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OGIC AND
ARGUMENT

THE LIBRARY

THE UNIVERSITY

OF CALIFORNIA

LOS ANGELES

PROFESSOR JOHN ELOF BOODIN

MEMORIAL PHILOSOPHY

COLLECTION

LOGIC AND ARGUMENT

LOGIC AND
ARGUMENT

JAMES H. HYSLOP

CHARLES SCRIBNER'S SONS
NEW YORK 1899

TROW DIRECTORY
NEW YORK

PREFACE

THIS work has been written to supply a double
want, namely, the combination of a purely ele-
mentary logic with the art of argumentative dis-
course. Nor has this last feature of the subject
been added out of deference to a revival of an in-
tellectual interest in collegiate debate, but it has
been suggested both by the practical value of
logic as mental discipline and its close connection
with the proper and orderly discussion of all sub-
jects in which educated men are expected to en-
gage. Logic as a practical art may be made quite
free from discussion of the theory of knowledge ;
and thus free from philosophic problems, may be
made most serviceable in the field of clear and
systematic thinking wherever a man is called upon
to form and express his opinions. The author has
long felt that formal and applied logic of the ele-
mentary kind can be taught as well in the earlier as
in the later part of a collegiate course, so that the
student can receive the benefit of it throughout
his whole academic career. It is especially a sub-
ject which ought to follow closely upon mathe-
matics. The value of this latter science lies in
the habit of reasoning which it fosters, but it
labors under one grave fault, if it is not supple-

1C9&595

vi PREFACE

mented by a knowledge of practical logic on other
data, and this is the encouragement which it may
unconsciously offer to over-confidence in the
legitimacy of our reasoning in subjects where our
propositions do not resemble those in mathema-
tics. Mathematics is the most important science
in which to begin our discipline in reasoning,
because we are not complicated with all those
modifications of meaning which the subjects of
distribution and equivocation introduce into the
process in other sciences. But it ought to be fol-
lowed closely by logic in a long and careful appli-
cation to practical examples that may contribute
to general knowledge while they also effect men-
tal discipline.

Fora somewhat similar reason I have connected
it with one department of rhetoric, but only that
which is concerned with the treatment of argu-
ments. But I have not more than merely outlined
this aspect of the subject, leaving to the instructor
the development both of detailed rules and of
practical work in themes. The outline and dis-
cussion of any thesis often depends upon a variety
of circumstances for which only the most general
rules can be given, and hence I have endeavored
only to assist the teacher in saving time by giv-
ing the student the general principles in order to
limit the amount of lecturing and dictation. The
practical exercises will afford all the opportunity
necessary for the special elucidation of principles.

The work has also been written so that the part
devoted to rhetoric can easily be omitted and the

PREFACE vii

remainder used for purely elementary logic. The
treatment of induction has been made very brief,
as not being adapted to as easy mastery as de-
ductive logic. But I have carefully outlined the
subject of fallacies and methods of argumenta-
tion. It is hoped that the work may encourage
an earlier study of logic than prevails in many in-
stitutions.

JAMES H. HYSLOP.

COLUMBIA UNIVERSITY,
May 22, 1899.

CONTENTS

CHAPTER I.
INTRODUCTION.

I. NATURE OF THE SUBJECT : Definition of Logic — Defini-
tion of Rhetoric. II. SCOPE OF LOGIC : Meaning of Law —
Meaning of Thought — Prelogical Processes — The Logical
Processes. III. SCOPE OF DISCOURSE : Divisions of Idea
Expression — The Functions of Discourse — Explanation — Con-
firmation. IV. SUMMARY, .... Pages 1-17

CHAPTER II.
CLASSIFICATION OF TERMS OR CONCEPTS.

I. DEFINITION OF TERMS. II. DIVISION OF TERMS:
Categorematic and Syncategorematic Terms — Singular and
General Terms — Collective and Distributive Terms — Concrete
and Abstract Terms — Positive and Negative Terms — Absolute
and Relative Terms, ..... Pages 18-30

CHAPTER III.
THE CONTENT OF TERMS.

I. INTRODUCTION. II. EXPLANATION OF THE PREDI
CABLES : Extension — Intension. III. ANALYSIS OF CON-
CEPTS: Definition — Division — Partition, . Pages 31-52

X CONTENTS

CHAPTER IV.
EXPLANATORY DISCOURSE.

