the sun. 6. Aryan, European, Frenchman. 7. Faith, hope, love.
8. Affection, desire. 9. Man, animal. 10. Plant, tree. 11. House,
barn. 12. Botany, Geology. 13. Mathematics, Astronomy.
Illustrate by three examples each: 1. Genus, species, differentia,
THE FORMATION OF CONCEPTIONS. 49
individual. 2. Highest class, lowest species, sub-class, sub-species,
superordinate, subordinate, co-ordinate, disparate. 3. The varying
relation of content and extent.
Section IV,— Denomination,
When, by the processes of conception, concepts and classes
have been formed, they need to be embodied in language in
order that they may be fixed and made subject to recall for
further use. This is the third essential element in Concep-
tion.
Topic First. — The Process of Naming.
Language is the expression of thoughts by means of
words spoken or written. It is the medium of communi-
cation between men. It fixes thoughts which would other-
wise be vague, or fleeting, or confined to some individual,
and makes them the property of all. It thus greatly facili-
tates the progress of our thinking. In short, while it is
true that some of our processes of thought may be carried
on without any language, it is nevertheless true that with-
out it thought would practically cease, while communica-
tion would become impossible.
I. Modes of Naming.
In giving names to our conceptions, the aim should be to
embody them as perfectly as possible and bring them as
fully as may be under the recall and control of ourselves
and others. It is evident that this aim is not always kept
in view. Things are named in various ways, and the names,
judged by the mode in which they are given, are oftener
non-logical than logical.
1. The name is sometimes purely arbitrary. This is often the case
with the strictly proper name. " It denotes an individual, but does
not indicate or imply any attribute of that individual. . . It is an
unmeaning mark or sign which we connect in our minds with an
object, so that when this sign meets our eyes or ears we may think of
5 D
50 PRACTICAL LOGIC.
that individual." The most profane of men may be named Christo-
pher, Christ-bearer.
2. The name is sometimes given from some accidental circumstance
or property. In proper names this is illustrated by such Bible names
as Moses, drawn out; Isaac, laughter. In common or class names, the
same process is illustrated by moon, measurer; planet, wanderer; vul-
ture, flyer; lord, loaf -keeper.
3. The name sometimes embodies some prominent essential property
or mark. This is illustrated by such words as sun, shiner; man,
thinker; animal, breather; barometer, weight-measurer.
4. The perfect or strictly logical name aims to embody as completely
as possible the entire essence of a conception. As such naming is
difficult in the case of complex conceptions, it is usually necessary to
fix upon some prominent essential property, in accordance with the
principle already given. The essential marks in the conception, man,
are rational and animal, but the Aryan people who named man seized
upon the essential mark, thought, and so called him man, i. e., thinker.
5. Names, as languages are constituted, are often, in fact, little more
than mere hints, which start the mind on its work of interpretation.
This has been shown by Hamilton to be one of the necessities of lan-
guage,— since, unless the vocabulary becomes almost infinite so as to
express all our single notions, the same words must be used to express
a multitude of thoughts, more or less differing from each other. See
Hamilton's Logic, p. 437.
II. Rules for Naming.
The Rules for giving names to our conceptions naturally
arise from the aim in naming.
Rule 1st. — Name a conception what it is.
The science of the human soul should be named, not mental philoso-
phy, nor intellectual philosophy, nor metaphysics, nor philosophy, but
psychology.
Rule 2d. — Make the name self-interpreting if possible.
A name is notative when it suggests its own marks (note), and thus
» becomes self-interpreting. It is symbolical when it serves as a symbol
or label of properties or marks which it does not suggest. Names
should be notative, if possible, in order to give the mind the best start
in its work of interpretation. It is a fact to be noted, that many
THE FORMATION OF CONCEPTIONS. 51
names which were originally notative have lost their power of sug-
gestion except to men who are educated. To one who would best
understand thought as expressed in English, acquaintance with the
languages from which the English has drawn its words becomes a neces-
sity. To one acquainted with Latin, triangle, quadruped, biped, become
notative and self-interpreting. To one having the mastery of Greek,
democracy, oligarchy, oxygen, mythology, philosophy, become self-
interpreting. To one understanding Anglo-Saxon, lord, wicked, battle,
war, orchard, become self-interpreting. To one versed in Philology
and History, heathen, villain, church, sincere, saunter, become self-
interpreting.
Rule 3d, — Make the name as simple as possible.
As the genius of our language is Saxon, let the preference be given
to Saxon, and, if possible, let the name be a single word. Pierce is
better than penetrate ; love is stronger than affection, and hate than
animosity ; working is more forceful than operation. Psychology, as
being one word, is better than intellectual philosophy ; arithmetic
than the art of computation.
Rule 4th. — In naming a system of conceptions or classes,
use a system of names.
In a system of names one may be made to suggest all the other
names and thoughts. Such system is thus of immense advantage,
especially in the various Sciences. In .the Natural History Sciences,
which deal largely with classes, a system of distinctions has been
adopted by which the precise place of each logical genus and species
in the great system of classes may be accurately fixed. In Zoology,
the Animal Kingdom is separated by Agassiz into Branches, Classes,
Orders, Families, Genera, Species, Varieties.
Praxis. — Test the following names by the rules for naming, stating
whether they are notative or symbolical: 1. Intellectual Philoso-
phy, for science of the human soul. 2. Paternal ancestor, for father.
3. Affection, for love. 4. Sierra Nevada Mountains. 5. Telegraph.
6. Geology. 7. Geography. 8. Academy. 9. School of herring. 10. Ac-
cident. 11. Blackboard. 12. Candlestick. 13. Ambition. 14. Navy.
15. Book. 16. Bible. 17. Volume. 18. Parchment. 19. Paper.
20. Pen.
52 PRACTICAL LOGIC.
Topic Second. — Products of Naming.
The products of naming concepts and classes are the
various kinds of terms in which our notions are embodied.
The divisions are based, (1), either upon something in the
term itself; or (2), upon something in the relations of
terms.
I. Kinds of Terms arising out of the Nature of the Term
itself.
The term involves in itself three elements, — mark or
property, object, name.
1. Considered as made up of marks, terms are divided,
(1), by the presence or absence of such marks into positive
and non-positive; (2), by the separation or connection of
the attributes with objects, into abstract and concrete.
(1.) All terms are either positive or non-positive. A positive term
is one that implies the presence of some real mark or property, as
man, tree, good. A non-positive term is one that implies the absence
of such mark or property, as not-man, uncertain, deaf. Non-positive
terms are either negative or privative. A negative term is one that
implies simply the absence of any real mark, as not-tree, not-good,
uncertain. Terms apparently negative are often positive in reality,
as immortal, the word meaning not only not subject to death, but
living for ever. So terms apparently positive are often negative,
as idle, which is equivalent to not working, or not disposed to work.
Privative terms are equivalent to a positive and negative term taken
together. They mark the absence of certain properties, and the pres-
ence of others, from which the presence also of the former might nat-
urally have been expected. Such terms are, blind, unkind, unholy.
Blind is not equivalent to not seeing, nor to not capable of seeing, but
signifies deprivation of sight in some being which might have been
expected to have it.
(2.) All terms are either abstract or concrete. Abstract terms are
those which embody abstracts or marks or properties as apart from
the objects to which they properly belong, as coldness, hardness. Of
the innumerable abstracts formed, the mind suffers the greater number
to pass without naming, but fixes some by names. Thus in observing
some individual man, the abstracts, life, intelligence, feeling, self-
THE FORMATION OF CONCEPTIONS. 53
activity, etc., are seized upon and fixed singly by names ; or several
of them together, under one name, as intelligence, feeling, etc., under
rationality; or all the marks together under humanity. Concrete
terms present the marks or qualities in connection with the objects to
which they belong, or (as indicated by the derivation of the word
from the Latin con and cresco, or con and cerno} with which they are
grown together or seen together, as the adjective terms, cold, hard, and
the substance terms or substantives, ice, iron, man.
2. Considered as embodying objects, terms are divided,
(1), by the number of objects embodied, into singular and
universal ; (2), by the connection of the objects with their
marks, into connotative and non-connotative.
(1.) All terms are either singular or universal. Singular terms are
those in which our percepts or simple apprehensions are embodied, or
our general notions as connected with our perceptions ; as, Shakespeare,
the Great Eastern, this man. They begin with embodying simple no
tions, but gradually rise toward the expression of thought proper or
general notions. They are of three kinds : proper names, individual-
ized common names, and collective names. Proper names are singular
concrete terms which denote an individual, but do not necessarily
indicate or express any properties of that individual; as, George
Washington, Alexander Hamilton. There is, however, a tendency in
the progress of thought to connect with and designate by the proper
term the peculiar qualities of the individual denoted by it. We say
of a man he is a Washington or a Caesar — meaning to bring out his
patriotism and equanimity or his ambition and universal genius. An
individualized common term is one which expresses the simple notion
of an object as it is presented to us in the concrete with more or less
of its properties; as, this table, this man, yonder mountain. It is
usually formed by adding some individualizing or limiting word to a
common or general term ; as, this table, that man, an organ, my hat.
The collective term is also properly a singular made up of many
objects brought together into the unity of a mass, rather than that of
a class ; as, the House of Commons, the army, a regiment, a forest.
The universal term is that in which the general notion, embracing
concept proper and class, is embodied. It is universal, as it embraces
all the objects possessing the common marks or properties involved in
it as an attribute term. It is common, or general, since it is applicable
to any and every one of these objects, as living, or man, is applicable
5*
54 PRACTICAL LOGIC.
to every individual of the human race. It differs from the collective
term, which embraces a number of things joined together in one mass,
as regiment, Congress, since the collective is not applicable to each and
every object under it. Every being embraced under the general term,
man, is a man ; but not every soldier embraced under the collective
term, army, is an army. When the concept proper, or complement of
ID arks or properties in a general term, is made prominent, it is used as
a concept, or attribute, term; when the class, or complement of objects
embraced in it, is made prominent, it is considered as a class term. In
he propositions, Jesus was man ; Jesus was a man, — the meaning of
the first is, that Jesus had the marks or properties of a man ; of the
second, that he belonged to the class, man. In the first proposition
man is a concept or attribute term ; in the second, a class term.
(2.) All terms are either connotative or non-connotative. A conno-
tative term is one which denotes an object, and notes along with it a
mark or property. A npn-connotative term is one which signifies an
object only or a property only. All proper names are non-connota-
tive, since they denote objects, but connote no property ; as, Wash-
ington, London. All abstracts of qualities, as whiteness, length, are
non-connotative, as they denote only properties without connoting
any objects. All adjectives, as white, just, and all concrete general
names, as bird, fish, are connotative, since they denote objects and
connote properties.
3. Considered as words, terms are divided, (1), by self-
interpretation, into notative and non-notative or symbol-
ical ; and (2), by the number of words constituting the
term, into simple and complex.
(1.) All terms are either notative or symbolical. This distinction
has already been defined and illustrated under the Second Rule of
Denomination.
(2.) All terms are either simple or complex. A simple term is one
which consists of only one word. But some words cannot be used as
terms, although they may form parts of terms. Hence arise complex
terms, which are made up of combinations of words. With reference
to their being used as terms, words are either categorematic (from a
Greek word, to assert or predicate), i. e., such that they can stand
alone as complete terms in propositions ; or syncategorematic (from
the Greek, to assert or predicate along with), i. e., such that they can
only form parts of terms, since they must be used with other words to
THE FORMATION OF CONCEPTIONS. 55
make up complete terms. To the former belong the noun, adjective,
and certain parts of the verb. There are, however, those who con-
tend that in the last analysis only nouns can form, terms. Such sen-
tences, as " Dictionaries are useful," must be completed by adding
books or things; thus, "Dictionaries are useful books" Adverbs,
prepositions, conjunctions, etc., are syncategorematic. We speak of
" the conservation of energy," " the conflict of religion and science,"
thus uniting many conceptions in one, and embodying them in a
phrase. In the statement, "This is a faithful saying, and worthy of
all acceptation, that Christ Jesus came into the world to save sinners"
the part italicized is a term expressed in a sentence. Complex terms
are formed by combining syncategorematic with categorematic words.
Any of the objects and properties included under the Predicables may
thus be combined in complex terms.
II. Kinds of Terms arising out of the Relations of Terms.
Terms are divided, 1, by their relation to one another,
into relative and non-relative or absolute ; and, 2, by their
relation to the objects of which they are predicated, into
compatible and incompatible.
1. All terms are either relative or non-relative. A relative term is
one which implies some other of which we may predicate it as its cor-
relative, as father, son ; ruler, subject; cause, effect. Non-relative or
absolute terms are such as do not imply any such relative object or
correlative, as tree, stone.
2. All terms are either compatible or incompatible. Compatible
terms are such as can be applied to the same object at the same time.
Contrary terms are the most opposed that can be conceived as appli-
cable to the same object at the same time, as wise and foolish, good
and bad. They are not compatible, however, when used in a strict
sense ; since anything which is absolutely good cannot be in any sense
bad. Incompatible terms are such as are entirely excluded from appli-
cation to the same object in the same sense at the same time. All
contradictory terms are incompatible, as wise and not- wise, black and
not-black.
These various distinctions of terms, embodying impor-
tant distinctions in thought, are to be met with more or
less frequently in all the profounder discussions in science,
philosophy, and theology. Most of them will be found to
66 PRACTICAL LOGIC.
be of value in the subsequent portions of Logic. They may
readily be presented in outline form by the student.
Praxis. — Apply all the foregoing distinctions, as far as possible, to
the following words : 1. Government. 2. Industry. 3. Art. 4. Agri-
culture. 5. Joy. 6. Jupiter. 7. This earth. 8. The consolations of
philosophy. 9. Intemperance. 10. Foolish. 11. Sobriety. 12. Hope-
fulness. 13. Psychology. 14. Virtue. 15. Non-relative. 16. Abso-
lute. 17. Immortal. 18. Deaf. 19. From. 20. Life.
Select, from the page preceding the praxis, the following kinds of
terms or words: 1. Negative. 2. Privative. 3. Simple. 4. Complex.
5. Concrete. 6. Abstract. 7. Relative. 8. Absolute. 9. Singular.
10. Universal. 11. Syncategorematic. 12. Notative. 13. Symbolical.
14. Connotative. 15. Non-connotative. 16. Abstract. 17. Concrete.
18. Collective. 19. Attribute. 20. Class.
CHAPTER II.
THE UNFOLDING OP CONCEPTIONS.
CONCEPTION, in its three essential elements, conception
proper, classification, and denomination, has been found to
result in three products :
First, the Concept Proper, embracing content or contained
properties ;
Second, the Class, embracing extent or included individ-
ual objects;
Third, the Term, embodying both concept proper and
class, and, therefore, to be regarded either as an attribute
term or as a class term.
The processes of unfolding these products, or of ascertaining accu-
rately and exhibiting systematically and completely what is con-
tained in them, are the processes at the foundation of all right and full
understanding of the materials of which discourse, whether spoken or
written, is made up. It is evident at once that a man who does not
understand what is involved in such conceptions as cause, force, expe-
THE UNFOLDING OF CONCEPTIONS.. 57
rience, persistence, can neither think nor discourse intelligently con-
cerning them, and can neither hear nor read intelligently anything
that others may say or write, which involves these conceptions.
As the products of conception are three, the processes of
unfolding are three :
First, the unfolding of the content of the concept proper.
This has been named Metaphysical Analysis, but has also
been called Logical Partition.
Second, the unfolding of the extent of the class. This is
known as Logical Division.
Third, the unfolding of the term. This will be known
as Logical Definition.
Logical Partition, Division and Definition will, there-
fore, furnish the subjects of the three Sections embraced
under the Unfolding of Conceptions.
Section I,— Logical Partition,
Logical Partition is that form of analysis which takes a
concept proper, as a complex of properties or attributes,
and unfolds the component properties. In other words,
Logical Partition is the complete and orderly statement of
the parts of the content of a concept, or the separation of
a complex attribute into its component attributes.
The thought-whole analyzed in partition is the concept
proper which is an attribute or intensive whole.
The mind contemplates the objects presented to it under three kinds
of wholes :
1st. Mathematical or Quantitative Wholes, or Wholes of strict In-
tuition. This inckides two kinds :
a. The Numerical, based on Time.
b. The Geometrical, based on Space.
2d. Essential orThysical Wholes, or Wholes of Observation. This
includes two kinds :
a. The Substance, as composed of substance and attributes.
b. The Causal, as composed of cause and effects.
58 PRACTICAL LOGIC.
3d. Logical Wholes, or Wholes of Discursion or Thought. This
includes two kinds :
a. The Attribute or Intensive Whole, or Whole of Content.
b. The Class or Extensive Whole, or Whole of Extent.
A mathematical whole, called also a quantitative, an intuitive, an
integrate, whole, is, according to Hamilton, one composed of integral,
or, more properly, integrant parts. It is a whole every part of which
lies out of every other part, while all the parts together make up the
integer or complete whole. Thus in the integrate spacial whole of the
human body, the head, body, and limbs, its integrant parts, are not
contained in, but each lies out of, each other. When the parts of an
integrate spacial whole are separate and accidentally thrown together,
the result is a mass whole, as a gallon of water, a pile of wheat, a
block of wood. When the parts of an integrate numerical whole are
thus separate and accidentally thrown together, the result is a collect-
ive whole, as an army, a forest. These wholes are analyzed by
mechanical or physical partition.
An essential whole, called also a physical whole and a whole of
observation, is the kind of whole with which observation brings us in
contact. It consists of substance and properties either of quality or
of action. The parts do not lie out of each other, but substance and
property permeate and modify each other. Thus in gold the material
substance is inseparably connected and blended with the properties of
quality and action, metallic and reflecting the yellow rays of light.
These wholes are analyzed by the process of mental analysis already
described.
A logical whole, called also a whole of thought, is the product of
the power of conception, and is, therefore, a creation of thought. As
a concept proper it is analyzed by logical partition ; as a class whole,
by logical division.
Logical analysis by partition and division, therefore,
deals with the logical whole in its two forms, partition
having particularly to do with the logical whole as an
attribute whole. The aim of partition, to unfold the con-
tent of an attribute whole, will, in connection with the
nature and make-up of this whole as already learned from
the formation of the concept proper, suggest the forms and
rules of the process.
THE UNFOLDING OF CONCEPTIONS. 59
Topic First.— The Forms of Logical Partition.
The purpose of the thinker in partition is to attain to
completeness in the work of unfolding the marks or prop-
erties of the concept. Such completeness may be either
relative or absolute. This gives the two forms of partition.
I. Relatively Complete Partition.
A partition is relatively complete when complete from
the thinker's point of view or for his special purpose. It
is obvious that it is not always the aim to bring out
all the possible properties included in the four predicable
classes. Thus the chemist may desire to bring out the
properties of gold as an element or as a metal ; the banker,
as a medium of exchange ; the encyclopaedist, in these
and all other aspects. It is thus manifest that any one
of many points of view may be made available, the choice
being always governed by the object of the thinker.
The point of view may be some one of the four kinds of properties,
and the aim to reach the component parts from this point of view.
The concept man may be parted by qualitative properties into ration-
ality and animality ; or by active properties, or as a causal agency,
into self-acting, thinking, feeling, etc. ; or by properties of condition,
into temporal, terrestrial, etc. ; or by relative properties, into depend-
ent, responsible, sinful, etc.
Or the point of view may be a single aspect of some one of the four
kinds of predicable properties. E. g., taking active properties as the
starting-point, man as a causal agency operates in many different
spheres, and may, therefore, have the properties unfolded with ref-
erence to any one of these spheres. The thinker may be a physicist
and so may regard man materially, as counterpoising more or less
weight and excluding other objects from the same space. He may be
a chemist and so may regard man chemically, as forming, by decom-
position, nitrogen, carbon, and other chemical elements. He may be
a physiologist and so may regard man organically, as breathing,
digesting, etc. He may be a political economist and so may regard
man industrially, as farming, manufacturing, trading, or as producing,
transporting, consuming, etc. He may be a psychologist and so may
60 PRACTICAL LOGIC.
regard man spiritually, as thinking, feeling, willing, etc. He may be
a theologian and so may regard man religiously, as recognizing, long-
ing after and worshipping God, etc.
II. Absolutely Complete Partition.
A partition is absolutely complete when the aim is to
give an exhaustive analysis of a concept, or to present all
the kinds of properties.
In such partition the various characteristics of man, as given from
the four points of view, would all be embraced. Or, to take another
example, gold may be parted by qualitative properties, as material,
solid, elementary substance, etc. ; by active properties, as reflecting the
yellow rays of light, conducting heat and electricity, counterpoising
great weight, etc. ; by relative attributes (including condition and
relation proper), as being mainly confined to particular regions of the
earth, being of great value as a precious metal, being the standard of
values in exchange, etc.
Topic Second. — The Rules of Logical Partition.
The rules for logical partition are determined by its aim
to unfold systematically, from some definite point of view,
the properties or attributes contained in a given concept.
Rule 1st. — The thinker in partition should first fix upon
a single complement of attributes, should then determine
upon the proper point of view for the purpose he has in
mind, and should finally adhere to this point of view
throughout the entire partition.
This is the law of unity. The danger of violating it arises from
the fact that language uses the same term or the same form of ex-
pression for very different concepts or bundles of properties. Man,
from the point of view of the physiologist, has very different marks
from man as considered in social science or in psychology or theology.
Physiology considers man as a material, organized, living being ;
social science, as a member of society and having certain social wants
and instincts ; psychology, as a spirit embodied ; theology, as a crea-
ture and subject of God. The law of unity requires that the proper
point of view be fixed upon and prohibits the mixing up of proper-
ties belonging to man from these various points of view.
THE UNFOLDING OF CONCEPTIONS. 61
Rule 2d. — A partition should be complete from its point
of view, or inclusive of the whole complement of proper-
ties divided.
This is a form of the general law of completeness or adequacy or
integrity. So far as a partition is incomplete it omits something essen-
tial to the conception, and thus fails to give that distinct view which
requires that all the parts be presented in their proper relation to each
other. Moreover, incomplete partitions are necessarily partial or one-
sided, and will inevitably lead to positive error. If, for example, in
analyzing faith as a Christian virtue, we recognize only the marks,
knowledge, assent or intellectual belief, and sentiment or response of
the heart, leaving out all moral disposition or purpose, we make faith
involuntary, and so take from it the essential element of all virtue.
Such faith ceases to be a virtue. Mr. Mill falls into a like error in
analyzing cause, as invariable antecedence, thereby omitting efficiency,
the principal and essential property involved in causation.
Prof. Day, in writing of the general Law of Adequacy in analysis,
says: " The practical importance of a careful observance of this Law
of Logical Analysis is to be seen in the fact that by far the greatest
part of erroneous opinion in all departments of knowledge arises from
the incomplete apprehension of the objects of knowledge. Most dis-
sensions in science and in belief would be ended by a complete survey
of all the constituent elements of the matter in dispute. It is mainly
because the parties look, one at one element, the other at another, and
each to the exclusion from his view of some element or character im-
portant to a correct opinion, that any dissension arises." This holds
with special force in partition, since this process deals with the prop-
erties, involved in the essential nature and make-up of things, upon
which all scientific classification depends.
If, for example, murder is analyzed into the elements, taking of
human life, deliberate purpose, then the act of the sheriff in hanging
a murderer, or the killing of another in self-defence, would be murder.
The essential element of malice is omitted in the analysis. Or, again,
if virtue is analyzed as embracing intelligence and conformity to the
law of right, omitting intention, then the act of every hypocritical
Pharisee in giving alms might be termed virtuous. On the other
hand, if right intention is embraced in the partition, and conformity
to the law of right omitted, the acts of the fanatic and enthusiast
might be termed virtuous. It is only by taking in all the elements
that error is escaped. Or, once more, if the characters of the rose are
6
62 PRACTICAL LOGIC.
given, as a shrub, producing flowers, having thorns, the rose might be
confounded with any thorn-bush. All such possibilities of error are
eliminated when the characters are fully enumerated as they are in
the scientific text-books of Botany.
Rule 3d. — A partition should be exclusive, i. e., it should
shut out all marks or characters not belonging to the sub-
ject.
This rule corresponds to the Law of Parcimony under observation.
It is violated if education is made to embrace, drawing out of the
powers, putting them to use by their proper exercise, in the study of
the physical sciences, in a scientific school. The use, the kind of study,
and the place are none of them essential to the process, and they should,
therefore, be excluded. So money may be analyzed into the charac-
ters, stamped metal, means of exchange. This, however, would not
apply to most of the money in use in civilized lands, as most of it is
not metallic. Money embraces the characters, representative of value,
means of exchange, passing current, so that metallic is not an essen
tial characteristic.
Rule 4th. — A partition should be orderly in the arrange-
ment of the component elements.
This requires that some principle of arrangement should
be seized upon and made use of in the statement of the
elements of the complex thought analyzed. It also requires
that in any continued process of partition the elements ob-
tained should be arranged so as to bring out the relations
of co-ordination and subordination.
In analyzing man, in its intrinsic elements, by partition, we may
begin with the visible and tangible and proceed to the higher invis-
ible and intangible. The resulting partition will be, animal attributes
or animality and rational attributes or rationality. Analyzing ani-
mality, we may again proceed from lower elements to higher. The
result will be, attributes of matter or corporeity, of organization, of
life, of sentiency, of voluntary motion. On the same principle of pro-
cedure, rationality will yield the properties of intelligence, emotion,
and endeavor. The rule given requires such orderly procedure and
arrangement in the work of partition. In the partition of man. it
THE UNFOLDING OF CONCEPTIONS. 63
would forbid the mingling of the two sets of attributes and the co-
ordination of any of the set of attributes resulting from the second
step in the partition, as sentiency, with animality or rationality.
In an exhaustive process of partition each of these elements should
be still further divided into its component properties, until the ulti-
mate elements are reached. For example, corporeity would give
extension in length, breadth and thickness, weight, etc. Organization,
life, etc., would each be found to yield component elements co-ordinate
with those of corporeity.
Praxis. — Give exhaustive Partitions of the following Concepts, test-
ing the work by the Rules: 1. Money. 2. Englishman. 3. The love
of God. 4. Life. 5. Salvation. 6. Genius. 7. Despair. 8. Forgive-
ness. 9. Heaven. 10. Duty. 11. Manliness. 12. Wisdom. 13. Jus-
tice. 14. Beauty. 15. Prophet. 16. Foresight. 17. Value. 18. For-
titude. 19. Egotism. 20. Selfishness. 21. History. 22. Philosophy.
23. Benevolence. 24. Charity. 25. Eternity. 26. Omnipotence.
27. Politeness. 28. Explanation. 29. Confirmation. 30. Design.
Give the component elements of the following Concepts, stating the
kind of whole and the point of view, and showing that the Partition
is in each case made in conformity to the Rules given : 1. The violet.
2. The diamond. 3. Botany. 4. Habit. 5. Hope. 6. Affection.
7. Religion. 8. Art. 9. Fine Arts. 10. The orange. 11. Carbon.
12. Monsoon. 13. Partition.
Examine the following Partitions, stating the kind of whole and
the point of view, showing whether they conform to the Rules, and,
in case they do not, correcting or completing the Partition according
to the Rules :
1. Government = Intelligent power, ordered by law, controlling
action.
2. Duelling = Fighting of two persons, mutual agreement, intent to
kill, deadly weapons.
3. Lie = Enunciation of what is false, intent to deceive, violation
of some obligation to give to others the truth.
4. Novel = Fictitious story, central interest in love, artistic con-
struction.
5. Contract — Two parties, mutual promise, mutual obligation.
6. Charity — Compassion and sympathy for the needy, kindly and
affectionate provision for the need, wise administering of the relief.
7. Circle = A curved line, drawn round a given point.
8. Planet = A star wandering in the heavens.
64 PRACTICAL LOGIC.
9. Triangle = A plane figure, three sides, three angles equal to two
right angles.
10. Parallelogram = A plane figure, four-sided, opposite sides equal
and parallel, opposite angles equal.
11. Fluid = Material substance, yielding easily to pressure, parts
readily changing relative position without separation, gaseous form.
12. Whale = A large fish, living in cold regions, useful, yielding oil.
13. Education = Instruction, moral discipline, training.
Section II,— Logical Division.
Logical Division is that form of logical analysis which
takes a conception as a genus or class whole and unfolds its
component species. In the words of Ueberweg : " Division
is the complete and orderly statement of the parts of the
extent of a notion, or the separation of a genus into its
species."
Note. — The student needs to distinguish carefully between partition and
division. The former takes a concept proper or attribute whole and separates
it into its component properties ; the latter takes a genus or class whole and
separates it into its component species made up of individuals.
The grounds or principles of division are found in the
concept proper, or the common properties by which the
objects in the class were originally classified. These prop-
erties embodied in the concept proper, and making up its
content, have been called the base, since they are at the
foundation of both concept and class. The possible prin-
ciples of division in any given case are, therefore, only
limited by the number of properties and combinations of
properties, intrinsic and extrinsic, contained in the base
and unfolded by partition.
Thus the class man has a content or base of two complex intrinsic
properties, animality and rationality. The class may he divided by.
any property embraced in these. It may be analyzed into animal
parts, — by the material properties, of extension in length, of weight
and of color, giving tall and short ; heavy and light ; white, tawny,
and black : by the properties of organization, giving sanguine, nerv-
ous, and bilious; etc., etc. Or man may be divided into rational
THE UNFOLDING OF CONCEPTIONS. 65
parts, — by different properties of intelligence, giving cultivated and
uncultivated ; enlightened and barbarous ; learned and unlearned ;
imitative and creative ; etc. : by the comparative prominence of the
intelligence, sensibility, and will, giving intellectual, sentimental, and
practical. Or it may be divided by both animal and rational parts
combined, — by language, giving Aryan, Semitic, and Turanian ; by
race constitution, giving Caucasian, Mongolian, etc. ; and the like.
Man has also a base of many extrinsic properties, or properties of con-
dition and relation, which may also furnish innumerable other prin-
ciples of division. It may thus be divided by relation to place, as
European, Asiatic, etc. ; islanders and dwellers on the continents ;
men of the torrid, temperate, and frigid zones ; and the like : by rela-
tion to time, into ancient and modern ; or ancient, mediaeval, and
modern ; antediluvian and postdiluvian ; old, middle-aged, and young ;
and the like : or by relation proper, into bond and free ; rulers and
ruled ; and the like.
Topic First. — The Forms of Logical Division.
The principal forms of logical division are the artificial
or dichotomous and the natural. Either of these may be
single and unextended or complex and extended.
1. The simplest form of division is the artificial or di-
chotomous, or that which arrives at two members which are
contradictories.
For example : animals are rational and irrational, or vertebrate and
invertebrate; angles are right and not-right or oblique; oblique
angles are acute and not-acute or obtuse ; the ancients were Jews
and Gentiles, or Greeks and barbarians, or bond and free.
Such division is said by the logicians to be strictly
logical, considering merely the form of the thought and
not requiring any knowledge of what the concepts mean
in order to assure us that the division is correct and ex-
haustive. But, as Ueberweg has remarked, "it labors
under the defect that the species classed under the nega-
tion are left indefinite. Through the unimportance of the
principle of division, or by reason of the number of species
included in the negative and contradictory notion, the
division may become worthless."
6* E
66
PRACTICAL LOGIC.
Substance.
Thus, the division of the universe into partridges and not-partridges
is of no value, both because of the worthlessness of the ground of
division and the indefiniteness of the negative notion.
The process of dichotomous division may be extended
until the lowest species or individuals are reached. There
are two forms of this extended dichotomous division, a loose
form and a strict one.
In the loose form the principles of division are seized upon suc-
cessively as the new occasions of division arise. This is illustrated
by what is known, from its author, the Greek logician Porphyrius, as
the Tree of Porphyry, which,
starting with substance as the
highest genus, closes with man
as the lowest species, and with
Socrates, Plato, etc., as the indi-
viduals.
It will be observed that the
successive principles of division
are the qualities implied in cor-
poreal, animate, sensible (or sen-
tient), and rational. It is evident
that the divisions on the nega-
tive side, incorporeal, insensate,
etc., are also capable of like sub-
division with those on the posi-
tive side.
In the stricter form of dichot-
omous division, one principle of
division is carried through the
entire series of subdivisions. In
this case it is necessary to select
at the outset some mark or attri-
bute of the original class, as the
principle on which the successive
divisions shall be made. This
Corporeal.
Animate.
Sensible.
Rational.
Incorporeal.
Inanimate.
Insensible.
Irrational.
Socrates, Plato, and others.
may be illustrated by dividing man or mankind by religion as the
principle of division.
THE UNFOLDING OF CONCEPTIONS. 67
Mankind
I
The ists Atheists
Mon otheists Polytheists
Chris
tians Non-Christians
Pa pists Anti-Papists
Jes uits Non-Jesuits
Loyola and others
In this example, religion, in the various forms in which it appears
among mankind, furnishes successive principles of division. The suc-
cessive marks or characteristics used are, a personal God, the one God,
God in Christ, the control of the Pope, Jesuitical principles.
2. The most perfect form of division is natural division.
"It founds itself," as Ueberweg has said, "on the essen-
tial modifications of the essentially constitutive (or intrin-
sic) attributes. It depends on the essential parts of the
notion or class to be divided. It is called natural division
in the same sense as the system which results from a con-
tinuous series of such divisions is to be called a natural
system."
It is evident that divisions of this kind cannot be formed in any
way according to an external uniform scheme. It is incorrect to look
for an equal number of members of division in all cases in divisions
of this kind. Thus the animal kingdom, divided by plan of structure,
gives, by the four distinct kinds of structure, vertebrates, articulates,
molluscs, and radiates. These four divisions are again taken up and
subdivided in the Natural System of Zoology. Confining the natural
subdivision to the vertebrates, we find at least five subdivisions recog-
nized by zoologists, — mammals, birds, reptiles proper, amphibians, and
fishes. Again, human duties, divided by the object toward which they
are directed, naturally fall into the divisions, individual, social, and
theistic. The student may also turn to the classification of the cupule-
bearing trees, as already given, for another illustration of natural
division. The natural divisions are seldom dichotomous.
68 PRACTICAL LOGIC.
3. From both dichotomous and natural division often arise
the trichotomy or threefold division, and the polytomy or
manifold division.
From the examples already presented, it is manifest that natural
division is often found to be trichotomous or polytomous. It is like-
wise true that these forms may arise from a condensed statement of
extended dichotomous division. Angles are divided, by the degrees
of difference in the direction of the sides, into acute, right, and obtuse.
This is a trichotomy condensed from an extended dichotomy, as fol-
lows : angles are right and not-right ; angles not-right are acute and
obtuse. The trichotomy is drawn from this. Mankind are Christians,
Jews, Mohammedans, polytheists, and atheists, is a polytomy con-
densed from an extended dichotomous process, as follows:
Mankind
I
The ists Atheists
Mon otheists Polytheists
Christians Non-Christians
Jews and Mohammedans
The trichotomy often arises because the parts of the class divided
are not sharply marked off or separated from each other. Thus, men
divided by color are white, tawny, and black. The present condition
of a sentient being may be one of pleasure, of indifference, or of pain.
Men divided by age are young, middle-aged, and old. Action con-
sidered morally is good, indifferent, or bad.
Topic Second. — The Rules of Logical Division.
The rules for division naturally arise out of its nature
and aim. They spring either from the principle of division,
from the various relations of the parts or species to the
whole or class divided, or from the relations of the divisions
and subdivisions to each other.
Rule 1st. — In a logical division the first requirement is
to fix upon the one principle of division suited to the pur-
pose in view, and the next to adhere to it throughout.
THE UNFOLDING OF CONCEPTIONS. 69
Several particulars need to be noted and emphasized in
connection with this rule.
1. There must be some principle of division in every
case as the reason or ground for the division. This is self-
evident, for, as Hamilton has said, " otherwise there would
be no division determined, no division carried into effect."
2. The principle of division is always to be sought in
some common mark or property, intrinsic or extrinsic, of
the class to be divided, and should be clearly and defi-
nitely grasped.
In general, it is manifest that the essential or intrinsic properties
(those of quality and action) have most to do with determining the
character pf the class and its species. These properties must, there-
fore, furnish the most important principles, or those of natural division.
In dividing man, rationality and animality furnish more character-
istic divisions than the extrinsic properties (those of relation).
The particular end which the thinker has in view must, however,
regulate the choice of the principle of division, so that in certain cir-
cumstances that principle is found in extrinsic or relative properties.
Man is divided by intrinsic properties, mental and physical constitu-
tion, into Caucasian, Mongolian, etc. Geographically, man may need
to be divided, by the relative property, place of abode, into European,
Asiatic, etc.
In all cases the principle of division, whether intrinsic or extrinsic,
should be clearly and definitely grasped. Failure in this inevitably
leads to incoherent, uncertain, and unsatisfactory results. Thus when
sentences are divided into indicative, interrogative, imperative, and
exclamatory, no principle of division is apparent ; we are left uncer-
tain whether these are all the kinds of sentences and whether they
should all enter into a proper division.
3. Every division should have only one principle.
The result of not complying with this requirement is what is called
cross-division. This fault brings confusion and perplexity. The
division of governments into monarchical, republican, despotic, aristo-
cratic, and hereditary, violates this principle. The first, second, and
fourth of these divisions have as their ground, the persons by whom
the authority is exercised ; the third has its ground in the extent of
70 PRACTICAL LOGIC.
the control ; the fifth in the tenure of office. Monarchy and aristoc-
racy may be despotic or hereditary, or b }th or neither. In short, the
divisions cross each other in various ways and the whole is hopelessly
confused. The same thing is illustrated by the division of books into
poetry, history, Latin, French, German, morocco, and cloth. Three
principles of division are made use of: the subject-matter, the lan-
guage in which written, and the kind of binding. This results in
many and perplexing cross-divisions.
4. The principle of division should always be one of
some importance and value.
This excludes all useless and foolish divisions, but especially the
counterfeit of dichotomy known as division by infinitation. To divide
the universe of being into man and not-man; or the animal kingdom
into parrots and not- parrots, may have a show of logic, but. the result,
as already seen, is absolutely worthless.
5. The principle of division should always be suited to
the purpose. Very different divisions of the same class
may be required for different ends.
For the purposes of Philology, a division of conjunctions, by the
words from which they are derived, into verbal, adjective, substantive,
phrase or prepositional, and composite, might possibly be of some
service ; but as a division for the purposes of grammar (which gives
attention to the thought embodied rather than the origin of words) it
has no relevancy and is of no value. For the purposes of Grammar,
the principle of division should be, by the relations of the sentences or
parts of sentences to each other, into co-ordinate and subordinate.
These again should be subdivided, by the special forms of co-ordination
and subordination, into copulative, adversative, etc., final, conditional,
etc. For the purposes of Philology it would be as absurd to divide
man into producers, transporters, and consumers, as it would to divide
man, for the purposes of Political Economy, into Aryan, Semitic, and
Turanian.
Rule 2d. — A division should be complete or inclusive of
all the species of the class divided.
These species into which a class is divided are called
the members of the division.
If these species or members of the division taken to-
THE UNFOLDING OF CONCEPTIONS. 71
gether do not exactly equal the class, then the division is
evidently only partial and imperfect. This rule may be
transgressed in various ways, as has been shown by writers
on logic.
1. The rule is transgressed when members of a division are left out.
For example, when we divide the actions of men into good and bad.
To this we should add, indifferent.
2. The rule is transgressed when a subdivision is co-ordinated with
a division, as when we divide mathematical figures into solids and
plane surfaces. It should be solids or surfaces, since this is the funda*
mental division (by the number of dimensions), and plane and curved
surfaces are subdivisions of surfaces by another principle.
3. We violate the rule when we bring in a dividing member too
much, as when we divide mathematical figures into solids, surfaces,
lines, and points. Here the last two elements, lines and points, must
be excluded, since lines and points, though elements of mathematical
figures, are not themselves figures.
Rule 3d. — The members of a division should be recipro-
cally exclusive.
This requires that each specific part brought out should
be entirely different from every other such part.
1. This rule is violated by placing a subdivision above or beside a
division under which it belongs, as when human actions are divided
into necessary, free, and moral. Free actions are either moral or
indifferent. In this case, therefore, a subdivision of free actions,
which is included under it, is placed by the side of it. Or, again,
when the sphere of Natural History is divided into the animal, vege-
table, and mineral kingdoms, and the vertebrates ; vertebrates is sub-
ordinate to animal, and as a subdivision of it should be excluded from
enumeration with it.
2. The rule is also violated when more principles of division than
one are used. For example, when we divide human actions into neces-
sary, free, useful, and detrimental, two principles of division are used,
necessity and utility, and the result is that the enumeration covers the
whole class of human actions twice.
Rule 4th. — A division should proceed immediately from
proximate genera to proximate species.
72 PRACTICAL LOGIC.
Divisions should, as far as possible, be continuous, that is, the notion
must first be divided into its proximate, and then into its remoter
parts, and this without overleaping any one part ; or, in other words,
each part must be immediately subordinated to its own whole. It is,
therefore, improper to divide animals into elephants, birds, fishes, etc.
According to Cuvier, as modified by Agassiz, the system of Zoology
which gives the true division of animal is as follows :
Kingdom Animal.
Branch Vertebrates, Articulates, Mollusfo, and Radiates.