I. INTRODUCTION. II. ANALYSIS OF THEMES: Applica-
tion and Use of Definition — The Application and Use of Di-
vision— The Application and Use of Partition — Methods of
Applying Analysis. III. SYNTHESIS OR COMPOSITION : Laws
of Composition or Synthesis — Forms of Composition. IV.
CONCLUSION Pages 53-71

CHAPTER V.
PROPOSITIONS.

I. DEFINITION. II. DIVISIONS: Univocal Propositions —
Equivocal Propositions. III. DISTRIBUTION OF TERMS,

Pages 72-92

CHAPTER VI.
OPPOSITION.

I. MEANING OF OPPOSITION. II. LAWS OF OPPOSITION.
III. SPECIAL CASES. IV. PRACTICAL APPLICATION OF OP-
POSITION, . . . . . . Pages 93-102

CHAPTER VII.
IMMEDIATE INFERENCE.

I. DEFINITION. II. DIVISIONS: Conversion — Obversion,
Contraversion or Contraposition — Inversion — Contribution —
Antithesis, ...... Pages 103-117

CONTENTS XI

CHAPTER VIII.
MEDIATE REASONING.

I. DEFINITION. II. DIVISIONS. III. ELEMENTS OF THE
SYLLOGISM. IV. RULES FOR THE SYLLOGISM : Rules Affect-
ing the Subject-Matter of the Syllogism — Rules Affecting
the Quantity and Quality of Propositions. V. MOODS OF THE
SYLLOGISM. VI. FIGURES OF THE SYLLOGISM. VII. REDUC-
TION OF MOODS AND FIGURES. VIII. PRACTICAL IMPOR-
TANCE OF THE FIGURES, . . . Pages 118-130

CHAPTER IX.

SIMPLE AND COMPLEX FORMS OF CATEGORI-
CAL REASONING.

I. CLASSIFICATION OF FORMS. II. EXPOSITION : Prosyl-
logism and Episyllogism — Enthymeme — Epicheirema —
Sorites, Pages 131-137

CHAPTER X.
HYPOTHETICAL REASONING.

I. NATURE AND DIVISIONS. II. SIMPLE HYPOTHETICAL
SYLLOGISMS. III. DILEMMATIC REASONING. IV. REDUC-
TION OF HYPOTHETICAL TO CATEGORICAL REASONING,

Pages 138-148

CHAPTER XI.
DISJUNCTIVE REASONING.

I. NATURE OF DISJUNCTIVE REASONING. II. FORMS OF
DISJUNCTIVE REASONING. III. REDUCTION OF DISJUNC-
TIVE SYLLOGISMS, Pages 149-154

XJi CONTENTS

CHAPTER XII.
FALLACIES.

I. DEFINITION AND DIVISIONS. II. FORMAL FALLACIES :
Illicit Process of the Middle Term — Illicit Process of the Ma-
jor Term — Illicit Process of the Minor Term — Illicit Process
with Negative Premises — Illicit Process with Mixed Premises
and Conclusions. III. MATERIAL FALLACIES : Fallacies of
Equivocation — Fallacies of Presumption. IV. GENERAL OB-
SERVATIONS, Pages 155-184

CHAPTER XIII.
INDUCTIVE REASONING.

I. GENERAL NATURE OF INDUCTIVE REASONING : Perfect
Induction — Imperfect Induction — Definition of Inductive Rea-
soning. II. FORMAL PROCESS IN INDUCTION. III. IN-
DUCTIVE FALLACIES, .... Pages 185-191

CHAPTER XIV.
PROOF AND ARGUMENTATION.

I. INTRODUCTION: Nature of Proof— Kinds of Proof. II.
PROCESS OF PROOF OR ARGUMENT: Definition — Analysis-
Probation. III. CLASSIFICATION AND ARRANGEMENT OF
ARGUMENTS: Forms of Argument— Arrangement of Argu-
ments, ....... Pages 192-214

QUESTIONS AND EXAMPLES, . . Page 215

LOGIC AND ARGUMENT

CHAPTER I
INTRODUCTION

I. NATURE OF THE SUBJECT.— Two sci-
ences or arts, as the case may be, are represented
in the title to this book. They are Logic and
Rhetoric. But the whole province of both of
them will not be comprised in this one treatise.
Only those portions of their territory which are
closely allied will be comprehended in the plan
before us, which will be to combine the principles
of correct reasoning with those of systematic and
orderly discourse. The more scientific portion of
Logic and the more literary aspect of Rhetoric
will be omitted, while we unite the practical func-
tions of the former with the systematic principles
of the latter. Discourse will thus get its treat-
ment from a point of view which involves both
a method of logical reasoning and a systematic
form of constructing the material of thought,
while the scientific object of the one and the
aesthetic object of the other give way to the one
purpose of teaching the student to logically sys-

2 LOGIC AND ARGUMENT

tematize the knowledge which he acquires. In or-
der to show the relation of the two subjects to
each other and the mode of their present com-
binations, a careful definition and explanation of
their contents is necessary.

ist. Definition of Logic. — Logic may be treated
either as a science or an art, or both. As a science
it seeks to determine what are called the laws of
thought, which is represented in the three processes
of conception, judgment, and reasoning. As an art
it applies these laws or rules to every-day thought.
Thus a science teaches us to know, and art to do.
But the distinction does not require to be urged
for present purposes. The object here is to se-
lect just those parts of both aspects that are suit-
able to systematic and logical discourse, as dis-
tinct from mere description, on the one hand, and
pure science on the other. Consequently we may
speak and think of logic from its practical side,
or so much of it as pertains to orderly methods of
statement and argument. Logic for this purpose
will consist of the rules that regulate correct
thinking and systematic presentation of ideas,
more especially in the form of argument. As a
whole it has two objects to fulfil : (i) To deter-
mine the general laws of thought which are called
the formal principles of thinking, and (2) To ex-
plain the conditions under which these laws are to
be applied and to be modified by the irregularities
of language and common speech. The first object
considers logic as a pure science, the second as an
applied science or art. Only the latter aspect will
enter into the purpose of the present treatise.

INTRODUCTION 3

2d. Definition of Rhetoric — Rhetoric may also
be considered as either or both a science and an
art. Like logic, it has to do with the form of dis-
course or the presentation of ideas. But it in-
cludes some things not considered by logic and
omits some things included in logic. In both
cases, however, it has a different object. It is not
directly concerned with the rules of reasoning,
nor with the truth of propositions and discourse,
but with their form of expression. It is, there-
fore, the science and art of the aesthetic and correct
expression of ideas. Consequently it will include
descriptive and narrative methods not found in
logic while it insists upon beauty of form, and
omits investigation of the laws of reasoning, while
it insists upon orderly construction of ideas in ac-
cordance with the principles of logical discourse.
There are also then two aspects to rhetoric : (i)
Beauty of form and expression, and (2) Systematic
and orderly expression with a view to efficiency in
imparting ideas. The former is the literary and
aesthetic aspect, and the latter the discursive and
persuasive function of the subject. But it is only
the latter aspect that will enter into the present
book, and only so much of it as directly relates to
logical method.

II. SCOPE OF LOGIC.— In common usage
logic is understood to treat of reasoning alone and
its laws. But it has a wider field. The laws of
thought apply to much more than reasoning, but
only because " thought " is more than inference.
It treats of all the complex processes of knowledge
as distinct from the simple and elementary func-

4 LOGIC AND ARGUMENT

tions of the mind, and in addition lays special em-
phasis upon the rules which determine the dis-
tinction between true and false thinking rather
than upon the causes of mental phenomena. It
omits the consideration of all elementary data of
knowledge, such as sensation, perception, associa-
tion, memory, and the mental states connected
with art and ethics, the emotions, desires, and voli-
tions, and confines attention to the three functions
which constitute "thought;" namely, (i) The
laws of Conception ; (2) The laws of Judgment,
and (3) The laws of Inference. Each of these
will come up for study in the proper place. At
present we must ascertain more definitely what is
meant by " laws of thought."