Class Mammals, Birds, Reptiles, Fishes, etc.
Elephants belong under mammals. In the division given, the inter-
mediate classes, vertebrates and mammals, are overleaped.
Such an overleaping is, however, sometimes allowed for the sake of
brevity ; but this only when the omitted members can be readily sup-
plied in thought. This is illustrated by the common mathematical
division, already given, of triangles, into right, acute, or obtuse.
Rule 5th. — A division should be orderly in the arrange-
ment of the specific parts into which the class is divided, —
i. e., the parts should be placed in proper co-ordination and
subordination.
This is simply the requirement that in the statement of a system of
division everything should be put in its own place. The rule may be
illustrated by the Intellect or Power of Cognition, beginning with the
Simple Cognitive Faculty.
COGNITIVE POWER OR INTELLECT (divided by progressive stages of
knowing) : —
1. Simple Cognitive Faculty (by kind of knowledges acquired), —
(1.) Internal Perception or Self-Consciousness, giving knowledge
of self;
(2.) External Perception or Sense, giving knowledge of external
world ;
(3.) Intuitive Perception or Intuition Proper, giving knowledge
of first truths.
2. Conservative Faculty or Memory (by psychological elements in
keeping knowledges), —
THE UNFOLDING OF CONCEPTIONS. 73
(1.) Retention, keeping knowledges, out of consciousness;
(2.) Reproduction or Association of Ideas, bringing back knowl-
edges by linking them together ;
(3.) Representation or Imagination, vividly imaging the knowl-
edges reproduced ;
(4.) Recognition, connecting the present imago with the past
knowledge.
3. Comparative Faculty or Thought (by material compared), —
(1.) Conception or Comparison of Objects, forming concepts,
classes, and terms ;
(2.) Judgment or Comparison of Concepts, forming judgments
and propositions ;
(3.) Reasoning or Comparison of Judgments, forming arguments
and conclusions.
4. Constructive or System-making Faculty (by law followed), —
(1.) Scientific Construction or Construction by the True, giving
scientific system ;
(2.) Artistic Construction or Construction by the Beautiful, giving
aesthetic system ;
(3.) Practical Construction or Construction by the Good, giving
practical system.
It will be observed that neither of the four main divisions can
change place with any other. Simple cognition, or the power of
acquiring our simple and fundamental knowledges, must act before
there can be anything for memory to conserve; conservation or
memory must act before comparison can have any material to elab-
orate ; comparison must do its work in order to furnish the materials
for construction. The powers subordinate to these four must likewise
take their proper places of subordination.
Praxis. — Give Divisions of the following Classes, stating clearly the
Principles of Division and whether Artificial or Natural, and testing
the work by the Rules : 1. The Races of Men. 2. The Nations of the
Earth. 3. Languages. 4. Fruits. 5. Heavenly Bodies. 6. Commerce.
7. Art. 8. Industries. 9. Governments. 10. Churches. 11. Emotions.
12. Desires. 13. Ships. 14. Triangles. 15. Quadrilaterals. 16. Laws.
17. Life. 18. Dogs. 19. Metals. 20. The Carnivora. 21. Plants.
22. Roses. 23. Stars. 24. Processes of Rhetorical Invention. 25. Phys-
ical Forces. 26. Colors. 27. Divisions of time. 28. Flowering Shruba
7
74 PRACTICAL LOGIC.
29. The ruminants. 30. Insects. 31. Forms of religion. 32. Civiliza-
tions. 33. Laws. 34. Societies. 35. Educational institutions. 36. Me-
chanic arts. 37. Wars. 38. International alliances. 39. Homicides.
40. Social conditions. 41. Human relationships. 42. The rocks.
43. Occupations. 44. Systems of unbelief. 45. Monotheistic systems.
46. Periods of human history. 47. Theistic systems. 48. Diversities
of genius. 49. Poets. 50. Phases of religious character. 51. Tem-
peraments. 52. Influences in formation of character. 53. Influences
of the Crusades upon European civilization. 54. Aims in life. 55. Mo-
tives influencing human conduct. 56. Benefits of international com-
merce.
Give extended and complete Divisions, Dichotomous or Natural, of
the following Classes, stating the Principle and testing by the Rules :
1. The vegetable kingdom. 2. Furniture. 3. Birds. 4. Cereals.
5. Fishes. 6. Creeds of Christendom. 7. The Sciences. 8. Foods for
man. 9. Views of the origin of the universe. 10. Forces of civili-
zation.
Examine each of the following Divisions, stating the Principle of
Division, showing whether the Division is Natural or Artificial and
whether it conforms to the Rules ; and, in case it does not, showing
wherein it fails and correcting and completing it:
1. Triangle = equilateral and equiangular.
2. Triangle = right-angled, isosceles, and scalene.
3. Literature = history, oratory, and poetry.
4. Literature = writings historical, religious, poetical, classical, and
current.
5. Government = democracy, oligarchy, aristocracy, and monarchy.
6. Government = absolute, limited, constitutional, and free.
7. Government = empires, kingdoms, dukedoms, and republics.
8. The fine arts = the arts of free beauty, the arts of dependent
beauty, and the arts of utility.
9. The arts of free beauty = music, sculpture, painting, and poetry.
10. The arts of dependent beauty = architecture, landscape-garden-
ing, embroidery, and decorative painting.
11. Rectilinear figures = triangles, quadrangles, rectangles, paral-
lelograms, and polygons.
12. Sentence = simple, compound, and complex.
13. Proposition = categorical, hypothetical, conditional, and dis-
junctive.
14. Proposition = affirmative, hypothetical, and negative.
THE UNFOLDING OF CONCEPTIONS. 75
15. Man = foot and horsemen.
16. Man = white, black, copper-colored, olive-colored, etc.
17. Thought — memory, conception, and reasoning.
18. Poetry = didactic, lyric, and epic.
19. Poetry = didactic, lyric, epic, and the ballad and sonnet.
20. Matter — solid, liquid, aeriform, and radiant.
21. Duties to self = self-conservation, self-culture, and self-conduct
or direction.
22. Carnivora = cats, dogs, civets, weasels, bears, seals, whales, etc.
23. Mental faculties = sense-perception, memory, conception, ab-
straction, judgment, reasoning, and taste.
Section III,— Logical Definition,
Definition in general is the mental separation of an object
of thought embodied in language from every other object
of thought. Logical definition is the accurate unfolding of
the signification of the terms which embody thought.
The various forms of definition and the indefiniteness of
view on the whole subject of definition make it necessary
to consider with greater care, the kinds of definition and
the rules of logical definition.
Topic First. — The Kinds of Definition.
The word definition is used in both a wide and loose and
in a narrow and strict sense. For definition in the former
sense, Hamilton has suggested the name of declaration,
signifying throwing light upon, clearing up. It may also
be called rhetorical definition, in distinction from definition
in the narrow and strict sense, which is called logical
definition.
I. Rhetorical Definition.
The object of rhetorical definition or declaration is to
give the meaning of a 'word loosely, or as it is popularly
understood and for common use, rather than exactly and
for scientific ends. It does not necessarily undertake to
unfold essential properties, but freely uses those that are
76 PRACTICAL LOGIC.
accidental, relative, or extrinsic. It is called description
when it makes use of a number of concrete characteristics,
as when we say that the Caucasian is tall, white, graceful.
1. Various popular modes of defining words may be in-
cluded under rhetorical definition. These should be dis-
tinguished in order to guard against certain common errors
and fallacies.
(1.) Etymological definition traces the root of a word
back to its origin and defines accordingly. It sometimes
throws much light upon the meaning of a word and adds
great force to the word.
There are, as has been shown by Trench in his "Study of Words,"
most important lessons of history, romance, poetry, and morals wrapped
up in even our commonest words. In bringing out this meaning by
etymological definition it is necessary, however, to guard very care-
fully against two errors in particular, — that of fixing upon a wrong
etymology, and that of assuming that what the word meant at the
beginning it means now. Home Tooke furnished an illustration of
the first error in confounding the root of truth with that of trow,
meaning think, and then concluding that " truth is what onetroweth,"
or simply a matter of opinion. A better philology finds for truth a
root which would make it signify reality. The second error may be
illustrated by assuming that villain is still simply a villager, because
that was the original meaning, or that knave is still merely a boy,
because that is what the word once meant.
(2.) Definition by word analysis, or by unfolding the
various roots of which a word is made up, bringing out
and combining their significations, — is also of value ; but,
since it involves, in most cases, a knowledge of the roots
of words, it is liable to lead to the same errors as etymo-
logical definition.
For example, the word edify, separated into its two component parts,
one meaning a temple and the other to make, would be defined etymo-
logically as the making or building of a temple. This may be strikingly
suggestive of the greater work of spiritual building signified by the
word as now used, but it can hardly be taken in the literal sense.
THE UNFOLDING OF CONCEPTIONS. 77
Note.— The subject of word analysis is treated of in such works as Webb's
" Manual of Etymology," and Swinton's " Word Analysis." The student of
Logic ought to be familiar with it.
2. Rhetorical Definition may also proceed by the vari-
ous thought wholes, already considered. It may define
words, in the looser way, as essential, as mathematical, or
as logical wholes, by giving concrete characteristics, by
using synonymes, or by casual substitution of phrases.
Such careless definition sometimes takes the form of mere descrip-
tion, or the naming of one or more concrete characteristics, as when
we say, " Man is a risible animal," " Man is a two-legged animal
without feathers," " The east is where the sun rises." It sometimes
becomes only the enumeration of synonymes, as in much of the defi-
nition of the Dictionaries, as, " Law is a rule, decree, or statute,"
" Religion is piety." It sometimes becomes little more than a careless
or casual substitution of phrases, narrative or descriptive, perhaps
presenting some consequence or attendant circumstance, as " Wisdom
leads to virtue and blessedness."
Some names are not definable except by rhetorical definition. It is
obvious that an individual cannot be logically defined, since practi-
cally we cannot form a notion comprising all the essential marks
which it has in common with any other notion or thing. Description
is the process applicable to individuals. On the other hand, simple
notions, or those containing a single or simple mark, cannot be logic-
ally defined, since they have only one mark and, therefore, no differ-
ential or distinguishing element. Being, for example, having only
one mark, existing, cannot be unfolded, as there is no complex content
to unfold. It can only be distinguished from nothing or non-entity,
which is a mere negation, or defined by some synonyme, as thing,
existence.
One office of Logic is to make plain the insufficiency of
all such loose forms of definition, while giving command of
the stricter forms of logical definition.
II. Logical Definition.
Logical definition separates a conception, as expressed by
a word, from all other conceptions by fixing upon and pre-
senting the essential and distinctive property or properties.
7*
78 PRACTICAL LOGIC.
1. Strict or perfect logical definition has two forms. —
The general term, as has been shown, may be considered
either as embodying a class or a concept proper, in other
words, either as a class term or as a concept term. Logical
definition should, therefore, regard the general term from
both these points of view. In other words, it is of two
forms : one defining the general term as a class term and
the other as a concept term ; the former dealing with extent
or contained objects, the latter with content or contained
properties.
Note.— The failure to recognize this twofold form has led to various differ-
ences of statement concerning the nature of logical definition. The old logical
definition was confined to the conception as a genus or class. Professor Davis
proposes to confine it to the conception as a concept proper. Logical definition
thus becomes substantially synonymous with Partition as that subject has
already been presented. Other logicians confine it to language or terms, and
make it apply chiefly to class terms. The view here taken is that it applies to
terms as embodying both classes and concepts. It is thus to be distinguished
from Logical Division and Partition, which deal with thought directly rather
than indirectly through language.
(1.) Definition of the Class Term. — If the term to be
defined is regarded or used as a class term, the definer is
required, by the principles of logical definition, —
First, to name the next higher genus to which the class,
considered as a species, belongs ; and,
Secondly, to name the difference (differentia), or specific
difference or that which distinguishes the class, considered
as a species, from all the other co-ordinate species under
that higher genus.
The genus and difference together make up the essence
of the term, because they embrace the essential character-
istics or marks of the class embodied in the term.
Thus, in the definition, Man is a rational animal, it is meant that
animal is the next higher genus to which man belongs as a species,
and that rational is the difference or that which distinguishes man
from the other co-ordinate species, irrational animal or brute.
(2.) Definition of the Concept Term. — If the term to be
THE UNFOLDING OF CONCEPTIONS. 79
defined is regarded or used as an attribute or concept
term, the definer is required, by the principles of logical
definition, —
First, to state the properties of the higher genus to which
the term, considered as a species, belongs ; and
Secondly, to state the properties which distinguish the
term, considered as a species, from other species under the
higher genus.
Thus, in the definition, Man is rational animal, the meaning is that
the concept term, man, includes animal properties or animality, and
rational properties or rationality. The properties of the higher
genus are included under animality, and those of the species under
rationality.
2. Certain imperfect forms of logical definition are also
distinguished by logicians. These are known as definition
by division, by colligation, by resolution, and by compo-
sition. They approach the strict standard of definition
more nearly than does rhetorical definition. They are in
fact statements of the results of Division and Partition.
The first two forms are simply different statements of the results of
Division as already treated. Definition by division unfolds a class
term into its constituent species or individuals, as when we state that,
" The animal kingdom consists of radiates, mollusks, articulates, and
vertebrates." Definition by colligation, which is the reverse of defi-
nition by division, gathers up and unites the constituent species or in-
dividuals of a genus or species, as when we say that, " The Earth, Mars,
Mercury, Venus, Jupiter, etc., are the planets." The second two forms
are simply different statements of the results of Partition as already
treated. Resolution brings out of a concept term its component prop-
erties, as when we say that, " Man is rational animal." Composition,
the reverse of resolution, gathers up and unites the component proper-
ties, as when we say that, " Rational animal is man."
3. By an extended process of logical definition an ulti-
mate and indefinable term is reached. In making such a
complete explication of a term it is necessary to proceed by
80 PRACTICAL LOGIC.
defining successively the genus of each new definition until
a simple notion is reached.
Professor Davis has illustrated this process in tabular form by an
extended definition of carnivore.
" A carnivore is a flesh-eating (= differentia] mammal (= genus).
A mammal is a vertebrate (= g) suckling its young (= d).
A vertebrate is an animal (=g) having an internal skeleton (— d).
An animal is a sentient (= d) organism (= g).
An organism is a living (= d) being (= g)."
The process comes to a close when the simple notion, being, is
reached. The result of the definition embraces all the properties con-
noted by the concept term, carnivore, and all that would be brought
out by a Partition of that term. Stated as a definition by resolution,
it becomes, "Carnivore includes flesh-eating, suck-giving, internal-
skeletoned, sentient, living, existing."
Ill, Nominal, Real, and Genetic Definition.
Logicians, from another point of view, distinguish defi-
nition as nominal, real, or genetic. The first has to do with
the mere name of the object of thought ; the second with
its reality or essential properties ; the third with the cause
which generates it.
Nominal or verbal definitions, or definitions of names or words,
comprise the loose forms given under rhetorical definition or declara-
tion, as when we say, " The word circle signifies a uniformly curved
line." A real definition is a definition of the thought or reality em-
bodied in a word. It unfolds essential marks, and is, therefore, strictly
analytic. It comprises the forms of logical definition already given.
Thus we define a circle as "a line returning upon itself, of which all
the parts are equidistant from a given point." A genetic or causal
definition is one which states the rise or production of a thing as the
result of some working cause. It adds something to what is contained
in the defined term, and hence is always synthetic. The genetic defi-
nition of a circle is, "A circle is formed when we draw around, and
always at the same distance from, a fixed point, a movable point which
leaves its trace, until the termination of the movement coincides with
the commencement." Only such notions as relate to quantities repre-
THE UNFOLDING OF CONCEPTIONS. 81
sented in space and time, in other words only mathematical notions,
can be genetically denned.
Topic Second. — The Rules of Logical Definition.
The rules for logical definition are determined by its
nature and aim. They spring either from peculiarities in
the origin and use of language, or from the nature of the
thought embodied in the language.
Rule 1st. — In logical definition the first step is to study
carefully the term to be defined.
The object of such study is to guard against the common
errors in defining, which arise from the ambiguities of lan-
guage. It is obvious, therefore, that logical definition
requires in general a knowledge of language and the prin-
ciples of interpretation. In particular it calls for a knowl-
edge of the kinds and sources of ambiguity in the use of
terms.
Professor Jevons has presented very forcibly the importance of a
thorough acquaintance with the great imperfections of language. He
says, " Comparatively few terms have one single clear meaning and
one meaning only, and whenever two or more meanings are uncon-
sciously confused together, we inevitably commit a logical fallacy. If,
for instance, a person should argue that ' punishment is an evil,' and
according to the principles of morality ' no evil is to be allowed even
with the purpose of doing good,' we might not at the first moment see
how to avoid the conclusion that ' no punishments should be allowed,'
because they are evil. A little reflection will show that the word
evil is here used in two totally different senses ; in the first case it
means physical evil or pain ; in the second, moral evil ; and because
moral evil is never to be committed, it does not follow that physical
evils are never to be inflicted, for they are often the very means of
preventing moral evil."
In studying the subtle variations in the meaning of even
our common words, it is necessary to distinguish between
terms as univocal and equivocal. Univocal terms are those
which can suggest to the mind no more than a single mean-
F
82 PRACTICAL LOGIC.
ing. Equivocal terms are such as have two or more differ-
ent meanings.
1. Strictly univocal terms are not liable to mislead. The names of
individual objects, persons, or events are usually fixed and certain in
their meaning, as George Washington, Westminster Abbey, the Atlan-
tic Ocean. The instances of univocal terms, outside of individual
names, are found chiefly in technical and scientific language. Steam-
engine, railway train, oxygen, hydrogen, sulphuric acid, etc., are
examples of what may be found in connection with every well-defined
science. It will be seen, however, on looking more closely, that gen-
eral terms are not strictly univocal. The same word has been found
to embody both the concept proper and the class. Hence the first
inquiry, even in the case of words commonly called univocal, should
be, 7s the term here used as a concept term or as a class term f The
word man may be used in one case to express the attributes of human-
ity, and in another to express the species or individual human beings,
and clear thinking requires that the thinker should know precisely
which is meant in any given case.
2. Equivocal terms are exceedingly numerous. Equivocal terms
are either properly ambiguous or homonymous.
(1.) A properly ambiguous (from Latin ambigo, to wander, hesitate,
or be in doubt) term is one that has come to be used in different sig-
nifications. Equivocation from ambiguity arises in two different ways :
1st. Through, association, i. e., from the transfer of the meaning from
the thing originally denoted by the word to some other thing habit-
ually and intimately associated with it. The word church originally
denoted the building in which religious worshippers assemble. It
has come to mean the particular body of worshippers accustomed to
assemble in any one place ; or any body of persons holding the same
opinions and connected in one organization, as the Church of Eng-
land, the Roman Catholic Church ; or the church of Christendom ; or
the clergy and religious authorities of any sect or country. The word
differs entirely in meaning as used by a member of the Anglican,
Greek, Roman Catholic, Congregational, Presbyterian, or any other
existing church.
2d. Through analogy, i. e., from the transfer of meaning to analo-
gous objects. We speak of a sweet taste, a sweet flower, a sweet
tune, a sweet face, a sweet poem, from the analogy or resemblance
between the pleasure given by the flower, tune, etc., and that given
by something sweet to the taste, as a lump of sugar.
THE UNFOLDING OF CONCEPTIONS. 83
The use of the same word in different significations renders it neces-
sary in many cases to ask the question, What is the signification in
which the word is here used? When the philosopher asserts that
" experience proves the eternity of matter," the first question gives
rise to such as follow : Whose experience ? The philosopher's ? All
men's? All men's in all ages? All human experience plus human
speculation ?
There are some ambiguous words which should be carefully studied
in order that an intelligent answer may be given to the question,
Precisely what does this word mean in the present instance f The word
all is an example of such ambiguity. In the proposition, " All these
soldiers are individual persons," all is used distributively, or one by
one. In the propositions, "Not all men are soldiers," "All men are
not soldiers," all with the negative attached is not equal to none, but
only to not some, so that the all in this case is only equal to some.
Words often change their meaning in the course of time, so that in
studying and testing the works of past thinkers, there is need to ask
the question, What was the meaning of the term to be defined, in the
day when this author wrote f When the authors of King James's ver-
sion of the Bible represent the Psalmist as praying, " Let thy tender
mercies speedily prevent us," careful inquiry should be made into the
use of the word prevent, about the opening of the seventeenth century.
Such inquiry will reveal the fact that the word, which now means to
go before one to hinder him, then meant to go before to anticipate or
supply his wants.
(2.) Homonyms are terms which, though of different origins, have
accidentally assumed the same form either in sound, or in spelling, or
in both. Examples of the first kind are seen in such words as right,
wright, write, rite, or rein, rain, reign, etc. Examples of the second
kind are such words as lead, the metal, and lead, as in following the
guidance of another. Examples of the third kind are such words as
mass, a heap, and mass, a Roman Catholic religious service. An im-
portant instance of this kind of equivocation is found in grammar, "as
between the numeral one, derived from an Aryan root, through the
Latin unus, and the indeterminate pronoun, one (as in, ' one ought to
do ones duty'), which is really a corrupt form of the French word
homme or man. The Germans to the present day use man in this
sense, as in, man sagt, i.e., one says."
Too great care cannot well be given to the study of the
terms to be defined. It is obvious, from the examples
84 PRACTICAL LOO 1C.
given, that any failure to grasp the precise signification in
which a single important word is used may utterly vitiate
a whole system of thought.
Rule 2d. — A logical definition should bring out the essence
of the term defined. This requires scientific accuracy.
The non-essential or accidental properties are not sufficiently charac-
teristic for a definition. The worthlessness of the well-known Platonic
definition, " Man is a two-legged animal without feathers," as contain-
ing only non-essential marks, was easily shown by Diogenes when he
presented a plucked chicken as Plato's man.
Since general terms embrace both concept and class, use
is to be made of both Partition and Division in framing
logical definitions. In the case of a class term the definition
should bring out the next higher genus, and the differentia,
or characteristic of the term defined considered as a species
under that genus. In the case of a concept term the defi-
nition should bring out the properties of the next higher
genus, and the differentia, or characteristics of the term
considered as the marks of a species under that genus.
Definition of the term as a class term is much the more common
form. Such definition becomes easy when the student has once learned
to put the term defined under the next higher class, and then to bring
out the distinguishing characteristics. Rhetoric is defined by first
putting it under the next higher class, art, or practical science, and
then distinguishing it from all other co-ordinate species of art by
stating its object, discourse, — "Rhetoric is the art of discourse."
Patriotism is defined by first putting it under the next higher class,
love, and then naming the special object, one's country, which distin-
guishes it from all other forms of love, — " Patriotism is love of one's
country."
Rule 3d. — A logical definition should be adequate or
precisely equal to the term defined. This forbids making
the definition too wide or too narrow, deficient or redundant.
It follows that a good definition may be tested by simple conver-
sion, or by letting the subject and predicate change places. If the
common definition, "Man is a rational animal," be adequate, then
THE UNFOLDING OF CONCEPTIONS. 85
the converse will be true, " Every rational animal is man." Strictly
speaking, we are not absolutely certain of the truth of this converse,
for although it may be true of this earth, there may be in other worlds
rational animals that are not men. The definition is, therefore, on
this supposition, said to be too wide, embracing not only man, but all
possible rational animals in other worlds. To make it perfectly ade-
quate it is necessary to add the relative property expressed by terres-
trial or some such term, as, " Man is a rational animal of this earth."
The converse will then be strictly true, " All rational animals of this
earth are men." On the other hand, if man be defined as a praying
animal, the definition is said to be too narrow. It is not true in the
strict sense that no animals that do not pray are men. The definition,
in other words, embraces only a part of men. Definitions are redun-
dant when they add to the essential characteristics derivative or unes-
sential marks, as, "Man is a rational animal that laughs;" they are
deficient when they omit some essential characteristic, as, " Man is an
animal." To the latter belong definitions by co-ordinate and subordi-
nate notions, as, " An odd number is that which is distinguished from
. an even by unity," " Man is an American."
Ride 4th. — A logical definition should be expressed in
language as perfect as possible.
This forbids absurdity, ambiguity, verbosity, tautology,
and obscurity of language, as well as circular, negative, and
figurative definitions.
The language in a definition should be clear and signifi-
cant and not vague, ambiguous, or senseless.
When Mr. Spencer defines the virtue of patriotism as national
egoism, his definition is probably accepted by the mass of readers
without thought. But egoism is selfishness, which of course is not a
virtue at all, and patriotism is not a national but an individual senti-
ment. The definition is, therefore, absurd. The same objection holds
against Mr. Spencer's definition of evolution, " Evolution is a change
from an indefinite incoherent homogeneity to a definite coherent hetero-
geneity, through continuous differentiations and integrations." The
definition is pronounced obscure both by common readers and by those
who understand the strict meaning of the scientific and mathemati-
cal phraseology. A British critic has translated the definition into
English, as follows: " Evolution is a change from a nohowish untalk-
8
86 PRACTICAL LOGIC.
aboutable-all-alikeness, to a somehowish and in-general-talkaboutable-
not-all-alikeness, by continuous somethingelsifications and stickto-
getherations."
The language in a definition should be precise and free
from surplus words.
Dr. Johnson's definition of oats, " Oats is a grain which in England
is generally given to horses, but in Scotland supports the people'' vio-
lates this principle. The specific difference, expressed by the words
italicized, is entirely unessential. Dr. James, in the " Anxious In-
quirer," says, " It is a great principle that subjective religion, or in
other words, religion in us, is produced and sustained by fixing the
mind on objective religion, or the facts and doctrines of the word of
God." Ruskin says of this, " Put entirely out the words I have put
in italics, and the sentence has a meaning, but by its verbosities it is
extended into pure nonsense; for 'facts' are neither ' objective ' nor
' subjective ' religion ; they are not religion at all. The belief of them,
attended with certain feelings, is religion ; and it must always be
religion 'in us,' for in whom else should it be (unless in angels ; which
would not make it less subjective)."
The language in definition should not be tautological,
i. e., a definition should not contain the name of the thing
defined, nor a derivative, synonymous, or correlative term,
for this would be to define a thing by itself.
This is violated by such definitions as " Life is the vital force." It
is also violated by what is called the circle or dialellon, as, " A board
is a thin plank," " A plank is a thick board." John Stuart Mill's
final definition of cause is a flagrant violation of this principle. It is
as follows : " We may define, therefore, the cause of a phenomenon to
be the antecedent, or concurrence of antecedents, on which it is conse-
quent invariably, and subject only to the absence of preventing or
counteracting causes." The essential idea of cause, efficiency, is left
out ; the last and perhaps the most emphatic word in the definition of
cause is causes ; and the affirmation that the consequent is invariable
is followed immediately by the assertion of a variable condition.
The language in a definition should be perspicuous.
The aim of definition is to place the thought before the mind with
more distinctness ; hence, terms more unintelligible than the one de-
THE UNFOLDING OF CONCEPTIONS. 87
fined should be avoided. This is violated by Aristotle's definition,
" The soul is the first entelechy or energy of a natural organized body
possessing life potentially." Definition by negative marks is also for-
bidden by this principle, where definition by positive marks is possible.
To define man as not a brute or not an angel gives no clear concep-
tion of what he is. Figures of speech are not ordinarily suitable for
definition, e.g., " Memory is the warder of the brain ; " " The Divine
nature is a circle whose centre is everywhere and the circumference
nowhere." Such definitions make thought obscure rather than distinct.
Praxis. — Define the following terms Etymologically, by Analysis
(where possible), Rhetorically and Logically, stating the kind of Whole
in each case : 1. Proposition. 2. Development. 3. Sincere. 4. Lord.
5. Heathen. 6. Tawdry. 7. Saunter. 8. Slave. 9. Faculty. 10. Op-
eration. 11. Education. 12. Vulture. 13. Instinct. 14. Virtue.
15. Patriotism. 16. Fanaticism. 17. Ox. 18. Gas. 19. Ice. 20. Oxy-
gen. 21. Diamond. 22. Electricity. 23. Sun. 24. Moon. 25. Load-
stone. 26. Gold. 27. Sophomore. 28. Voyage. 29. Battle. 30. War.
31. Sentence. 32. Grammar. 33. Rhetoric. 34. Logic. 35. Arith-
metic. 36. Straight line. 37. Circle. 38. Point. 39. Sphere. 40. Vice.
41. Ghost. 42. Spirit. 43. Tribulation. 44. Passion. 45. Vexation.
46. Rage. 47. Love. 48. Desire. 49. Expectation. 50. Loafer.
Note.— See Trench " On the Study of Words"
Define the words from number 36 to number 39 inclusive, nominally,
really, and genetically.
Examine each of the following definitions, stating of what kind it
is, showing whether it conforms to the Rules, and, in case it does not,
showing wherein it fails, and correcting and completing it :
1. Grammar is the science of language.
2. Philology is the science of language.
3. A triangle is a rectilinear figure having three sides and three
angles.
4. A square is a quadrilateral having all the angles right angles,
all the sides equal, and the opposite sides parallel.
5. Malaria is that which induces fever.
6. A cone is a solid generated by the revolution of an angle about
one of its sides.
7. Virtue is a voluntary act done in obedience to the law of God for
the sake of everlasting happiness.
8. Logic is the art of reasoning. — WHATELY.
88 PRACTICAL LOGIC.
9. Logic is the light-house of the understanding.
10. Truth is the agreement of a cognition with its object. — HAM-
ILTON.
11. Truth is accordance with the reality.
12. A whale is a large fish inhabiting the polar seas, and furnishing
oil and whalebone as articles of commerce.
13. Happiness is the reflex of unimpeded energy. — HAMILTON.
14. Life is that condition of an organized being in which it is
capable of performing its functions. — PORTER.
15. Life is definable as the continued adjustment of internal rela-
tions to external relations. — SPENCER.
16. Science is systematized knowledge.
17. Mind is the unextended. — BAIN.
18. Matter is the permanent possibility of sensation. — MILL.
19. Mind is a conscious string of sensations.
20. A sphere is a solid generated by a revolution of a semicircle
about its diameter as an axis.
21. A sphere is a solid or volume bounded by a surface, every point
of which is equally distant from a point within, called the centre. —
WORCESTER.
22. Education is the training of the intellectual powers, principally
by the study of the physical sciences.
23. Knowledge is power.
24. Net-work is anything reticulated or decussated at equal dis-
tances with interstices between the intersections. — DR. JOHNSON.
25. A saunterer is one who is going to the Holy Land.
26. Law is a lawful command.
27. Gratitude is a lively sense of future favors.
28. Gratitude is a virtue of acknowledgment.
29. A ruler is one who establishes laws.
30. A circle is a curved line returning upon itself, the parts of which
are at an equal distance from the central point.
31. Logic is the electric light of the intellect, the cynosure of truth,
the physic of the mind.
32. Man is an animal walking on two feet.
33. Man is a bimanous mammal.
34. Monarchy is a form of political government in which one man
is sovereign.
35. Wealth is that which furthers the well-being of man.
36. The soul is the principle by which we live, feel, move, perceive,
and understand. — ARISTOTLE.
THE UNFOLDING OF CONCEPTIONS. 89
37. Beauty is the feeling we experience in recognizing unity amidst
variety.
38. A dragon is a serpent breathing flame.
39. Fine Art is the embodiment of thought in sensuous form.
40. Man is a rational being.
41. A cat is a domestic animal.
42. A dog is a digitigrade quadruped, having fixed claws, four toes,
and a recurved tail.
43. Memory is that power of the human soul which recalls past
knowledge.
44. Philosophy is the science of principles. — UEBERWEG.
45. Philosophy is the love of wisdom.
46. Dirt is matter in the wrong place. — LORD PALMERSTON.
47. A perception is an impression made on the mind.
48. Mathematics is the science of extension.
49. Snow is frozen mist.
50. A carnivore is flesh-eating, suck-giving, internal-skeletoned,
sentient, living, existing.
51. A seal is a species of fish.
52. Honesty is a species of policy distinguished from other co-
ordinate species by being the best.
53. Dancing is a refined and sublimated modification of circum-
ambulatory locomotion.
54. Man is physically a living machine.
55. A conjunction is a word that connects words and sentences.
56. Matter is that in which is discerned the promise and potency of
all terrestrial life. — TYNDALL.
57. God is the not-ourselves which makes for righteousness. — MAT-
THEW ARNOLD.
58. Religion is cosmic emotion. — CLIFFORD.
59. Evolution or development is essentially a combination of causes
working toward a particular end. — McCosH.
60. The conic section is that mathematical figure which divides into
these four forms — circle, ellipse, parabola, hyperbola.
61. The sensibility takes that to be good which warrants or prom-
ises pleasure, and affects us pleasantly ; — the desires rest on pleasant
feelings.
62. The feeling of the pleasant is the immediate consciousness of
the furtherance of life. — UEBERWEG.
63. Justice is a square number.
64. The idea of the good is the sun in the kingdom of ideas. — PLATO.
8*
90 PRACTICAL LOGIC.
65. Nature (Heaven and earth and all that is therein) is the body
of God.
66. The state is man writ large.
Define the principal Terms used in the following Sciences, testing
the definitions by the Rules: 1. Arithmetic. 2. Geometry. 3. Botany.
4. Zoology. 5. Grammar. 6. Physical Geography. 7. Rhetoric. 8. Psy-
chology. 9. Natural Philosophy. 10. Astronomy. 11. Geology. 12. Eth-
ics. 13. Political Economy. 14. Science of Government.
SUMMARY OF RESULTS
THE aim of the Logic of Conception is to train to the
best thinking and fullest appreciation of thought in the
first form. The degree of perfection or imperfection with
which the mind grasps its conceptions constitutes what is
called the logical quality of conception, Our grasp of con-
ceptions is perfect in proportion as it is clear, distinct, and
adequate : imperfect in proportion as it is obscure, confused,
and inadequate.
A conception is clear when it is simply distinguishable from others ;
obscure when it is not. This may be illustrated by experience in
gazing upon a tree. When the light falls upon it we readily distin-
guish it from other trees and objects of the landscape, and the view is
clear ; but when the mist or the twilight settles around it we can no
longer distinguish it from other objects, and the view becomes obscure.
We have a clear conception of man when we distinguish it from inor-
ganic matter, plant, animal, etc. ; so long as we are unable to do this
our conception of it is obscure.
A conception is distinct when we not only distinguish its object
from all others, but also grasp the constituent marks or parts of that
object. In every-day life we may know the hand-writing or features
of a person from those of all others and yet not be able to give the
characteristics of either. This is true in conception, — we may be able
to discriminate man from mineral, plant, animal, etc., and yet not be
able to give the characteristics of man. Our conception is confused or
indistinct. Distinctness requires us not only to discriminate between
THE UNFOLDING OF CONCEPTIONS. 91
an object and all others, but also to know the distinctive marks or parts
of that object. Our conception of man becomes distinct when we see
that it includes animality, rationality, and terrestriality ; until then
it is confused.
A conception is adequate when we not only grasp the constituent
marks, but also the marks of these marks ; inadequate when we fail
to do this. Perfect adequacy of conception is reached by carrying out
the complex processes of Partition, Division, and Definition until the
lowest component attributes, constituent species, and characteristic
marks are reached. The extent to which these processes must be car-
ried to reach a practical adequacy of conception in any given case will
depend upon the exigencies of the thinking or the aims of the thinker.
The conception of man is adequate when we not only know the three
marks given above, but have also gone further and grasped the marks
of animality, as corporeity, organization, life, sentiency, voluntary
motion ; of rationality, as intuition of first truths and the power of
thinking and acting in the light of such truths ; of terrestriality, as
limitation to the earth with its conditions of time and space.
It will be readily seen that clearness is chiefly attained
through Definition ; distinctness through Partition and
Division ; adequacy through the extended processes of Par-
tition, Division, and Definition.
A conception is true when it corresponds with the reality.
The aim of the Practical Logic of conception is fully at-
tained when the training results in the ability of the thinker
to reach true conceptions which are clear, distinct, and
adequate.
PART II.
THE LOGIC OF JUDGMENT OR THE PROPOSITION.
THE aim of the Logic of Judgment is to train the mind
to skill in dealing with the second Form of Thought.
Definition.— (Judgment is that form of thought in which
we compare two notions and mentally affirm their union or
disunion, on the ground of a like union or disunion appre-
hended in the objects or realities which the notions repre-
sent The result of the operation of judging is a complex
form of thought known as a Judgment, the verbal expres-
sion of which is called an Assertion or Proposition. The
connection between judgment and proposition is so intimate
that the two terms are used interchangeably.
Note. — The definitions of judgment have been various. Some have defined
it to be, the affirmation of the agreement or disagreement, or of the congruence
or confliction, of two notions. According to Thomson, it is " an expression
that two notions can or cannot be reconciled— that the mark of the one may
or may not henceforward be assigned to the other." Manifestly judgment as
thought is much more than mere affirmation, whether mental or verbal, of the
agreement or disagreement of two notions. The question whether the form
of words, "Man is intelligent," or, " Man is patent elliptic," is a judgment or
embodies a judgment, is not to be decided by affirmation of any kind. It de-
pends upon the knowledge of connection existing or not existing between the
realities or objects represented by the words and notions.
Ueberweg comes nearer the presentation of the essence of judgment, when
he makes it the comparison of two notions, whose forms are different from
but belong to each other, and the mental affirmation of their union or disjunc-
tion on the ground of like relation apprehended between the objective realities
92
THE FORMATION OF JUDGMENTS. 93
which the notions represent. The all-important thing is " the consciousness,
whether or not the analogous combination exists between the corresponding
objective elements. As the individual conception corresponds to the individ-
ual existence, so the judgment in its various forms corresponds to and is the
subjective copy of the various objective relations."
The desired skill in judgment can only be acquired by
the knowledge and use of the principles which govern the
forming and unfolding of judgments. The subject will,
therefore, be considered under two Chapters, one treating
of the formation of judgments, the other of their unfolding.
CHAPTER I.
THE FORMATION OP JUDGMENTS OR
PROPOSITIONS.
THE formation of judgments is manifestly a most impor-
tant work of thought. Processes of reasoning and systems
of science and philosophy are made up of combinations of
judgments, and if the judgments are not properly and
thoroughly established, i. e., if they are not true, then the
arguments and systems cannot be expected to prove true.
It is, therefore, necessary to inquire carefully into both the
process and products of judgment-forming.
Section I, — The Process of Judgment-Forming.
The definition of judgment already given suggests for
consideration the following Topics : first, ascertaining and
combining the elements of judgment; second, finding the
reasons or grounds upon which the truth of judgments de-
pends, or the verification of judgments.
Topic First. — The Elements of Judgment.
The elements of judgment are ascertained by analyzing
judgment either as embodied in the proposition or as a
form of thought. From the former point of view, it is
94 PRACTICAL LOGIC.
made up of two terms (so called because they are the ter-
mini or boundaries of the proposition) united by the verb
to be as copula (bond) ; from the latter point of view, it is
composed of two notions united by some connecting link of
thought.
I. The Terms or Notions in Judgment.
The terms or notions are distinguished as the Subject or
Subject Notion, or that about which the assertion is made,
and the Predicate or Predicate Notion, or that whose union
or non-union with the subject is affirmed. In logical form-
ulas the subject is usually expressed by S and the predicate
byP,
The various notions, already considered, resulting from the processes
of conception, constitute the material which may possibly form the
terms of judgments. The following kinds have already been distin-
guished : (1.) The simple notion, called also simple apprehension, and
percept. This is the result of immediate cognitions by the senses
and consciousness. In observation this notion has as yet no name
given, but may be known by the indefinite " it." An orange, as an
object hitherto unseen and unknown, might be called "it." (2.) The
simple abstract notion, or part abstracted from the object observed,
but not yet combined with others into a concept. By observation we
get, from the hitherto unseen and uninvestigated orange, the abstracts,
yellow, round, sweet, juicy, etc. (3.) The general notion, as the con-
cept proper or bundle of properties or marks expressed in the concept
term. By conception proper the various abstracted properties are
gathered up in thought in the concept, orange. (4.) The general no-
tion, as the class or group of objects to which the bundle of attributes
in the concept applies. By classification the concept orange is applied.
It will be seen that only part of these can enter into the strictly
logical judgment.
II. The Connecting Links of Judgment.
The two terms of a proposition are always united by the
copula, which, according to the view of most logicians, is
always the present tense indicative of the verb to be, either
with or without the negative particle. The real quality of
THE FORMATION OF JUDGMENTS. 95
judgment, however, or that which makes it what it is, is
the mental union or separation of two terms or notions, on
the ground of a more or less clearly apprehended connec-
tion or absence of connection between them. The various
links by which this union in judgment is affected are to be
found in the predicables already given.
1. While the connecting link of judgment in language is
always the verb to be, which to the logician signifies connec-
tion rather than existence, it is obvious that the copula does
not always appear in this form in propositions as we find
them. E. g.,
" Columbus discovered America ; " " Napoleon was the emperor of
France." Hence arises the necessity for the practical application of
the Second Logical Postulate, in reducing judgments to the normal
form, S is P, or S is not P. Under this any change of logical form is
permissible, provided it brings out the thought more fully, without
changing it. "I am," means "I am existing," or, "I am a being."