ist. Meaning of Law. — The term "law" has
three meanings, one in politics and ethics, and
two in science. They are (i) A command or pro-
hibition, an injunction either by government or by
conscience to do or not to do ; (2) The uniformity
of events, or the fixed regularity with which events
occur under conditions determining them ; and
(3) A rule which serves as a criterion of what is
true or false. This is sometimes called a princi-
ple, and is distinguished from a cause in the or-
dinary sense of that term. With the first of
these senses logic has nothing to do. It concerns
only the other two with special reference to the
third inasmuch as it is mainly occupied with the
means of distinguishing between truth and error,
so far as conception, judgment, and reasoning are
connected with them. In science "law" is either
a name for mere uniformity of events beyond our

INTRODUCTION 5

ability to modify them, or it is a name for a prin-
ciple or rule of our own action in which we en-
deavor to shape our thinking, feeling, and willing
to the conditions of things outside of us as well
as in the mind. Logic thus tries to find the uni-
formities of mental operations and to put us in
the way of conforming to them correctly, or ap-
plying them so that illusion and error in knowl-
edge and belief may not occur. In the present
treatise, however, we shall not occupy ourselves
with the determination of these laws as mere uni-
formities of events, but as rules to be kept in
mind when engaged in discourse or argument,
and hence as helps to systematic and clear think-
ing. For this purpose we do not require to study
the most general " laws " of thought, but only
those minor and subordinate rules connected with
the use of conceptions, judgments, and reasoning,
and which may be understood without a profound
acquaintance with our subject.

2d. Meaning of Thought. — This term has more
than one meaning, only one of which is of in-
terest in logical discourse. We may enumerate
four of its meanings : (i) Consciousness, (2) Med-
itation, (3) Comparison, (4) Reasoning. The first
means merely " to have in mind," and involves no
special laws of importance in logic. The second
denotes reflection, or holding the attention upon
some object of consciousness. The third and
fourth usually imply this reflection, but denote
more at the same time. They do not, however,
represent the most comprehensive idea of the
term which combines them and which may be

6 LOGIC AND ARGUMENT

called synthesis. Thought or synthesis, as a log-
ical process, may be defined as the mental act
which compares, combines, and unifies experience
so as to produce clear knowledge. This idea in-
cludes more than mere inference, and so compre-
hends all the processes that are connected with
the formation of complex as distinct from simple
ideas. Consequently in logic it is a term that
comprehends all the mental actions connected
with conception, judgment, and reasoning. These
are occupied with complex ideas. The earlier and
prelogical processes are connected with simple
ideas, as they are often called : the mental states
which do not compare, discriminate, or unite ex-
periences to form thought wholes. Both classes of
mental action may come in for brief consideration.

1. Prelogical Processes. — These are : (i) Sen-
sation, the definite states of consciousness effected
by the mind's reaction upon stimulus from the ex-
ternal world ; (2) Apprehension or Perception, the
act of being aware of a fact that it is, not neces-
sarily what it is ; (3) Memory, involving the reten-
tion, reproduction, or association and the recogni-
tion of past experiences. These are all elementary
acts of the mind, not involving comparison or
unification of any kind. They represent simple
states of consciousness and simple subject-matter.
They are the material or the occasion for calling
into action the higher exercise of the understand-
ing, but they are not themselves logical processes
in the technical sense of the term.

2. The Logical Processes — These are one and
all acts of the mind which conceive a connection

INTRODUCTION 7

between facts, or involve synthesis. They repre-
sent the mind as holding two or more objects of
consciousness before it and affirming or denying
some sort of connection or relation between them.
When I see or think of an object I conceive it per-
haps as a group of attributes or as belonging to a
class. In one case I perceive it, in the other I ap-
perceive it ; the former denoting the process of
bringing the properties to inhere in the same sub-
ject and the other the process of seeing what a
thing is. In both I compare and unify experiences
or things. Also when I reason. In all I am dis-
covering relations in a series or multiple of facts
that make them some kind of definite whole. This
may be made clearer by considering the three pro-
cesses with which logic is concerned — Conception,
Judgment, and Reasoning.

(a) Conception. — Conception is the act of mind
which in some way unites facts or experiences to
form definite ideas. The product may be called
a concept. This is of two kinds: (i) Individual
wholes and (2) class wholes. The former may
also be called attribute or substance wholes, and
the latter general concepts. But the individual
whole is found by conceiving a group of attributes
as belonging to the same thing or subject. It is
illustrated most clearly by a proper noun, such as
" Plato," " Bucephalus," etc. A general term will
also represent such a group of attributes, usually
if not always, but it also stands for more than
this at the same time. A class whole represents
a group of individuals, thought together and de-
noted by the same term on the ground of common

8 LOGIC AND ARGUMENT

attributes. Thus "man," "quadruped," "tree,"
"animal, "are concepts that denote an indefinite
number of individuals of like kind and applicable
equally to each individual in the class. They are
names for objects grouped together distributively,
as it is called, and not collectively, by an act of
comparison and abstraction. The common prop-
erties are noted and the differences are ignored.
But in both kinds of concepts an act of synthesis
takes place. In individual or attribute wholes the
synthesis is of different attributes or qualities in the
same thing or subject, and in class wholes or gen-
eral concepts the synthesis is of the same or like
qualities in different things or individual subjects.
The same distinction can be expressed in another
way. The former may be considered a group of
different attributes in the same subject or indi-
vidual, and the latter a group of different indi-
viduals or subjects with similar attributes, only
the common qualities being considered, while the
differences are neglected. The acts of mind in
each case are both unifying acts, involving a judg-
ment of connection, though they differ in respect
of the object-matter about which they are em-
ployed. Both seize upon the constant facts or
groups of facts and qualities for the purpose of
giving them a name which may always denote
them and be their logical equivalent in discourse.
All conceptions whatsoever may fall under one or
the other of these forms. No exception is pos-
sible until a subject is found with only one prop-
erty, and this could still be called an individual
whole, though we should not speak of a synthesis

INTRODUCTION 9

of different qualities, but merely the idea of a
single quality in a subject.

(b) Judgment. — Judgment is the act of mind
which perceives and asserts a relation between
things. It may be a relation of identity or differ-
ence, of agreement or disagreement, an affirmative
or a negative relation. The term is also used to
denote a proposition which is in reality the prod-
uct of the act. But here the emphasis is upon
the mental act which connects affirmatively or
negatively objects of consciousness. These ob-
jects will be attributes and subjects. The relations
will be between attributes and attributes, subjects
and attributes, and subjects and subjects. Thus
I may affirm or deny a connection between various
attributes, or between various subjects and attrib-
utes, or between various subjects. For instance,
" White is not blue," " Plato is wise," " Men are
bipeds," or "Lincoln was not Socrates." The act
of judgment involves a connection or exclusion
which cannot always be expressed by a single term
or concept, and hence is often defined as the asser-
tion of agreement or disagreement between con-
cepts. For practical purposes this definition can
be accepted, though the more technical account of
it may be considered in order to evade objections
based upon the desire for theoretical completeness
and accuracy. The fact that most judgments in
discourse are judgments of relation between in-
dividual and general concepts, as defined techni-
cally, may justify the reference to them in that
form as typical of practical usage, and we may
either stretch the term "concept " to include in-

I0 LOGIC AND ARGUMENT

dividual attributes as such, or permit the action
of judgment to relate or connect properties that
are sometimes called percepts or individual ob-
jects of apprehension in distinction from individ-
ual and class wholes. But aside from the question
of its subject-matter the judgment is still a unify-
ing act or assertion of relation of some kind. It
represents consciousness as looking at two facts
or things at the same time, and pronouncing upon
this agreement or disagreement, likeness or un-
likeness, connection or disconnection with each
other.

(c) Reasoning. — This process is simply a little
more complex in its object-matter than conception
and judgment. It is still an act of discovering
or asserting relations, but most usually between
judgments, though it may be involved in the for-
mation of concepts themselves. In usual discourse,
however, it is the movement of the mind from one
proposition to another in which the act discovers
and asserts, and agreement or disagreement be-
tween relations noticed in judgments. Thus if I
know that metals have a metallic lustre and am
told that sodium is a metal, I am likely to infer
that sodium has a metallic lustre, though I have
not seen the fact. I expect to find this fact to be
true on the fact that the asserted connection be-
tween sodium and metals, on the one hand, and
metals and lustre on the other, is true. The in-
ference or reasoning is the transition to connec-
tions that are not suggested by a single proposition
in this case, though in one kind of reasoning a
new order of connection may come out of even a

INTRODUCTION 1 1

single statement. But in all cases the same act of
noting identity and difference, agreement and dis-
agreement as in judgment, characterizes reason-
ing, only the matter is more complex than in the
other two logical processes. It is a process which
usually or always affects the degree of certitude
or probability in regard to propositions which may
not carry with them satisfactory conviction until
this relation is seen. Consequently it becomes a
means of proof and discovery, if not of new mat-
ter of knowledge, then of new relations between
known facts.