"Columbus discovered America," means, "Columbus is the one who
discovered America." " Napoleon was the emperor of France," means,
" Napoleon is he who was the emperor of France." " Stars twinkle,"
means, " Stars are things that twinkle." The same postulate permits
the restoration of all inversions and displacements of parts of sen-
tences to the normal form, S is P, or S is not P. E. g., " Great is
Diana of the Ephesians " becomes " Diana of the Ephesians is great."
2. A judgment, however, is not a mere form of words,
two terms joined by the verb to be. " Man is intelligent."
" Man is round-square horizontal." One of these is a judg-
ment ; the other is not. The difference is that in the one
case there is a connection in thought, while in the other
there is none. This connection has been variously pre-
sented.
(1.) It has been said that the affirmative judgment is
always based upon the Axiom of Identity ; the negative on
the Axiom of Contradiction. In accordance with this view
judgment has been defined to be the affirmation of agree-
ment or disagreement.
96 PRACTICAL LOGIC.
This is true, but it is necessary to go below these generalities to the
special features in which the agreement or disagreement is found. E.
g., in the judgment, " Man is a terrestrial, rational animal," the copula
represents equality or identity. This is true in all perfect definitions.
Or again, in the judgment, " Man is intelligent," the copula expresses
the relation of substance and property, or genus and species, and the
judgment is interpreted as meaning, either that intelligence is an attri-
bute of humanity, or that man is a species of the genus intelligent
beings. Or again, in the judgment, " The life was the light of men,"
the copula may express the relation of substance and active property
or cause and effect. The judgment is thus seen to involve certain spe-
cial principles of connection which underlie the mere agreement or
disagreement.
(2.) According to the Aristotelian logic, every judgment predicates
of the subject either a genus, or a property, or a definition, or an
accident.
These forms of predication have been illustrated by suitable judg-
ments. " Envy is a passion." The relation is that of genus to species.
"Man has the faculty of speech." The relation is that si peculiar
property to substance or subject. "A state is a community governed
by its own laws." The relation is that of identity of the essential
properties, or essence of a thing, — by which the definition is consti-
tuted,— with the thing itself. " Life is sweet." The relation is that
of an accidental property to its subject.
These predicable classes have been reduced by Thomson to definition
and attribute, the latter including genus, property, and accident.
(3.) The Predicables as given, page 30, furnish the sim-
plest statement of what may be predicated in any judgment.
Of any subject may be predicated its substance and what-
ever belongs to it as its properties.
Thus of man may be predicated the substance of the thing itself,
as " Man is man ; " or some of the properties of quality, as " Man is
rational," or all of them (the essence or definition), "Man is rational
animal ; " or active properties, as " Man is the moulder of nature ; " or
relative properties, as " Man is of few days," " Man is terrestrial,"
" Man is finite," etc.
When notions or terms are thought together by one or
other of these various connections the product is a judgment.
THE FORMATION OF JUDGMENTS. 97
III. The Elements Combined.
The various notions or terms are united either in judg-
ments of observation or in strictly logical judgments.
These are both included under logical judgments in the
wider sense.
Note.— Hamilton gives the name of primitive judgment to the judgment of
existence implied in all our cognitions. This is not, however, judgment as thought,
and, therefore, is not to be treated in Logic.
1. The judgment of observation follows upon observation. In start-
ing with an orange, assumed to be a thing never before known, the
observer has no name for the object. The mental analysis by which
the abstracts are formed may be looked upon as made up of a succes-
sion of judgments : " It is yellow ; " " It is sweet ; " " It is round ; "
etc. All the predicates of these judgments, when gathered up, give
the concept, which is finally embodied in the word orange, and then
used in classifying all like objects as oranges. The judgment of obser-
vation may be seen to be the mental union of simple apprehensions
or percepts and abstracts.
2. The judgment of observation thus prepares the way for and
gradually approaches the strictly logical judgment, which makes use
of the concept and class, as, " The orange is yellow ; " " Oranges are
yellow." It will readily be seen that the strictly logical judgment
will take different forms, as the subject and predicate are concept or
class notions. The various relations of the notions in logical judg-
ments as embodied in propositions may be brought out in the following
form, using the notions man and mortal:
Subject. Copula. Predicate.
Concept proper, Concept proper, '
(Man = humanity) r is -j (mortal.)
Class, ) or I Class»
(Man=. mankind) I is not' (a mortal.)
The strictly logical judgment is the form of judgment of
which Logic mainly treats. In the logical proposition the
two terms may both be concept terms, giving a proposition
of content, as, " Man is mortal ; " or both class terms, giv-
ing a proposition of extent, as, " Man is a mortal."
The subject term in the latter form may be either an individual, as,
9 G
98 PRACTICAL LOO 1C.
" Garibaldi ; " or an individualized general term, as " this man ; " or
a general term taken partially, as " some men ; " or a general term
taken universally, as " all men." This form of logical judgment may,
therefore, be either, " Garibaldi is a mortal," or " This man is a mor-
tal," or " Some men are mortals," or " All men are mortals."
Note.— The strictly impersonal judgments, expressed in the classical lan-
guages without subject (except as the subject in the third person singular is
involved in the termination of the impersonal verb) and in the English with
" it" as the subject, as, " it rains," " it thunders," properly come under the logi-
cal judgments. Says Ueberweg, " In the so-called judgments without subjects
the sum total of the existence surrounding us, thought of indefinitely, or an
indefinite part of it, takes the place of the subject."
Praxis. — Examine carefully the following judgments, stating them
in the normal form (S is P, or S is not P), naming the subject and
predicate, and bringing out the precise connecting link in each case :
1. Truth is stronger than error. 2. The human race was one in its
origin. 3. A square is rectangular. 4. A square is an equilateral
rectangle. 5. " Few and short were the prayers we said." 6.
" Flashed all their sabres bare." 7. Man is risible. 8. Not all the
ills of earth can mar my joy. 9. Not all men are virtuous. 10. A
horse may be white. 11. He that destroys a usurper does right. 12.
Great is the work of life. 13. There was no possibility of substan-
tiating the allegations. 14. " In jewels and gold men cannot grow
old." 15. " From peak to peak the rattling crags among leaps the
live thunder." 16. It is wrong to put an innocent man to death.
17. There is no place like home. 18. " None but the brave deserve
the fair." 19. " The most sublime act is to put another before thee."
20. Life every man holds dear.
Topic Second. — Verification or Proof of Judgments.
When a so-called judgment, expressed in a proposition,
is brought before the mind, the question is naturally asked
concerning it, What reason is there for believing it to be
true? A so-called judgment is decided to be true, doubt-
ful, or false, by the presence or absence of proof, i. e., of
something which makes the reality of the connection of the
two notions more or less evident to the mind.
Practically, in all our intercourse with men and books, judgments
of every form are constantly being presented to our minds for con-
THE FORMATION OF JUDGMENTS. 99
sideration. " Geometry is the science of extension." " Things which
are equal to the same thing are equal to each other." " Logic is the
art of reasoning." " The weather is cold." " If the weather remains
as at present, the streams will be frozen over." In short, every sen-
tence read, heard, or uttered involves one or more judgments, and no
such judgment is anything more to us than an empty assertion until
we have grasped some proof that the expressed connection of its parts
agrees with the corresponding reality. The verification or confirmation
of judgments is, therefore, a most important part of this form of thought.
Judgments have been divided, by the sources from which
the predicate is drawn, into analytic and synthetic. The
predicate notion may either be brought out of the subject
notion by analysis, or brought to it from without. Proofs
are accordingly either analytic or synthetic, the former
being drawn by analysis from the terms of the proposition
itself; the latter being brought from outside the terms of
the proposition.
An analytic or explicative judgment is one in which what is affirmed
in the predicate is already contained in the definition of the concept
or general term which forms the subject. " Man is rational," is an
analytic judgment; since the predicate, rational, is involved in the
notion, man, as brought out by partition or by the definition, "Man
is a rational animal." Such judgments are also called a priori, or
judgments not grounded on but prior to experience. The simple study
of what is contained in the subject notion gives the predicate without
resort to the testimony of experience. E. g., in the judgment, " Body
is extended," the instant the thinker understands what is meant by the
term "body," he knows that "extended" is comprehended in it. A
synthetic or ampliative judgment is one in which the predicate adds
something which is not contained in the conception or definition of the
subject. E. g., "Man is a sinner," "Neptune is the most remote of
the planets," are synthetic judgments. The predicate adds to the
subject something which it brings from outside and which no analysis
could have discerned in the subject.
In connection with the various forms of judgment analytic
and synthetic the nature of the proof, and the canons or
rules governing it, will be set forth.
100 PRACTICAL LOGIC.
I. Proof of Analytic Judgments.
Analytic judgments furnish within themselves the ma-
terial for their own verification. This is to be brought out
by analysis, i. e., by partition or division of the subject or
predicate or both.
The proposition, "All trees are organic," is proved by analyzing
" organic." The proposition is regarded as one of extent, affirming
that the genus, " organic beings " includes the species, " trees." Or-
ganic beings are divided, by the presence or absence of a nervous sys-
tem and power of causation, into animals and plants. Plants are
divided, by the size and duration of the stem or ascending axis, into
herbs, shrubs, and trees. The result reached may be expressed in tab-
ular form :
Organic beings = j Animals, / Herbs,
( Plants = | Shrubs,
( Trees ;
froDi which it is apparent that the lower species " trees " is included
under the higher genus " organic." The proposition, " Duelling is
murder," is analytic. Regarded as a proposition of content, its proof
is reached by partition of the terms. " Murder " includes the generic
mark, taking of human life, and the differential or specific marks, de-
liberately, unlawfully, maliciously. "Duelling," where it results in
death, is found to include the same marks, taking of human life, de-
liberately, unlawfully, maliciously. The two are thus found to agree.
Duelling is, therefore, murder, i. e., the relation affirmed to exist between
the two, in the proposition to be proved, corresponds to the reality.
The proof of the proposition, "Labor is a blessing to man," is to be
found by an analysis of the terms. Regarded as a proposition of ex-
tent, it affirms that "labor" is one species of the genus or class
"blessings to man." By partition "blessing to man" has the active
properties or characteristics, meeting some fundamental and natural
need of man, giving satisfaction or happiness. There are, therefore, as
many "blessings to man " as he has fundamental and legitimate needs
to be satisfied. Analyzing " blessings to man " by division, we, there-
fore, find that the genus includes the desires for habitual activity
physical and rational, for knowledge, for power, for property, for help
in dependence and helplessness, for deliverance from sin, etc. Any-
thing which meets and satisfies any one of these desires is a blessing
THE FORMATION OF JUDGMENTS. 101
to man. " Labor " analyzed by partition is found to include the
marks, exertion of the powers, habitual, with rational aim, or, in other
words, habitual rational activity. " Labor," as meeting the funda-
mental and legitimate need for habitual rational activity is a " blessing
to man." Continuing the process of thought still further, we may
conclude from the analysis, that " knowledge " is a blessing to man,
"power" is a blessing to man, "wealth" is a blessing to man, "the
sustaining power of divine providence" is a blessing to man, "sal-
vation from sin " is a blessing to man, etc.
General Rule. — The analysis must be accurate and com-
plete.
It is obvious that this method of proof must render cer-
tain the truth of the propositions which admit of its appli-
cation. All analytic proof is, therefore, said to be demon-
strative in its force.
II. — Proof of Synthetic Judgments.
Synthetic judgments require that their proofs be sought
outside of the judgments themselves. No analysis of terms
will furnish the proof that, " Duelling is a relic of barbar-
ism," or that, " The Feudal System was beneficial." The
proof must be brought from outside sources.
The precise source or place outside will depend upon the
species of synthetic judgment to be proved. Synthetic
judgments are divided, by the place outside the proposition
from which the predicate is brought, into intuitive and em-
pirical.
Intuitive, or a priori, judgments are those whose predicates are
brought from within the mind itself, from some fundamental or thought
necessity. In these the predicate could never be unfolded from the
subject, as in the judgment, " Every event must have a cause." It is
a law of our thinking that compels us to connect " must have a cause "
with the subject, " every event." Empirical, or a posteriori, judg-
ments are those of which the predicates are brought from outside the
mind. They have their ground in experience. The judgment, " Body
is extended substance," is analytic, since " extended substance " is seen
to be comprehended in "body," or to be identical with it; but the
102 PRACTICAL LOGIC.
judgment, " Body is heavy," is a synthetic judgment, since the mark
"heavy " is not comprehended in " body." The latter is an empirical
judgment, since only experience, examining bodies and measuring
pressure by muscular effort, enables us to predicate " heavy " of " body."
1. Proof of Intuitive Judgments. — These draw their
proofs from the mind itself. The proofs are intuitions or
fundamental truths, accepted by all, and lying at the foun-
dation of all human knowledge and activity.
For the proposition, " Suicide is wrong," the proof is to be found
in man's intuitive convictions of duty. Every one knows intuitively
that man, as a creature under the moral government of God, is bound
to make the most and the best of himself, and that to fail in this is
wrong. Duty is intuitively seen to require that he should preserve
himself, improve himself, and use his powers for the true end of life.
"Suicide" is intuitively seen to break the first of these requirements,
and, therefore, seen to be " wrong." The propositions, " I exist," " I
am thinking," rest upon the intuitive belief in the veracity of our
consciousness.
As so-called intuitions are often urged in proof of various
false judgments, it becomes necessary to keep clearly in
mind the tests of intuition, These may be given in the
following rules :
Rule 1st. — Every intuition is self-evident. The mind, on the bare
contemplation of it, must see its truth at once, without requiring any
foreign evidence or outside proof.
Rule 2d. — Every intuition is necessary. The mind cannot help be-
lieving and acting upon its truth. That " Space exceeds my widest
imagination of space," and that " Every event must have a cause,"
one cannot help believing.
Rule 3d. — Every intuition is catholic or universal. It must be en-
tertained by all men intelligent and understanding what is meant by
it. An intuition is sometimes described as being " What all men
everywhere and always believe."
Rule 4th. — Every intuition is accepted by all men practically. In-
tuitive truths may not be consciously apprehended and stated by the
majority of mankind, but they are assumed and acted upon by all
men, even by those who deny their belief in them.
THE FORMATION OF JUDGMENTS. 103
The notions of being, personal identity, time, space, causation, the
axioms of Mathematics, Logic, Ethics, etc., are among these self-evi-
dent, necessary, and universal cognitions of men.
It is evident that all such proofs, properly tested, must
render certain the truth of propositions based upon them.
Intuitive proofs are, therefore, said to be, like analytic
proofs, demonstrative in force.
2, Proofs of Empirical Judgments. — Empirical judg-
ments, or those based upon something outside of the propo-
sition and of the mind itself, rest for their proofs upon the
experience of the thinker himself or of others. Knowledge
in the form of experience has been seen (p. 16) to include
the observation and thinking of the man himself, and the
observation and experience of others given in testimony
and authority. This suggests the kinds of empirical judg-
ments to be established.
(1.) Judgments from Observation. — When the judgment to be veri-
fied is based upon our own observation of things external or internal,
its truth is tested by careful application of the Rules of Observation
already given (p. 33). Thus, " I see my uplifted hand in all its parts ; "
" I am conscious of exertion in lifting my hand," are judgments of
observation. Their truth evidently depends upon the trustworthiness
of the senses and consciousness, assumed in all observation, and upon
strict compliance with the Rules of Observation.
(2.) Judgment from Thought. — Many empirical judgments are
reached by the processes of Reasoning Inductive and Deductive.
These must be tested by the Canons of Reasoning, which will be
presented in Part III.
(3.) Judgments from Testimony and Authority. — Testi-
mony is the statement of others concerning matters of fact
which they have observed in their own consciousness or in
the world around them. Authority is the statement of
others concerning matters of opinion which they have
reached by the processes of conception, judgment, and rea-
soning. The testimony or authority may be recorded on
104 PRACTICAL LOGIC.
monuments or in writings, books, etc., or given by word of
mouth.
As almost all human knowledge is received on testimony
or authority, the question, What are the tests of testimony
and authority ? becomes a most important one. The tests
are to be found either, first, in the ability, character and
number of witnesses or authorities, or, secondly, in the
character of that which they present. Out of these arise
the Rules to be observed in judging of the truth or falsity
of judgments received from others.
Rule 1st. — A witness or authority must be competent,
i. e., must have the opportunity, the ability, and the dispo-
sition to know the facts testified to, or to think out the
judgments presented on his authority.
a. Want of opportunity to observe destroys the value of any so-
called testimony. The testimony of A concerning what B says that C
did is mere hearsay, and of little evidential value. Negative testi-
mony is of little value. The testimony of a thousand witnesses that
they did not see A kill B is not sufficient to countervail the statement
of one good witness that he did see A kill B. Want of ability to ob-
serve the facts in any given case may make the testimony worthless.
A blind man's testimony to mere objects of sight is worthless. Cer-
tain spheres of observation require special skill, so that only the testi-
mony of experts, or those trained for the purpose, may be of value
in those spheres. A man acquainted with the phenomena of electricity
will be able to detect important facts which would entirely escape the
notice of the ordinary observer. Testimony regarding the distance,
size, form, and appearance of any object requires a trained judgment
to make the observation trustworthy. Thus the testimony of an ex-
pert,— e. g., of a practical astronomer to the fall of a meteor, — may
become of more value than that of hundreds of ordinary observers.
Want of disposition to observe accurately vitiates testimony. This
may result, through habitual carelessness, in imperfect observation, or,
through prejudice, in warped views of things. There are men who,
from the first cause, never see anything worth seeing, and others who,
from the second cause, always see things double or quadruple or as
they expect or wish to see them.
b. Want of opportunity or ability or disposition to think out the
THE FORMATION OF JUDGMENTS. 105
conclusions for which one is quoted as an authority must, of course,
destroy the weight of the authority. In order to be an authority in
any department of thought a man must have had special opportunity
of acquaintance with that department, must have shown himself pos-
sessed of extraordinary ability to deal with it and of unusual mastery
of it, and must be disposed to seek and discern the truth in it. The
authorities in Law are the men who have shown themselves masters
of legal science. The authorities in Physical Science, are, accord-
ing to Professor Tait, " the advanced, best, ablest scientific thinkers."
The "competent authorities "" in Physics are not the men who simply
observe and experiment, but the men of exact science, who, largely by
the aid of mathematics, have advanced the bounds of the science.
Professor Tait names as such authorities in Great Britain, " Brewster,
Faraday, Forbes, Graham, Rowan Hamilton, Herschel, and Talbot,"
in the immediate past, and "Andrews, Joule, Clerk Maxwell, Balfour
Stewart, Stokes, William Thomson, and such like," in the present. The
authorities in Theology, Philosophy, etc., are the men who are masters
in these departments.
The utterance of a competent authority in any department has great
weight even when not accompanied with the reasons, because he is
rightly supposed to know whereof he affirms. The word of the aver-
age man, even if he is admitted to be familiar with his subject, has
just as much weight as the reasons by which he supports it, and it has
weight at all only as he presents his reasons along with it. He is not
an authority. Assertions made concerning Theology, Metaphysics,
etc., by experimental physicists who have given absolutely no attention
to those difficult departments, are worth just as much as the counter
assertions made concerning Experimental Physics by theologians who
know nothing of that department. In all such cases, however dis-
tinguished a man may be in his own department, his words concerning
the unknown department should have only so much weight as is given
by the reasons with which he accompanies them.
Rule 2cL — A witness or authority must be credible, i. e.t
must be of such a character as to be worthy of belief.
a. Whatever the opportunities or natural ability of a witness, if
he is shown to be careless in observing, credulous in receiving state-
ments, addicted to falsehood, under the influence of prejudice, or
swayed by motives that would warp his view of the facts, the value
of his testimony is just so far impaired.
106 PRACTICAL LOGIC.
b. The value of arthority is equally affected by the credibility of
the one giving the opinion. If the judge who renders a certain de-
cision can be shown to be corrupt, or to be in any way wanting in
principle, his decision will come so far short of commanding assent as
authority.
Rule 3d. — Concurrence in testimony or authority in-
creases the probability of its truth.
a. The force of concurrence in testimony is broken when there is
evidence of collusion or pre-arrangement. Precise agreement in stat-
ing the general facts and all the details of any occurrence is looked
upon as proof of collusion ; whereas incidental variation in non-essen-
tial particulars, along with general agreement, shows the absence of
collusion and the truthfulness of the witnesses. Where there has been
no opportunity for collusion, concurrent testimony may become abso-
lutely conclusive even where all the witnesses are noted liars. In
such cases we cannot account for the agreement except on the ground
that what the witnesses independently state is true.
b. The force of concurrence in authority is subject to the same limi-
tations as that in testimony. Too precise agreement in statement of
matters of opinion indicates probable collusion. No weight is to be
attached to the concurrence of many judges, if it can be shown that
the successive decisions have all followed some one original and lead-
ing decision. If, however, there is evidence that each arrived at his
decision by independent thought, the authority may become of the
greatest weight, even when the word of each one separately could
command little or no respect. The cumulative force of convergent
evidence or argument is also to be considered. The convergence of
several lines of proof is often sufficient to render certain what perhaps
no.one of these lines alone would fully establish. This is illustrated
in the proof that there is a personal God. The consent of mankind,
the principle of causation, the order of the universe, the intuition of
the infinite, the voice of conscience, and the yearnings of the affections,
all converge towards the common centre, a personal God, and the
strength of the proof lies in this convergence, rather than in the sep-
arate arguments taken alone.
Rule 4th. — Things absurd or impossible are not to be be-
lieved on the ground of testimony or authority, although
THE FORMATION OF JUDGMENTS. 107
things strange, wonderful, or even miraculous may be be-
lieved on such ground.
Whatever is absurd or impossible, i. e., logically contradictory or
beyond the reach of power to accomplish, cannot, of course, be believed.
No testimony or authority could make one believe in a triangle with
four sides, or in Mill's conceived world in which two and two make
five. It must be observed, however, that what is merely contrary to
experience is not necessarily absurd or impossible. The King of Siam
had never in his experience known water to be transformed into a
solid upon which men could walk ; but every one sees that this was
not sufficient reason for his pronouncing the missionary, who told him
of such a thing, a liar and impostor, since human experience is very
limited.
There is need to note especially the natural inclination of men to
pronounce everything absurd and impossible which contradicts their
settled convictions, their preconceptions or their prejudices, or which
is repugnant to their feelings. It was once, by the majority of man-
kind, pronounced impossible for the earth to turn on its axis and move
through space with incredible rapidity without our perceiving it. It
was declared absolutely impossible that information should be trans-
mitted thousands of miles in the fraction of a second, or that a man
should converse with his friend hundreds of miles away. It must be
borne in mind that the impossible is only that which is logically con-
tradictory or beyond the reach of power ; and that, therefore, before
any particular thing can be pronounced impossible, the laws and limi-
tations of thought and power must be comprehended and found to
forbid its accomplishment. A thing may, therefore, be perfectly cred-
ible, though it be strange, unaccountable, or even unintelligible.
" What is strange or unaccountable to one mind may be perfectly
familiar and plain to another. For the most limited intellect or ex-
perience to make itself the standard of the possible, would be as absurd
as a man's making his visible horizon the limit of space." Even tes-
timony to supernatural and miraculous events may be entirely worthy
of belief, if there be any Supernatural Power in the universe, and
such events may and ought to be believed if the witnesses are com-
petent and credible and concur in their statements. It is a remarkable
fact that the greatest scientists and philosophers, — such men as Bacon,
Locke, Descartes, Newton, Herschel, Brewster, and Faraday, — have
unhesitatingly believed in miracles on the ground of such testimony,
regarding them, not as events without any adequate cause, but as
108 PRACTICAL LOGIC.
events into whose production a higher, Unseen Cause entered. In all
such cases, however, the witnesses to the supernatural events should
be subjected to the most rigid scrutiny and cross-examination, accord-
ing to the established rules of testimony.
It is evident that the proofs of empirical judgments never
give the judgments the absolutely demonstrative force which
belongs to the proofs of analytic and intuitive judgments,
but simply render them more or less probable. As the
entire practical ongoing of human life depends upon such
judgments from experience, i. e., from observation, thought,
testimony, and authority, the meaning and truth of Butler's
statement, that "probability is the guide of life," becomes
apparent.
Probability varies in different cases. It may in one case practically
amount to certainty ; in another the balance may be as a thousand, or
a million, or vastly more, to one, against the truth of the judgment.
The rational conduct of human affairs varies accordingly. Where
the balance of probabilities is in favor of the truth of a judgment,
men base their action upon it, in all the ordinary affairs of life, with
a confidence increasing as the degree of probability rises. When the
probabilities are as fifty-one to forty-nine that certain goods will
greatly advance in price, the enterprising merchant hesitatingly in-
vests in them ; as the probabilities become as seventy-five to twenty-
five, he invests more eagerly ; as the probabilities approach certainty,
he secures control of all that his capital will enable him to command.
Where great and permanent practical interests are involved, even
the lowest degree of probability should, in accordance with the dic-
tates of common sense, be acted upon. The man wrecked in mid-
ocean wisely clings to his solitary plank even when the probabilities
that he will be saved are only as one to a thousand or even one to a
million. The balancing of probabilities and deciding the course in
view of them is manifestly an essential part of man's rational and
moral discipline in this world.
Note. — Professor Jevons says of the Theory of Probabilities : " It is the very
guide of life, and hardly can we take a step or make a decision of any kind
without correctly or incorrectly making an estimate of probabilities. . . . The
whole cogency of inductive reasoning rests upon probabilities. The truth or
untruth of a natural law, when carefully investigated, resolves itself into a
THE FORMATION OF JUDGMENTS. 109
high or low degree of probability, and this is the case whether or not we are
capable of producing precise numerical data."— Jevons' Principles oj Science,
p. 217.
Praxis. — Examine critically the following judgments or proposi-
tions,— first, stating of each whether it is analytic or synthetic ;
secondly, if analytic, developing the proof from the judgment itself;
thirdly, if synthetic, showing whence its proofs are to be derived and
bringing the proofs of the judgments from observation, testimony, and
authority from the proper sources :
1. Washington is the capital of the United States.
2. George Washington was a true patriot.
3. Columbus discovered America.
4. New Orleans is situated on the Mississippi.
5. England is across the Atlantic Ocean.
6. There is such a country as China.
7. Madagascar is inhabited.
8. Civilization has been progressive from the earliest ages.
9. The Aztecs reached a high degree of civilization.
10. Lying is never justifiable.
11. The Allegheny Mountains were formerly submerged.
12. The Himalayas are the highest mountains on the globe.
13. The feudal system was beneficial.
14. Honesty is the best policy.
15. Education cannot be effected by mere class-room instruction or
lecturing.
16. The sum of the three angles of a triangle is equal to two right
angles.
17. Two straight lines cannot inclose a space.
18. The earth is between 93,000,000 and 94,000,000 miles from the
sun.
19. Wrong-doing blinds the conscience.
20. Falsehood is dangerous.
21. The story of Christ's life and death is true.
22. Joan of Arc was a religious enthusiast.
23. In a right-angled triangle the hypothenuse is the longest side.
24. Any two sides of a triangle are together greater than the third.
25. Christianity is of divine origin.
26. The study of the classics is necessary to the highest culture.
27. North America was once inhabited by a race of Indians of
higher civilization than the existing tribes.
10
110 PRACTICAL LOGIC.
28. Christianity is the religion which meets the needs of man.
29. A triangle cannot have more than one angle as great as a right
angle.
30. The moon revolves round the earth.
31. The best science recognizes a God.
32. Probability is the guide of life.
Section II,— The Products of Judgment,
The process of judging results in judgments which are
embodied in propositions. These products need to be care-
fully classified and divided, since the unfolding of judg-
ments depends upon a knowledge of their kinds and char-
acteristics, and since judgments constitute the material of
Reasoning, the third Form of Thought.
Judgments of content and extent and analytic and syn-
thetic judgments have already been considered in treating
the process of judgment (pp. 97-99). For further logical
purposes the chief divisions of judgments are based on the
various ways of making the predication or assertion, since
the assertive element is the main one in judgment. This
gives rise to the following divisions :
First, by the quality of the predication, whether affirmative or not,
into affirmative and negative judgments. This division is treated
under Quality of Judgments.
Second, by the extent of the predication, whether total or not, into
universal or total and particular or partial judgments. This division
is treated under Quantity of Judgments.
Third, by the directness of the predication, whether direct or indi-
rect, into categorical and hypothetical. This division is treated under
Relation of Judgments.
Fourth, by the degree of certainty of the predication, whether
certain or not, into certain including demonstrative and assertory, and
not-certain including probable and possible. This division, as it has
reference to the results in the mind of the thinker himself, will be
treated, in summing up the results of thinking in its second form, at
the close of Part II., under Modality of Judgments.
Since the divisions of scientific syntax in Grammar depend upon the
forms and combinations of logical judgments or logical propositions,
THE FORMATION OF JUDGMENTS. Ill
for grammatical purposes there is still another division of judgments,
which needs to be considered :
Fifth, by combination, whether single or not, into simple, and mul-
tiple or combined including complex and compound. This is treated
under Grammatical Combination of Judgments.
Topic First. — Quality of Judgments.
By the quality or character of the predication judgments
are either affirmative, as, " Belgium is populous; " or nega-
tive, as, " The vicious are not wise." In the former there
is indicated the union of the two notions by some link of
connection, and they are, therefore, said to agree, by the
principle of Identity ; in the latter there is indicated by the
negative the separation of the two notions, which are, there-
fore, said to disagree, by the principle of Contradiction.
It follows from the nature of negation that a negative copula always
excludes everything in the predicate, — the whole, the species, the indi-
viduals,— entirely from the subject. E. g., " No men are angels" cuts
off the entire class " angels " and all that is included in it from the
class "men." "Some men are not artists" cuts off the entire class
" artists " from these " some men." This is called the distribution of
the predicate, or the taking of it in its entire signification.
It should be observed that the negative particle is not always con-
nected with the copula, but may be placed in other parts of the propo-
sition ; yet in every judgment really negative it belongs only to the
copula. By the second Logical Postulate it is always permissible to
put the negative into its proper place, with the verb to be, in reducing
any proposition to the normal form, S is not P. " No human knowl-
edge is perfect " may thus be changed into, " All human knowledge
is not perfect." In many apparently negative propositions the force
of the negative particle does not fall on the copula, but upon one of the
terms. E. g., "Not to submit is madness " is really an affirmative prop-
osition, since the force of the "not" falls on the words "to submit."
The meaning is, "Non-submission (or resistance) -is madness." Again,
"A person not vicious is virtuous" is equivalent to, "A non-vicious
person is virtuous," and is, therefore, an affirmative proposition. In
like manner propositions apparently affirmative may be really nega-
tive, the force of the negative particle being in some way involved in
the thought, if not in the form of expression. E. g., " Only a few
112 PRACTICAL LOGIC.
men are wise ; " " Few men are wise ; " " But few men are wise," are
all substantially negative propositions, since they are equivalent to,
" Most men are not wise." On the other hand, " A few men are wise,"
is an affirmative proposition. Great care should manifestly be exer-
cised in ascertaining the precise quality of all such propositions.
Topic Second. — Quantity of Judgments.
The quantity of judgments depends upon the extent of
the predication. Certain logical distinctions, which arise
from the combination of quantity with quality, may also
be most conveniently treated under this Topic.
I. Kinds of Judgments by Quantity.
The predicate notion of a judgment may be affirmed or
denied either of the whole of a subject or of a part of it
only. Having once formed the notion, "orange," we may
affirm that, "This orange is yellow," or, "Some oranges
are yellow," or, "All oranges are yellow." Hence judg-
ments by this division are universal or total and particular
or partial.
1. Universal or total judgments include the strictly uni-
versal, or those in which the notion of the subject is taken
in its entire extent ; the judgments in which a definite part
of the notion of the subject is taken; the judgments with
individualized, singular, or collective subjects ; and equiv-
alent or substitutive judgments.
Universal judgments in the strict sense are those in which the pred-
icate notion is affirmed or denied of the entire subject notion, i. e., of
all that is comprehended or contained under it, whether attributes or
objects. The subject is, in this case, a logical whole taken in all its
parts. "All men are mortal;" "Every man is mortal," are univer-
sal judgments, the subject embracing the total number of objects in the
class "man." The subject in all universal judgments, whether affirm-
ative or negative, is said to be distributed, because what is predicated
is predicated of each and every object in the entire whole. Universal
judgments include those in which a definite part of the subject is taken,
as, "These men are Japanese." They also include judgments with
individualized subjects, as, " This man is sober ; " and judgments with
THE FORMATION OF JUDGMENTS. 113
singular subjects, as, "Bucephalus is a horse;" "France is not an
empire." This follows from the fact that the predicate notion is af-
firmed or denied of the whole subject. The same is true of judgments
whose subjects are collective wholes, as army, forest; mass wholes,
as, wheat, rice ; material wholes, as gold, stone.
From the predication of the definition, or essence, of a notion, there
arises a peculiar kind of universal judgment in which the subject and
predicate are equal and identical. This is known as the equivalent, or
substitutive judgment, in distinction from the simple attributive judg-
ment or ordinary universal. For example, " Body is extended sub-
stance ; " " Man is a rational animal." In all such judgments the
notions or terms of both subject and predicate are taken in their entire
meaning, or distributed.
The signs of universal judgments are all, every, each, both, any, none,
neither, always, never, whoever, wherever, whatever, etc. Care must be
taken, however, to guard against the ambiguous use of such signs,
especially against such use of the word all. The word all in its proper
logical sense means " each and every ; " but it stands sometimes for
"all taken together," as, "All these claims upon my time overpower
me." Hence may arise an ambiguity, since instead of all, in its proper
sense of "all taken together," we are liable, in our interpretation, to
put all in its logical sense of " each and every." The example could
not mean, " Every single claim upon my time overpowers me."
2. Particular or partial judgments embrace the ordinary
form including the purely indefinite and the semi-definite
judgments; and the more unusual forms called numerically
definite and plurative judgments.
Particular or partial judgments are those in which the predicate
notion is affirmed or denied of a number of objects less than the whole
denoted by the subject notion, as, "Some men are poets," "Some rulers
are not just." In particular judgments the naked subject must always
be restricted either by implication or by some restrictive term. The
signs of particular judgments, are, some, not all, not every, a few, there
are — that, a or an, one, two, three, etc., sometimes, somewhere, etc.
The word some, as used in introducing particular judgments embod-
ied in propositions, is, as Hamilton has shown, ambiguous. In some
instances it introduces a semi-definite judgment, as, " Some men are
poets," i. e., some at most, not all. In other instances it introduces a
strictly indefinite judgment, as, "Some men reason," i. e., some at
10* H
114 PRACTICAL LOGIC.
least, perhaps all The latter is the old logical meaning of some, and
the judgment is wholly indefinite ; the former meaning makes the judg-
ment semi-definite, since it excludes all. In which sense the word is
used in any given instance must be determined by examining the
thought or, in connected discourse, the context. Numerically defi-
nite judgments, are those in which the predicate notion is affirmed
or denied of a definite number or proportion of the objects included
in the subject, as, " Ten men in a thousand are wise." Considering
the " ten men " alone as the subject, the judgment would be regarded
as universal, since the predicate is affirmed of all the ten. Of like
nature are plurative judgments which embrace more than half but
not all the subject. These may be numerically definite, as, " Forty
men out of the fifty on the steamer perished ; " or indefinite, as, " Most
men are not poets." In the numerically definite form the sign is found
in numbers expressing more than half of the whole embraced in the
subject. In the indefinite plurative judgment the signs are found in
such expressions as, more than half, the majority, many, etc.
"When the predication approaches more nearly to covering the whole
of the subject, as in approximately universal judgments, such terms
are used as most, almost every one, the large majority, etc. On the
other hand the following signs are nearly total negatives : few, very
few, hardly or scarcely any, little, small, slight, rare, seldom, etc.
II. Logical Distinctions from Quantity and Quality Com-
bined.
Two subjects — the normal forms of judgments as they
appear in the syllogism, and the distribution of terms — are
dependent upon both Quality and Quantity, and will be
most naturally treated and best understood in immediate
connection with these topics.
1. Normal Forms of Judgment. — Men in their thinking
combine quality and quantity in judgments. To facilitate
the use of judgments in the syllogism logicians have formed
a complete scheme of judgments combining quality and
quantity, and have affixed to each form a symbol by which
both quality and quantity are briefly expressed. The pos-
sible combinations are four, two of which are subdivided as
shown in the following form :
THE FORMATION OF JUDGMENTS. 115
Quantity. Quality. Symbol. Formula.
Universal Affirmative,
Attributive, A, All S is (some) P.
[ Substitutive, U, All S is (all) P.]
Universal Negative, E, No S is (any) P.
Particular Affirmative,
•§ Attributive, I, Some S is (some) P.
[ Substitutive, Y, Some S is (all) P.]
Particular Negative, 0, Some S is not (any) P.
These may be illustrated by examples:
All men are (some) mortals .... A.
[ All men are (all) rational animals . . . U.}
No men are (any) angels . E.
Some men are (some) mortals .... I.
[ Some men are (all) the poets Y.]
Some men are not (any) artists ... 0.
The judgments in most common use are A, E, I, and 0, and the log-
ical processes are usually confined mainly to these.
2. Distribution of Terms. — As already indicated, a term
is said to be distributed when it is taken in its entire sig-
nification embracing each and every object included under
it. From the principles already presented a general state-
ment of the terms distributed, or taken in their full extent,
in the various judgments and also of those undistributed,
or not taken in their full extent, can readily be made.
These may be embodied in Rules.
Rule 1st. — All universals, — A, U, and E, — and no par-
ticulars,— I, Y, and 0,- — distribute the subject.
Rule 2d. — All negatives, — E and 0, — and all substitutive
affirmatives, — U and Y, — but no attributive affirmatives, —
A and I, — distribute the predicate.
From the nature of quantity and quality, as seen in the statements
made and examplep given, it appears that the six kinds of judgment*
have their terms distributed or undistributed, as follows :
116 PRACTICAL LOGIC.
A distributes the subject only.
U " both subject and predicate.
E " both subject and predicate.
I " neither subject nor predicate.
Y " the predicate only.
0 " the predicate only.
Praxis. — State of each of the following judgments, — first, to which
of the six forms it belongs, and whether its terms are distributed or
undistributed and why, marking the judgment by its appropriate
letter ; secondly, if the judgment is particular, whether it is definite,
semi-definite, numerically definite, plurative, etc., and if universal,
whether singular, attributive, substitutive, etc.; and, thirdly, if am-
biguous, wherein the ambiguity consists :
1. All oaks are trees. 2. Some men have genius. 3. Poets are men
of genius. 4. Body is extended substance. 5. This inkstand is made
of glass. 6. The senate has adjourned. 7. Birds breathe and fly. 8.
" All Jerusalem went out to meet him." 9. Salt is chloride of sodium.
10. Some men reason. 11. Some men seek reputation. 12. A few were
saved. 13. He that does not heed, stumbles. 14. Nine boys out of ten
prefer play to study. 15. Forty of the fifty sailors perished. 16. Not
every mistake is culpable. 17. Milton was blind. 18. All men are
not liars. 19. God is good. 20. Gold is a heavy metal. 21. With rare
exceptions men are selfish.
Topic Third.— Relation of Judgments.
The relation of judgments depends upon the manner of
predication. The predication may be made either simply
and positively or may be made to depend upon something
else. The first gives rise to the categorical judgment ; the
second to the hypothetical.
Note.— The ordinary grammatical division of propositions as embodied in
sentences is based upon the mental states embodied. It embraces the follow-
ing kinds of sentences :
/Expressing Cognition or Intellect, including,—
I ( Interrogative, showing search for ground of judgment,
m\l Hypothetical, showing certain grounds only as still in doubt,
8 1 ( Categorical, showing the comparison and connection completed ;
v /Expressing Emotion or Sensibility, —
g J Exclamatory, embodying feeling ;
w /Expressing Conation or Will, including, —
I ( Optative, indicating wish or choice,
V 1 Imperative, indicating determination or volition.
THE FORMATION OF JUDGMENTS. 117
Interrogative sentences may have the same terms as the other sentences ex-
pressing cognition, and are treated in Logic in the same manner as those sen-
tences. The elements of emotion and will do not enter into the thought of the
proposition, in the strict sense. In so far as the sentences based upon them ex-
press thought in the proper sense, they may be treated as propositions express-
ing cognitions, and so become either categorical or hypothetical. See Davis'
Logic, p. 82.
1. A categorical judgment is one in which the predicate
is affirmed or denied of the subject simply and absolutely
or without condition, as, " Captain Jack was a Modoc chief; "
" Benedict Arnold was not a patriot." The affirmatives
are based on the principle of Identity, the negatives on
that of Contradiction.
2. A hypothetical judgment is one in which the predica-
tion is based upon some circumstance " which must be
granted or supposed before the assertion becomes applicable."
The supposition may be either a condition or an alternative
or both these combined ; and hypothetical judgments are,
therefore, of three kinds, conditional, disjunctive, and di-
lemmatic.