Logic will then have to do with the laws that
regulate the formation and correct use of concep-
tions, propositions, and reasonings, the processes
involved in the comparison and unification of ideas.
Its main object is to establish conviction when it
is employed as an art, and to formulate laws for
correct thinking when it is a science. Its scope,
however, covers all the acts of mind comparing
and connecting phenomena for the sake of know-
ing their relations as subject to constancy and
proof.

III. SCOPE OF DISCOURSE — The general
meaning of thought expression, as comprehending
every kind of presentation of ideas, has already
been mentioned, and also the aspect of it which
will come under notice here. We found it to rep-
resent both aesthetic and systematic form, and
stated that only the latter feature would be in-
cluded in the present treatise, as the field for the
application of logical as distinct from literary or
rhetorical method proper. That is to say, we

12 LOGIC AND ARGUMENT

intend here to examine the principles which regu-
late the systematic construction of discourse as
distinct from elegance of expression or of forms
designed merely to please the feelings of taste.
But it will conduce to a better understanding of
our purpose if we briefly sketch the whole field of
idea expression comprising the literary, historical,
scientific, and philosophic modes of thought. We
can then clearly observe the limited conception to
be taken of discourse for our purposes.

ist. Divisions of Idea Expression. — The expres-
sion of ideas divides itself into two general forms,
namely : Poetry and Prose. This distinction is
based merely upon the mode of literary and
grammatical construction. Both are governed by
the two functions of rhetoric, aesthetic principles
designed to please the feelings, and systematic
principles to influence the intellect. Each divi-
sion, however, can be further sub-divided : Poetry
into Didactic, Lyric, Epic, and Dramatic, and
Prose into the Literary or Polite, and the Explana-
tory. The Literary or Polite Prose may be divided
into Oratory, Essay, and Fiction, and the Explana-
tory into History, Science, and Philosophy. The
tabular outline below gives a bird's-eye view of
this field.

f Didactic.

f Poetry J £>Tic-
Epic.

[ Dramatic.

Thought Products . . . •{ ( Oratory.

f Literary . . . . -^ Essay.

Prose.. \ \ ?*tion.

f History.
(. Explanatory. \ Science.

t Philosophy.

INTRODUCTION 13

Now the conception of Discourse as it is here to
be cultivated will cover the whole field of Prose
where the rules for systematic construction of
thought are the same for the literary as for the
explanatory forms of expression ; but special
reference will be made to the explanatory branches
of idea expression. Perhaps even the same prin-
ciples are applicable to Poetry, as I think they are ,
but as we are not considering either the special
principles that distinguish poetry as such, nor the
aesthetic object of all expression we may limit the
idea of Discourse or systematic construction to
Prose, and thus keep in view the logical side of
the subject. Hence we shall speak of Discourse
as the systematic expression of thought, and illus-
trate it exclusively for the field of prose, ignoring
that aspect of rhetoric which has aesthetic expres-
sion for its object.

2d. The Functions of Discourse. — Discourse,
like logic, has an object. This object is to discuss
and present a theme. The theme is some subject
of thought, and may be either an idea or a truth,
a single object of thought requiring analysis and
exposition, or a proposition requiring demonstra-
tion. The object to be served by discourse will
thus have a range limited by the nature of the
theme. The range will be less in the case of
an idea than in that of a truth, while the latter
will include one additional function and all that is
required by the former. An idea or single con-
ception requiring explanation and analysis will be
any individual or class whole, such as "metals,"
"cathedral," "architecture," " art," " science,"