(1.) A conditional or conjunctive judgment suspends the predication
upon some supposed circumstance (called a condition), as, " If the sun
shines the snow melts." This may be put into the form, " The snow
is, — if the sun shines, — melting." " Melting " is predicated of " snow "
upon the condition that " the sun shines." If it be true that " the
sun shines," then it is true that " the snow melts." The supposed cir-
cumstance, " If the sun shines," is called the antecedent ; the judg-
ment suspended upon the condition is called the consequent. The rela-
tion between the two is that of reason and consequent, or cause and
effect. The conditional judgment is, therefore, based upon the princi-
ple of Sufficient Reason. The signs of conditionals are, if, when, in
case of, etc.
Conditional judgments may be converted into categorical form by
changing the signs, if, when, in case of, etc., into such phrases as "the
case of," " the circumstances in which," etc. Thus the conditional,
" If the sun shines the snow melts," becomes " The case of the sun's
shining is the case of the snow's melting."
(2.) A disjunctive judgment suspends the predication upon some
alternative introduced by "either — or." It involves two or more
118 PRACTICAL LOO I C.
judgments, all of which cannot be true, but one or more of which, by
the principle of Excluded Middle, must be true. Thus in the disjunc-
tive, " Either the Bible is false or holiness ought to be followed," there
are two alternative judgments, " The Bible is false; " and " Holiness
ought to be followed." " Either London is in England or it is not,"
contains two alternative judgments, " London is in England; " " Lon-
don is not in England." One or other of them must be true ; the
other cannot be. The disjunctive needs to be carefully distinguished
from the partitive judgment, which, under the form of a disjunctive,
simply predicates of a genus its several species ; as, " All Africans are
either bond or free." The genus, Africans, is in this case made up of
the component species, bond and free, which are affirmed of it not
alternatively nor disjunctively, but concurrently. The affirmation of
the one is not a denial of the other.
Disjunctive judgments may be converted into categorical form by
using all their members for one of the terms, and the phrase " possible
cases," or, " the only alternative," or one like it, for the other term.
The disjunctive, " This season is either Spring, Summer, Autumn, or
Winter," becomes, " All the possible cases regarding this season are
Spring, Summer, Autumn, and Winter." Disjunctives may also be
converted into conditionals by taking the contradictory of one of the
members for the antecedent and making the other members conse-
quents. Thus, "If it is not Summer, it is either Autumn, Winter, or
Spring."
(3.) A dilemmatic judgment is a hypothetical involving a combina-
tion of the conditional and the disjunctive. The disjunctive may fall
either in the antecedent or in the consequent. Thus, " If a man falls
into the sea, he will either sink or swim ; " " If man is either praise-
worthy or blameworthy, he must be a free agent."
A dilemmatic judgment may be converted into categorical form by
changing each of its elements, according to the principles laid down
under hypotheticals and disjunctives.
Topic Fourth.— Grammatical Combination of Judgments
or Propositions.
Judgments embodied in propositions are either single or combined.
Combined judgments are combined by subordination or by co-ordina-
tion. Propositions are, therefore, simple, complex, or compound.
A simple proposition consists of only one subject and predicate. Both the
subject and predicate may, however, be grammatically very complex, e. g., "A
THE FORMATION OF JUDGMENTS. 119
legitimate and forcible argument may fail to win the assent of a prejudiced
man." The kinds of judgments thus far treated are chiefly forms of simple
judgments embodied in simple propositions.
A complex proposition consists of a principal judgment with one or more
subordinate judgments, e. g., " Man who is born of a woman is of few days."
The subordinate elements appear as substantive, adjective, or adverbial elements,
so that in logic the complex sentence is treated as embodying a simple judg-
ment. The office of the subordinate clauses is explicative, as, " Whoever is
right, is safe ; " or restrictive, as, " Men who are avaricious are discontented."
A compound proposition is made up of two or more co-ordinate judgments, as,
" Art is long, and time is fleeting." For logical purposes the constituent judg-
ments of a compound proposition require separate and independent statement.
Co-ordination is either copulative, adversative, disjunctive, or causal. The co-
ordination is copulative when two or more thoughts, which are considered
independent, are so united together that the thought expressed in the co-ordi-
nated judgment gives a greater extent to the thought of the preceding judg-
ments, e. g., " Socrates and Plato were wise ; " " Plato was a philosopher and
Sophocles was a poet." The copulative connection may be either annexive, en-
hansive, intensive, or ordinative. The co-ordination is adversative when the
judgments united in thought stand in opposition to one another, e. g., "Not
the rich are happy, but the good." The opposition may be contradictory, con-
trary, or restrictive. The co-ordination is disjunctive when the judgments
united in the one thought exclude one another, e. g. " Either he is here or he
is not here." The disjunction is either exclusive as in the ordinary disjunctive
judgments, or separative as in comparisons. The co-ordination is causal when
the last of the co-ordinate judgments denotes the ground of the preceding judg-
ment, or the conclusion from it, as, " Aristotle was an accurate thinker, for he
formed conceptions and judgments well." The causal relation in the wide
sense, may be either reason, or cause proper, or conclusion from reason, or conse-
quence from cause.
Note. — For a full presentation of the principles of subordination and co-or-
dination, see Kiihner's Latin and Greek Grammars, and Becker's German
Grammar.
Praxis. — Examine and characterize the following judgments, — First,
reducing them to the normal form ; secondly, bringing out the connect-
ing links; thirdly, indicating the sources of proof; fourthly, giving
the quantity, quality, and relation, and showing the distribution of
the terms ; fifthly, stating whether simple or combined, and if com-
bined showing whether complex or compound, and bringing out the
particular relations of subordination or co-ordination :
1. No reptiles have feathers.
2. Grace is unmerited favor.
3. None are free who do not govern themselves.
4. He that ruleth his own spirit is greater than he that taketh a
city.
5. George Eliot was the wife of George H. Lewes.
120 PRACTICAL LOGIC.
6. He that getteth silver is not satisfied with silver.
7. Thomas Jefferson prepared the first Anglo-Saxon Grammar pro-
duced in America.
8. There is no fireside, howsoe'er defended,
But has one vacant chair.
9. Never morning wore to evening but some, heart did break.
10. The rich are not necessarily happy, for happiness is not the
result of external circumstances.
11. Those here present constitute the class in Logic.
12. All that glitters is not gold.
13. Man was originally a long-eared animal of arboreal habits.
14. A miracle is impossible.
15. No such thing as a miracle has ever been experienced.
16. Who steals my purse, steals trash.
17. Life every man holds dear.
18. If Christ rose from the dead, then Christianity is true.
19. Either Richard III. was a monster or Shakespeare was wrong.
20. If Socrates was innocent, Anytus was either deceived or per-
jured.
21. Wherever thore is smoke, there is fire.
22. If Caesar lives, he will rule or ruin.
23. He would have gone, but was prevented by sickness.
24. Goliath uttered his challenge and David accepted it.
25. First, the dawn ; then, the rising sun ; and last, the busy tide
of life.
26. There are studies much vaunted, yet of little utility.
27. Some democracies are unstable.
28. Some honest men become bankrupt.
29. The world's no neuter ; it will wound or save.
30. The country is generally flat or but slightly undulating.
31. Wealth may seek us ; but wisdom must be sought.
32. He had the air of dignity, yet of deep feeling.
33. For man to tell how human life began is hard ; for who him-
self beginning knew ?
34. Thy father slew my father ; therefore die.
35. We have no slaves at home — then why abroad ?
36. He is very great in knowledge, and accordingly valiant.
37. I have the wish, but want the will to act.
38. The widow and her child returned to England, and lived almost
hopeless in their old home.
THE UNFOLDING OF JUDGMENTS. 121
CHAPTER II.
THE UNFOLDING OP JUDGMENTS.
THE best use of judgment in the practical work of think-
ing requires that the thinker should be able to unfold what
may be contained in any judgment, or implied in it, or im-
mediately inferred from it. Hence the following Topics:
First, the development of contained judgments.
Second, the development of implied judgments.
Third, the development of inferred judgments.
Note.— Some logicians consider this subject as a part of Reasoning. Ac-
cording to these, Reasoning is, either by inference from one judgment to an-
other derived from it ; or from two judgments to a third, which could not be
derived from either alone but is drawn from both combined. The latter is
called Mediate Inference ; the former Immediate Inference. The subjects of
the present Chapter are, according to this view, treated under the head of Rea-
soning. They are, however, properly to be treated under Judgment, for they
all flow from the nature of conceptions as already presented and from the re-
lations of these conceptions in judgments and propositions.
Section I,— Development of Contained Judgments,
That which is contained in any judgment may be brought
out by analysis of the content or extent of its terms, the
subject and predicate.
This form of analysis is of great service in careful thinking and
especially in confirmation of judgments. It is applicable, of course,
only to judgments in which at least one of the terms is complex or
has component attributes or species. The process must conform to the
laws of Partition and Division.
The proposition, " The highest civilization is dependent on Chris-
tianity," may be analyzed, as a proposition of content, either by par-
tition of the subject or of the predicate. The subject, "the highest
civilization," includes as marks or attributes : the most righteous civil
government ; the completest development of the arts industrial and
aesthetic ; the broadest and most liberal education ; the best manners
and morals, or conduct in all relations ; the highest spirit of enter-
prise and progress. The proposition may therefore be unfolded into
the following : The most righteous civil government is dependent on
11
122 PRACTICAL LOGIC.
Christianity ; The completest development of the arts industrial and
aesthetic is dependent on Christianity ; The broadest and most liberal
education is dependent on Christianity ; The best form of manners and
morals, or conduct, in all relations is dependent on Christianity ; The
highest degree of enterprise and progress is dependent on Christianity.
The predicate element, " Christianity," may be analyzed to meet the
requirements of these propositions for proof. From this point of view,
it includes the following marks : the perfect standard of justice ; the
true theory of activity and beauty ; the grandest system of truth ;
the complete theory of responsibility and duty ; the inspiring prin-
ciples of progress. The proposition may, therefore, be unfolded into the
following : The highest civilization is dependent upon Christianity as
a perfect standard of justice ; The highest civilization is dependent
upon Christianity as the true theory of activity and beauty; The
highest civilization is dependent on Christianity as embracing the
grandest system of truth ; The highest civilization is dependent on
Christianity as the complete theory of responsibility and duty ; The
highest civilization is dependent on Christianity as containing the in-
spiring principles of progress.
Propositions of extent may be unfolded by the principles of division.
Thus, " Free institutions are conducive to progress,'' may be unfolded
through the subject as a genus, as including free governmental institu-
tions,, free educational institutions, free social institutions, free religious
institutions, etc. ; and through the predicate, as including political prog-
ress, educational progress, social progress, religious progress, etc.
To the development of contained judgments manifestly belongs also
what Thomson names, " Immediate Inference by the Sum of several
Predicates." "Copper is a metal, red, malleable, ductile, etc.," is in
no proper sense an immediate inference from the judgments, " Copper
is a metal," " Copper is red, etc.," but a simple compounding of them.
So these component judgments are simple constituents of the general
judgment, and may be unfolded from it.
Praxis. — Develop the following propositions by Subject and Pred-
icate, and suggest the sources of proof for the resulting propositions:
1. The studies of the High School Course are best fitted to prepare
for the pursuits of business life.
2. The studies of the College Course are best fitted to prepare for
the work of the professions.
3. The Fine Arts are favorable to a pure morality.
THE UNFOLDING OF JUDGMENTS. 123
4. The study of the Ancient Classics is the best discipline for the mind.
5. Manly qualities are becoming to a student.
6. Proper protection of the various industries is essential to national
prosperity.
7. The discipline of life is essential to man's development.
8. Division of labor is essential to national wealth.
Section II,— Development of Implied Judgments,
The implied judgment, according to Davis, " is one that
actually exists together with the given judgment, either
merely in thought or involved covertly in the expression."
Several simpler and less important forms of implication
need to be noted, but especially the more important form
named obversion.
Topic First— Simpler Forms of Implication.
These are chiefly forms of interpretation of the language
or thought.
Such judgments may be covertly implied in the language. Thuc,
in the proposition, " Few men are wise," it is covertly implied by the
language that " Most men are not wise." " Some men are rich," im-
plies that " Some men are not rich." Such judgments are sometimes
implied in the thought. Thomson places under immediate inference,
what he names, " Immediate Inferences of Interpretation." It is not
strictly inference but rather implication. Thus, in the judgment, " John
loves Mary," it is implied that " John lives," that, "Mary lives," and
that, " there is such a thing as love."
. The development of active and passive forms of judgments from
each other may also be placed here. In the active form, " Napoleon
conquered Europe," is implied the passive form, " Europe was con-
quered by Napoleon."
In any simple proposition many other propositions may be implied.
Thus, " Yesterday I lifted one hundred pounds," implies judgments
of the existence of yesterday, of the one hundred pounds, of myself, of
the lifting, 6f memory, of time, of personal identity, of will power, etc.
Topic Second, — Obversion.
Under implied judgments belongs also what Bain calls
obversion. It is sometimes termed, " Immediate Inference
124 PRACTICAL LOGIC.
by Reciprocal Change of Positive and Privative Concep-
tions." In affirming one thing we impliedly deny the op-
posite. Obversion is the bringing out and denying of this
opposite or reverse form.
Thus, " The road is level ; " " The road is not inclined ; " are not
two facts, but the same fact from different sides. The second is not an
inference from the first, but something implied in the first, — an obverse
form of the first. "Whoever is wise is not foolish ; " we must grant
the obverse form if we grant the positive. In obversion the negative
form may be taken either as infinitated or as simply privative. " Wise "
implies the infinitated notion, " not-wise " or " non-wise," the two to-
gether making up the universe of being ; and also the privative, " not-
wise " or " unwise."
Each of the normal forms of judgment, — A, E, I, 0, —
has its obverse form. For developing these obverse implied
judgments we have the following
Rule. — Obvert the predicate (i. <?., change it to the infin-
itated or privative form) and then change the quality of the
judgment.
Note.— To avoid awkward compounds with non and not, in obverting and
changing the quality of judgments, various prefixes and suffixes are often used,
as, in-, un-, dis-, less-, etc. ; and uncompounded negatives, as unwise and foolish,
instead of not- wise. Great care needs, however, to be taken, as these terms
are often not privatives, but only signify the existence of the quality in a low
Taking the four principal judgments as embodied in
propositions, in the order of the letters representing them,
and applying the Rule given above, we get the obverse
forms :
1. The normal form of the universal affirmative, A, is as follows:
Every x is y; Every man is mortal.
Obverting the predicate, this becomes :
Every x is not-y ; Every man is (not-mortal) immortal.
Changing the quality of the judgment from affirmative to negative,
it becomes :
No x is not-y ; No man is (not-mortal) immortal.
THE UNFOLDING OF JUDGMENTS. 125
2. The normal form of the universal negative, E, is as follows : No
x is y ; No men are angels.
Obverting the predicate, this becomes :
No x is not-y ; No men are not-angels.
Changing the quality of the judgment from negative to affirmative,
it becomes :
Every x is not-y ; All men are not-angels (excluded from angels).
3. The normal form of the particular affirmative, I, is as follows :
Some x is y ; Some men are wise.
Obverting the predicate, this becomes :
Some x is not-y; Some men are (not-wise) foolish.
Changing the quality of the judgment from affirmative to negative, it
becomes :
Some x is not not-y ; Some men are not foolish.
4. The normal form of the particular negative, 0, is as follows :
Some x is not y ; Some men are not wise.
Obverting the predicate, this becomes :
Some x is not not-y ; Some men are not (not-wise) unwise.
Changing the quality of the judgment from negative to affirmative, it
becomes :
Some x is not-y ; Some men are (not- wise) unwise.
Praxis. — State what is implied in the following propositions by the
various forms of implication just explained :
1. Napoleon was an ambitious conqueror. 2. The diligent student
will become wise. 3. Wellington was the soldier of duty. 4. John
Howard was philanthropic. 5. Greece is a name of glory. 6. War
is productive of evil. 7. The peacemakers are blessed. 8. Cold kills
animals.
Section III,— Development of Inferred Judgments,
An inferred judgment, according to Davis, is " one that
only virtually or potentially exists in the given judgment,
and is derived from it." Its statement contains "something
new, there is a step forward, a progress of thought. In the
inferred judgment there is always either a different subject,
or a different predicate, from that of the premise, and per-
haps both."
The so-called inferred judgments may be reached from
11*
126 PRACTICAL LOGIC.
other judgments either by Addition, Disjunction, Conver-
sion, or Opposition. Of these forms the last two are the
most important.
Topic First. — Inferred Judgments by Additions.
Determinants may be added to both terms of a judgment which is
thereby rendered more definite, e. g., " A negro is a fellow-creature ;
therefore, a suffering negro is a suffering fellow-creature." The orig-
inal terms of the judgment may themselves be made determinants or
marks of new conceptions introduced into the judgment, e. g., " Oxy-
gen is an element ; therefore, the decomposition of oxygen is the de-
composition of an element." On the same principles two judgments
may be amalgamated ; as, " Honesty deserves reward, and a negro is
a fellow-creature ; therefore, a negro who shows honesty is a fellow-
creature deserving of reward." Care must be taken in all these forms
of addition to keep the distribution of the terms unchanged.
Topic Second. — Inferred Judgments by Disjunction.
Since the members of a disjunctive judgment are. 'mutually exclusive,
we may infer from the disjunctive, " The teeth are either incisor,
canine, bicuspid, or molar teeth," the judgment, " The molar teeth are
neither incisor, canine, nor bicuspid." As the dividing members in a
disjunctive judgment exhaust the whole subject divided, we may infer
that the part of the whole not contained in one member must be in
some other. Hence from the judgment just given come such inferred
judgments as, " All teeth which are not molar are either canine, inci-
sor, or bicuspid teeth."
Topic Third. — Inferred Judgments by Conversion.
Illative Conversion of judgments is such a transposition
of the subject and predicate of a judgment that the con-
verse or transposed form is a legitimate inference from the
convertend or original judgment. Three general Rules must
be observed in conversion :
Rule 1st. Before conversion reduce the proposition to the
strict logical form, in which subject, copula, and predicate
distinctly appear.
Rule 2d. No term not distributed in the convertend must
be distributed in the converse. We may infer from all to
THE UNFOLDING OF JUDGMENTS. 127
all, from all to some, and from some to some, but not from
some to all.
Rule 3d, The transfer of the terms should be total. In
other words, the whole naked subject (i. e., the subject
without its sign of quantity, every, all, some, etc.) must be
transferred to the predicate, and the whole naked predicate
must be transferred to the subject.
Confining attention mainly to the four attributive judgments, A, E,
I, 0, — since these are all the forms of which any special use is ordina-
rily made in compendiums of Logic, — it will be seen that there are
three principal forms of conversion.
First, Simple Conversion when neither the quantity nor the quality
is changed ;
Second, Conversion by Limitation when the quantity is changed.
Third, Conversion by Negation or Contraposition, when the qual-
ity is changed.
1. Simple Conversion is where the terms can be trans-
posed without change of either quantity or quality. This
can, of course, occur only when both subject and predicate
are distributed, as in E, and where both are undistributed,
as in I,
(1.) Let E, "No one without a love of beauty can be an eminent
artist," be given for conversion. The Rules should be applied in order.
By Rule 1st, the proposition becomes, " Every one without a love of
beauty is not any one who can be an eminent artist." By Rule 2d
and Rule 3d, the converse becomes, " Any one who can be an eminent
artist is not any one without a love of beauty." The converse is
still E.
(2.) Let I, " Some good men are bad poets," be given. The propo-
sition is already in strict logical form. By Rules 2d and 3d the con-
verse becomes, " Some bad poets are good men." The converse is
still I.
(3.) Substitutive and equivalentjudgments, TJ and Y, are, of course,
converted by simple transposition of tbe terms. " All bodies are ex-
tended substances " becomes, " All extended substances are bodies."
2. Conversion by limitation (per accidens) takes place
128 PRACTICAL LOO 1C.
where it is necessary, in order to an illative transposition,
that the quantity of the proposition should be changed
from universal to particular, while the quality remains
unchanged. This will, of course, occur where the subject
is distributed and the predicate undistributed, i. e., in A.
As some may be inferred from all, E may also be converted
by limitation.
(1.) Let A, "All poets are men," be given for conversion. It is
already in strict logical form. In order to conform to Rule 2d, the
predicate must be limited to " some men." By Rule 3d the converse
becomes, " Some men are poets ; " or, " Some men are all the poets."
The converse of A is I.
(2.) Let E, " No men are perfect," be given for conversion by limi-
tation. Completing the form, limiting the quantity of the predicate,
and then making a total transfer of the terms, the converse becomes,
" Some perfect things are not men." The converse is 0. By simple
conversion it would be E.
3. Conversion by Negation or Contraposition takes place
where it is necessary in order to illative transposition, that
the quality of the judgment should be changed, while the
quantity remains unchanged. This occurs in 0.
Let 0, " Some quadrupeds are not horses," be given for conversion.
If converted simply, it would be, " Some horses are not quadrupeds,"
which is absurd. This result is avoided by obverting, or infinitating
the proposition, and then converting simply. Infinitating the predicate,
the proposition becomes, " Some quadrupeds are (things) not-horses ; "
and by conversion, " Some things not- horses are quadrupeds." Thus
the converse of 0 is I.
Topic Fourth. — Inferred Judgments by Opposition.
Opposition is the name given to the differences in quan-
tity or quality, or both, between judgments having the
same naked subject and predicate. Legitimate inferences
follow from opposition.
Between the judgments, A, E, I, 0, to which attention is
here chiefly confinecj, there are four kinds of opposition,
THE UNFOLDING OF JUDGMENTS. 129
which are exhibited by the following diagram, called the
Square of Opposition.
All men are true, A Contrary E No men are true.
(Subalternans)
(Subalternans)
Some men are true, • .-*" *'• • Some men are not true.
(Subalternate) I Subcontrary 0 (Subalternate)
1. Contradictory Opposition, which is the only perfect
form, exists between the propositions A and 0, E and I,
which differ both in quantity and quality. By the principles
of Contradiction and of Excluded Middle, of two contra-
dictory propositions both cannot be true and both cannot
be false.
Rule. — From the truth of either of two contradictories
the falsity of the opposite follows; and from the falsity of
either the truth of the opposite follows.
If A, "All men are true," be sublated (denied) then we can posit
(affirm) 0, " Some men are not true." If it be not true that " All
men are true," then it is certain that, (at least) "Some men are
not true." If 0, " Some men are not true," be denied, then A, " All
men are true," may be affirmed ; but if the former be affirmed, the
latter may be denied.
Contradictory opposition is of special service in indirect proof.
Instead of showing an opponent's arguments false and his position,
therefore, unsustained, it is often better to prove the truth of the con-
tradictory and then infer the falsity of his position. E. g., if one
affirms that " All scientists are extreme evolutionists," which is A,
the best way to meet it is by establishing the contradictory 0, " Some
scientists are not extreme evolutionists ; " or, " Some one scientist, as
Prof. Tait, is not an extreme evolutionist." If this be established the
necessary inference is that A is false. The form of indirect proof
known as reductio ad absurdum, largely used in geometrical demon-
strations, instead of demonstrating a proposition directly, demonstrates
I
130 PRACTICAL LOGIC.
that its contradictory is absurd, and thence immediately infers the
truth of the proposition.
2. Contrary Opposition is between the universal proposi-
tions A and E, which differ in quality only.
Rule. — From the truth of a judgment the falsity of its
contrary opposite follows ; from its falsity nothing follows.
Both A and E cannot be true. From the truth of A the falsity of
E follows, and vice versa. E. g., if A, " All men have conscience," be
true, then E, " No man has a conscience," is false ; and if the latter be
true then the former is false. From the falsity of one contrary nothing
follows with regard to the other. If it be false that, " All men are
poets," it does not follow that, " No men are poets." But both may
be false. E. g., the propositions, A, "All men are poets," and E, "No
men are poets," are both false, since the truth lies between the two
and is expressed in I, " Some men are poets." In individual proposi-
tions, as, "Shakespeare was a poet," the opposition appears as the sim-
ple negative, " Shakespeare was not a poet."
3. Subcontrary Opposition is between the particular prop-
ositions I and 0, which differ in quality only.
Rule. — If one sub-contrary be true, nothing follows in
regard to the other ; but if one be false, then the other must
be true.
For example, if I, "Some wars are evil," be true, it does not follow
from this that 0, " Some wars are not evil," is true. But if I, " Some
wars are evil," be false, then " Some wars are not evil," must be true.
4. Subalternate Opposition is between the propositions
A and I, E and 0, differing in quantity only.
Rule. — If the universal, A or E, be true, the particular
I or 0, must be true ; and if the particular I or 0, be false,
then the universal, A or 0, must be false.
If A, " All men are liars," is tr.ue, then I, "Some men are liars," is
also manifestly true. If I, " Some men are perfect," is false, then A,
" All men are perfect," is false.
The results may be summed up as follows :
<D
THE UNFOLDING OF JUDGMENTS. 131
Contradictories. Contraries. Subalterns.
^H i If A is true, O is false,.... E false, I true.
g ) If E " I " ,....A " , O " .
If A is false 0 is true, E undetermined,...! undetermined.
If E " I " ...... A " ,...0
Contradictories. Subcontraries. Subalterns.
If I is true, E is false 0 undetermined, ...A undetermined.
If O " A " ,....! " ,...E
If I is false, E is true,....0 true, A false.
IfO " A " ' I " , E " .
Praxis. — Apply exhaustively the principles of implication and al&o
the principles of immediate inference in its four kinds, to the follow-
ing judgments, giving the quantity and quality of the judgments:
1. All the righteous are happy. 2. No human virtues are perfect.
3. Some possible cases are probable. 4. The just are (all) the holy.
5. Some men are all the poets. 6. All the insincere are dishonest.
7. No unjust act is unpunished. 8. Some unfair acts are unknown.
9. The unlawful is the (only) inexpedient. 10. No brutes are re-
sponsible. 11. Heaven from all creatures hides the book of fate. 12.
Fair promises are not often to be trusted.
SUMMARY OF RESULTS.
THE aim of the Logic of Judgment is to train to the
best thinking and fullest appreciation of thought in the
second form. The perfection of thinking in judgment de-
pends upon the certainty of the connection of the subject
and predicate. This gives rise to what is called the Modal-
ity of Judgments.
1. By the degree of certainty of the predication to the
mind of the thinker or others, all judgments have been
divided into Demonstrative, Assertory, and Problematic.
(1.) A demonstrative or apodictic judgment is one that is certain to
him who holds it, and that may be made certain to all sane minds suf-
132 PRACTICAL LOGIC.
ficiently intelligent to understand the signification of the judgment
itself and its evidence. All analytic judgments are demonstrative, or
are certain to him who holds them, and may be made certain to all
other sane minds of sufficient intelligence to understand the signifi-
cance of the terms. All intuitive judgments are also demonstrative, or
have both subjective and objective certainty. These include the truths
of Mathematics, the fundamental principles of Logic, the axioms of
Ethics and Metaphysics. All judgments reached by immediate infer-
ence from these are also demonstratively certain.
(2.) An assertory judgment is one that announces what is known
as actual. It is certain only to him who holds it, but not capable of
being made certain to others of different moral disposition. " It com-
mends itself to our moral nature, and in so far as other men are of the
same disposition, they will accept it likewise." This holds especially
of higher moral and religious truths. Moral and religious deterio-
ration prevents their acceptance.
(3.) " A problematic judgment is one that is neither held with entire
certainty by the thinking subject, nor can we show that it truly rep-
resents the object about which we judge. It is a mere opinion"
Problematic judgments constitute one of the necessary stages in the
progress towards truth. " Great discoveries are problems at first . . .
Whenever we judge about variable things, as the future actions of
men, the best course of conduct for ourselves under doubtful circum-
stances, historical facts about which there is conflicting testimony, we
can but form a problematical judgment, and must admit the possibility
of error at the moment of making our decision."
2. A simpler division of j udgments, by the degree of cer-
tainty in the mind of the thinker, is into Certain, Probable,
and Doubtful.
(1.) A certain judgment is one in which the knowledge that the
connection between the subject and predicate corresponds to the reality
is absolute and unquestionable. All analytic judgments, all intuitive
judgments, all immediate inferences from certain judgments, all strict
deductions from certain or necessary premises may become certain to
the thinker.
(2.) A probable judgment is one in which the knowledge that the
connection between the subject and predicate corresponds with the re-
ality is not absolute and unquestionable. The boundary line between
the probable and doubtful is not always clearly marked, since, in com-
THE UNFOLDING OF JUDGMENTS 133
mon language, the degrees of probability may reach all the way from
the nearest approach to certainty that a judgment is true, down to
the nearest approach to certainty that it is not true, i. e., from the
nearest possible to absolute certainty, to the nearest possible to abso-
lute uncertainty ; while the degrees of doubtfulness may have the
same wide scope. It may be said, however, in general, that a strictly
probable judgment is one which has the balance of proof in its favor,
and that a doubtful judgment is one which has the balance of proof
against it. As has already been seen, man receives most of the knowl-
edge used in the conduct of life, in such a way that it is not certain,
but at best only more or less probable. All the acquired perceptions
of the senses and consciousness are mixed with inferences, and, there-
fore, only probable ; while only the original or intuitive perceptions
are certain. The conclusions of finite reason, especially by the induc-
tive processes, are liable to error, and, therefore, cannot rise to certainty.
The judgments based on testimony and authority can at best reach
only a high degreee of probability. A judgment may be possible when
it is not probable. " A thing is said to be possible when, though not
actually in existence, all the conditions necessary for realizing its ex-
istence are given." It is possible, for example, that aerial transporta-
tion may some day take the place of transportation by steamer and
railway, but not perhaps probable.
The aim of the Practical Logic of Judgment should be
to train the thinker to skill in distinguishing clearly be-
tween the certain, the probable, and the doubtful ; and in
arriving at sound judgments, on the basis either of cer-
tainty or of probability, by which to govern the entire con-
duct of human life.
12
PART III.
THE LOGIC OF REASONING OR THE SYLLOGISM.
THE aim of the Logic of Reasoning is to train the mind
to skill in dealing with the third Form of Thought.
Definition. — Reasoning is that form of thought in which
we compare various judgments and, on the ground of some
medium or cause, reach other judgments as inferences or
conclusions from them. Reasoning may, therefore, be used
as synonymous with Mediate Inference. The product of
reasoning, as embodied in language, is usually known as
the Syllogism.
Note.— Mediate inference is inference by a medium, or middle notion or term.
It is thus distinguished from immediate inference which, as has been seen (p.
121), does not make use of any such third or middle term. The middle term
is used where we cannot compare two things directly. We cannot compare
two lots directly by placing one upon the other, but we can measure them both
with a surveyor's chain, or other common measure, and thus ascertain their
relative dimensions. So when two notions or terms cannot be directly compared
and connected they may be indirectly by the use of a third notion or term.
We may, e. g., wish to connect " John Baptist" and " priest " in the judgment,
" John Baptist was a priest." Having no direct statement to that effect in the
Bible, we must reach the conclusion by reasoning from the fact that the sons
of priests were also priests. The process of thought is stated as follows :
Analytic Form. Synthetic Form.
f John Baptist was a priest ; f The son of a priest was a priest ;
•j For he was the son of a priest ; 4 John Baptist was the son of a priest ;
( And the son of a priest was a priest. (. .'. John Baptist was a priest.
Both terms are connected with a third term, "son of a priest," and thus
connected with each other.
134
THE FORMATION OF REASONING. 135
The most helpful logical presentation of Reasoning must treat of
both the formation of reasonings or syllogisms and the unfolding of
syllogisms. The present subject will, therefore, embrace two Chapters.
CHAPTER I.
THE FORMATION OF REASONING OR
MEDIATE INFERENCE.
THE formation of thought as reasoning must manifestly
be placed at the foundation in all training to thought in its
third form. It will be necessary to consider, in successive
Sections, the nature of reasoning or mediate inference in
general, and the fundamental forms of reasoning1, — deduc-
tion and induction. The process and the products will be
considered under each of the forms of reasoning.
Note.— Much of the modern depreciation of Logic, and especially of the
Logic of the Syllogism, is doubtless due to the fact that the Science has been
confined largely to the mechanical testing of barren forms. If this be all there
is in the Logic of Reasoning, it would have to be admitted that it is not a very
valuable means of knowledge ; the old objection would hold, that " the prem-
ises, so far from being able to establish the truth of the conclusion, presup-
pose it." Take in illustration a syllogism commonly given: "All Cretans are
liars ; this man is a Cretan ; therefore he is a liar." How do we know all before
we know each f How do we know all before the character of this particular
Cretan is decided? That is, until we are certain that this particular Cretan is
a liar, we cannot be certain that all Cretans are liars.
The all-important thing in reasoning is the finding of middle terms
or connecting links of argumentation ; and even the testing of the
various products of reasoning cannot proceed intelligently without
some skill in finding these connecting links.
Section I,— The Process of Reasoning or Mediate Inference
in General,
Topic First. — The Forms of Reasoning.
All reasoning necessarily proceeds from general princi-
ples to particulars or individuals, or from facts or particu-
lars to general principles. Mediate Inference is, therefore,
136 PRACTICAL LOO 1C.
divided into two chief kinds : Deduction, or Specialization,
or Syllogism in the stricter sense ; and Induction, or Gen-
eralization, or Syllogism in the looser sense.
Syllogism in the stricter sense in its chief forms is inference from
the general to the particular or individual, and in all its forms infer-
ence proceeding from the general. Induction is inference proceeding
from the individual or particular to the general. Inference by anal-
ogy, which proceeds from the individual or particular to a co-ordinate
individual or particular, is a third form distinct from both, though
able to be reduced to a combination of the other two. See Ueberweg's
Logic, p. 333.
Deduction has also been called " the inference of subordination," or
" inference by analysis of notions ; " induction, " the inference of su-
perordination ; " analogy, " the inference of co-ordination."
The difference between deduction and induction may be illustrated
by the methods of proving that the interior of the earth is in a molten
condition. From the volcanic phenomena, i. e., from the facts that
the earth is in a molten condition under Mount Vesuvius, Mount Hecla,
Mauna Loa, etc., it is inferred inductively that the whole interior is in
such condition. From the process of the earth's formation by the con-
densation of intensely heated material (an origin probable on astro-
nomical grounds), it is inferred deductively or syllogistically that the
interior is in a molten condition. The one process starts from facts ;
the other from a general principle. They are usually thrown into
syllogistic form, as follows :
Inductive Process. Deductive Process.
The interior of the earth is
molten ;
For, it is molten under Vesu-
vius, etc. ;
And Vesuvius, etc., fairly rep-
resents the whole.
The interior of the earth is
molten ;
For the solar system was formed
by condensation ;
And the earth is a part of the
solar system.
The nature of analogy, as made up of induction and deduction, may
be shown from the following example : " The Earth, a planet revolv-
ing in an orbit round our sun, turning on its axis, having an atmo-
sphere, change of seasons, etc., supports organic life ; Mars is a planet
revolving in an orbit round our sun, turning on its own axis, having
an atmosphere, change of seasons, etc. ; hence Mars also will probably
support organic life." It will be seen by examination that this consists
THE FORMATION OF REASONING. 137
of an apparent induction and a deduction combined. This may be
exhibited, in full, as follows :
[~ The Earth supports organic life ;
The Earth is a planet revolving, etc., and fairly represents that
class of planets ;
.*. All planets revolving, etc., probably support organic life ;
^ |~~ Mars is a planet so revolving, etc. ;
P [_.'. Mars probably supports organic life.
According to the common view both deduction and in-
duction may be embodied in syllogistic form (as in the
examples given). The elements of the reasoning, as em-
bodied in the syllogism, need, therefore, to be considered.
As the validity of the reasoning depends, however, not
upon the syllogistic forms, but upon the connecting link of
thought embodied in the middle term, the subject of find-
ing middle terms needs to be specially considered.
Note.— The question whether all reasoning can be reduced to the syllogism
is one into which we have not space to enter. Nor is there need to discuss it
here, since it is freely admitted that the validity of the reasoning depends upon
the connecting links of thought and not upon the form; and that the syllogism is
of no special value in the formation of processes of reasoning, but only in
formulating and testing them after they are formed.
Topic Second. — The Elements of Reasoning.
The elements of reasoning are ascertained by analyzing
the process as embodied in the Syllogism. The syllogism
is composed of three terms and three propositions ; and
underlying the form, as the real basis of thought, is some
mediating notion or cause.
I. The Terms and Propositions.
The terms or notions in the syllogism are distinguished
as the major term, the minor term, and the middle term.
The propositions in the usual form of statement are the
major premise and the minor premise, constituting the ante-
cedent or proof, and the conclusion or consequent.
The conclusion is the judgment to be proved. In the formal syllo-
gism it is placed last. Its subject, represented by S, is the minor term ;
12*
138 PRACTICAL LOGIC.
its predicate, represented by P, is the major term. The middle term,
represented by M, is that with which the major and minor are com-
pared in the premises.
The major premise is the judgment in which the major term or
predicate of the conclusion is compared with the middle.
The minor premise is the judgment in which the minor term is
compared with the middle.
This may be illustrated in concrete form and in formula, as follows :
All conquerors (M) are tyrants (P) ;~| f M is P ; Major Premise.
Napoleon (S) was a conqueror (M) ; < S is M ; Minor Premise.
Napoleon (S) was a tyrant (P). J l.'.S is P. Conclusion.
The conclusion is reached by comparison of both its terms
with the third or middle term, " conqueror."
II. The Middle Term or Connecting Link.
The middle notion or term (originally called the argu-
ment) always represents the link of thought by which the
two terms of the conclusion are brought together and the
judgment proved. It furnishes the sufficient reason for
connecting the major and minor terms. Reasoning is prop-
erly, therefore, finding the sufficient reason— in case of in-
duction the cause — for the connection of the terms in the
conclusion.
Various maxims have been formulated to express the connection
embodied or implied in the middle term. The principal are those of
Aristotle and Kant, which apply respectively to propositions of extent
and content, or to propositions made up of class terms and those
made up of attribute terms. The axiom of Sufficient Reason, or of
Reason and Consequent, is, however, the best and most complete
expression of this connection.
The so-called dictum of Aristotle places the relation of genus and species at
the foundation of reasoning. Whatever can be predicated affirmatively or
negatively of any genus or class distributed can be predicated likewise of all
or any of the species or individuals included under it. If it can be affirmed
of the genus man, that it is included in the higher genus person, then it can
be affirmed of the species slaves, included under man, that it is included under
person. Or if it can be affirmed of the genus man, that it is excluded from the
genus brute, then the same can be affirmed of the species poets, included under
the genus, man.
THE FORMATION OF REASONING. 139
The formula of Kant places the relation of a complex property to its compo-
nents at the foundation of reasoning. Whatever is a component of a complex
property of a tiling is a property of the thing itself. The mark brave, which
is a component of the complex mark conqueror, is also a mark of Caesar,
the object to which the complex conqueror applies.
Others make the relation at the basis of reasoning that of whole and part. A
part of a part is also a part of the whole.
The real connecting principle or basis in reasoning, i. e., the real
sufficient reason, is, perhaps, best expressed by the relation of reason
and consequent, which, as has already been seen (p. 20), embraces
whole and part, cause and effect, substance and attribute, genus and
species, etc. Any form of reason and consequent may be at the basis
of deduction; while the basis of induction is the strictly causal rela-
tion only.
Topic Third.— Finding and Verifying Arguments or Mid-
dle Terms.
From what has been thus far considered, it is obvious
that reasoning essentially consists in finding and verifying
arguments, or middle terms and causes, under the principle
of Sufficient Reason or Reason and Consequent. This pro-
cess differs in deduction and induction, inasmuch as these
forms of reasoning differ.
Section II. — Deductive Keasoning.
Topic First. — Process of Finding and Verifying the
Argument in Deduction.
Three things are essential in deduction: first, finding the
proper middle term ; second, verifying the premises formed
by the aid of it ; third, testing the conclusion.
I. Finding the Middle Term.
The first question is, By what middle term can the two
given terms be bound together or disjoined in the conclu-
sion ? The following Rules will guide the thinker in his
quest :
Rule 1st. — Examine carefully, by the principles laid down in the
Logic of Conception, the two terms to ba connected or disjoined, m
140 PRACTICAL LOGIC.
order to ascertain which of the relations under reason and consequent
is applicable to them.
Rule 2d. — Seek the proper mediating whole, concept proper, class,
or cause, as the case may require.
Rule 3d. — Bring the middle term thus found into proper connection
with the other terms and these with each other in syllogistic statement.
The application of these Rules may be illustrated by examples.
Thus, in seeking a middle term to prove that "The Persians worship a
thing insensible" we find, by the first Rule, that this term must be an
individual under the genus, " things insensible." By the second Rule,
"the sun" furnishes such an individual. By the third Rule, these
are brought together in syllogistic statement, in the order of proof, as
follows :
The Persians worship a thing insensible ; Question.
For the Persians worship the sun ; ) jx. /
And the sun is a thing insensible. I
Again, in finding a middle term to prove that "Judas was not a true
apostle," we find, by the first Rule, that the major term, " true apos-
tle," is a genus or class term. By the second Rule, "thief" furnishes
a "genus" excluded from the genus, "true apostle." By the third
Rule, this takes shape as follows :
Judas was not a true apostle ; Question.
For Judas was a thief ; \ P f
And no thief was a true apostle. )
Once more, in proving that "Plato is mortal," we find, by the first
Rule, that the major term, " mortal," is a concept or attribute term.
By the second Rule, we find that the complex concept, " man," in-
cludes "mortal" as a component property; and, therefore, since the
mark of a mark is a mark of the thing itself, " mortal " is a mark of
" Plato." By the third Rule, this gives, stated in twofold syllogistic
form:
f Plato is mortal ; Question. r Man is mortal ; 1 p /•
< For Plato is man ; 1 <j Plato is man ; )
I And man is mortal. / 1 .'. Plato is mortal. Conclusion.
II. Verifying the Premises.
When the middle term has thus been found and con-
nected with the major and minor terms, the question arises,
Are these premises true ? Hence the following Rule :
THE FORMATION OF REASONING. 141
Rule 4th. — Test the premises by the principles already presented
for the verification of judgments (p. 98), in order to be sure that only
correct judgments have been grasped.
It is all important that correct judgments should be grasped and
placed at the foundation as premises, since otherwise any inferences
from them would be logically worthless. The sources of the judgments
made use of in deduction are the following : intuition ; thought proper
inductive and deductive ; and testimony and authority. The prem-
ises must be tested by the principles by which judgments from these
various sources are proved.
III. Testing the Conclusion,
When the premises have been found to be true or prob-
able, the question arises, Does the conclusion follow from
the premises f Hence the following Kule :
Rule 5th. — Test the whole process by the principles of analysis pre-
sented in the Logic of Conception, and by the laws which govern the
Syllogism as presented in the next Chapter under the Unfolding of
Reasoning.
Partial understanding of the terms may lead to false conclusions.
This may be prevented by a careful study and analysis of the con-
cepts and terms involved, by means of Partition, Division, and Defi-
nition. False conclusions may also be drawn from correct premises.
This may be prevented by the careful use of the formal rules of the
Syllogism.
In all deductive reasoning, it should be remembered,
that the conclusion can never be any more certain than the
premises. Forgetfulness of this is the source of many and
great errors in both Science and Philosophy.
Topic Second,— Products of Deductive Reasoning.
The product of deduction is the Syllogism proper in its
various forms. Syllogisms are divided, by the form of the
judgments embodied in them, into categorical and hypo-
thetical. Categorical syllogisms are either simple or com-
bined,— simple when they contain but one argument with
its major and minor premises expressed or understood and
its conclusion ; combined when more than one process of
142 PRACTICAL LOGIC.
argument is involved. The former may be called the mono-
syllogism ; the latter the polysyllogism.
I. Categorical Syllogisms.
A categorical syllogism is one in which the judgments
are categorical (p. 117).
1. The mono syllogism may be in its statement either
complete or incomplete.
The complete form is the ordinary form in which both the premises
and the conclusion are expressed. The incomplete form or the enthy-
meme (Greek, meaning in the mind) is that form in which one premise
is unexpressed, or left to be supplied by the mind. Thus :
" Alexander the Great was brave ;
For he was a conqueror."
In this case the major premise, "All conquerors are brave," is omitted.
The minor premise may also be omitted. Thus :
" Conquerors are brave ;
Therefore Alexander the Great was brave."
Note. — The enthymeme is the usual form in ordinary speech. The premise
left unexpressed is easily supplied in completing the syllogistic statement.
It will also be seen that in common speech there are to be found many abridged
and disguised forms of argument. For example : " Hard study strengthens the
mind, but wearies the flesh ; so that what wearies, strengthens ; " " Theft is a
crime ; yet some kinds were legal in Sparta." In such cases the first step is to
reduce the argument to the normal form.
2. The polysyllogism includes the various forms in which
separate syllogisms are combined into wholes of connected
reasoning. Syllogisms may be attached, as prosyllogisms,
to premises to prove them, or, as episyllogisms, to conclu-
sions, making the conclusions premises for reaching further
conclusions. In the former case the prosyllogisms are sub-
ordinate to a principal syllogism, and the whole constituted
is, therefore, a complex syllogism, which may be known as
the epichirema; in the latter case the episyllogisms are
co-ordinate with that to which they are attached, and the
whole is, therefore, a compound syllogism.
(1.) The Complex Syllogism, or Epichirema, or reason-rendering
THE FORMATION OF REASONING. 143
syllogism, is either manifest (i. e., having all the parts fully expressed),
or occult (i. e., having some of the parts suppressed). Both the mani-
fest and occult forms may be " either single or double, according as
one or both of the premises are furnished with an auxiliary reason."
The single epichirema, in both its occult and manifest forms, may be illus-
trated by the following example :
Main Syllogism. Occult Prosyllogism. Expanded Prosy llogism.
Vice is odious ; f Whatever enslaves is a vice ;
Avarice is a vice, for [it enslaves ;] J Avarice enslaves ;
.-.Avarice is odious. ( .'.Avarice is a vice.
Omitting the expanded prosyllogism, we have the ordinary single epichi-
rema in its occult form ; omitting the occult prosyllogism, we have the same
in its manifest form.
The double epichirema, in both its occult and manifest forms, may be illus-
trated by the following example :
Main Syllogism. Occult Prosyllogisms. Expanded Prosyllogisms.
Man has a spirit ; for [he is rational ; =] r Every rational being has a
J spirit;
j Man is a rational being ;
V. .'. Man has a spirit.
Man has a body ; for [he fills space ; =1 f Whatever fills space has a
J body;
j Man fills space ;
Something that has a spirit has body. (. /. Man has a body.
Omitting the expanded prosyllogisms, we have the double epichi-
rema in its occult form; omitting the occult prosyllogisms, we have
the same in its manifest form.
(2.) The compound syllogism, made up of successive co-ordinate
syllogisms, includes the double syllogism, in which the episyllogism
is attached to the conclusion of a syllogism, making that conclusion a
premise for reaching a new conclusion ; and the chain syllogism,
which is made up of successive co-ordinate syllogisms. In both these
forms it may be either manifest or occult.
The double syllogism of the compound form does not need to be
further subdivided. The chain syllogism in its occult form is usually
known as the sorites (Greek, meaning a heap}. The successive syllo-
gisms in it are all equally abridged.
Both the manifest and occult forms may be illustrated by the following ex-
amples, in which the occult forms are contractions of the manifest forms :
Double Syllogism, Manifest Form.
Useful studies ought to be pursued ;
1st, \ Logic is a useful study ;
Logic ought to be pursued.
I
144 PRACTICAL LOGIC.
{A course which omits what ought to be studied is deficient ;
A course which omits Logic omits what ought to be studied ;
.*. A course which omits Logic is deficient.
Double Syllogism. Occult Form.
Useful studies ought to be pursued ; )
Logic is a useful study ;
.• Logic ought to be pursued ; J Syllogism.
Hence an educational course l
which omits Logic is deficient. / EPlsy"°glsm-
Chain Syllogism, Occult, Sorites. Chain Syllogism, Manifest.
Bucephalus is a horse ; I. f Bucephalus is a horse ;
A horse is a quadruped;
/. Bucephalus is a quadruped.
A horse is a quadruped; II. f Bucephalus is a quadruped ;
A quadruped is an animal ;
Bucephalus is an animal.
A quadruped is an animal ; III. f Bucephalus is an animal ;
An animal is a substance ; An animal is a substance ;
Bucephalus is a substance. [ v Bucephalus is a substance.
The sorites proper is of two kinds, — the progressive or Aristotelian,
in which the argument descends from whole to part ; and the regres-
sive or Goclenian, in which the argument ascends from part to whole,
as in the following examples :
Regressive Sorites. Progressive Sorites.
Bucephalus is a horse ; An animal is a substance ;
A horse is a quadruped ; A quadruped is an animal ;
A quadruped is an animal ; A horse is a quadruped ;
An animal is a substance ; Bucephalus is a horse ;
.•. Bucephalus is a substance. /. Bucephalus is a substance.
The sorites can thus readily be expanded into a manifest compound
syllogism. It consists of "as many simple syllogisms as there are
middle terms between the subject and predicate of the conclusion, i. e.t
intermediate wholes and parts between the greatest whole and the
smallest part, which the reasoning connects." In the example given, —
taking the progressive form, — the greatest whole and smallest part are
substance and Bucephalus; the middle terms are horse, quadruped,
animal. This gives three simple syllogisms, by using successively
these middle terms.
II. Hypothetical Syllogisms.
The hypothetical syllogism is that form of syllogism in
which the reasoning turns upon some hypothetical judg-
ment (p. 117) embodied in the major premise. Hypotheti-
THE FORMATION OF REASONING. 145
cal syllogisms, whether monosyllogisms or polysyllogisms,
are, therefore, primarily divided into conditional or con-
junctive and disjunctive. These, as in the case of cate-
goricals, may be either manifest or occult.
1. A hypothetical monosyllogism is one which contains
but one argument, with its major and minor premises ex-
pressed or understood, and its conclusion. The suppressed
or disguised premise gives the hypothetical enthymeme
which is the most common form in ordinary speech. Both
manifest and occult hypothetical arguments may be either
conditional or disjunctive.
(1.) A conditional, or conjunctive hypothetical syllogism is one in
which the reasoning turns upon a conditional or conjunctive judg-
ment embodied in the major premise. This may be illustrated in both
its manifest and occult forms by the following example :
Manifest Form. Enthymeme.
If rains are plenty, the crops will be f If rains are plenty, crops will be
plenty ; J plenty ;
Rains are plenty : 1
/. Crops will be plenty. (. So crops will be plenty.
(2.) A disjunctive hypothetical syllogism is one in which the rea-
soning turns upon a disjunctive judgment embodied in the major
premise. This may be illustrated by the following example :
Manifest Form. Enthymeme.
{Man is either an automaton or free ; f Man is either an automaton or free;
He is a free being; J
.-. He is not an automaton. [ And so he is assuredly free.
2. The hypothetical polysyllogism includes the various
forms in which hypothetical arguments may be brought to-
gether into wholes of connected reasoning. These wholes
may arise from combining hypothetical and disjunctives
in the premises, or by combining entire arguments. The
former gives rise to dilemmatic syllogisms; the latter to
compound hypothetical syllogisms, including the double
form and the sorites.
(1.) A dilemmatic syllogism is one having a dilemmatic judgment
(p. 118) for its major premise, with a minor premise so affirming or
13 K
146 PRACTICAL LOGIC.
denying some member or members of the major as to lay the founda-
tion for an inference. The forms depend upon the various combina-
tions in the major premise. The combinations are as follows :
1st. A single conditional antecedent with a disjunctive consequent,
as in the example :
If the Senator aspires to a place, he will either rule or ruin :
The Senator aspires to the place of President :
.*. He will either rule or ruin.
Or, If A is B, either C is D or E is F ;
But A is B, ... /. either C is D or E is F.
2d. A plurality of conditional antecedents all having one common
consequent, as in the example :
"If things are what we can help, we ought not to fret about them; and if
they are what we cannot help, we ought not to fret about them ;
But all things are either what we can or cannot help ;,
/. They are what we ought not to fret about."
Or, If A is B, X is Y, and if C is D, X is Y;
But either A is B or C is D ; ... .-. X is Y.
This form is what has been known as the dilemma in the strict sense,
or the horned syllogism. It is so called because it confronts an oppo-
nent with two assumptions, on which it tosses him as on horns from
one to the other, each being equally fatal to him.
3d. A plurality of conditional antecedents each with its own con-
sequent, as in the example :
f If men are virtuous they are wise, Or, If A is B, C is D, )
I And if they are vicious they are unwise ; And if E is F, G is H ; /
But they are either virtuous or vicious ; But either A is B, or E is F ;
.-. They are either wise or unwise. .'. Either C is D, or G is H.
(2.) The compound hypothetical syllogism includes the double form,
in which the latter of two syllogisms is abridged, and appears as an
episyllogism; and the hypothetical sorites, in which the successive
syllogisms are all equally abridged. These may be illustrated by ex-
amples :
Double Form.
{If the people are industrious, wealth increases;
They are industrious ; Episyllogism.
.'. Wealth is increasing (and hence the nation mil become power/til).
Hypothetical Sorites.
If Gladstone is virtuous, he is brave ; Or, If A is B, C is D ;
If brave, he is magnanimous ; If C is D, E is F ;
If magnanimous, he will relieve the Irish ten- 1 T „ _ . _, _ . _
ants; / IfEisF.GisH;
But Le is virtuous, and /. will relieve the Irish ) _, .
tenants. f 1S B> '*'
THE FORMATION OF REASONING. 147
Praxis. — Find middle terms for the following conclusions, according
to the Rules given ; verify the premises and test the conclusion ; and
mark by the appropriate vowels the quantity and quality of all the
judgments: 1. Jupiter is a planet. 2. Education is valuable. 3.
Religion is indispensable. 4. The crocodile is a reptile. 5. Few
patriots have been disinterested. 6. No brutes are responsible. 7.
Perseverance is a condition of success. 8. A sensualist is not truly
free. 9. The elk is ruminant. 10. Good logicians are not true poets.
11. The immoral man is not happy. 12. The inactive man cannot be
happy. 13. Astrology is not a science. 14. Astronomy is a science.
Give a complete outline of the kinds of Syllogisms, as presented in
the preceding Section, and then construct one or more original syllo-
gisms illustrating each of the kinds.
Section III,— Inductive Seasoning,
Topic First.— Process of Finding and Verifying the Cause
in Induction.
Two things are essential in induction : first, fixing upon
some assumed cause which works in the facts from which
the inference is sought, and which furnishes the basis for
a working hypothesis ; second, testing and verifying this
hypothesis.
Note.— Ueberweg has said truly: " Hypotheses are necessary in all sciences
if the knowledge of causes is to be reached. Causes as such are not accessible
to observation, and, therefore, at first can be thought only under the form of
hypotheses, until, with the advance of the sciences, the previously problem-
atic suppositions pass over into knowledge apodictically certain. . . Scientific
hypotheses . . . are the results of regular reflection on experience, and, as
premises in tentative deductions, form the necessary preliminaries to ade-
quate knowledge."
I. Finding the Working Hypothesis.
In finding the cause in induction, the first question to be
asked is, What working hypotheses, in themselves possible,
can be formed, which agree with the facts of experience, so
that the phenomena may all be taken into account and ex-
plained ?
Induction derives its data from experience. Experience is the ex-
amination which is necessary to furnish us the facts from which to
148 PRACTICAL LOGIC
make inferences. Such experience is obtained either by observation or
by experiment.
Observation is the act of the mind in seizing upon facts as they are sponta-
neously presented in nature. Its nature and methods have already been
unfolded (p. 26). Experiment is the process of voluntarily " putting in action
causes and agents over which we have control, and purposely varying their
combinations and noticing what effects take place." It vastly multiplies the
possibilities of observation, and is thus of the greatest importance to science.
The data drawn from experience for use in induction consist of facts or phe-
nomena. A phenomenon means literally " that which appears to, or is known
directly by, the senses," and then " that which is known as a fact to the mind."
The word, therefore, includes all facts whether made known by the senses or
consciousness. The word fact is substantially its equivalent in usage. It sig-
nifies literally "something done," and maybe defined to be anything that
exists or happens, whether in the world of matter or of mind.
Equally important with the data of induction is the correct logical
method of dealing with the facts. This Bacon sought to furnish in
his Novum Organum or New Instrument. Its aim is to direct the mind
in seizing upon the facts in any given region, constructing hypotheses
for their explanation, and, through the verification of these, reaching
perfected theories or general truths.
" The correct construction of hypotheses," says Ueberweg, " is a
life and death question with Philosophy ; for it is the science of the
principles which underlie all the sciences, and requires more than
any other to pass beyond mere experience, and to bring together by
comparison very different departments of knowledge." Hence the
importance of correct Rules carefully applied.
Bale 1st. — Observe, analyze, and classify the facts to be generalized
and explained, in order to ascertain their reality and their various
elements and relations.
This Rule guards against two common sources of error in induction. The
first is that of assuming what is not fact to be fact. This is illustrated by the
problem presented by Charles II. to the Royal Society : " Why does a live fish
in water increase the weight while a dead fish does not?" The answer to the
question, " Is it a fact ?" would have saved the time spent in endeavoring to
solve the imaginary problem. The second is the error from getting only a
partial view of the facts or from failure to get them in their relations. This is
illustrated in Stahl's method of accounting for combustion, by the extrication
of a substance supposed to be contained in all combustible matter, called
phlogiston, which went up in the flame. Combustion results in the visible
residue of ashes and the invisible phlogiston which passes off. The error was
in the non-observation of an important part of the actual residue, — the gas-
eous products of combustion. When these were at last taken into account, it
was found that the gases with the ashes weighed much more than the sub-
stance burned, so that there was no room for phlogiston. See Mill's Logic,
Book V., Ch. iv.
THE FORMATION OF REASONING. 149
"Rule 2d. — Correctly interpret the facts, i. e., seek to find the appro-
priate cause for the facts and basis for the generalization.
By cause in induction is meant " operating power," or, more
strictly, " power which in operating originates new forms of being."
It is anything which has efficiency and exerts it in producing change,
and hence is often called efficient cause. It should be carefully dis-
tinguished from law, which has no efficiency, but is merely an expres-
sion of an established sequence of facts, or of the regular order in
which a cause operates. A condition is " that which is prerequisite
in order that something may be, and especially in order that a cause
may operate." It is " prior to the production of an effect; but it does
not produce it. It is fire that burns ; but, before it burns, it is a
condition that there be an approximation of the fire to the fuel, or
the matter that is burned. . . The cause of burning is the element of
fire, fuel is the con-cause, and the condition is the approximation of
the one to the other."
The cause may be sought, first, in some known, or. secondly, in some un-
known, force or forces. The search in the former case has to do with some
real cause and is guided by the so-called Methods of Induction, and in the
latter case must be reached by inductive assumption or assumption of strictly
hypothetical cause. In the former case the results tend to take shape in contri-
butions to exact science ; in the latter they belong to the region of scientific
question or metaphysical speculation. The quarrels of scientists and theolo-
gians very often arise from confounding the two.
(1.) Inductions of Real Cause. — The Canons of the In-
ductive Method used in the search for the real cause for
any phenomenon, whether that cause is simple or complex,
may have reference either to the preliminary consideration
of the happening or not happening of the event, the cause of
which is sought; or to the more advanced problem of meas-
uring the exact quantity of an effect, if it be capable of being
more or less, and connecting it with the quantity of the cause.
To the first stage belong the methods of agreement and of
difference ; to the second, the methods of concomitant vari-
ation and of residues.
A. What can be learned of the real cause of an event
from the happening or not happening of that event ?
The Method of Agreement is applied in case of the uniform hap-
pening of an event. This gives rise to —
13*
150 PRACTICAL LOGIC.
Canon First. — If in all observed cases of an effect or phenomenon
one condition is uniformly present, that is probably the cause, or in-
cludes the cause, of the phenomenon or effect. In other words, " the
sole invariable antecedent of a phenomenon is probably its cause."
" To apply this method we must collect as many instances of the phenom-
enon as possible, and compare together their antecedents. Among these the
causes will lie, but if we notice that certain antecedents are present or absent
without appearing to affect the result, we conclude that they cannot be neces-
sary antecedents."
The method of agreement is subject to a serious difficulty. An antecedent
may not be a cause. Night or the cock-crowing or the rising of some diligent
workman may uniformly precede the coming of the day without being the
cause of it. Hence the necessity for tests by which to distinguish between
simple antecedent and real cause.
The Method of Difference is applied in case of the uniform happen-
ing of an event in the case of the presence of some condition, and the
uniform failure of it in case of the absence of that condition. This
gives rise to
Canon Second. — If, in all instances in which a phenomenon does
occur, one single condition is present, which is uniformly absent
whenever such phenomenon does not occur, this constantly present or
absent condition is presumed to be the cause of the phenomenon.
Thus we can clearly prove that friction is one cause of heat, because when"
two sticks are rubbed together they become heated ; when not rubbed they do
not become heated. Sir Humphrey Davy showed that even two pieces of ice
when rubbed together in a vacuum produce heat, as shown by their melting,
and thus completely demonstrated that the friction is the source and cause
of the heat. We prove that air is the cause of sound being communicated to
our ears, by striking a bell in the receiver of an air-pump, as Hawksbee
first did in 1705, and then observing that when the receiver is full of air we
hear the bell ; when it contains little or no air we do not hear the bell.
B. What can be learned of the Real Cause of an event
from the varying degree or quantity of an event ?
" Every science and every question in science is," as Jevons has
said, " first, a matter of fact only, then a matter of quantity, and by
degrees becomes more and more precisely quantitative. Thirty years
ago most of the phenomena of electricity and electro-magnetism were
known merely as facts ; now they can be for the most part exactly
measured and calculated.
" There is in fact a natural course of progress through which we
proceed in every such inquiry, as may be stated in the following se-
ries of questions.
THE FORMATION OF REASONING. 151
1. Does the antecedent invariably produce an effect?
2. In what direction is that effect?
3. How much is that effect in proportion to the cause ?
4. Is it uniformly in that proportion ?
5. If not, according to what law does it vary ? "
The Method of Concomitant Variations is applied, after phenomena
begin to be measured, in cases where there is an increase or decrease of
an event with a corresponding increase or decrease of the condition
which, by the other methods, has been assumed to be the cause. This
gives rise to
Canon Third. — Increase or diminution of t'he effect, accompanied by
the increased or diminished intensity of the assumed cause, in cases
which admit of increase and diminution, increases the assurance of
the causal relation.
By the method of difference it may be shown that air is the cause of the
transmission of sound, by striking a bell in the air and in a vacuum. Instead
of this, the method of concomitant variations may be applied, by striking a
bell in the receiver of an air-pump with a very little air, and then increasing
and decreasing the density of the air. The sound, which is very faint with a
little air, grows fainter and disappears as the air is exhausted, and becomes
louder and fuller as air is added.
This method is made use of in seeking causes for events which go through pe-
riodic changes, alternately increasing and decreasing. It leads us to search for a
cause which undergoes like periodic changes. The tides are thus proved to
be due to the combined attraction of the moon and sun, since the periods of
high and low, spring and neap, tides succeed each other in intervals corre-
sponding to the apparent revolutions of those bodies round the earth.
But all these methods are subject to difficulty from the fact that
causes are usually complex, or, in other words, that there is usually
a plurality of causes co-operating in the production of any given
effect. This gives rise to
The Method of Residues or of Eesidual Variations. — When there
are several causes each producing a part of the effect, we desire to
know how much is due to each cause. This leads to
Canon Fourth. — Subtract from any phenomenon such part as is
known by previous inductions to be the effect of certain of the causes,
and the residue of the phenomenon is the effect of the remaining causes.
This is illustrated by the method of ascertaining the exact weight of a load
of hay or any other commodity in a cart, by weighing the cart and load to-
gether, and then subtracting the tare or weight of the cart alone, previously
ascertained. Almost all the remarkable modern predictions in astronomy
have been made by the use of the method of residues. Thus, after the effects
of all known attractions were calculated in the case of Uranus, it was still
152 PRACTICAL LOGIC.
found that the planet was sometimes before and sometimes behind its calcu-
lated place. This residual effect pointed to the existence of some cause of
attraction not then known, and the exact place and size of the disturbing
body was calculated and the planet Neptune discovered.
" The motions of several comets have in this way been calculated, but it
is observed that they return each time a little later than they ought. This re-
tardation points to the existence of some obstructive power in the space
passed through, the nature of which is not yet understood."
When the same phenomenon may be the effect of any one of various
causes, there arises the necessity for excluding all the causes but that
which really operates in the given case. Ordinarily this is not a
difficult matter. It requires, however, that the attendant circum-
stances should be carefully noted and understood. A room may be
heated by the August sun, or by a fire in furnace or grate or stove, or
by any one of various other causes. Which is the operating cause
may be ascertained by the proper inspection, the real cause being
thus found and all others excluded.
(2.) Inductions of Hypothetical Cause, — When the cause
of any given phenomenon is unknown or beyond our reach,
the assumption of some hypothetical cause becomes a ne-
cessity of the human mind. Such cases are in the region
of tentative science or scientific speculation, rather than in
that of exact science. Rule 2d requires in such cases that
the cause or causes assumed should be appropriate and ade-
quate to account for all the facts.
Eule 3d. — When the facts have been sufficiently investigated com-
bine them all under the cause, simple or complex, which seems best
suited to produce them, and which is at work in all similar facts.
This gives the working hypothesis, which must be modified to suit the
further developments of investigation.
As the observation may be more or less complete, various working
hypotheses may be reached by the same thinker or by different
thinkers.
When the facts concerning the movements of bodies on the earth and in the
heavens have been to some extent observed, they may be referred to gravity
as the cause. When the investigation has been carried still further, the work-
ing hypothesis of universal gravitation, of Newton, may be stated : "Any two
masses in the universe, whatever their material, attract each otlier by gravitation with
a force which varies directly as the mass and inversely as the square of the dis-
tance."
THE FORMATION OF REASONING. 153
This is the work of the constructive imagination or of
the power of scientific construction, and must always pre-
cede complete and established scientific theory.
II. Testing the Working Hypothesis.
Scientific thinking requires that to the most ingenious
boldness in forming working hypotheses should be united
the most cautious accuracy in testing them before their
acceptance as truth. The tests of hypotheses are found in
connection with the cause assumed, the facts to be explained,
or the application of the deductive method.
"A riper inquiry," says Ueberweg, " recognizes that in all problems where
we must proceed upon mere observation, and not with mathematical certainty,
the scientific correctness of distinct hypotheses must be the first object of
investigation. An essential advance in method in this sense was made in
Astronomy, when in the Platonic school, and especially by Heraclides of Pon-
tus, the question to be investigated was not stated in this way : What positions
and motions of the heavenly bodies are to be necessarily accepted on empir-
ical and speculative grounds? but in this : What hypotheses of regular motions,
in themselves possible, can be formed which agree with the facts of observa-
tion, so that the phenomena may be ' preserved ' ? "
Rule 1st. — See that the hypothesis in each case embodies a cause
or complex of causes which is appropriate, sufficient, and, if possible,
known and true. This is the cause test.
All rival hypotheses should be considered and fairly tested accord-
ing to this Rule. The direction of Ueberweg is as follows : " Let all
the opposing fundamental qpinions be brought under the view of dif-
ferent thoroughly testing hypotheses, and do not let the one opinion
(as too often happens if it is the traditional one) be treated from outset
as correct, necessary, sound, and rational, and those of opponents con-
sidered to be false, arbitrary, unsuitable, or foolish."
The Rule suggests various particulars to be noted in settling the
claims of rival hypotheses.
1st. The hypothesis which is to be of service must embody a cause.
The hypothesis of evolution, as stated by Spencer, embodies no cause : " Evo-
lution is a change from an indefinite, incoherent homogeneity to a definite,
coherent heterogeneity through continuous differentiations and integration."
" A change " is not a cause, but is rather the very thing to be explained. This
is true of a vast region of so-called inductions, which are not inductions at all,
because there is no cause at the foundation of the facts. For example, it might
readily be concluded, from the fact that man and all the animals with which
154 PRACTICAL LOGIC.
we come in contact move the lower jaw in masticating food, that all animals
do the same. The fact, however, is that the crocodile moves the upper jaw.
This is mere generalization, and not induction in the proper sense.
2d. The hypothesis is to be preferred which embodies an appro-
priate cause.
The universe is found by scientific investigation to be a thought-system. Of
various hypotheses concerning its production,— by chance, by self-origination
through blind matter and force, by an Intelligent Author capable of planning
and constructing such a thought-system, etc.,— the hypothesis of an Intelli-
gent Author is the only scientific one, since such a cause is the only appro-
priate one for the effect.
3d. The hypothesis is to be preferred which embodies a known
cause.
Induction assumes the simplicity of nature. That is, the Author of nature
works as man would work, using the simplest means to attain the end in view,
never introducing a new force where some already existing force will accom-
plish the object. On this principle Newton extended the familiar action of
the known force of gravity on the earth's surface to the phenomena of the
heavens.
4th. The hypothesis is to be preferred which embodies a true cause.
Newton's view of gravitation made use of a true cause, which " had been
already known as an actual power in nature, in the power of weight upon the
earth."
When no known agent can be found, it becomes necessary to assume some
unknown, but appropriate and adequate, cause. Thus, the physicist in
accounting for the phenomena of light, electricity, etc., assumes the existence
of ether, an extremely tenuous substance, pervading all bodies and extending
through the universe, which is the vibratory medium in the transmission of
all these forms of energy. This is, of course, a strictly hypothetical cause.
Some other hypothesis may, at some future time, take its place.
5th. The hypothesis is to be preferred which takes into account the
complex nature of causes and makes the right ones prominent.
Almost universally in nature causes are manifold and complex, and none
of the complex elements can be overlooked without falling into error. For
example, about 1854, some excavators broucht up some burnt brick and pot-
tery from the depth of 60 and 72 feet, in the valley of the Nile. Assuming
that they were found where they were made, and that the alluvium had been
deposited upon them at the rate at which the Nile now makes its deposit, and
that this was the only cause at work, it was calculated mathematically that the
relics must be from 12,000 to 60,000 years old. One causal element omitted
was the weight of the brick-bats in connection with the fact (also causal) that
all the region is a vast quagmire during the inundation which covers it with
water during a large part of the year. Sir Robert Stephenson afterwards
found in the Delta near Damietta, at a far greater depth, a brick bearing the
stamp of Mohammed AH (1808). Some one said satirically that the main ques-
tion in the first case should have been : How long will it take a brick to sink
72 feet in a quagmire? But although this might be the main question, all
causes should be given their due weight in reaching the correct result.
THE FORMATION OF REASONING. 155
Bale 2d. — See that the hypothesis in each case combines and ex-
plains all the facts. This is the fact test. This embraces various
particulars.
1st. The hypothesis must embrace the facts.
This is the object in forming hypotheses, and forgetfulness of it is fatal to
correct thinking. The question in inductive science should not be, what must
be ? but, what is ? The old science, putting assumption and deduction in the
place of induction from facts, taught that the orbits of the heavenly bodies
must be circular, because " the circle is the perfect figure ;" the true science
teaches that the orbits of the heavenly bodies are, in fact, ellipses, because this
alone agrees with the facts as explained by the laws of centrifugal and cen-
tripetal force in connection with gravitation and the motion of the bodies.
2d. The hypothesis must explain all the facts. A single fact clearly
contradictory to any hypothesis calls for the modification or abandon-
ment of the hypothesis.
It is manifest that even a single fact clearly contradictory to any
hypothesis proves the hypothesis untenable, as that single fact, though
there were no other such fact, would prove the principle embodied in
the hypothesis not universal. The place occupied by exceptional facts
is thus seen to be very important. As Jevoiis has said, " they are
commonly the points from which we start to explore new regions of
knowledge." As all exceptions are not equally fatal to the hypotheses
to which they appear to be exceptional, Jevons (Principles of Science,
pp. 644-672) has arranged them under eight classes :
(1.) " Imaginary, or false, exceptions, that is, facts, objects, or events which
are not really what they are supposed to be.
(2.) "Apparent but congruent exceptions, which, though apparently in con-
flict with a law of nature, are really in agreement with it.
(3.) " Singular exceptions, which really agree with a law of nature, but ex-
hibit remarkable and unique results of it.
(4.) " Divergent exceptions, which really proceed from the ordinary action
of known processes of nature, but which are excessive in amount or monstrous
in character.
(5.) " Accidental exceptions, arising from the interference of some entirely
distinct but known law of nature. This is the largest class of exceptions.
(6.) " Novel and unexplained exceptions, which lead to the discovery of a
new series of laws and phenomena, modifying or disguising the effects of pre-
viously known laws, without being inconsistent with them.
(7.) " Limiting exceptions, showing the falsity of a supposed law in some
cases to which it has been extended, but not affecting its truth in other cases.
(8.) " Contradictory or real exceptions, which lead us to the conclusion that
a supposed hypothesis or theory is in opposition to the phenomena of nature,
and must therefore be abandoned." These exceptions are the most important
of all, " since they lead to the entire rejection of a law or theory before ac-
cepted." No law of nature can fail; there are no such things as real excep-
tions to real laws. Where contradiction ex-ists, it must be in the mind of the
156 PRACTICAL LOGIC.
experimentalist. Either the law is imaginary or the phenomena which con-
flict with it ; if, then, by our senses we satisfy ourselves of the actual occurrence
of the phenomena, the law must be rejected as illusory.
Rule 3d. — Apply the principles of deduction to the hypothesis, as-
certaining what ought to happen in any given circumstances if the
hypothesis he true, and test the predicted results by observation and
experiment. This is the prediction test.
When any hypothesis embodies a real cause, it gives the thinker the power
of predicting by deduction the particular phenomena which come under it.
The verification of such predictions is one of the last and highest tests of an
induction. "There is no more convincing proof of the soundness of knowl-
edge than that it confers the gift of foresight." Astronomy furnished the
earliest development of this power. Thales, the Father of Philosophy, pre-
dicted the eclipse which suddenly turned day into night during a battle be-
tween the Medes and Lydians. The recent discovery of Neptune is the most
remarkable instance of this prevision. The method of prediction by deduction
is equally applicable to all the physical and mental sciences.
" As we deduce more and more conclusions from any hypothesis and find
them verified by trial, the probability of the theory increases in a rapid man-
ner; but we never escape the risk of error altogether. Absolute certainty is
beyond the powers of inductive investigation, and the most plausible supposi-
tion may ultimately be proved false.
"Such is the groundwork of similarity in nature, that two very different
conditions may often give closely similar results. We sometimes find our-
selves, therefore, in possession of two or more hypotheses which both agree
with so many experimental facts as to have great appearance of truth. Under
such circumstances we have need of some new experiment, which shall give
results agreeing with one hypothesis but not with the other." This gives rise
to what Bacon called an Experimentum Crucis, an " Experiment of the Fin-
ger Post." In Pascal's day his own hypothesis, that the mercury rose in the
tube because of the pressure of the atmosphere, had as its rival the doctrine,
that this phenomenon was due to nature's abhorrence of a vacuum. His ex-
periment of causing a barometer to be carried to the top of the Puy-de-D6me
was the crucial experiment which established his own theory and negatived
the rival hypothesis.
Rule 4th. — Avoid the common error of assuming unverified hypoth-
eses, or such as are based upon other unverified hypotheses, as true.
The failure to conform to this general rule has been the bane of sci-
entific investigation in both its physical and mental spheres in all ages.
The spirit of speculation and the determination to believe one's own
dreams to be the reality have overborne the spirit of the true philoso-
pher. "The philosopher," says Faraday, "should be a man willing
to listen to every suggestion, but determined to judge for himself. He
should not be biased by appearances ; have no favorite hypothesis ;
be of no school ; and in doctrine have no master. He should not be
a respecter of persons, but of things. Truth should be his primary
THE FORMATION OF REASONING. 157
object. If to these qualities be added industry, he may indeed hope
to walk within the veil of the temple of nature."
Topic Second. — Products of Inductive Reasoning.
The product of induction is a generalization. The pro-
cess may be expressed in quasi-syllogistic form, as follows :
Mars, Jupiter, the Earth ......... move in elliptical orbits round the sun;
These are (as good as— or fairly represent) all the planets ;
/. All the planets move in elliptical orbits round the sun.
Or letting Mj, M2, etc., represent the different instances from which
the inductions are made, we have the formula:
M,, as well as M2, is P;
M1? as well as M2, is S ;
• T?TTQ1-TT Q id P
Every S is P.
I. Varieties of Induction,
Inductions are divided by logicians into perfect and im-
perfect.
1. The so-called perfect induction takes place " when, by
a perfect enumeration of all individuals or particulars, the
whole sphere of the universal is exhausted." For example:
Mercury revolves on its axis ; so do Venus, the Earth, Mars, Jupiter,
and Saturn. But these are all the old planets. .'. All the old planets
revolve upon their axes.
This, however, is enumeration and addition rather than inference.
It is ordinarily applicable, of course, only to spheres of objects so
limited that all the individuals may be successively examined.
2. The so-called imperfect induction includes the cases
in which the general is reached by inference, without the
complete enumeration of objects. Sometimes only a very
few objects out of an indefinite number are examined.
The conclusion in such cases may be made universal, first, by the
pure assumption of a real causal nexus between the subject and pre-
dicate of the conclusion, — giving what may be called an inductive
guess, often mistaken for induction ; or, secondly, by the strictly
inductive method of finding some real, adequate and, if possible, true
cause, to connect the subject and predicate of the conclusion, — giving
what may be called a true induction.
14
158 PRACTICAL LOGIC.
(1.) The inductive guess or primary induction may be illustrated by
the following example :
Iron is heavier than water, so is silver, quicksilver, gold, etc.
/. All the metals are heavier than water.
The primitive inductions thus formed are mostly false, as in this
example, since some of the metals, as sodium and potassium, are lighter
than water. A vast amount, not only of the thinking of common
life but also of the so-called scientific induction, is of this nature, and,
therefore, at the best only the work of the imagination, and at the
worst mere crude guess-work.
(2.) The true induction is that in which a causal nexus, found in
the nature or essential relation of the objects examined, is more or
less completely established. The generalizations in such cases vary in
degree of probability. The highest degree of probability is reached
where some true and known cause is at work producing like effects in
the various individual instances. The probability decreases as the
cause recedes into the region of the unknown and hypothetical. The
true induction may be illustrated by the following examples :
Mercury, Venus, Jupiter, etc., appear to be wanderers among the fixed stars ;
These represent all the planets (since this apparent wandering is due to the
motion of these stars and the earth) ;
. • . All the planets will probably appear to be wanderers among the. fixed
stars.
3. Analogy has already been shown (p. 136) to involve
both induction and deduction, the inductive being the prin-
cipal element. As analogy depends upon some assumed
likeness, its kinds may be indicated by the kinds of prop-
erties (pp. 28-9) in which the likeness is found. That like-
ness may be in either essential or non-essential properties.
(1.) Analogy based upon resemblance in essential properties is the
most valuable kind. The reasoning in this case rests upon the generic
and essential nature of the objects coordinated in the analogy. This
may be illustrated by the inference made by Franklin in November,
1749, which must be reckoned among inferences from analogy, since
lightning and electrical phenomena were not yet known to be the
same but only similar :
" The electric fluid, as it shows itself in experiments made by us, is attracted
by projecting metallic points;
THE FORMATION OF REASONING. 159
" This electric fluid and lightning agree in the properties, that they give light
of the same color, have a quick motion, are conducted by metals, etc., etc. ;
" Hence it is to be presumed that lightning will also be attracted by project-
ing metallic points."
(2.) Analogy based upon resemblance in peculiar or accidental prop-
erties is of comparatively little value, since these properties do not
indicate any essential or causal principle lying back of them. This
may be illustrated by the following examples :
" The American swan is white; therefore, the Australian swan is white."
" John Smith, a man with a red nose, is a drunkard ; therefore, Timothy
Jones, another man with a red nose, is a drunkard."
But the Australian swan, though in all essential respects the same
as the American, differs in the non-essential property of color, being
found to be black. In like manner the red nose may be the result of
exposure to the sun, or of any other of many causes.
(3.) Analogy based upon the resemblance of relations is the most
difficult to deal with of all the forms of analogy. This is analogy in
the strictest sense. It is necessary in all inferences of this kind to
consider with great care how far the analogy holds. In the direct
form these characteristics of analogy may be illustrated by the rela-
tions of a foot to a man and a mountain. It is under the man as a
support and under the mountain as a support, but its being that upon
which man walks does not warrant the extension of this relation to
the foot of a mountain. Analogy from contradictories is illustrated
when, from the fact that virtue produces happiness, it is inferred by
analogy that its contradictory moral quality, vice, will produce unhap-
piness.
II. Fallacies in Induction,
The most common fallacies in induction arise from fail-
ure, first, in dealing with the facts ; or, secondly, in finding
the cause.
The most common fallacy is that of false generalization
(fictae universalitatis, or unreal universality*}. This makes a
show, at least, of complete and conclusive induction.
(1.) This may result from careless and incomplete observation of facts,
and may then be called the fallacy of insufficient observation. Thus,
a French physician, it is said, once gave a Frenchman, who had
typhoid fever, chicken soup ; the patient recovered, and on the basis
160 PRACTICAL LOGIC.
of this one fact the doctor made the generalization, — "Chicken soup
will cure a man who has typhoid fever." He afterwards used the
same remedy in the case of an Englishman who had the same disease ;
the patient died, and the doctor reached and recorded the further gen-
eralization,— " Chicken soup cures a Frenchman, but kills an English-
man."
(2.) The false generalization may also result from the hasty assump-
tion of something as the cause which is not the cause (non causa pro
causa}. That which is assumed as the cause in such cases may be
either a simple concomitant or a mere antecedent (post hoc ergo propter
hoc). The fallacy of assuming that a simple concomitant is a cause
(cum hoc ergo propter hoc) is illustrated by the conclusion of the
materialist, that since chemical action in the brain accompanies mental
action, it is the cause of mental action ; which is paralleled by the
assumption, that because the small boy's boots always accompany the
small boy, therefore, they are the small boy. The fallacy of assuming
that a mere antecedent is a cause (post hoc ergo propter hoc) is illus-
trated by the inference, among the ancient Romans, that when a
general engaged the enemy where the response of the augurs had been
unfavorable, and suffered defeat, the cause of the disaster was the
unfavorable character of the auspices.
Praxis. — Test the following conclusions reached by induction ; state
whether the induction is valid or not in each case ; verify the induction
when valid, and when not valid show what is the fallacy involved :
1. " The Jews are rogues,— The Carthaginians, faithless,— The Cretans, liars,
— The French, braggadocios, — The Germans, mystics, — The rich, purse-proud, —
The noble, haughty, — Women, frivolous, — The learned, pedants." 2. Matter
is eternal. 3. Spirit is essentially immortal. 4. The Irish are malcontents. 5.
All human languages had a common origin. 6. The great civilizations have
all flourished in the North Temperate Zone. 7. Man is what circumstances
make him. 8. " There 's a divinity that shapes our ends, rough hew them how
we will." 9. That which survives is fittest. 10. All the planets revolve on
their axes. 11. Conceited men are always shallow. 12. Ignorant men are con-
ceited. 13. Selfish men are not men of principle. 14. Man is born sinful. 15.
The Christian nations are the progressive nations. 16. The Protestant nations
are the foremost nations in the world. 17. The reach of gravitation is univer-
sal. 18. The best education is secured by means of the Classics. 19. The best
education is secured by means of the Natural Sciences. 20. The best edu-
cation is secured by means of the combined study of the Classics, Natural
Sciences, and Mathematics. 21. The appearance of a comet is the harbinger
of famine, pestilence, and war. 22. Friday is an unlucky day.
State, in the following cases, whether the facts are exceptional, and,
if so, to what class each belongs ; and show whether and how they
eTHE \
RSITY J
RMATION OF REASONING. 161
can be reconciled with the hypotheses to which they appear to be ex-
ceptional :
1. The rotation of the earth upon its axis gives to all the stars an apparent
motion of rotation from east to west. The Pole Star seems not so to revolve.
2. According to the Newtonian view of gravitation all bodies are heavy. But
flame, bubbles, clouds, etc., ascend, and were, therefore, regarded by the an-
cients as essentially light. 3. The Copernican theory teaches that the earth in
revolving moves toward the east at the rate of a thousand miles or more an
hour. It has been objected to it that, if this be so, then a stone dropped from
the topmast of a ship at anchor ought to fall behind toward the west, just as a
stone dropped from the mast-head of a moving ship would fall behind, owing
to the motion of the ship. 4. The ancients held that the general tendency of
bodies on the earth is downward. In the case of the loadstone held over iron,
the iron had a tendency upward. This could not be explained by the hypoth-
esis of essential lightness, since iron is one of the heaviest substances. 5.
According to the theory of Torricelli and Pascal, the mercury ought to stand
at a height of about 31 inches in the barometer. Boyle showed that in a
perfectly cleansed tube it could be made to stand as high as 75 inches. 6.
According to the hypothesis of the materialistic evolutionist, the development
of the universe has been a continuous change and progress from the primor-
dial atom, without break or interference of any other than material forces.
Dr. McCosh, in Christianity and Positivism (Appendix, p. 344), enumerates
eleven breaks in the continuity, among which are the following : " Chemical
action cannot be produced by mechanical power." " Life, even its lowest
forms, cannot be produced from unorganized matter." " Protoplasm can be
produced only by living matter." "A living being can be produced only from
a seed or germ." "An animal cannot be produced from a plant." " Sensation
cannot be produced by insentient matter." The genesis of a new species of
plant or animal has never come under the cognizance of man, either directly
or indirectly. Consciousness cannot be produced out of mere matter or sensa-
tion. " We have no knowledge of man being generated out of the lower ani-
mals." "All human beings, even savages, are capable of forming certain high
ideas, such as those of God and duty ;" the brute is not.
State and test the following hypotheses :
1. The Wolffian hypothesis of the origin of the Homeric Poems. 2. The
hypotheses concerning the origin of the Four Gospels. 3. The hypotheses
concerning the nature of Electricity. 4. The hypotheses concerning the
nature of Heat. 5. The hypotheses concerning the composition of Comets.
6. The hypotheses concerning the origin of Life on our globe. 7. The hypoth-
eses concerning the nature of Man. 8. The hypotheses concerning the nature
of Beauty. 9. The hypotheses concerning the origin of the Universe.
Note.— For a complete and extended treatment of Induction, the teacher
and student are referred to the following works : Jevon's Principles of Science;
Mill's System of Logic, Ratiocinative and Inductive.
14* L
162 PRACTICAL LOGIC.
CHAPTER II.
THE UNFOLDING OF REASONING OR THB
SYLLOGISM.
THE treatment of the formation of reasoning is naturally
followed by the consideration of the unfolding and testing
of its various kinds, as embodied in the Syllogism, and the
presentation of the various forms of Fallacy or unsound
reasoning.
Practical Logic should train the thinker to distinguish
readily between a true syllogism and one that only seems
to be a true one. This requires the treatment, in successive
Sections, of the Forms and Tests of Categorical and Hypo-
thetical Syllogisms, and the kinds of Fallacies.
Section I,— The Categorical Syllogism Unfolded,
In unfolding the categorical syllogism, the nature and
kinds of which have already been presented (p. 141), the
following Topics will be considered :
Topio I, — The Possible Forms of the Syllogism, or Figure and Mood.
Topic II.— The Testing of the Valid Forms.
Topio III. — Complex and Abnormal Forms.
Topic First.— -The Possible Forms of the Simple Categor-
ical Syllogism.
The possible forms of the single syllogism are determined
by the various positions of the middle term, in the premises,
with reference to the major and minor terms, and the pos-
sible combinations of the four normal judgments, A, E, I,
0, in groups of three. The first gives rise to Figure, the
second to Mood.
I. Figure of Syllogisms.
Syllogisms are divided into different Figures by the posi-
THE UNFOLDING OF REASONING. 163
tion of the middle term. The possible positions are four,
which give rise to as many Figures :
Figure I, middle term subj. of maj. prem. and pred. of minor.
Figure II, " " pred. of both maj. and min. premises.
Figure III, " " subj. " " " "
Figure IV, " " pred. of maj. prem. and subj. of minor.
This may be expressed and illustrated as follows :
f M * P Every virtue is praiseworthy ; = A
l%' ' J g ^ M Eloquence is a virtue ; = A
ig. I. f
b prae. j
P /. Eloquence is praiseworthy. = A
f P ^|- M No vice is praiseworthy ; = E
l%' \ 4 S • M Eloquence is praiseworthy ; = A
prae prae. [ ^ g ^ p ^ Eloquence is not a yice == E
f M * P Every virtue is praiseworthy ; = A
sub sub. [ ^ g ^ p ^ gomething useful is praiseworthy. = I
c P ^ M Every virtue is praiseworthy ; — A
lg' 'X M • S Everything praiseworthy is useful ; = A
prae sub. ^ . g ^ p . gomething usefoi is a virtue. = I
In these examples the mnemonic sub and prae stand for subject and
predicate. The wedge-shaped figure or line (^ — ) denotes a judg-
ment. Its thick end turns toward the subject of extension, which is
contained as a species under the predicate as a genus. The perpendic-
ular stroke drawn through the line (^ ) indicates negation. In
the Hamiltonian Notation, of which this is a part, the heavy horizon-
tal line (••••) used in the unfigured syllogism (p. 165), indicates
equality between subject and predicate, or a substitutive judgment.
Note.— The syllogisms ordinarily used in the examples in Logic are made
up of propositions of extent, and are, therefore, called extensive syllogisms.
Hamilton introduces and insists upon the intensive syllogism. This is ex-
pressed by reversing the wedge-shaped figure, which in this case represents
the copula as meaning "comprehends," instead of "is contained under,"
which is its meaning in the extensive syllogism. The two forms may be illus-
trated :
The notion responsible is contained under the notion free-
agent; M» P
The notion man is contained under the notion responsible
agent ; S » M
The notion man is contained under the notion free-
agent. .'. S i
164 PRACTICAL LOO 1C.
•jj, ( The notion man comprehends the notion responsible ;
* -I The notion responsible comprehends the notion free ;
t: [ .-. The notion man comprehends the notion free.
In the first form the notions are class notions; in the second, concepts proper.
In the second form the premises of the first form are transposed. With this slight
change extensive and intensive syllogisms conform to the same rules, and are
so nearly identical that the intensive form does not need separate treatment.
In fact, both propositions of extent and of content are often used in the same
syllogism. Thus:
All of the metals are positive ; Proposition of content.
Silver is one of the metals ; Proposition of extent.
/. Silver is positive. Proposition of content.
II, Mood of Syllogisms.
The Mood of a Syllogism is the arrangement of its prop-
ositions according to their respective quantity and quality.
There are as many possible Moods as there are combinations
of the four normal propositions, A, E, I, 0, in syllogistic
form.
It will be seen on examination that in the premises each of the four
may be placed first, and then followed by each of the four successively,
giving 4X4 = 16 combinations. Each of these 16 combinations may
then be followed successively in the
The 16 Premise Forms. conclusion by each of the four judg.
AE EE IE OE ™>>te, A, E, 1,0, giving 16X4 = 64
possible syllogistic combinations. These
forms will be presented later, in gath-
ering up the results of the application
of the Rules, and need not, therefore, be here given. The student,
moreover, will be able readily to form the combinations for himself.
It will be found, when the proper tests are applied, that compar-
atively few of these combinations give valid syllogisms.
Topic Second. — The Testing of the Valid Forms.
Two methods have been employed in testing the validity
of the various combinations :
First, By what Hamilton calls " the thorough-going quan-
tification of the predicate."
Second, By comparing the spheres of the notions in the
THE UNFOLDING OF REASONING. 165
various combinations and framing and using Rules based
upon the results. This is the logical method.
ist. The Unfigured Syllogism. — By quantifying the predicate, Hamilton
has sought to dispense with Figure altogether. By the explicit quantification
of the terms the exact quantity of each is brought out. After the quantifica-
tion the relation between the terms of the judgments may, according to Ham-
ilton, be expressed by the sign of equality, and the subject and predicate may
indifferently change places. The figured and unfigured form may be illustrated
by example :
Figured. —Fig. I. Unfigured.
A Men are rational ; All men = some rational ;
A Negroes are men ; All negroes = some men ;
A .'. Negroes are rational. .'. All negroes = some rational.
If the object in introducing this new method is to simplify reasoning i*, is
not attained, since while it apparently simplifies it really complicates it. The
fatal objection to its general introduction is found in the fact, that the instant
the predicate of a judgment is quantified, it ceases to be a logical or qualitative
•whole and becomes a simple* quantitative or mathematical whole. The judgment
is no longer a logical, but a simple mathematical, judgment. Davis enforces this
position in " The Theory of Thought," p. 124:
" For, consider the meaning of ' all ' in the predicate. It is not, it cannot be,
the distributive, divisive, exemplar ' all,' but is always the total, indivisible,
cumular ' all,' a mathematical whole. E. g., 'All men are bimana ;' this is
the distributive ' all,' meaning that all, each, and every man is in the class, or
has the mark, bimana. But let us say 'All men are all bimana ;' this does not
mean ' Every man is all bimana,' nor 'All men are every bimana,' nor ' Every
man is every bimana,' which is nonsense. It means 'All men (as a mathemat-
ical, total, collective whole) are all bimana' (as ditto). Thus ' all' in the "pred-
icate is never distributive, but cumular, and enforces the ' all ' of the subject
also to be cumular. So also the total predicate of a negative is a mathemat-
ical, not a distributed total ; and ' some ' in the predicate is a mathematical
part. More generally, whenever the quantity of the predicate is designated,
both terms are individuals, and the judgment is mathematical."
The decision whether a given combination leads to a valid inference, and
the proof of the validity or non-validity, must depend upon the comparison
of the spheres of the notions as given in the premises of the apparent syllo-
gism. The reciprocal relations of notions, already presented (pp. 40 and 45),
comprehend all the relations essential in the comparison of notions in reason-
ing. These relations, as has been seen, may be made apparent to the senses
by the use of geometrical figures.
2d. The proper method of testing the validity of the
various combinations of judgments as premises is by com-
paring the spheres of the notions involved in these judg-
ments. The valid forms are determined by General Princi-
ples arising out of the Logical Axioms ; by General Rules
166 PRACTICAL LOO 1C.
arising out of the relations of the terms and propositions
of the Syllogism ; and by Special Canons arising out of the
nature of the particular Figures. Figure I. has always been
considered the normal form of the syllogism, to which the
other forms may be reduced. Hence, the principles which
govern the Reduction of Syllogisms to this Figure need to
be presented. For convenience of reference, a Conspectus
of Results will also be given.
I. The General Principles.
At the foundation and applying equally to all the figures
are three general principles embodying the axiom of Iden-
tity or Affirmation and of Contradiction or Negation.
First General Principle. Affirmative Conclusion. — If, when the
major and minor terms are compared with the same middle term, they
both agree with it, they may agree with each other. This is the basis
of affirmative conclusions.
Second General Principle. Negative Conclusion. — If, on such com-
parison, one term agrees and the otfear disagrees with the same middle
term, they disagree with each other. This is the basis of negative
conclusions, which, therefore, result from the combination of one af-
firmative and one negative premise.
Third General Principle. No Conclusion. — If, on such comparison,
both terms disagree with the same middle term, it is uncertain whether
they agree or disagree with each other, and, therefore, no valid infer-
ence can be drawn in such cases. This is the case where both prem-
ises are negative.
II. The General Rules.
The general rules arising out of these general principles
depend upon the relations of the terms and propositions of
the syllogism. They may be reduced to seven, and are
equally applicable to all the figures.
Rule 1st. — There must be three, and only three, terms in any valid
syllogism. The major and minor terms would not otherwise be logi-
cally connected at all. This needs no illustration. It guards against
the common Fallacy of Four Terms, which oftenest arises from the use
THE UNFOLDING OF REASONING. 167
of equivocal terms (p. 82) or want of clear thought. In all cases the
middle term needs to be carefully examined in order to make sure that
it is used in precisely the same sense in both premises. Whenever it
is not so used the case is one of substantially four terms. E. g. »
" What we eat grows in the fields or is the flesh of animals ;
Cooked food is what we eat ;
/. Cooked food grows in the fields or is the flesh of animals."
This is a case of two middle terms. In one premise, " what we eat"
is used with reference to its mere essence ; in the other, with reference
to the accident or property of being cooked. This is the Fallacy of
Accident (Fallacia Accidentis).
Rule 2d. — The middle term must be distributed at least once. The
necessity for this arises from the fact that without it the major and
minor terms might be compared with different parts of the sphere of
the middle term, and so fail of being brought into logical connection.
E.g.:
All poets (P) are men (M) ; = A
All orators (S) are men (M). = A
We cannot infer that " All poets are orators," or that "Some poets
are orators," since the universal affirmative, A, does not distribute the
predicate (p. 115), which is here the middle term. Such conclusions
would result in the Fallacy of Undistributed Middle.
Rule 3d.— A term undistributed in the premises must not be dis-
tributed in the conclusion. Otherwise the conclusion would include
more than is involved in the premises. The violation of this rule is
called the Fallacy of Illicit Process. The fallacy may occur either
with the major term or with the minor.
Illicit Process of the Major Term.
All birds (M) are winged (P) ; = A
A bat (S) is not a bird (M) ; = E ($)
.'. A bat (S) is not winged (P). = E
The major term, " winged," is undistributed in the major premise
(A), and distributed in the conclusion (E). Hence the inference is not
valid, as may be seen from the above presentation of the relation of
the spheres of the notions.
Illicit Process of the Minor Term.
Persons without imagination (M) are not true poets (P) ; = E
Good logicians often (S) are without imagination (M) ; = I
.'. Good logicians (S) are not true poets (P). = E
168 PRACTICAL LOGIC.
In this case the word " often" makes the judgment equivalent to,
" Some good logicians are not true poets ;" while the universal neg-
ative conclusion denies of "all good logicians" that they are "true
poets."
Rule 4th. — The conclusion must always follow the weaker part.
By this is meant that, if one premise is negative the conclusion must
be negative, and, if one premise is particular the conclusion must be
particular. This does not need illustration.
It follows that universal conclusions can be reached only from uni-
versal premises. It will appear subsequently that universal conclu-
sions are not warranted in all cases by universal premises, since they
would often involve the fallacies of undistributed middle or of illicit
process.
Rule 5th. — No valid inference can be drawn where both premises
are negative. This follows from the Third General Principle. The
relation of the major and minor terms to each other is left wholly un-
determined by the form of the judgment.
Three cases come under this Rule : where both premises are universal neg-
ative ; where one is universal negative and the other particular negative ;
where both are particular negatives. The Rule, therefore, excludes, as invalid
in all instances, four of the sixteen possible combinations,— E E, E O, O E, 0 O,—
leaving only twelve possibly valid combinations.
A single illustration, coming under the first case, will suffice to assist the
student in presenting for himself in diagram the various forms which the in-
determinate relations of the major and minor terms may take.
No poets (P) are angels (M) ; No P is M ; = E
No men (S) are angels (M) ; NoSisM; =E
By the terms of the judgments both " poets" and " men " are excluded from
" angels," but they may stand to each other in any one of at least the five fol-
lowing relations (p. 40) : 1st. They may be independent or coordinate. 2d.
They may be coextensive. 3d. S may include P. 4th. P may include S. 5th.
S and P may intersect each other.
2
It will be found that, in the second and third cases of negative premises, the
possible relations of the terms become even more complicated.
Rule 6th. — No valid inference can be drawn where both premises
are particular. In such instances the precise connection of the spheres
of the major and minor terms with that of the middle cannot be deter-
mined from the form of the judgments.
THE UNFOLDING OF REASONING. 169
Three cases come under the Rule : where both premises are particular affir-
mative ; where one is particular affirmative and the other particular negative ;
where both are particular negative.
The first case, 1 1, will furnish a sufficient illustration.
Some poets (M) are intellectual (P) ; Some M is P ; =1
Some poets (M) are emotional (S) ; Some M are 8; •= I
In this case the " intellectual " and " emotional " poets might stand in either
of the following relations : 1st. They might exactly coincide. 2d. They might
wholly exclude each other. 3d. They might intersect each other, etc.
3
"f '" i \
etc.
The same indeterminateness, in the relation of the major and minor terms
to each other through the middle term, may be shown to exist in the other
cases. The third case is likewise excluded from valid syllogistic forms by the
Rule for negative premises.
The Rule, therefore, excludes three combinations not excluded by the pre-
vious Rule : 1 1, 1 O, O I ; leaving but nine possibly valid combinations.
Apparent Exceptions. — Two apparent exceptions to this Rule need
to be noted: first, syllogisms involving plurative judgments (p. 114);
secondly, those in which one or both of the premises are substitutive
judgments (p. 113). These are not, of course, strictly particular
judgments.
Plurative Judgments, whether indefinite or numerically definite, give
valid conclusions, as seen in the following examples :
Most men (M) are conceited (P) ; A Ignorailt 1 D
I r> L>
Conceited.
Most men (M) are ignorant (S) ; E Ignorant and conceited. | Q
/. At least some conceited men (S) are ignorant (P).
It is obvious in this case that " most men " in the major premise may coin-
cide more or less fully with "most men" in the minor, as illustrated in the
diagrams. In the first case, the line A C represents the " ignorant," B D the
" conceited," and AD" all men." The line B C represents the minimum of
agreement, in the given case, when the " ignorant" and " conceited" differ to
the utmost. In the second case, E F represents both the " ignorant" and the
" conceited," and EG" all men." The line E F represents the maximum of
agreement, when the "ignorant" and "conceited" agree to the utmost, i. e.,
coincide.
If this be given the numerically definite or proportional form, it may become
80 out of every 100 men are conceited ;
80 out of every 100 men are ignorant ;
:. At least 60 out of every 100 conceited men are ignorant.
15
170 PRACTICAL LOGIC.
In this instance the "80" of the major premise may agree more or less fully
with the " 80 " of the minor, as illustrated by the diagram. The minimum of
agreement, as shown in the following diagram, is D B, or 60 out of every 100 ;
the maximum, E F, 80 out of every 100.
Ignorant = 80 B Ignorant-conceited = 80
I I I I I I I I 1 I I I I I I I I I I I I I
A D | Conceited = 80 C E | F G
Substitutive Judgments, even when particular (Y), often result in
making conclusions valid that would be invalid if the premises were
mere particular attributives. Such judgments, whether universal or
particular, always distribute the predicate (p. 115). They are not, how-
ever, strictly particular judgments. For example :
Some trees (P) are (all the) oaks (M) ; = Y Some P is all M ;
Some oaks (M) are white oaks (S) ; = I or Y Some M is (all) S;
/.Some white oaks (S) are trees (P). = I .-. All S is P.
Eule 7th. — No valid inference can be drawn from the combination
of a particular major premise with a negative minor premise. This
will appear from the comparison of the spheres of the notions in the
four possible cases : IE; OE; 10; 00.
The Rule may be sufficiently illustrated by the first case, I E. The other
combinations have also been already excluded from the valid combinations,—
O E and O O by negative premises ; I O and O O by particular premises.
Some iron ores (P) are magnetic (M) ; = I
No lead ores (S) are magnetic (M) ; = E
It is not determined whether the sphere of S is quite separated from the sphere
of P, or intersects it, or falls wholly within it. If the attempt were made to
draw the conclusion, " No lead ores are iron ores," the negative would dis-
tribute the predicate, "iron ores" (P), which is not distributed in the major
premise, and would thus result in illicit process of the major term.
This Rule, therefore, excludes the combination I E, and leaves only eight out
of sixteen, which can be valid in any case. These may be stated (numbered
for convenient reference in treating the four Figures) as follows :
1. A A. 2. E A. 3. I A. 4. O A. Only part of the remaining eight will
5. A E. be found to hold true in any one of the
6. A I. 7. E I. Figures.
8. A O.
III. Special Canons of the Figures.
Each of the four Figures has its special rules resulting
from the relations of the terms, which may be embodied in
a Canon for that Figure.
1. Figure I. is that which has the middle term as the sub-
THE UNFOLDING OF REASONING. 171
ject of the major premise and the predicate of the minor.
There follows, from the resulting relations of the terms, —
Canon 1st. — In Figure I. the requirements are :
f Major prem. universal to avoid fallacy of undistributed middle;
1 Minor prem. affirmative to avoid fallacy of illicit process of maj. term.
Testing by this Canon the eight possible combinations left by the
General Rules, only six syllogistic forms are found valid in Figure
I.: AAA, AAI, EAE, EAO, All, EIO. These are reducible to four,
since AAI and EAO are but cases of particular or weakened conclu-
sions, included in the universals, AAA and EAE.
Note.— In this Figure the process of testing by the General Rules and the
Canon will be applied to the eight combinations successively, in order to pre-
pare the student to apply the like process to the remaining three Figures.
No. i, A A, by the successive addition of the four propositions, A, E, I, O,
gives AAA, AAE, AAI, AAO. The second and fourth of these forms, AAE,
AAO, drop out since the affirmative premises indicate agreement, while the
negative conclusion would infer disagreement. The third, AAI, is included
in AAA. Only one valuable form, AAA, remains. It conforms to the Canon,
since its major premise is universal and its minor premise affirmative, and the
syllogism thus guarded against fallacy. This valid mood is known among
logicians by the mnemonic word, Barbara, the meaning of the consonants in
which will be subsequently explained under Reduction. It is illustrated in
the following example :
2 All that is composite is dissoluble ; = A All M is P;
ja All material things are composite ; = A All S is M ;
« .-. All material things are dissoluble. = A /. All S is P.
No. a, E A, by the successive addition of the four propositions, A, E, I, O,
gives EAA, EAE, EAI, EAO. The first and third of these forms, EAA and
EAI, drop out, since the one negative premise always requires a negative con-
clusion by Rule 4th. The fourth, EAO, is included in EAE, drawing a partic-
ular conclusion when the universal is permissible. The valid mood, EAE, is
known among logicians by the mnemonic word, Celarent. It stands the test
of the Canon. It is illustrated in the following example :
No finite being is exempt from error ; = E No M is P ; ~
g All men are finite beings ; = A All S is M ;
"5 /. No man is exempt from error. = E .-. No S is P.
No. 3, 1 A, gives IAA, IAE, IAI, IAO, none of which are valid, since, besides
the breach of the General Rules, the particular major premise, I, violates the
Canon, and always results in undistributed middle.
No 4, OA, gives OAA, OAE, OAI, OAO, none of which are valid for the rea-
sons given under No. 3.
No. 5, AE, gives AEA, AEE, AEI, AEO, none of which are valid, since the
negative minor premise, E, violates the Canon, and results in illicit process of
the major term.
172 PRACTICAL LOO I C.
No. 6, A I. gives AIA, AIE, All, AIO. The first form, AIA, violates Rule
4th ; the second and fourth, AIE and AIO, violate the General Principle of all
affirmatives. The fourth, All, is valid, standing the test of the Canon. The
valid mood is known among logicians by the mnemonic word, Darii. It is
illustrated as follows :
X p
..: All virtues are laudable ; = A All M is P ;
£ Some habits are virtues ; = I Some S is M ;
Q .'. Some habits are laudable. = I /. Some S is P.
No. 7, E I, gives EIA, EIE, EII, EIO. The first, second, and third forms, EIA,
E1E, EII, violate Rule 4th. The fourth, EIO, is valid, standing the test of the
Canon. The valid mood is known among logicians by the mnemonic word,
Ferio. It is illustrated as follows :
g- No virtue is reprehensible ; = E No M is P ;
Some habits are virtues ; = I Some S is M ;
fe .-. Some habits are not reprehensible. = O .*. Some S is not P. x--^-K P
No. 8, A O, gives AOA, AOE, AOI, AGO, none of which are valid, since the
negative minor premise, O, violates the Canon.
The valid moods in Figure I. are Barbara, Celarent, Darii, Ferio.
The Figure is naturally and unconsciously used, according to Lambert,
to prove qualities. It follows from the " Dictum de omni et nullo."
2. Figure II, is that which has the middle term as the
predicate of both premises. There follows, from the result-
ing relations of the terms, —
Canon 2d. — In Figure II. the requirements are :
f Major prem. universal, to avoid illicit process of maj. term;
1 One prem. negative, to avoid undistributed middle.
Testing by this Canon the eight possible combinations left by the
General Rules, only six syllogistic forms are found valid in Figure
II. : EAE, EAO, AEE, AEO, EIO, AOO. These are reducible to four,
since EAO and AEO are but cases of particular conclusions, included
in the universals, EAE and AEE.
Leaving the student to test the various possible forms, it will be suf-
ficient to illustrate the valid moods by examples. The moods are
known among logicians as Cesare, Camestres, Festino, Baroko.
S Nothing material has free will ; = E No P is M ; HP J
g All spirits have free will ; =A AllSisM; ^~^l
<-> .-. No spirit is material. = E .-. No S is P. V f S
M ^^i=rf
Cesare is a valid mood, as is seen by its conforming to the Canon, in its uni-
versal negative major premise, E.
I
THE UNFOLDING OF REASONING. 173
All colors are visible ; = A All P is M ;
No sound is visible ; = E No S is M ;
/. No sound is a color. = E No S is P.
Camestres is a valid mood, since it conforms to the Canon in its universal
major premise, A, and negative minor, E.
S No vice is praiseworthy; =E NoPisM;
g Some actions are praiseworthy ; = I Some S is M ;
fa .-. Some actions are not vices. = O /. Some S is not P. VLV M
Festino is a valid mood, since it conforms to the Canon in its universal neg-
ative major premise, E.
5 All birds are oviparous ; =A AllPisM;
Jj Some animals are not oviparous ; = O Some S is not M .
m .*. Some animals are not birds. = O /. Some S is not P.
*r
Baroko is a valid mood, since it conforms to the Canon in its universal major
premise and negative minor.
Figure II. is naturally and unconsciously used, according to Lambert,
to prove di/erences. It follows from a "Dictum de diverse:" "Things
which are different do not belong to each other."
3. Figure III. is that which has the middle term as the
subject of both premises. There follows, from the resulting
relations of the terms, —
Canon 3d. — In Figure III. the requirements are :
( Minor prem. affirmative to avoid illicit process of maj. term;
\ Conclusion particular to avoid illicit process of min. term.
Testing by this Canon the eight combinations of premises, six are
found to be valid in this Figure: AAI, IAI, All, EAO, OAO,
EIO. These are known among logicians as Darapti, Disamis,
Datisi, Felapton, Bokardo (Dokamok), Ferison.
M
a All gilding is metallic ; =A AllMisP;
«g All gilding shines ; = A All M is S ;
Q /. Some things that shine are metallic. = I .'. Some S is P.
Darapti is a valid mood, since it conforms to the Canon, in its affirmative
minor premise, A, and its particular conclusion, I.
en
'g Some acts of homicide are laudable ; = I Some M is P
3 All acts of homicide are cruel ; = A All M is S ;
Q /. Some cruel acts are laudable. = I /. Some S is P.
* 15*
174 PRACTICAL LOGIC.
Disamis is a valid mood, since it conforms to the Canon, in its affirmative
minor premise, A, and its particular conclusion, I.
!» All acts of homicide are cruel ; " = A All M is P ;
^ Some acts of homicide are laudable ; = I Some M is S ;
/. Some laudable acts are cruel. = I .-. Some S is P.
CO
Datisi is a valid mood, since it conforms to the Canon, in its affirmative
minor, I, and its particular conclusion, I.
c"
Q
*£ No material substance is a moral subject; =E NoMisP;
.2 All material substance is extended; = A All M is S;
fit .'. Some extended thing is not a moral subject. = O/. Some S is not P.
Felapton is a valid mood, since it conforms to the Canon, in its affirmative
minor premise, A, and its particular conclusion, O.
d
"2 Some syllogisms are not regular ; = O Some M is not P
J4 All syllogisms are things important ; = A All M is S ;
ffl .'. Some important things are not regular. = O .'. Some S is not P.
Bokardo is a valid mood, since it conforms to the Canon, in its affirmative
minor premise, A, and its particular conclusion, O.
JNo truth is without result ; = E No M is P :
Some truths are misunderstood ; = I Some M is S ;
£ .'. Some things misunderstood are
not without result. = O /. Some S is not P.
Ferison is a valid mood, since it conforms to the Canon, in its affirmative
minor premise, I, and its particular conclusion, O.
Figure III. is naturally and unconsciously used, according to Lam-
bert, to prove examples and conceptions (concepts proper). He founds
it on a " Dictum de exemplo :" " When one finds things A which are B,
then there are A which are B."
4. Figure IV. is that which has the middle term as the
predicate of the major premise and the subject of the
minor. There follows, from the resulting relations of the
terms, —
Canon 4th. — In Figure IV. the requirements are :
C If either prem. neg., maj. prem. universal to avoid illic. major;
< If maj. prem. affirm., min. prem. universal to avoid undistrib. mid. ;
( If min. prem. affirm., conclusion particular to avoid illicit minor.
Testing by this Canon the eight combinations of premises, five are found to
be valid in this Figure : AAI, AEE, IAI, EAO, EIO. These are known among
logicians as Bram-antip, Camenes, Dimaris, Fesapo, Fresison.
THE UNFOLDING OF REASONING.
175
All greyhounds are dogs ; = A All P is M ;
All dogs are quadrupeds ; = A All M is S ;
Some quadrupeds are greyhounds. = I /. Some S is P.
Bramantip is a valid mood, since it conforms to the Canon, in its universal
minor premise, A, with particular conclusion, I.
All ruminating animals have four
stomachs ; = A All P is M ;
No animal with four stomachs is
carnivorous ; = E No M is S ;
No carnivorous animal ruminates. = E .'. No S is P.
Camenes is a valid mood, since it conforms to the Canon, in its universal
major premise, A, and its universal minor premise, E.
Some practically virtuous men are
necessarians ; — I Some P is M ;
•~ All necessarians speculatively sub-
vert the distinction of vice and
2 virtue; =A AllMisS;
.-. Some who speculatively subvert
" the distinction of vice and vir-
tue are practically virtuous. = I /. Some S is P.
Dimaris is a valid mood, since it conforms to the Canon, in its universal
minor premise, A, and its particular conclusion, I.
No negro is a Hindoo ; = E No P is M ;
All Hindoos are blacks ; - A All M is S ;
Some blacks are not ne-
groes.
= 0 /. Some S is not P.
Fesapo is a valid mood, since it conforms to the Canon, in its universal major
premise, E, its universal minor premise, A, and its particular conclusion, O.
No moral principle is an
animal impulse ; = E No P is M ;
•55 Some animal impulses are
principles of action ; = I Some M is S ;
^ /. Some principles of action
10 are not moral principles. = O .'. Some S is not P.
Fresison is a valid mood, since it conforms to the Canon, in its universal
major premise, E, and in its particular conclusion, O.
Figure IV. is the reverse of Figure I. It is naturally and uncon-
sciously used, according to Lambert, to prove reciprocities. He founds
it on a " Dictum de reciproco :" " If no M is B, no B is this or that M ;
if C is or is not this or that B, there are B which are or are not C."
176 PRACTICAL LOGIC.
IV. Collected Results.
For convenient reference the results of the testing of the
o
various forms may be gathered up and tabulated.
1. Table of Moods, Valid and Invalid.
•5i
*§,
£X
Conclu.
Moods.
Tested.
•s?|
Ȥ,
= i
S|
Conclu.
Moods.
Tested.
A
A
E
I
0
AAA
AAE
A AI
A AO
V. C. i.
I. C. 2. 3. 4.
I. P. 1.
y.c.2i(W).3.4.
L R I.
A
A
E
I
O
E A A
EAE
E AI
EAO
I. P. 2.
V. C. I. 2.
I. C. 3. 4.
I. P. 2.
V.cC.2(W,3.4.
E
A
E
I
0
AE A
AEE
AEI
ABO
I. P. 2.
V. C. 2. 4.
I. C. 1. 3.
I. P. 2.
V.C.2(W>4.(W).
I. C. 1. 3.
E
A
E
I
0
EEA
EEE
EEI
EEO
I. P. 3. R. 5.
I. P. 3. R. 5.
I. P. 3. R. 5.
I. P. 3. R. 5.
A
V,
AIA
AI E
I. R. 4.
I P 1 R 4
A
F
El A
E I E
I. P. 2. R. 4.
I R 4
I
I
O
All
AIO
V. C. i. 3.
I. C. 2. 4.
I. P. 1.
I
I
O
EH
EIO
I. P. 2.
V. C. i. 2. 3. 4-
A
V,
AO A
AO E
I. P. 2. R. 4.
I. R. 4.
A
F,
EGA
EOE
I. P. 3. R. 4.
. P. 3. R. 4. 5.
O
I
O
AOI
AGO
I. P. 2.
V. C. 2.
I. C. 1. 3. 4.
O
I
0
EOI
EOO
. P. 3. R. 5.
. P. 3. R. 5.
A
A
E
I
O
I A A
IAE
I AI
IAO
I. R. 4.
I. P. 1. R. 4.
V. C. 3. 4-
I. C. 1. 2.
I. P. 1.
A
A
E
I
O
O A A
O A E
OAI
OAO
. P. 2. R. 4.
.R.4.
.P. 2.
V. C. 3.
. C. 1. 2. 4.
E
A
E
I
O
I EA
IEE
IEI
IEO
I. P. 2. R. 4.
I. R. 4.
I. P. 2.
I. R. 7.
E
A
E
I
O
OE A
OEE
OEI
OEO
P. 3. R. 4. 5.
P. 3. R. 4. 5.
. P. 3. R. 5.
.P.3. R.4.5.
A
F
IIA
HE
I. P. 3. R. 6.
I. P. 1. 3. R. 4. 6.
A
F
OIA
O1E
. P. 2. 3. R. 4. 6.
. P. 3. R. 6.
1
I
O
III
HO
I. P. 3. R. 6.
I. P. 1. 3. R. 6.
I
I
O
Oil
OIO
P. 2. 3. R. 4. 6.
P. 3. R. 6.
A
F
IO A
I O E
I. P. 2. 3. R. 4. 5.
I P 3 R 4. 6.
A
F
OO A
OOE
P. 3. R. 4. 5. 6.
P. 3. R. 4. 5. 6.
O
I
O
101
IOO
I. P. 2. 3. R. 4. 6.
I. P. 3. R. 6.
O
I
O
001
OOO
P. 3. R. 4. 5. 6.
P. 3. R. 4. 5. 6.
Note.— In the column headed "Tested," V denotes valid; I, invalid; P,
principle; R, rule; C, both canon and figure; W, weak (indicating a partic-
ular conclusion where a universal might be drawn). The student will find
profitable exercise in applying the tests to all the forms and figures.
THE UNFOLDING OF REASONING.
177
2. Things Proved by the Figures.
Fig. Proved.
I. Attribute.
II. Difference.
III. Example.
IV. Eeoiprocity.
Process.
Ascribes to the thing what we
know of its attribute. It con-
cludes from the genus to the
species.
Leads to the discrimination of
things, and relieves perplex-
ity in our notions. Affords
only negative conclusions.
Affords examples and excep-
tions in propositions which
appear general. Gives only
particular conclusions.
Finds species in a genus in Bra-
mantip and Dimaris; shows
that the species does not ex-
haust the genus in Fesapo
and Fresison ; denies of the
species what was denied of
the genus in Camenes.
Dictum.
Dictum de Omni et
Nullo. What is
true of all A is
true of every A.
Dictum de Diverso.
Things which are
different are not
attributes of each
other.
Dictum de Exem-
plo. When we find
things A which
are B, in that case
some A are B.
Dictum de Recip-
roco. If no M is B,
no B is this or that
M ; if C is (or is
not)thisorthatB,
there are B which
are (or are not) C.
3. Valid Moods in the Four Figures.
The valid moods in all the Figures have been embodied in five Latin
hexameter lines :
Fig. 1. Barbara, Celarent, Darii, Ferio^we prioris;
Fig. 2. Cesare, Camestres, Festino, Baroko (or Fakofo), secundce;
Fig. 3. Tertia Darapti, Disamis, Datisi, Felapton,
Dokamok (Bokardo), Ferison habet. Quarto, insuper addit
Fig. 4. Bramantip, Camenes, Dimaris, Fesapo, Fresison.
V. Reduction of Figures.
Figure I. has been looked upon by logicians as the normal Figure,
to which all the others may be reduced. The object of Logical Reduc-
tion is to bring arguments of the last three Figures into the form of
Figure I., and thus bring all alike to the test of Aristotle's Dictum. It
is thus shown that this Dictum, which is clearly the regulating prin-
ciple in Figure I., is also the regulating principle in all deductive rea-
M
178 PRACTICAL LOGIC.
soning, and that the process is, therefore, always substantially the
same (p. 138).
Note.— Reduction is usually described as being of two kinds: Direct or Os-
tensive, and Indirect (Eeductio ad impossibUe). The latter method was the re-
sult of a mistaken notion of the logicians that Baroco and Bocardo could not
be directly reduced, and is of no value theoretical or practical. Fakofo and
Dokamok will be substituted for Baroco and Bokardo, and may be reduced
by the direct method.
The mnemonic words in the last three Figures were designed to in-
dicate not only the mood of syllogisms, but also the principles by which
they are to be reduced. The valid forms in the four Figures must be
kept in view in reduction.
The initial consonant, B, C, D or F, in the last three Figures indi-
cates the mood in the first Figure to which the syllogism reduces.
Thus, a syllogism in the mood Cesare, Fig. II., reduces to Celarent.
The inserted consonants, s, p, k, f, m, indicate the various processes
in reduction. S indicates that the proposition symbolized by the vowel
preceding it is to be converted simply (p. 127); p, by limitation or per
accidens (p. 127) ; k, by contraposition (p. 128) ; f, by infinitation or
obversion (p. 124). The letter m (mutari) indicates that the premises
of the given syllogism are to be transposed. The p in Bramantip
shows that, after converting simply, the premises warrant a universal
conclusion.
The other consonants, b, d, 1, n, r, t, a,re not significant, but are in-
serted for the sake of euphony, or of the metre in the mnemonic hex-
ameters invented, to keep the moods and figures in mind, by Petrus
Hispanus, who died in 1277 as Pope John XXII.
The process of reduction may be illustrated by the following examples:
Figure II. Figure I.
NoPisM; f NoMisP;
Cesare = ^ All S is M ; Celarent = \ All S is M ;
No S. is P. I .-. No S is P.
Bashfulness is not something thor-
oughly good ;
Modesty is something thoroughly
good;
/. Modesty is not bashfulness.
Nothing thoroughly good is bash-
fulness ;
Modesty is something thoroughly
good;
Modesty is not bashfulness.
The C in Cesare indicates that the mood reduces to Celarent ; the s, that the
major premise is to be converted simply.
Figure III. Figure I.
AllMisP; C AllMisP;
Darapti = -| AllMisS; Darii = j Some S is M;
, Some S is P. (. /. Some S is P,
THE UNFOLDING OF REASONING.
179
All whales are mammalia ;
All whales are water animals ;
Some mammalia are water animals.
All whales are mammalia ;
Some water animals are whales ;
.'. Some mammalia are water animals.
The D in Darapti indicates that the mood reduces to Darii ; the p, that the
preceding proposition, A, is to be converted by limitation.
Note.— The student can readily carry the work of reduction through all the
figures and moods.
Topic Third. — Complex and Abnormal Forms.
In books and in conversation arguments usually appear
in incomplete or irregular forms, and often combined as
polysyllogisms manifest or occult. In dealing with these,
the incomplete forms, except in the case of such regular
forms as the Sorites, need to be completed and the irreg-
ular forms reduced to regularity. The general rules then
become applicable.
The greater part of this work the student may be left to carry out
for himself by aid of the principles already laid down. There is need,
however, to present the principles which govern the Sorites, to con-
sider briefly some peculiar forms of argumentation, and to exhibit
especially the calculation of probabilities.
I. The Sorites Tested.
The Sorites, or chain of Enthymemes in Fig. I., has al-
ready been denned and illustrated (p. 143). There are two
ways of testing the Sorites : by completing all the abridged
syllogisms (p. 144), and then applying the usual tests ; or by
using a system of rules which may be immediately applied.
The former method may be left to the student himself ; only
the latter needs to be illustrated.
From the nature of the Sorites the following principles result :
1. The first proposition furnishes the major premise of the first com-
pleted syllogism ; the last proposition is the conclusion of the last syl-
logism and of the whole chain ; the intermediate propositions are the
minor premises of the successive syllogisms. The number of syllogisms
must, therefore, equal the number of minor premises.
2. The major premise of each successive syllogism after the first is
furnished by the conclusion of the preceding syllogism.
The reasoning must conform to the Canon of Fig. I.
180 PRACTICAL LOGIC.
Rule 1st. — Every major premise must be universal in order to avoid
undistributed middle. It follows that only the last proposition in the
progressive sorites and the first in the regressive may be particular, since
any other particular premise would result in making the conclusion
of its syllogism, or the next major premise, particular also.
Kule 2d. — Every minor premise must be affirmative in order to
avoid illicit process of the major term. It follows that only one
premise may be negative, the last proposition in the regressive sorites
and the first in the progressive, since these only are not minor premises.
The Sorites and its Rules may be illustrated by the following examples,
which are abridged to admit of compact parallel statement :
Regressive Sorites.
Some prosperous are avaricious ;
The avaricious are intent on gain ;
The intent on gain are discontented ;
The discontented are not happy ;
.*. Some prosperous are not happy.
Progressive Sorites.
No discontented are happy;
All intent on gain are discontented ;
All avaricious are intent on gain ;
Some prosperous are avaricious ;
, Some prosperous are not happy.
It has been often asserted that Sorites cannot occur in any other than Fig. I.
It has been shown, however, by Mill, that one step, and only one, step in a So-
rites may be either in Figure II. or Figure III.
II. Peculiar Forms of Argumentation.
The usual form of direct proof of propositions is known
among logicians as the argumentum ad rem, or proof of the
thing itself. As variations from it or in contrast with it may
be noted the argumentum a fortiori, the argumentum adjudi-
cium, the argumentum ad populum, the argumentum ad
verecundiam, the argumentum ad ignorantiam, the argumen-
tum ad homincm, and the reductw ad absurdum.
The argumentum a fortiori, or, " by a stronger reason," is one involving com-
parative judgments. It is based upon the maxim, " What is greater than a
greater is greater still than the thing." The argument is essentially mathe-
matical or quantitative. Thus :
Asia is larger than Africa ;
Africa is larger than Europe ;
.*. By much more is Asia larger than Europe.
This may also be presented as follows :
The Atlantic Ocean is as large as Lake Superior (and more) ;
Lake Superior is as large as the Dead Sea (and more) ;
.'. The Atlantic Ocean is as large as the Dead Sea (and still more).
The argument a fortiori is also denned as " the proof of a conclusion deduced
from that of a less probable supposition that depends upon it." For example,
see Matthew vi. 30 and vii. 11.
THE UNFOLDING OF REASONING. 181
The argumentum ad judicium is based upon the common judgments of man-
kind. Its maxim is, " What all men everywhere and always believe, is true,"
or the so-called principle of common sense on which the Scottish philosophy
of Reid rests. The argument has great force when it is really based on the
common judgment of mankind. The danger of appealing to this principle
without sufficient grounds is, however, very great. Under the confident asser-
tions, " Everybody says," " No one pretends to think," the greatest fallacies
are often covered. The argument may be illustrated as follows :
The material world is a reality and our perception of it immediate, because
all men, everywhere and always, have so believed.
The argumentum ad populum is based on an appeal to public opinion, or to
passion or prejudice, rather than intelligence. It is often employed because
no really good arguments are to be found, or because it is easier to appeal to
the passions and prejudices of the masses than to their intelligence. It often
puts forward as its major premise the false maxim, " Vox popuM Vox Dei,"
" The voice of the people is the voice of God."
The argumentum ad verecundiam is an appeal to the feelings of reverence
for certain persons or objects, instead of proceeding to prove the point in hand.
The Scholastics used as a standing major premise the maxim, " It is foolish to
affirm that Aristotle erred."
The argumentum ad ignorantiam is addressed to the ignorance of men. It
sometimes consists in assuming that a position is correct because an adversary
cannot show the contrary ; sometimes, in taking advantage of men's ignorance
to impose upon them by some shallow sophism, false statement, or confident
assertion.
Under this may be included the Fallacy of Interrogation, in which a question
is so put as to be equivalent to a confident assertion of some error. The de-
mand for an adequate conception (p. 91) or description, often made by a brow-
beating lawyer upon a witness in court, is of the same character. It is only a
few experts who can give anything more than a clear notion (p. 91) of the
handwriting, features, or dress of the most intimate friend.
The argumentum ad hominem is an appeal to the practice, principles or
professions of an opponent as confirming our own position or destructive to
his. An opponent may thus be silenced, since the argument is good against
him, even though it be not good against the views he advocates. As soon as he
renounces such practice, principles or professions, the argument ceases to be
of value as against him. Our Lord often used this method to silence the cavils
of the Jews ; for example, Matthew xxii. 41-45.
The reductio ad absurdum proves a proposition indirectly by proving the
absurdity of its contradictory. It has already been considered (p. 129).
III. Calculation of Probabilities.
The theory of probabilities, or of chances, as it is some-
times designated, has in recent times received increased
attention. In an elementary work there is only space for
the simplest rules and cases.
Thomson has described chance as " the amount of belief with which we
expect one or other, out of two or more uncertain events." Uncertain,
16
182 PRACTICAL LOGIC.
or merely probable, events are " those wherein no cause or law appears
to determine the occurrence of one rather than another." Jevons pro-
poses " to dispense altogether with this obscure word ' belief,' and to
say that the theory of probability deals with quantity of knowledge."
An event is merely "probable when our knowledge of it is diluted
with ignorance, and exact calculation is needed to discriminate how
much we do and do not know."
At the basis of the rules for the calculation of probabilities are the common-
sense principles which underlie all reasoning. " We must treat equals equally,
and what we know of one case may be affirmed of every case resembling it in
the necessary circumstances. The theory consists in putting similar cases on
a par, and distributing equally among them whatever knowledge we possess.
Throw a penny into the air, and consider what we know with regard to its
way of falling. We know that it will certainly fall upon a side, so that either
head or tail will be uppermost; but as to whether it will be head or tail, our
knowledge is equally divided. Whatever we know concerning head, we know
also concerning tail, so that we have no reason for expecting one more than
the other. The least predominance of belief to either side would be irra-
tional ; it would consist in treating unequally things of wkich our knowledge
is equal."
The Rules concern either simjda 9r combined probabilities.
Bale 1st. — A single probability of any uncertain event is ascer-
tained by dividing the number of chances favorable to the event by
the total number of chances favorable and unfavorable.
Thus the probability that the head will fall uppermost, when a penny is
thrown into the air, is expressed by ^. The probability that a man blind-
folded will draw a white ball out of an urn containing 2 white balls and 8
black ones is expressed by ^ or £. To take a different case, if the letters of the
word Roma are thrown down casually in a row. what is the probability that
they will form a significant Latin word ? The possible combinations of the
four letters are 4 X 3 X 2 X 1 = 24. If all the combinations are examined, 7 will
be found to have a meaning, namely, Roma, ramo, oram, mora, maro, armo, and
amor. Hence the probability sought is &.
Bule 2d. — The probability of the independent recurrence of an
event is found by multiplying together the fractions expressing the
single probabilities.
Thus the probability of throwing head twice with a penny is % X % = % :
the probability of throwing it three times is yz X Yz X Yz = Y& This Rule will
be seen to rest on Rule 1st, since the denominator represents the possible com-
b' nations in the case, or the whole number of ways of the happening of the
compound event, and the numerator the number of ways favorable.
Bule 3d. — " In order to calculate the probability that an event al-
ready observed will be repeated any given number of times, divide
the number of times the event has been observed, increased by one,
TEE UNFOLDING OF REASONING. 183
by the same number increased by one and the number of times the
event is to recur."
" Thus, if the tide had been observed 9 times, the chance that it would recur
10 times more would be f + j 0 +j = ^ — J. This is the same thinS as if
each reproduction of the observed event corresponded to putting a white ball
in an urn where there were already, before commencing the trials, a white
ball and as many black balls as it is supposed that the event observed should
re-occur times."
Two or more probabilities if mutually dependent weaken each other,
while if independent they strengthen each other.
Eule 4th. — In case of mutually dependent probabilities, or prob-
abilities of probabilities, the total probability is reached by multiply-
ing together the several single probabilities.
Thus, if the credibility (p. 105) of a witness be %, and his competency (p.
104), or ability to know the facts of which he testifies, be %, the total probabil-
ity of his telling the truth is % X % = § = Y& As certainty is represented by
unity, the testimony will, in this case, be twice as likely to be false as it is to
be true.
Kule 5th. — In case of independent probabilities the total probabil-
ity is reached by subtracting each separate probability from unity
(which gives the probability of the opposite event, in each case, or the
probability of a probability), multiplying the separate results together
(according to Rule 4th), and subtracting this product from unity
(thus arriving at the probability of the original compound event).
Thus, the total probability that the Gospels are true may be made up from
the probability arising from the character of the authors, represented by % .
from the absence of any motive on the part of the authors to fabricate such
accounts, represented by % ; from the influence of the Gospels themselves
upon the world, represented by $. Subtracting each of these from unity and
multiplying the results together, we have, as the probability of imposture,
1A X VA X \ = sV This subtracted from unity gives fg as the probability of the
truth of the Gospels.
Note. — See Thomson's Laws of Thought; Jevon's Principles of Science; New-
comb's Algebra.
Praxis. — In the following syllogisms show whether the premises
are true. Name the middle, minor, and major terms. Name the mood
and figure of each, showing whether valid or not. Reduce any mood
in the other Figures to Fig. I. Bring out the relation of reason and
consequent involved in connection with the middle term in each case,
substituting the letters, S, P, M, for the terms in the general formula,
and giving the relation of the notions by the circular notation.
1. No human weakness can belong to God ; some attributes imputed
184 PRACTICAL LOGIC.
to the Deity by mythology are human weaknesses ; hence (at least)
some attributes imputed to the Deity by mythology cannot belong to
Him.
2. Some who act in accordance with law do not do what is right
with right intention ; .*. some who act legally are not morally disposed.
3. Every real, natural poem is naive ; those poems of Ossian which
Macpherson pretended to discover are not naive (but sentimental) ;
hence they are not real, natural poems.
4. The sum total of the worlds belonging to our solar system must
completely determine the orbit of Uranus ; the known worlds of our
solar system do not fully account for the orbit of Uranus ; hence the
whole of the worlds of our so.lar system are not known.
5. Passive mental states make men neither noble nor base, worthy
of praise or of blame ; the virtues do this ; .*. the virtues are not pass-
ive mental states.
6. All squares are rectilineal plane figures ; some parallelograms
are squares ; /. some parallelograms are rectilineal plane figures.
7. No form of knowledge, which corresponds to a peculiar form of
existence, is of merely didactic value ; syllogism is a form of knowledge
which corresponds to a peculiar form of existence (viz., to the real con-
formability to law) ; hence the syllogism is not of mere didactic worth.
8. All cetaceous animals are water animals ; all cetaceous animals
are mammalia ; hence some mammalia are water animals.
9. Some persons accused of witchcraft have not believed themselves
to be free from the guilt laid to their charge ; all those accused of
witchcraft were accused of a merely feigned crime ; hence some who
were accused of a merely feigned crime have not believed themselves
free from the guilt laid to their charge.
10. Jubeo is not a verb sentiendi vel declarandi ; jubeo takes the con-
struction of the accusative and infinitive ; hence at least one or some
Latin verbs which take the construction of accusative and infinitive
are not verbs sentiendi vel declarandi.
11. All squares are regular figures ; some parallelograms are squares ;
.•. some parallelograms are regular figures.
12. Some parallelograms are squares ; all squares are regular figures;
.*. some regular figures are parallelograms.
13. All squares are parallelograms ; no parallelogram has converg-
ing opposite sides ; .*. no square has converging opposite sides.
14. Good non-conductors of heat retain heat longer ; woollen clothes
are good non-conductors ; .'. woollen clothes retain "heat longer.
15 Some things which retain heat longer are woollen clothes ; things
THE UNFOLDING OF REASONING. 185
which retain heat longer are good non-conductors ; .'. woollen clothes
are good non-conductors.
Supply the conclusions to each of the following pairs of premises,
and show whether the conclusion is valid, or why no conclusion can
be drawn. Treat the syllogisms as required in the preceding examples.
1. All good reasoners are candid ; some infidels are not candid ;
2. The ox, deer, sheep, goat, etc., are ruminant ; the ox, the deer,
etc., are as good as all horned animals ; .•
3. Oaks are vegetables ; oysters are not oaks ; .•
4. No good action results in evil ; some alms-giving results in evil ;
5. Animals are bodies having organization and sensation; frogs
have organization and sensation ; /
6. Some of our tax laws are oppressive measures; all oppressive
measures should be repealed ; .•
7. Reptiles bring forth their young by eggs ; the rat does not bring
forth its young by eggs ; /
8. The connection of soul and body is to be believed ; the connec-
tion of soul and body is incomprehensible ; /
9. True poets are men of genius ; very unwise men have proved
true poets ; .*
10. All good men are sincere ; Rousseau was sincere ; .•
11. Political Economy is a profitable study ; profitable study
sharpens the intellect ; .*
12. No truth is worthless ; many truths are misapplied ; /
13. Most people are careless ; most people are destitute of perfect
health; /
14. 90 out of every 100 men are imprudent ; 90 out of every 100
are unsuccessful ; .*. . '. . . .
15. Elephants are stronger than horses ; horses are stronger than
men ; /
Section II,— Unfolding of the Hypothetical Syllogism,
Hypothetical syllogisms have already been defined and
divided (pp. 144-146). They will now be considered in the
order of the division given.
Topic First — The Conditional or Conjunctive Syllogism.
The conditional syllogism may either be tested as it is,
186 PRACTICAL LOGIC.
or reduced to categorical form and then tested by the prin-
ciples of categorical reasoning.
I. The Tests of Conditional Syllogisms.
The tests of conditional syllogisms arise out of their na-
ture as directly embodying the principle of Reason and
Consequent. From this it follows that, if the reason be
present in any given case we may be sure of the presence
of the consequent ; and if the consequent be absent we may
be sure of the absence of its reason. Hence the two forms
of conditionals, the constructive and destructive, and the
Rules applicable to these forms of reasoning.
Bale 1st. — Affirming the antecedent or reason affirms the conse-
quent (modus ponens] ; while denying the consequent denies the ante-
cedent (modus tollens).
The first part of the Rule gives the constructive conditional, which
affirms the reason or antecedent, and then on the ground of this af-
firms the consequent. The second part gives the destructive condi-
tional, which denies the consequent, and on the ground of this denies
the reason. The two forms may be illustrated as follows :
.£ Antecedent. Consequent.
3 If General Grant has a fever, he is sick ; Major premise.
•g He has a fever ; (Modus ponens). Minor premise.
o •'. He is sick. Conclusion.
o
Antecedent. Consequent.
3 If General Grant has a fever, he is sick ; Major premise.
*j He is not sick; (Modus tollens.) Minor premise.
Q /. He has not a fever. Conclusion.
The absence of the particular reason or antecedent mentioned in any
given case does not render certain the absence of the consequent, since
antecedents or reasons are manifold and the consequent may follow
from other antecedents. So the presence of the consequent does not
argue the presence of a particular antecedent or reason, since it may
be the consequent or effect of some other antecedent. Hence
Rule 2d. — Denying the antecedent does not deny the consequent;
and affirming the consequent does not affirm the antecedent.
THE UNFOLDING OF REASONING. 187
Antecedent. Consequent.
{If there is fire in the stove ; the room will be warm ; Major premise.
There is no fire in the stove ; (Deny Ant.) Minor premise.
.• No conclusion.
If there is fire in the stove ; the room will be warm ; Major premise.
The room is warm. (Affirm Conseq.) Minor premise.
.• No conclusion.
In the case of the denial of the antecedent the conclusion that the
room will not be warm does not follow, since it may be warmed by a
grate, or a furnace, or steam apparatus, or a warm sun in summer, or
the presence of a large audience, or by being on fire, etc. In the case
of the affirmation of the consequent, the particular antecedent does
not follow, since the same thing may result from any one of the ante-
cedents enumerated.
The whole may be illustrated by diagram :
® Furnace. ~~ -- — '~^~^
Heated %
3 Steam.
I •• £pa
_*5b_ Room. I
The dotted lines may represent the possible lines of reason or causa-
tion ; the heated room, the consequent or effect. If the stove is pres-
ent, then the heated room will be present, because that is a sufficient
reason. If the stove is not present, the room may still be heated, since
the grate, furnace, etc., may furnish the sufficient reason. If there is
not the heated room, then all the antecedents must be absent, — stove, etc.
If there be the heated room, no definite a priori conclusion concerning
the agency of the stove is possible, since the consequent may result
from any other of the antecedents.
II, Reduction of the Conjunctive Syllogism.
The conjunctive or conditional syllogism may readily be
reduced to the categorical form, as already shown (p. 117),
188 PRACTICAL LOGIC.
and then tested by the Rules which apply to the various
Figures.
Applying the principles of reduction to the syllogism just given, it
becomes :
i st. The case of the presence of the heated stove is the case of a warm room ;
The present is the case of a heated stove ;
M* .'. The present is the case of a warm room.
gj Or A. : Every room in which a stove is heated is warm ;
£ A. This is a room in which a stove is heated ;
A. .*. This room is a warm room.
£ 2d. A. Every room in which the stove is heated is warm ;
3 E. This room is not warm ;
•£ E. /. The stove is not heated in this room.
£» 3d. A. Every room in which the stove is heated is warm ;
E. This is a room in which the stove is not heated ;
.5« E. .'. This room is not warm. (Not valid.)
M
This form corresponding to the denial of the antecedent, under Rule 2d, in-
volves illicit process of the major term.
u 4th. A. Every room in which the stove is heated is a warm room ;
3 A. This room is a warm room ;
•S? A. .*. This room is one in which the stove is heated. (Not valid.)
This form corresponding to the affirming of the consequent, under Rule 2d,
involves undistributed middle, or substantially four terms.
Topic Second. — The Disjunctive Syllogism.
The tests of the disjunctive syllogism arise out of the na-
ture of the disjunctive judgment, as embodying the prin-
ciple of Excluded Middle, in connection with Reason and
Consequent the principle of all reasoning.
A perfect disjunctive judgment embodies a complete division of some
genus or class, and the alternatives presented are the species under
that class, and are reciprocally exclusive (p. 71).
The major premise presents these species as alternatives.
The minor premise makes a categorical predication concerning one
or other of the species or alternatives.
The conclusion draws an inference concerning the other species.
Kule 1st. — See that the disjunction exhausts the division, and that
the disjunctives are reciprocally exclusive.
Kule 2d. — Affirming a part of the disjunctives, wholly or disjunc-
tively, in the minor premise, denies all the others in the conclusion.
THE UNFOLDING OF REASONING. 189
Rule 3d. — Denying a part of the disjunctives, in the minor prem-
ise, affirms the rest, in the conclusion, wholly or disjunctively, ac-
cording as one or more may remain.
These may be illustrated by the following examples :
The Apostles must have been fanatics, or impostors, or true men;
They were neither fanatics nor impostors ;
.*. They were true men.
The season of the battle of Lexington must have been spring, or summer, or
autumn, or winter ;
It was neither summer nor winter ;
/. It was either autumn or spring.
In the first example the character of the Apostles is analyzed into
three possible exclusive phases, and we affirm that if they do not be-
long to one or other of the first two they must belong to the third. In
the second example the seasons are analyzed into the four, and we af-
firm that since it was neither the second nor fourth it was one of the
other two.
Topic Third. — The Dilemmatic Syllogism.
The dilemma tic, or conjunctive-disjunctive, syllogism is
subject to the Rules of conditionals and disjunctives. The
most common forms are the following :
I. One Antecedent in the Major with Disjunctive Consequent.
This takes the form : If A is B, either C is D or E is F. By the
rules of conditionals and disjunctives we have the following possible
cases and results :
Affirm Antecedent. A is B ; /. either C is D or E is F.
Deny Cons, wholly. Neither C is D nor E F ; /. A is not B.
Deny Cons, disjunctively. Either C is not D or E is not F. No conclusion.
Denial of Antecedent. A is not B. No conclusion.
Affirmation of Consequent. C is D or E is F No conclusion.
II. Plurality of Antecedents in the Major with Common Consequent.
This takes the form : If A is B, X is Y, and if C is D, X is Y. This
gives the following oases and results :
Affirm Antec. wholly. A is B and C is D ; .-. X is Y.
Affirm Antec. disjunct. A is B or C is D ; .'.X is Y.
Deny Consequent. X is not Y ; .'. neither A is B nor C is D.
Deny Antecedents. A is not B nor is C D. No conclusion.
Affirm Consequent. X is Y. No conclusion.
III. Plurality of Antecedents in Major, each with its own Conse-
quent.
190 PRACTICAL LOGIC.
This takes the form : If A is B, C is D, and if E is F, G is H. This
gives the following oases and results :
Affirm Ant. wholly. A is B and E is F ; /. C is D and G is H,
Affirm Ant. di&junct. A is B or E is F ; .'. C is D or G is H.
Deny Cons, wholly. C is not D and C is not H ; /.A is not B and E is not F.
Deny Cons, disjunct. C is not D and G is not H ; /.A is not B or E is not F.
Deny Antecedent. A is not B and E is not F. No conclusion.
Affirm Consequent. C is D and G is H. No conclusion.
Note.— All the forms enumerated are called dilemmatic syllogisms, but. as
already stated (p. 146), the dilemma, in the strict sense, is only that form which
has a plurality of antecedents in the major, and a disjunctive minor. This
dilemma is sometimes rebutted by another with an opposite conclusion. Aris-
totle illustrates the process of rebuttal thus : " An Athenian mother said to her
son, ' Do not engage in public affairs ; for if you do what is just men will hate
you, and if you do what is unjust the gods will hate you.' This the son re-
butted by the following retort : ' I ought to enter into public affairs ; for if I do
what is unjust men will love me, and if I do what is just the gods will love
me.' "
Praxis. — In the following examples, complete the syllogisms if in-
complete. Name the kind in each case and formulate with letters and
illustrate by diagram. Test each example by the Rules.
1. If men are virtuous they are wise, and if they are vicious they
are unwise ;
But they are either virtuous or vicious ;
/. They are either wise or unwise.
2. If the classics teach how to produce wealth they ought to be
studied ;
They do not so teach ;
/. They ought not to be studied.
3. Mahomet was either an enthusiast or an impostor;
He was an enthusiast ;
/. He was not an impostor.
4. If there be no future life, then either virtue receives its due re-
ward in the present world, or there is no perfect government admin-
istered over men ; neither of which is admissible.
5. The fact that I defended him is a proof that I hold him innocent.
6. If pain is severe, it will be brief; and if it last long, it will be
slight ; hence it should be borne patiently.
7. If this man were wise, he would not speak irreverently of Scrip-
ture in jest, and if he were good, he would not do so in earnest ;
But he does it either in jest or in earnest;
THE UNFOLDING OF REASONING. 191
Section III.— Conspectus of Fallacies,
A fallacy is any unsound or delusive mode of reasoning.
The principal fallacies in induction and deduction need to be
particularized and distinguished.
In order to acquire a complete command of the principles of reason-
ing and to guard against error, the thinker must make himself familiar
with the most common kinds of fallacy. In the previous Sections, as
Jevons has said, " we have considered, as it were, how to find the right
road ; it is our task here to ascertain the turnings at which we are
most liable to take the wrong road."
Note.— With respect to the knowledge or intention of the reasoner, fallacies
have been divided into paralogisms and sophisms. A paralogism is a fallacy
which is unknown to the reasoner himself; a sophism is a false argument, un-
derstood to be so by the reasoner himself and intentionally used to deceive.
This is not, however, a logical distinction, since it is not based upon the thought,
but upon the mental and moral condition of the reasoner, and is, therefore, of
no logical value.
Topic First. — Fallacies in Induction.
In induction we deal with matters of fact. The require-
ments of induction are summed up in two things :
1st. Exact Observation of the facts.
2cL Correct Interpretation of the facts.
All fallacies in induction arise from failure to conform to
these requirements.
I. Fallacies from Failures in Exact Observation.
1. Neglect of observation, or ignoring of all facts (pp. 26-34, 148,
155).
2. Partial observation, giving incomplete view of the facts (pp. 33,
148, 155).
3. Neglect of exceptional, and especially contradictory, facts (p. 155).
4. Assuming what is not fact to be fact (pp. 33, 148).
5. Mixing illegitimate inferences with the facts (p. 33).
II. Fallacies from Failures in Correct Interpretation.
1. Neglect of all cause, or confounding induction with mere general-
ization (pp. 147, 153), including groundless universal conclusion from
few unimportant facts (fictce universalitatis) (p. 159).
2. Partial explanation of the facts, by assuming an improper or in-
sufficient cause, including:
192 PRACTICAL LOGIC.
(1.) Assuming inappropriate cause (p. 154).
(2.) Assuming inadequate cause (p. 154).
(3.) Assuming a single cause where there is a complex of causes (p. 154).
3. Neglect of real cause for hypothetical cause (p. 154).
4. Fallacy of unreal reason, or assuming what is not a cause to be a
cause (non causa pro causa) (p. 160), including:
(1.) Confounding antecedent and cause (post hoc ergo propter hoc) (p. 149).
(2.) Confounding concomitant, condition or occasion and cause (cum hoc ergo
propter hoc) (p. 149).
(3.) Confounding law and cause (p. 149).
Note.— The most noted forms of the fallacy of unreal reason are the lazy
reason (ignava ratio), the reaper (ratio mctens), and the controlling reason (ratio
dominans). These are all of the same character, and may be illustrated by an
example of the first, which gave it its name :
Sumption.—" If I ought to exert myself to effect a certain event, this event
either must take place or it must not;
Sub-sumption. — " If it must take place, my exertion is superfluous; if it must
not take place, my exertion is of no avail ;
Conclusion. — " Therefore, on either alternative, my exertion is useless."
In regard to the vice of this sophism, Krug, as quoted by Hamilton, says:
11 It is manifest that it lies in the sumption, in which the disjunct members are
imperfectly enounced. It ought to have been thus conceived : If I ought to
exert myself to effect a certain event, which I cannot, however, of myself
effect, this event must either take place from other causes, or it must not take
place at all. It is only under such a condition that my exertion can, on either
alternative, be useless, and not if the event depend wholly or in part for its
accomplishment on my exertion itself, as the conditio sine qua non."
This shows that this so-called syllogism formally violates Rule 1st under
disjunctives (p. 188), as applied to the dilemma.
5. Assuming unverified hypotheses as truth (pp. 156, 160).
Topic Second. — Fallacies in Deduction or Syllogism.
Deductive reasoning deals with truths or general princi-
ples. Its requirements are, therefore, summed up in two
things :
1st. Correct Matter or Thought, or the grasping of true
premises.
2d. Correct Form in Reasoning, or the proper unfolding
of what is contained in the premises.
All fallacies in deduction result, therefore, from failure to comply
with one or both these requirements. Those which result from some
failure in the matter or thought are known as Material Fallacies ;
those resulting from some failure in the form of reasoning are known
THE UNFOLDING OF REASONING. 193
as Logical or Formal Fallacies ; those resulting from failure in both
matter and form are known as Semi-Logical Fallacies.
I. Material Fallacies.
Material fallacies are those which arise outside of the
mere form of thought, or verbal statement (extra dictionem),
in the subject-matter or thought itself. They may take the
form of unwarranted assumption of premises, or of irrelevant
conclusion from the proper premises.
1. Unwarranted Assumption of Premises.
(1.) Begging the question (petitio principii), or virtual assumption
of the thing to be proved or of that by which it is to be proved. This
includes :
a. Petitio principii proper, where the assumption is openly made without
show of proof.
b. Arguing in a circle, where the conclusion is virtually used to prove the
premise.
E. g., John Knox and John Witherspoon are excellent men because they be-
longed to an excellent church, the Presbyterian Church ; and the Presbyterian
Church is an excellent one because it has contained such good men.
c. Assuming a resemblance without proving it, or where there is no such
resemblance (non tale pro tali).
E. g., «' All other religions are delusions ; therefore, Christianity is a delusion."
(2.) Failure in Estimating Probabilities.
a. Over-estimation of dependent probabilities (p. 182).
b. Under-estimation of independent probabilities (pp. 108, 188).
2. Irrelevant Conclusion from Proper Premises.
(1.) Fallacy from arguing to the wrong point. This is also called
ignoratio elenchi, or " ignoring the refutation," which refutation in-
volves the establishment of the contradictory (p. 129). This includes:
a. Perverted argument from common consent (argumentum ad judicium)
(p. 181).
b. Argumentum ad populum (p. 181).
c. Argumentum ad verecundiam (p. 181).
d. Argumentum ad ignorantiam (p. 181).
e. Argumentum ad hominem (p. 181).
(2.) Fallacy from simple Confusion of Thought. This includes:
a. Fallacy of accident (fallacia accidentis) and the converse (p. 167). This
includes :
(a.) Arguing from a general rule to a special case, where some accidental cir-
cumstance renders the rule inapplicable.
(b.) Arguing from a special case to a general one. This is described by the
17 N
194 PRACTICAL LOGIC.
Latin phrase, " a dicto secundum quid ad dictum simpliciter," meaning " from a
statement under a condition to. a statement simply or without that condition."
(c.) Arguing from one special case to another special case.
b. Fallacy of the consequent, or non sequitur, where the reasoning is so loose
and inconsequent that no one can discover any force in it.
c. Fallacy of many questions (plures interrogationum), which results from so
combining two or more questions that no true answer can be given to them.
II. Logical or Formal Fallacies.
Logical fallacies are those which occur in the mere form
of the statement (in dictione) . They may ordinarily be dis-
covered by the aid of the rules of deduction or the syllo-
gism, without any knowledge of the subject-matter of the
argument. They are violations of the Rules of Reasoning
categorical and hypothetical.
1. Fallacies in Categorical Reasoning.
(1.) Violation of the Rules for Terms.
a. Four Terms (quaternio terminorum). Breach of Rule 1st (p. 166).
b. Undistributed Middle. Breach of Rule 2d (p. 167).
c. Illicit Process of Major or Minor. Breach of Rule 3d (p. 167).
(2.) Violation of the Rules for Premises.
a. Failure of conclusion to follow weaker part. Breach of Rule 4th (p. 168).
b. Conclusion from two negative premises. Breach of Rule 5th (p. 168).
c. Conclusion from particular premises. Breach of Rule 6th (p. 168).
d. Conclusion from particular major with negative minor. Breach of Rule
7th (p. 170).
2. Fallacies in Hypothetical Reasoning.
(1.) Violation of Rules for Conditionals.
Conclusion from denying antecedent or from affirming consequent.
Breach of Rule 2d (p. 186).
(2.) Violation of Rules for Disjunctives.
a. Confounding partitive and disjunctive judgments (p. 118).
b. Disjunctive elements not exclusive and inclusive. Breach of Rule 1st
(p. 188).
c. Conclusion not in accordance with the affirmation or denial of disjunction.
Breach of Rules 2d and 3d (pp. 188, 189).
III. Semi-Logical Fallacies.
Semi-logical fallacies are fallacies partly material and
partly formal.
These fallacies arise largely from the ambiguous use of terms. In
such cases the term used in two senses is substantially equivalent to
THE UNFOLDING OF REASONING. 195
two terms. The ambiguity must first be detected by examining into
the meaning of the terms. The fallacy is so far material. When the
ambiguity is fairly detected, the fallacy is at once transformed into the
formal or logical fallacy of four terms. It includes :
1. Fallacy of Equivocation, consisting in the use of the
same word in two distinct senses.
(1.) Fallacy of ambiguous middle (p. 82).
(2.) Fallacy of homonymous terms (p. 83).
2. Fallacy of Amphibology, consisting in ambiguous gram-
matical structure of a sentence.
E. g., " The Duke yet lives that Henry shall depose."
3. Fallacy of Composition and Division, arising from using
a term distributively (pp. 112, 115) in one premise, and col-
lectively (pp. 54, 113) in the other.
This is especially common in the use of " all" (p. 113), " not all" (p. Ill), etc.
4. Fallacy of Etymology. This includes :
(1.) Fixing upon a wrong root (p. 76.)
(2.) Assuming that the original meaning of the root of a word de-
cides the present meaning of the word (p. 76).
Note.— For enumerations of the sources of human error, see Bacon's Novum
Organum, Lib. i. ; Mill's Logic, Book V., ch. ii. ; Hamilton's Logic, Lect. xxiii.
Praxis. — Examine the following arguments, completing them if in-
complete, and reducing to regular form if irregular. Examine and de-
fine the important conceptions or terms. Name the kind of argument
in each case, formulating with letters and illustrating by diagram.
Present the proof of the premises. Test each example by the Rules,
naming and explaining the fallacy, material, logical or semi-logical,
wherever such fallacy exists. If categorical, reduce to Fig. 1.
1. A science which furnishes the mind with a multitude of useful
facts deserves cultivation; but Logic is not such a science; .•. Logic
does not deserve cultivation.
2. Nuisances are punishable by law ; to keep a noisy dog is a nui-
sance ; .*. to keep a noisy dog is punishable by law.
3. Twice two and three are seven; twice two and three are ten;
/. seven is equal to ten.
4. If motion is possible, a body must move either in the place where
it is, or in a place where it is not ; but a body cannot move in a place
196 PRACTICAL LOGIC.
where it is, and of course it cannot move where it is not ; /. motion is
impossible.
5. What you bought yesterday you eat to-day ; you bought raw
meat yesterday ; /. you eat raw meat to-day.
6. The Jews are avaricious; .'. the prophet Daniel was avaricious.
7. All bodies that move themselves are animated ; the stars move
themselves ; /. the stars are animated.
8. Mouse is a syllable ; but a mouse eats cheese ; .'. a syllable eats
cheese.
9. If it be fated that you recover from your present disease, whether
you call in a doctor or not you will recover ; again, if it be fated that
you do not recover from your present disease, whether you call in a
doctor or not you will not recover ; But one or other of the contra-
dictories is fatal ; .'. To call in a doctor is of no consequence.
10. Episcopacy is of Scripture origin; the Church of England is
the only episcopal church in England ; .*. the Church established is
the Church that should be supported.
11. Carbon is combustible ; diamonds are composed of carbon ;
/. diamonds are combustible.
12. Rain has fallen, if the ground is wet; but the ground is not
wet ; .*. rain has not fallen.
13. None but mortals are men ; monarchs are men ; .'. monarchs
are mortals.
14. Logic as it was cultivated by the Schoolmen proved a fruitless
study ; .-. Logic as it is cultivated at the present day must be a fruit-
less study.
15. Men can live without animal food, and they can live without
vegetable food, as has been often demonstrated ; but all food is either
animal or vegetable; /. men can live without food.
16. All birds are animals ; no reptiles are birds ; .*. no reptiles are
animals.
17. He who is most hungry eats most; he who eats least is most
hungry ; /. he who eats least eats most.
18. If rain has fallen, the ground is wet ; but rain has not fallen ;
.*. the ground is not wet.
19. Night must be the cause of day, for it invariably precedes it.
20. If Brandreth's pills are of any value, those who take them will
improve in health ; my friend who has been taking them has im-
proved in health ; /. they are of value.
21. He that can swim needs not despair to fly ; for to swim is to fly
in a grosser fluid, and to fly is to swim in a subtler.
THE UNFOLDING OF REASONING. 197
22. The ground is wet, if rain has fallen; the ground is wet; /. rain
has fallen.
23. All stars are self-luminous ; all planets are not self-luminous ;
/. no planets are stars.
24. Some flowers are tulips ; all flowers are beautiful ; /.all the tu-
lips are beautiful.
25. The probability of the existence of a God, derived from the ex-
istence of the universe, may be stated as f ; from order in the universe,
f ; from conscience, f ; from common belief of mankind, f, etc. These
all fall far below unity or full proof ; .'. the proofs of the existence of
a God are insufficient to warrant belief.
26. If the books in the Alexandrine Library be in conformity with
the doctrines of the Koran, there is no need of them ; if adverse, then
also they should be burned.
27. If the ground is wet, rain has fallen ; but rain has fallen ; /. the
ground is wet.
28. The hope of immortality is either a rational expectation or an
illusion ; but that belief cannot be an illusion which all the most en-
lightened peoples have adopted.
29. Personal deformity is an affliction of nature ; disgrace is not an
affliction of nature ; /. personal deformity is not disgrace.
30. No idle person can be a successful writer of history ; .*. Hume,
Macaulay, Hallam, and Grote must have been industrious.
31. Bacon was a great lawyer and statesman ; and as he was also
a philosopher, we may infer that any philosopher may be a great
lawyer and statesman.
32. Nothing is better than wisdom ; dry bread is better than noth-
ing; .'. a fortiori is dry bread better than wisdom.
33. If classical education is worth the cost, either it must be pre-
eminently fitted to develop the mental powers, or it must furnish ex-
ceedingly valuable information ; but neither alternative can be main-
tained, and so classical education is not worth the cost.
34. Men love to be humbugged ; the President of the Bible Society
is a man ; /.he loves to be humbugged.
35. All power proceeds from will as its antecedent ; a steam-engine
has no will ; /. it has no power.
36. What produces intoxication should be prohibited ; the use of
spirituous liquors produces intoxication; .'. the use of spirituous
liquors should be prohibited.
37. All the trees in the park make a thick shade ; this tree is one
of them ; .'. this tree makes a thick shade.
198 PRACTICAL LOGIC.
38. The object of war is durable peace ; /. soldiers are the best
peacemakers.
39. Improbable events happen almost every day ; but what happens
almost every day is a very probable event; .'. improbable events are
very probable events.
SUMMARY OF RESULTS.
THE aim of the Logic of Reasoning is, in general, to train
to the best thinking and fullest appreciation of thought in its
third form. The perfection of thinking as reasoning depends
upon the degree of certainty that the right cause or mid-
dle term has been fixed upon. As the finished result of Con-
ception is clear and distinct thinking, and that of Judg-
ment connected thinking, so that of Reasoning is continuous
thinking.
The conclusions from induction are probahle truths (judg-
ments, p. 132), varying in probability all the way from mere
hypotheses to perfected theories. The conclusions from
deduction are always certain truths (judgments, p. 132)
when the premises are certain and the reasonings correct,
and probable truths when the premises are only probable.
The special aim of the Practical Logic of Reasoning
should be to train the thinker to the highest degree of
skill and certainty in using the various processes of induc-
tion and deduction in his own thinking, and to the greatest
readiness and accuracy in grasping and testing these pro-
cesses and their products as they are presented in the think-
ing of others.
PART IV.
THE LOGIC OF CONSTRUCTION OR THE SYSTEM.
THE aim of the Logic of Construction should be to train
the student to skill in dealing with the Fourth Form of
Thought.
Definition. — Construction is that higher form of thought
in which we combine mutually related products of the lower
forms of thought, according to some rational principle, into
one relatively complete whole (pp. 11-13). The product
of construction is known as the System.
Ueberweg defines system as "the orderly combination of mutually-
related knowledge into one relatively complete whole." System is
either mechanical or rational. Rational system is that in which the
combination is a result of the application of some rational principle ;
mechanical system, that in which such rational principle is wanting.
The alphabet, as arranged in the order, a, b, c, etc., is a mechanical
system ; as arranged in classes, — as vowels, semi-vowels, and conso-
nants; or tonics, subtonics, and atonies, — it is a rational system.
There are three forms of rational system : scientific system ; artistic
system ; practical system. These all imply orderly arrangement, but
they differ in the law by which that arrangement is effected ; that of
scientific system being according to the law of the true ; that of artistic
system according to the law of the beautiful ; that of practical system
according to the law of the good.
In scientific system the aim is to combine the related thoughts in
199
200 PRACTICAL LOGIC.
such a way that the totality will exactly express the truth and the
whole truth. It is, therefore, said to be governed by the Law of the
True. In artistic or aesthetic system the aim is to combine the related
truths in such a way as to produce a totality which will express di-
versity in unity, or beauty. It is, therefore, said to be governed by
the Law of the Beautiful. In practical system the aim is to combine
forces and agencies as means so as to secure a whole by which some
desired end or good may be secured. It is, therefore, said to be gov-
erned by the Law of the Good.
Artistic or aesthetic system belongs to ^Esthetics ; the other forms
may be regarded as properly belonging to Logic (p. 12), and will be
briefly considered.
Constructive thinking is manifestly the highest act of the
human intellect, and should, therefore, be made prominent
in the later stages of higher education. The formation and
unfolding of systems will be briefly treated in successive
Chapters.
CHAPTER I.
THE FORMATION OP CONSTRUCTION
OR SYSTEM.
AN understanding of the combination of mutually related
thoughts into systems, by the constructive faculty, must
prepare the way for unfolding and testing such systems.
The process and the products will be considered briefly
under each of the forms of construction.
Section I,— Scientific Construction.
Scientific construction is construction according to the
law of the true. Its product is Scientific System.
Topic First. — Process of Forming and Verifying Scien-
tific System.
Three things are essential in thinking in the form of
scientific system : First, fixing upon some one sphere of
THE FORMATION OF CONSTRUCTION. 201
mutually related thoughts, or thoughts constituting a whole ;
secondly, maintaining logical consistency in the joining of
all the parts under this whole ; thirdly, verifying the agree-
ment of the resulting combination, in its parts and as a
whole, with the entire reality of the sphere which is being
systematized.
These give the Laws of Scientific Construction ; the Laws
of Logical Unity or Logical Totality ; of Logical Consis-
tency ; and of Logical Truthfulness.
I. The Law of Logical Unity or Totality.
The unity and totality of a system are determined by
this, that all the individual thoughts contained in it depend
on a common principle. A principle, in this sense, has been
defined as " an absolutely or relatively original element on
which a series of other elements depends." It is the unify-
ing thought which binds together the otherwise disconnected
and unorganized mass of thoughts. Hence arises
Rule 1st. — Seek a principle which will bring the thoughts to be
systematized into unity under one sphere or whole.
The Law of Totality may also be presented as the Law of Numer-
ical Completeness, which requires that a scientific view of any region
of fact or truth shall present all the essential facts and truths, none
added and none omitted. Any so-called science, e.g., astronomy, may
be rendered so far false by an addition to the facts or truths or sub-
traction from them.
Various principles, or points of view, may be made use of in system-
atizing any region of truth. The sphere may thus be enlarged or
diminished. For example, the astronomer may aim to present the
astronomy of the solar system or of the universe ; he may give his
work a mathematical or a descriptive form ; he may present the solar
system and universe as they are, or treat them historically, giving the
stages in their development.
II. The Law of Logical Consistency or Correlation.
The logical consistency of a system requires the proper
joining or correlation of all the parts under the whole or
202 PRACTICAL LOGIC.
totality. All the truths combined should be in their proper
relation to each other.
The main relations to be kept in mind in such work are those of
substance and properties, as brought out under Observation (p. 29) ;
those of content of concepts (p. 40) and extent of concepts (p. 45) ;
those of reason and consequent, as involved in induction and deduc-
tion (pp. 138-9). There should be perfect accuracy of thought in all
the parts and relations of the system. Hence arises
Rule 2d. — See that all the parts are properly joined or articulated
under the one whole.
Any science, e. g., zoology, may be rendered false by any departure
from the facts or laws of succession ; or from the relations of co-ordina-
tion, subordination, etc., brought out by logical and scientific division;
or from the relations of reason and consequent, as involved in induc-
tion and deduction.
III. The Law of Logical Truthfulness.
The logical truthfulness of a system requires that the
entire system so constructed shall, in all its parts and as a
whole, be in accordance with the reality, or the entire
sphere or whole which is being systematized. This con-
formity with the reality is the crucial test of a system.
From it arises
Rule 3d. — Test the system of thought constructed by the reality
which it represents.
In any scientific system any want of conformity to the sphere of
reality renders the system so far false. Imaginary schemes, such as
the scheme of organized being as unfolded by Haeckel in his History
of Natural Evolution, have no claim to the name of scientific system.
Topic Second. — Products of Scientific Construction.
Systems, as the products of scientific construction, are
either absolutely or relatively complete.
Scientific System has sometimes been confounded with systems of
classes (p. 44), but it is manifest that these merely form one of the
elements used in constructing scientific systems. Science is used in
various senses: "exact knowledge;" "classified knowledge;" etc.
Ueberweg defines it as a " whole of knowledge in the form of the sys-
THE FORMATION OF CONSTRUCTION. 203
tern," in which sense it is substantially equivalent to scientific system.
According to this view, " scientific knowledge finds its perfection in
the combination of thoughts, one with the other, into a whole, which
in its content and form represents the objective reality." " Science as
such has its true existence only in the systematic form."
I. Relatively Complete System.
The Sciences, as we find them, usually deal with some
relative whole and not with the entire universe of truth.
They are inductive, deductive, or mixed, according to the
method of thought employed.
1. The inductive sciences result from the employment of the induc-
tive method of thought.
The Inductive Method involves three elements :
First, The scientific investigator starts with matters of fact.
Secondly, In reaching the materials for the science, he makes use
of the principles of inductive reasoning chiefly.
Thirdly, These materials are given their proper systematic form by
the principles of scientific construction (p. 201). Its steps are, as has
been seen (pp. 148-9, 200-3) : exact observation, correct interpreta-
tion, and scientific construction. The product is a system of thought
wrought out from the facts.
2. The deductive sciences result from the employment of the deduc-
tive method of thought.
The Deductive Method involves three elements :
First, The scientific investigator starts with ideas or relations of
ideas.
Secondly, In gathering the materials for the science he makes use
of the principles of deduction chiefly.
Thirdly, These materials are given their proper systematic form by
the same general principles of scientific construction made use of in
the inductive method.
Its steps are, therefore : proper grasp of truth, or right judgments or
general principles ; correct unfolding of truth ; and scientific construc-
tion of the results.
In it induction may be used in subordination whenever matters of
fact are incidentally taken into account.
The product is a system of thought unfolded from fundamental
thoughts or truths.
2(M PRACTICAL LOO I C.
3. The mixed sciences arise from the joint employment of the in-
ductive and deductive methods. This results from the presence of
both facts and truths, both of which need to be wrought into the sys-
tem. Astronomy furnishes an illustration of mixed scientific method.
II. Absolutely Complete System.
The absolutely complete science deals with all things, or
the universe. It aims to construct the universal scientific
system and the universal philosophy, both of which are in-
cluded under complete scientific system in the wide sense.
Herbert Spencer distinguishes between knowledge, science, and phil-
osophy as follows : " Knowledge of the lowest kind is ununified knowl-
edge ; science is partially unified knowledge ; philosophy is completely
unified knowledge." The distinction usually made between science
and philosophy is as follows : science deals with facts and their order,
or with the " what;" philosophy deals with general principles and rea-
sons, or the " why." It is impossible, however, to have any science so
completely empirical as not to involve more or less of the principles
or reasons of things, and equally impossible to have any philosophy
so entirely transcendental as not to embrace a solid basis of fact or
reality. In the highest sense science, as scientific system, embraces
both facts and their reasons, both the "what" and "the why," or
both science proper and philosophy.
1. The Complete Science. — Great thinkers have sought to
construct the one universal scientific system, and with va-
rious success. The system of Comte may be presented as
one of the best.
Comte starts with the suggestion of Descartes, that " sound knowledge
should advance from the simpler to the more complex phenomena." In
this suggestion "-lay the germ of a sound arrangement of the sciences,
which scarcely, however, seems to have begun to bear fruit before the
time of Ampere and Comte." Thomson, in his Laws of Thought, pp.
316-319, has presented the system drawn from Comte in brief form.
«' Mathematics, or the science of quantity, is at once the most simple in its
elements and the most general in its application, entering more or less into all
the sciences of nature, and constituting almost the whole of that which comes
next it in the order of dependence. Astronomy, or the science of the heav-
enly bodies, is the application of mathematical truths to the laws of matter
and motion, matter and the motions of material bodies being the new concep-
THE FORMATION OF CONSTRUCTION. 205
tion which belongs to this science. Physics, being the science, or rather group
of sciences, which is conversant with the general laws of the world so far as
they relate to beings without life or organization, would come next ; and it
imports, in addition to the conceptions of Astronomy, those of light, of heat,
of sound, of electricity, of magnetism, and many others. Chemistry would
rank next, which is the science of the decomposition and combinations of
the various substances that compose and surround the earth. Next in order
of complexity would rank Physiology, founded on the additional conception
of vegetable and animal life. To this would succeed Anthropology, or the
science of man's nature ; and to this Social Science, which ascertains the laws
that govern men when combined in cities and nations.
Each of these departments may be divided into many branches, as Physics
into Acoustics, Optics, Electricity, and the like ; or Social Science into Morals,
Politics, Political Economy, Law, and the like There is a
general correspondence between this classification and the order in which the
various objects of science came into being. The heavenly bodies were first
appointed their paths in the celestial spaces ; then the surface of our earth
was prepared for living creatures ; then they were created after their kind,
and man the last. The social life of man grew up last of all, when his race
was multiplied on the globe ; and ever as new elements appear, the conditions
of society are being modified even to the present time."
We are now in a position to sketch the table of the Sciences.
"CLASSIFICATION OF THE SCIENCES.
Group. Mode of Treatment.
1. MATHEMATICS Theoretical. Historical. Applied.
II. ASTRONOMY " " "
III. PHYSICS •• "
IV. CHEMISTRY " " "
V. PHYSIOLOGY " •*
VI. ANTHROPOLOGY M " "
VII. SOCIAL SCIENCE " M "
RELIGIOUS PHILOSOPHY."
2. The Complete Philosophy. — Thinkers have also aimed,
in dealing with the question " Why?" to construct the uni-
versal philosophic system, and with equally various success.
The common-sense philosophy may be accepted as the best.
The philosopher must seek to give a rational explanation of the ul-
timate facts to which all scientific investigation of phenomena leads.
These ultimate facts are three : consciousness ; the cosmos of matter
and spirit ; the being back of all on which all depends. A complete
18
206 PRACTICAL LOGIC.
philosophy must, therefore, have its psychological theory, its cosmo-
logical theory, and its ontological theory. The three are embraced in
THE COMMON-SENSE PHILOSOPHY.
I. PSYCHOLOGICAL THEORY.. ..Consciousness is made up of two ele-
ments of knowledge: experience
and intuitioji.
II. COSMOLOGICAL THEORY The Cosmos is made up of two ele-
ments: spirit and matter.
III. ONTOLOGICAL THEORY The Ultimate Being, or First Cause
of the Cosmos, is the infinite, per-
sonal Spirit, God.
Section II,— Practical Construction,
Practical construction is construction according to the
law of the good. Its product is Practical System.
Topic First. — Process of Forming and Verifying Practical
System.
Three things are essential to thinking in the form of prac-
tical construction : First, the intelligent fixing upon some
one complex plan or aim ; secondly, the careful preparation
or gathering of ideas and forces which will serve as means
to this end; thirdly, the best arrangement and adjustment
of the means to secure the end in view. These give the
laws of practical aim, practical adaptation, and practical
unity.
I. The Law of Fraotical Aim.
Practical aim in constructive thinking requires that the view be
fixed upon some beneficent, useful, rational, or moral end to be attained.
Hence arises
Rule 1st. — Fix upon and define clearly in the mind the end to be
attained.
II. The Law of Practical Adaptation.
Practical adaptation in constructive thinking requires that all the
material made use of be such, and only such, as is suited to secure the
proposed end. Hence arises
THE UNFOLDING OP SYSTEMS. 207
Rule 2d. — See that the suitable means are provided for attaining
the proposed end.
III. The Law of Practical Unity.
Practical unity in constructive thinking requires that all the means
be combined, arranged, and adjusted in such system as best to secure
the end proposed. Hence arises
Rule 3d. — See that the means are properly correlated so as to
secure the proposed end.
Topic Second. — Products of Practical Construction.
The Laws of Practical Construction govern in the pro-
duction of all inventions, ideals, plans of life, etc. Success
in life depends largely upon the possession of this power in
proper development.
One of the highest forms of practical construction is found in oratory,
in which the aim is to arrange thought in such a system as shall induce
a change of view, of judgment, of feeling, or of purpose in an audience.
Illustrations will suggest themselves to the teacher and student.
For the purpose of directing in the work, a few examples will suffice.
Praxis. — Study as practical systems: 1. A steam-engine. 2. A
telephone. 3. A plough. 4. The speech of Daniel Webster, in the
trial of John Francis Knapp, for the murder of Joseph White. 5.
The oration of Demosthenes on the Crown.
CHAPTER II.
THE UNFOLDING AND TESTING- OF SYSTEMS.
THE best use of the power of construction in the work of
thinking requires that the thinker should be able to grasp
and unfold what may be contained in any system, and to
test such system by the principles of construction, scientific
and practical.
For the purposes of the brief discussion here proposed, the two forms
of logical system need not be separated. Two things are of prime
importance: first, the ascertaining of the elements of systems, and
secondly, the testing of systems.
208 PRACTICAL LOGIC.
Section I,— Ascertaining the Elements,
The elements of any system may be learned from the
Laws of Construction. In unfolding scientific constructions
(to which attention will be confined) three things are
embraced : First, the grasping of the totality involved in
the system ; secondly, the study of the relations of the parts
or the articulation of the system ; thirdly, the comparison
of the system with the objective reality. The careful study
of these elements is requisite to prepare for the testing of
systems.
Topic First. — The Whole and its Principle.
In studying any system it is necessary first to seize upon
it as a whole by ascertaining the principle which unites its
elements.
A system is " an organized body of truth, or truths arranged under
one and the same idea, which idea is as the life or soul which assim-
ilates all those truths." In studying and unfolding any system, it is,
therefore, necessary to inquire first for this organic idea or principle,
which is the soul of the system. This holds in all three forms of sys-
tem, scientific, aesthetic, and practical.
Trendelenburg distinguishes " systems of arrangement," correspond-
ing to systems of classes (p. 47); and "systems of development,"
corresponding to the products of scientific construction (p. 202).
The former arise under Conception, by Classification or Division ; the
latter, under Reasoning, by Induction and Deduction. The former
take the form of the descriptive, classificatory, or natural history
sciences, — as Botany, Zoology, etc. ; the latter, of explanatory natural
and mental sciences, — as Physics, Chemistry, Psychology, etc.
The principle or organic idea in systems of classes, is simply the
principle of classification (p. 47) or division (p. 68), which has already
been considered. E. g., in Zoology the system of the animal kingdom
is a system of classes and sub-classes, based on plan of organic structure.
The principle or organic idea in the higher form of system, or sys-
tem in the stricter sense, is the central truth to which the inductive
method leads, and with which the deductive method starts out.
Accordingly, Ueberweg has said : " The principles of knowledge are of two
kinds, according as the individual or particular, or the universal, serves as the
THE UNFOLDING OF SYSTEMS. 209
starting-point of knowledge. The former do not correspond to the real prin-
ciples, but form the natural foundations of propaedeutic knowledge; the
latter distinctly correspond to real principles and, accordingly, form the
foundations of strictly scientific knowledge.
"The propaedeutic or method of investigation proceeds regressively or
analytically to the knowledge of real principles ; the purely scientific or con-
structive method proceeds progressively or synthetically from principles to
particulars or individuals. But it is by no means always desirable, in an
exposition of the sciences, to thoroughly separate the analytic from the
synthetic elements. Both are often to be combined with each other in the
treatment of individual problems."
The construction and value of a system will, therefore, manifestly depend,
in any given case, first of all, upon the correctness and completeness of the
principle which unites its parts into a whole. Hence, in examining systems,
Rule 1st. — Ascertain the principle or organic idea of the system.
In a system of Ethics the idea of right or virtue is the principle.
In the Moral System of the universe the idea of right as embodied in
the control of the Moral Governor is the principle.
Topic Second. — The Articulation or Relation of the Parts.
In studying any system it is necessary, in the second place,
to seize upon the relations of the parts to each other.
Every truth has relation to some other. In a system the various
connections of related truths are brought out. Bishop Butler says,
in his Sermons : " A System, Economy, or Constitution, is a one or a
whole, made up of several parts, but yet the several parts even con-
sidered as a whole do not complete the idea, unless in the notion of a
whole you include the relations and respects which these parts have
to each other."
The relations of the thoughts to each other, in any system, may in-
clude any or all the possible relations of conception, judgment and
reasoning. The aim in all systematic knowledge is " to unite the facts
of knowledge so as to see them in their several bearings." Hence
Rule 2d. — See that the parts of the system are logically connected
throughout.
Topic Third. — The Relation to the Objective Reality.
In studying any system, it is necessary, in the third
place, to compare the thought-system with the reality
which it represents.
18* O
210 PRACTICAL LOGIC.
"System applies not only to our knowledge, but to the objects of
our knowledge. Thus we speak of the planetary system, the muscu-
lar system, the nervous system. We believe that the order to which we
would reduce our ideas has a foundation in the nature of things. And
it is this belief that encourages us to reduce our knowledge of things
into systematic order."
The final test of the correctness of any system must be found, there-
fore, in its exact truthfulness. Hence arises
Bule 3d. — See that the system agrees exactly with the reality.
Section II,— Testing of Systems.
As the highest process in the formation of thought is the
construction of systems, so the highest process in the un-
folding of thought is the testing of systems.
The possibilities and dangers of error have been seen to be very
great in Conception, Judgment and Reasoning, but they must evi-
dently be as much greater in Systematizing, as this form of thought
is higher and more difficult than the others. Mohammedanism and
Buddhism in religion, Epicureanism and Utilitarianism in morals, and
numberless other systems in all departments of thought, maintain their
hold upon mankind simply because of the inability of the masses of
mankind to ascertain their elements and put the systems themselves
to the test.
Some examples of the testing of systems will best illustrate the kind
of work to be done in order to avoid error. In a text-book of the
scope of the present, it is impossible to find space for presenting such
examples in detail. The work must, therefore, be confined to giving
directions for testing systems, and referring the teacher and student
to examples of such testing to be found elsewhere.
Topic First, — Directions for Testing.
The first inquiry, resulting from the carrying out of Rule
1st, is, What is the organic thought or principle which holds
together the parts of the system ?
The second inquiry, resulting from Rule 2d, is, Are the
parts logically connected ?
The third inquiry, resulting from Rule 3d, is, Does the
system of thought agree with the facts or the reality ?
THE UNFOLDING OF SYSTEMS. 211
Archbishop Whately has clearly marked out the course to be pur-
sued in testing a system of argument. We quote his directions, which
are as follows :
" First, then, of whatever length the reasoning may be, whether treatise,
chapter, or paragraph, begin with the concluding assertion,— not necessarily
the last sentence expressed, but the last point established,— and this, whether
it be formally enunciated or left to be understood. Then, tracing the reason
backwards, observe on what ground that assertion is made. The assertion
will be your Conclusion ; the ground on which it rests your Premises. The
whole Syllogism thus obtained may be tried by the rules of Logic.
" If no incorrectness appear in this syllogism, proceed to take the premises
separately, and pursue with each the same plan as with the conclusion you
first stated. A premise must have been used as such, either because it required
no proof, or because it had been proved. If it have not been proved, consider
whether it be so self-evident as to have needed no proof. If it have been
proved, you must regard it as a conclusion derived from other assertions
which are premises to it, so that the process with which you set out will be
repeated, viz., to observe on what grounds the assertion rests, to state these
as premises, and to apply the proper rules to the syllogism thus obtained.
Having satisfied yourself of the correctness of this, proceed, as before, to state
its premises, if needful, as conclusions derived from other assertions. And
thus the analysis will go on (if the whole chain of argument be correct) till
you arrive at the premises with which the whole commences, which of course
should be assertions requiring no proof; or, if the chain be anywhere faulty,
the analysis will proceed till you come to some proposition, either assumed as
self-evident though requiring proof, or incorrectly deduced from other asser-
tions." See Whately's Logic, pp. 418, 419.
Topic Second. — Examples Illustrative.
The teacher of Logic will be able to furnish illustrations
of this subject in every department of thought.
I. Familiar Subjects.
The tests should be applied first to familiar subjects.
These are found in the text-books of Arithmetic, Geography,
Physical Geography, Grammar, Rhetoric, Psychology, Ethics,
etc., used in the study of these various departments.
One of the most important and useful of all mental processes is that
of studying and grasping a science in its entirety as a system. It
trains all the mental faculties, — simple cognition, memory, compar-
ison and construction. Until a science is so grasped, it is not in any
proper sense mastered, since the main thing in a science is not its sep-
arate facts and truths, but its whole of related facts and truths.
212 PRACTICAL LOGIC.
The best preparation for grasping and testing large and complex
systems of thought is secured, by constantly training the student to
analyze, outline, and test the parts and chapters of the text-books
used.
II, More Difficult Subjects.
The logical training of the young is not, however, com-
plete until this process of testing has been extended to more
difficult and abstruse subjects. The following illustrations
of such testing, found in various works, — some of which at
least will be within the reach of every teacher of Logic, —
may be of service. The illustrations may be extended at
pleasure by the teacher.
1. Analysis of Part First of Paley's Evidences of Christianity. See
Whately's Logic, Appendix III., pp. 421-427.
2. Mill's Criticism of the Theistic Argument for a First Cause, in
Three Essays on Religion. Criticised in Princeton Review, September,
1878, Article "John Stuart Mill and the Destruction of Theism."
3. Herbert Spencer's First Principles. Criticised in The Philosophy
of Herbert Spencer, by Professor Borden P. Bowne ; and in Mr. Spen-
cer's Formula of Evolution, by Malcolm Guthrie.
GENERAL SUMMARY.
THE last aim of all training in thinking should be to pre-
pare for and lead to constructive thinking. The safe con-
duct of life, in the largest and best sense, will depend upon
the thinker's power to know in system, — that is, to distin-
guish between true systems and false systems, as presented
by others, and to construct true systems scientific and prac-
tical for himself. To help to prepare man intellectually
for such conduct of life should be the aim of the Practical
Logic of Construction.
INDEX.
Absolute, terms = non-relative, 55 ;
being, 28.
Abstract, or abstract notion, 31.
Abstraction, 31.
Accident, separable and inseparable,
29.
Accidental definition = description,
76.
Added determinants, 126.
Additions, inference by, 126.
Adequate knowledge, 91 ; perfectly
and practically, 91.
A dicto secundum quid, 193.
Affirmative propositions or judg-
ments, 111.
Ambiguity, of terms, 82 ; of negative
particles, 111; of all, some, etc., 113;
fallacy from, 195 ; sources of, 82.
Amphibology, fallacy of, 195.
Ampliative judgments, 99.
Analogy, 137, 158.
Analysis, logical, 58; two kinds, 58.
Analysis! phyqiralt 32; ™onfa^ ft2j_y
^Analytic judgment, 99.
Antecedent, 117; not cause, 150.
Argument, as middle term and cause,
138.
Argumentum, ad ignorantiam, 181 ; ad
hominem, 181 ; adjudicium, 181 ; ad ver-
ecundiam, 181 ; a fortiori, 180.
Argumentum ex concesso, a proof
derived from a proposition already con-
ceded.
Aristotle's Dictum, 138.
Art, definition, 14.
Artificial Classification, 42, 65.
Assertion == a statement or proposi-
tion, affirmative or negative, 92.
Association, ambiguity from, 82.
Assumption, any proposition taken
for granted as the basis of an argu-
ment ; unwarranted, 193.
Attribute, 28 ; term, 54 ; proved, 177.
Attributive, term = connotative term,
54; judgment, 113.
Authority, defined, 105; competency
of, 104 ; credibility of, 105 ; concurrence
of, 106.
Axioms of Logic, 18.
Baconian Method, or inductive
method, 148.
Barbara, Celarent, etc., 177.
Base, logical, 64.
Begging the question, 193.
Belief, 16 ; see Probability. •
Calculation of Probabilities, 181 ;
overestimation in, 193.
Canons, of Inductive Method, 149 ; of
syllogism, 170-175.
Canons of Syllogism, 170.
Categorematic words, 54.
Categorical, propositions, 117; syllo-
gisms, 141 ; syllogisms tested, 162.
Categories, 27 ; Aristotle's, 30.
Cause, 149, 86 ; in induction, 138 ; test,
153; complex, 154; hypothetical, 152.
"Aristotle distinguished four kinds
of causes for the existence of a thing.
— 1. The Material Cause, the sub-
stance or matter composing it; 2.
The Formal Cause, the pattern, type,
or design, according to which it is
shaped ; 3. The Efficient Cause, the
force employed in shaping it ; 4. The
Final Cause, the end, motive, or pur-
pose of the work."
213
214
INDEX.
Chain syllogisms, 143.
Chance, definition, 181.
Changes, in meaning of words, 82;
periodic, 151.
Characteristics = marks or proper-
ties, 28.
Circulus, in definiendo, 86 ; inprobando,
193.
Classes, single, 42 ; systems of, 42 ; ex-
tent of, 44 ; relations of, 44 ; distinc-
tions arising from, 45.
Classification, process, 41 ; rules, 42 ;
results, 44; special relations from, 45 ;
artificial and natural, 65, 42.
Clearness of knowledge, 90.
Cognition or knowing, 10.
Collective terms, 53; undistributed,
113.
Colligation, definition by, 79.
Comparison, faculty of, 12 ; of objects,
34; of notions or terms, 92; of judg-
ments, 134; by similar properties, 34.
Compatible terms, 55.
Complex, concept, 35 ; proposition, 119 ;
syllogism, 142.
Complex conceptions, development
of, 121.
Composition of Causes, in complex
cause, 154.
Composition, fallacy of, 195.
Compound, proposition, 119; syllo-
gism, 142.
Comprehension of terms, 39.
Concept proper, 37 ; rules for form-
ing, 37, 38; distinctions, 39; relation
to class, 47.
Conception, definition, 12, 25 ; forma-
tion of, 25 ; unfolding of, 56 ; elements
of, 26 ; proper, 34 ; products, 56 ; logical
quality, 90.
Conclusion, of syllogism, 138; false,
141, 193 ; weakened, 171 ; from plura-
tive judgments, 169; principles govern-
ing, 166; from substitutive judgments,
170.
Concrete terms, 53.
Concurrence, of testimony and au-
thority, 106.
Condition, 149.
Conditional, propositions or judg-
ments, 47 ; syllogisms, 145, 185.
Confusion of words, sources of, 81.
Connotation of terms, 54.
Consequence = the connection be-
tween the antecedent and consequent.
Consequent, reason and, 20 ; fallacy of
the, or non sequitur, 194 ; in conditional
propositions, 117 ; as effect of cause, 20.
Consilience of Inductions = " the
agreement of inductions derived from
different and independent series of
facts, as when we learn the motion of
the earth by entirely different modes of
observation and reasoning."— Whewell.
Consistent terms = compatible terms.
Conspectus, of relations of concepts,
40 ; of relations of classes, 45 ; of judg-
ments, 115; of grammatical proposi-
tions, 116 ; of opposing judgments, 131 ;
of figures of syllogism, 163 ; of moods,
176 ; of things proved by the figures,
177 ; of valid moods, 177 ; of fallacies,
191.
Construction, Logic of, 199-212.
Content, of concepts or terms, 39.
Contradiction, law of, 18; of judg-
ments, 129.
Contradictory, terms, 55; proposi-
tions, 129; opposition, 129.
Convergent evidence, 106.
Converse fallacy, of accident, 193.
Conversion of propositions, 126;
simple, 127 ; by limitation, 127 ; by con-
traposition, 128; by opposition, 128.
Convertend, 126.
Coordinate, conceptions, 44 ; proposi-
tions, 119.
Copula, 94.
Criterion = of truth, 15.
Cross division, 69.
Data, the facts from which a conclusion
is to be drawn, 147.
Declaration, 75.
Deduction and Induction, 136.
Deductive or Combined Method,
203.
De facto = what actually or really
happens, as opposed to de jure, what
ought to happen by law or right.
Definition, 75 ; rhetorical, 75 ; etymo-
logical and by word analysis, 76 ; loose,
77 ; logical, 75, 77 ; perfect, 78; of class
terms, 78; of attribute terms, 78; im-
perfect, 79 ; extended, 79 ; nominal, real
and genetic, 80 ; rules, 81.
Demonstrative judgments, 131.
Demonstrative, or absolutely conclu-
sive, proof, analytic, 101; intuitive,
103; indirect, 129.
INDEX
215
Denomination, or naming, 49 ; pro-
cess and modes, 49 ; rules, 50 ; products
of, 52.
Denotation of terms = extent, 44.
Depth of a notion ; see Content.
Description, or accidental definition,
76.
Destructive conditional syllo-
gism, 186.
Diagrams, of content, 40 ; of extent,
45; of opposition, 129; of syllogism,
167-175.
Dichotomy, 65.
Differences and resemblances, 41.
Differentia, or specific difference, 46.
Dilemma, 145; rules of, 189.
Dilemmatic, judgments, 118; syllo-
gisms, 145, 189.
Discovery, or investigation, method of,
209.
Discursive faculties, 11.
Disjunction, inference by, 126.
Disjunctive, propositions, 117 ; distin-
guished from partitive, 118 ; converted,
118; syllogisms, 145, 188.
Distinct knowledge, 90.
Distribution of terms, 111-113; rules,
115.
Division, logical, 57, 64 ; principle of,
64; forms, 65; dichotomous, 66 ; natu-
ral, 67 ; rules, 68.
Divisions of Logic, 22; principle of,
24.
Doubt = hesitation between various
views, 181.
Empirical judgments and proofs, 103.
Enthymeme, 142.
Epichirema, 142.
Episyllogism, 142.
Equivocal terms, 82.
Equivocation, sources of, 82 ; fallacy
of, 195.
Essence, 29.
Essential propositions — explica-
tive, 99.
Euler's Notation, 45.
Evidence = any facts apprehended by
the mind and made the grounds of
knowledge and belief. As testimony
and authority, 103; convergent, 106.
Exceptional facts, 155.
Excluded middle, law of, 19.
Exhaustive division, 70.
Experience, 16, 103, 147.
Experimentum crucis, 156.
Experts, definition, 104.
Explanation of facts, in induction,
148, 155.
Explicative propositions, 99.
Extension, or extent, 44 ; relations of
to content, 48.
Extensive Syllogism, 163.
Extremes, or terms, of a proposition,
52,94.
Fact, or phenomenon, 148.
Faculties, of intellect, 12, 72 ; discur-
sive, 13.
Fallacies, classification of, 191 ; in in-
duction, 159, 191 ; in deduction, 192 ;
material, 193; logical or formal, 194;
semi-logical, 194.
False cause, 160, 192.
Figures of speech, in definition, 87.
Figures, of the syllogism, 162 ; canons
of, 170.
Forms of thought, 11.
Fundamental principle of syllo-
gism, 138.
Fundamentum divisionis, or prin-
ciple of division, 68.
General, notion, 44 ; term, 53.
Generalization, 41 ; as product of in-
duction, 157 ; false, 159 ; mere, 154.
Genus, 46.
Grammatical combination of propo-
sitions, 118.
Grammatical sentences, 116; co-
ordination of, 119; subordination of,
119.
Hamiltonian Notation, 163.
Hearsay, definition and value, 104.
Homonymous terms, 83.
Hypothesis, finding the working, 147;
testing, 153.
Hypothetical, propositions, 117; syl-
logisms, 144, 185.
Identity, law of, 18 ; of concepts, 39.
Ignoratio Elenchi, 129, 193.
Illative Conversion, 126.
Illicit Process, of the major term, of
minor term, 167.
Immediate inference, 134.
Imperfect figures, of the syllogism,
177.
Imperfect induction, 157.
216
INDEX.
Inconsistent propositions = con-
tradictory, 129.
Inconsistent terms, or incompatible
terms, 55.
Indefinite use of some, 114.
Indirect demonstration, 129.
Indirect reduction, 178.
Individual, 46.
Induction, 136; unfolded, 147; pro-
ducts of, 157; perfect and imperfect,
158; fallacies in, 159, 191 ; true, 156.
Inductive syllogism, 157 ; guess, 156.
Inference, mediate and immediate, 134.
Infima species, 46.
Infinitation, judgments from, 124.
Inseparable accident, 29.
Instances, exceptional, 155.
Intellect, faculties of, 13, 72.
Intension, 39.
Intensive syllogisms, 163.
Intention, first and second. " Of the
first intention are the names of things,
a man, stone, etc. ; of the second are the
names of names and species, as univer-
sal, particular, genus, species, syllogism,
and the like."— Hdbbes. Terms of the
second intention express the mode in
which the mind regards or classifies
terms of the first intention.
Intuitive knowledge, 31.
Inversions restored to normal form,
95, 111.
Irrelevant conclusion, 193.
Judgment, definition, 12, 92; forma-
tion of and elements, 93 ; primitive and
logical, 97 ; of extent and content, 97 ;
impersonal, 98; verification or proof,
98; analytic and synthetic, 99 ; intui-
tive and empirical, 101 ; products, 110 ;
quality, quantity, relation, and modal-
ity, 110; normal forms, 114; categor-
ical and hypothetical, 117; unfolding
of, 121; contained, implied, and in-
ferred, 121 ; conversion of, 126; demon-
strative, assertory, and problematic,
131 ; of observation, 97.
Language, its relation to thought, 50 ;
ambiguities of, 81 ; in definition, 85.
Law, 149.
Law of thought, special and general,
17; fundamental, 18; of Identity, 18;
of Contradiction, 18 ; of Excluded Mid-
dle, 19 ; of Sufficient Reason, 20.
Limitation, conversion by, 127.
Logic, definitions, 8 ; practical aim, 13;
postulates, 21 ; divisions, 22.
Lowest species, 46.
Major term, 137; premise, 138.
Many questions, fallacy of, 194.
Material fallacies, 193.
Mediate inference, 134.
Members of division, 70.
Metaphysical division = Logical
Partition, 57.
Method, logical, 23.
Methods of indviction, agreement,
149; difference, 150; concomitant vari-
ations, 151 ; residual variations, 151.
Metonymy = transfer of meaning, 82.
Middle term, 137.
Minor term, 137 ; premise, 138.
Miracles, credible, 107.
Mnemonic verses, 177.
Modal propositions = those assert-
ing that the predicate does or does not
belong to the subject, with an intima-
tion of the mode or manner.
Modality of judgments, 110, 131.
Modus, ponens, 186; lollens, 186.
Moods of the syllogism, 164 ; valid and
invalid, 176.
Names or terms, notative and symbol-
ical, 50 ; systems of, 51 ; positive and
non-positive, abstract and concrete, 52 ;
singular and universal, 53; attribute
and class, connotative and non-conno-
tative, simple and complex, categore-
matic and syn-categorematic, 54 ; rela-
tive and non-relative, compatible and
incompatible, 55 ; univocal and equiv-
ocal, 82 ; homonymous, 83.
Natural Classification, 65, 42.
Negation, conversion by, 128.
Negative, term, 52; definition, 87;
judgment, 111 ; copula, 111 ; premises,
168 ; conclusion, 166 ; testimony, 104.
Nominal definition, 80.
Non causa pro causa, 192.
Non sequitur, 194.
Notion, 39 ; simple, 31 ; identical and
different, congruent and conflictive,
contrary and contradictory, 39 ; con-
tent of. 39.
Novum Organum, aim of, 148.
Numerically definite, judgment,
114; syllogism, 169.
INDEX.
217
Object, 28.
Objective, 28.
Obscure knowledge, 91.
Observation, definition, 26, 148; dis-
tinguished from experiment, 148 ; in-
struments and forms of, 26 ; objects of,
27 ; processes and products, 31 ; exact,
32 ; rules, 33.
Occasion, of an event = condition,
149.
Occult forms of syllogism, 143.
Opposite terms = different or con-
flictive,39.
Opposition of propositions, inference
by, 128.
Paralogism =» purely logical fallacy,
191, 194.
Parity of reasoning, used to denote
that when one case has been demon-
strated, other similar cases can be dem-
onstrated by a like course of reason-
ing.
Particular premises, 168 ; fallacy of,
194.
Particular propositions, 113.
Partition = metaphysical division,
57.
Partition, logical, 57; matter of, 57;
forms, 59 ; rules, 60 ; physical, 31.
Partitive judgments, 118.
Per accidens, conversion, 127.
Percept, 31.
Perfect figure, of the syllogism =
Figure I., 177.
Perfect knowledge, by conception,
90 ; by judgment, 131 ; by reasoning,
198 ; by construction, 212.
Periodic changes, 151.
Petitio principii, 193.
Phenomenon, 148.
Philosophy, definition, 204 ; complete,
205.
Physical definition = statement of
physical parts.
Plurative propositions, 114; syllo-
gisms, 169.
Polysyllogism, 142.
Polytomy, 68.
Porphyry, tree of, 66.
Positive terms, 52.
Post hoc, ergo propter hoc, 192.
Postulates of Logic, 21.
Predicables, 27; scheme of, 30; use
of, 30 ; observation of, 30.
19
Predicaments = Categories.
Predicate, quantified, 164.
Premise in reasoning, 138.
Principle, of division, 64 ; of system,
208.
Privative conception, inference by,
124.
Privative, terms, 52.
Probability, degrees of, 108 ; the guide
of life, 108 ; calculation of, 181 ; in in-
duction, 158; overestimation and un-
derestimation of, 193.
Problem =* an assertion put forward for
proof or dis-proof.
Proof of judgment, 98 ; analytic, 100 ;
synthetic, 101; intuitive, 101; empir-
ical, 103 ; from testimony and authori-
ty, 103.
Proper names, 53.
Property, definition, 28; kinds, 27;
distinguished from attribute, quality,
etc., 28 ; intrinsic and extrinsic, 28 ; es-
sential and non-essential, 28 ; peculiar,
29; accidental, 29.
Propositions, or judgments, classifica-
tion of, by quality, 111; by quantity,
112 ; by relation, 116 ; by modality, 131 ;
by grammatical form, 118 ; by source
of predicate, 99.
Prosyllogism, 142.
Proximate genus, 47.
Quantification of predicate, 164.
Quantity of propositions, 112.
Quaternio termiiiorum, 166, 194.
Ratiocination =» Syllogism or Deduc-
tion.
Reason = middle term, 139 ; lazy and
controlling, 192.
Reason and Consequent, principle
of, 20 ; forms of, 20.
Reasoning, logic of, 134-198.
Reductio, ad absurdum, 129, 181 ; ad
impossible, 178.
Reduction, of figures, 177; of con-
junctive syllogisms, 187.
Relation = any connection in thought
or fact between things. Category or
properties of, 27.
Relative terms, 55.
Residues, method of, 151.
Rules, of observation, 33 ; of concept-
forming, 37 ; of classification, 42 ; of
naming, 50 ; of partition, 60 ; of divi-
218
INDEX.
sion, 68 ; of definition, 81 ; of intuition,
102; of testimony and authority, 104;
of obversion, 124 ; of illative conver-
sion, 126 ; of illative opposition, 129 ; of
verifying deduction, 139 ; of induction,
148; of hypothesis, 153; of categorical
syllogism, 166 ; of sorites, 179 ; of cal-
culating probabilities, 182 ; of condi-
tional syllogism, 186; of disjunctive
syllogism, 188 ; of forming system, 201 ;
of testing system, 209.
Science, definition, 13, 204 ; complete,
204; practical, 14.
Semilogical fallacies, 194.
Sentence, grammatical forms, 118.
Separable accident, 29.
Signs of judgments, universal, 113;
particular, 113 ; approximately univer-
sal, 114.
Similars, grasped in conception, 35.
Simple, apprehension, 31 ; conversion,
127.
Singular, terms, 53 ; judgments, 113.
Sophism, 191.
Sorites, or chain syllogism, 143; classi-
fied, 144; tested, 179.
Specialization, or deduction, 136.
Species, in Logic, 46 ; in Natural His-
tory, 46 ; distinctions of, 46-48.
Subaltern, genera and species, 46;
propositions, 129.
Subalternans, subalternates, 129.
Subcontrary, 129.
Subject, 28; and predicate, 94; naked,
127.
Subjective, 28.
Subordinate, genera and species, 47 ;
propositions, 129.
Substance, definition, 28; properties
of, 28.
Subsumption = bringing a special case
under the general rule or law ex-
pressed in the major premise or sump-
tion, 192.
Sufficient Reason, law of, 20; basis
of reasoning, 138.
Summum genus, 46.
Sumption = major premise, 192.
Syllogism, 24, 134 ; inductive, 157.
Symbolical terms, 50.
Syncategorematic terms, 54.
Synthesis, or synthetic method, 209.
Synthetic syllogism, 134.
System, definition and forms, 12, 199 ;
of classes, 46 ; natural, 67.
Tacit or occult premise, 142.
Tautology, in definition, 86.
Terms, or names, formation of, 52;
classification of, 52-56 ; distribution of,
115.
Testimony and Authority, nature
of, 16 ; proof from and rules for, 103.
Theory = verified hypothesis, 148.
Thing, 32.
Thought, definition, 10 ; forms, 11 ; law,
17.
Transfer of meaning of terms, 82.
Tree of Porphyry, 66.
Trichotomy, 68.
Trilemma=dilemmatic syllogism (145)
with three alternatives.
Truth, definition and criterion, 15;
modes of arriving at, 16; degrees in
assurance of, 16.
Universal, terms, 53; propositions, 112.
Univocal terms, 82.
Variations, method of, 151 ; periodic,
151.
Weakened conclusion, 171.
Weaker part, in syllogism, 168.
Whole, kinds of, 57.
Witnesses, competency, 104; credibil-
ity, 105; concurrence of, 106; inci-
dental variations of, 106; noted liars,
106.
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