14 LOGIC AND ARGUMENT

" Greece," " Plato," " British Museum," " The
Papacy." All of these are objects to be described
and explained, and not to be proved. But the
second class of conceptions either imply judg-
ments or state them, and in addition to explana-
tion require proof. They are concerned with the
establishment of the truth, or reality of an idea or
proposition. The former concerns only what it is,
or its nature as an admitted or conceivable fact ;
the latter concerns the truth of some law, fact, or
principle embodied in judgments. The proposi-
tion may not always be expressed formally. It
may only be implied, even in a single term, as in
titles, headlines, etc. But a theme is subject only
to explanation when it is merely a conception, in-
dividual or general, and becomes subject to proof
in addition to explanation only when it expresses
or implies a proposition to be affirmed or denied.
Such are " protection," " free trade," " Malthus
law of population," " patent laws," "single tax,"
"punishment," "private property," "the impor-
tance of the family," " the necessity of quarantine,"
"the existence of God," "immortality," "the
freedom of the will," etc. In propositions these
conceptions take the form, " protection is inde-
fensible," or " protection is necessary," " God
exists," " the will is free," etc. In them we
have judgments whose terms are to be explained,
and whose assertions are to be proved or dis-
proved, while in individual conceptions the proc-
ess stops with exposition. The whole process
of discourse, however, of logical discourse, as
here defined, consists of two fundamental forms

INTRODUCTION 1 5

of method with their subordinate divisions.
They are Explanation and Confirmation. Each of
these can only be briefly outlined at this stage of
the work.

ist. Explanation. — The explanation of a theme
is the exposition of the characteristics or facts
which constitute the object of thought. It states
what a thing is and shows all the qualities or
events which it represents, and involves two gen-
eral processes. They are Analysis and Synthesis.
Each is the complement of the other, and both
processes are necessary to complete the process
of explanation.

(a) Analysis. — The analysis of a theme is the
separation of a conception or whole of thought
into its constituent parts, qualities or relations,
in order to find all that it means or implies. It is
a process that discriminates between the essential
and non-essential attributes expressed by a thing.
Its object is to render clear the parts that make
up a whole. Three processes are involved in it.
They are Definition, Division, and Partition. The
discussion of them will come up in the proper
place.

(If) Synthesis. — Synthesis is a constructive proc-
ess, and consists in the systematic arrangement
of the parts of a whole in order to give a clear
and complete conception of it as a whole. As
analysis shows only the parts that constitute a
thing, synthesis shows the manner in which those
parts constitute an orderly whole. Synthesis ex-
hibits a coherent totality, a finished product, and
analysis the raw material out of which it is com-

!6 LOGIC AND ARGUMENT

posed. There are two forms of synthesis, ac-
cording as the theme or object of thought repre-
sents a space whole, or a time whole. They are
Description and Narration. Both are processes of
systematization, and aim to give an orderly ac-
count of the qualities or facts expressed or im-
plied by a theme. They will be further discussed
at another time. Possibly Exposition might be
added as a third form of synthesis, for what may
be called thought wholes.

ad. Confirmation. — Confirmation is proof, a
process of establishing conviction. The previous
processes only show what a conception means, or
what a thing is : they do not determine conviction.
They impart instruction as to facts and form ideas
of real or possible things, but they do not aim to
dissolve doubts, to decide beliefs, to fix the truth
or falsity of propositions. Proof is the process
by which the truth of a judgment is established.
There are two forms of this proof or confirmation,
according as it determines certitude or probability.
They are Deductive, or Analytic, and Inductive, or
Synthetic Proofs. They represent the reasoning
processes of discourse, and are superadded to
those of explanation. They also will come up for
more careful exposition.

IV. SUMMARY — We have now found that
logical discourse comprises a knowledge of the
laws of thought and of the laws of constructive
arrangement. We thus combine in this treatise
the practical part of logic and the logical part of
rhetoric. The laws of thought will be considered
only in so far as they are necessary for regulating

INTRODUCTION 1 1

the correct interpretation and use of conceptions,
judgments, and reasoning, and the principles of
rhetoric will be considered only in so far as they
deal with clear and systematic treatment of
themes, the art of aesthetic expression being left
to others for discussion. Discourse then, as it is
here conceived, denotes the logical analysis and
synthesis of the ideas expressed by a theme, and
all subsequent investigations will concern the
laws and conditions under which those processes
can best be applied.

CHAPTER II
CLASSIFICATION OF TERMS OR CONCEPTS

I. DEFINITION OF TERMS. -- The words
" Term " and "Concept " are identical in logic, but
in general usage their synonymous meaning is not
so apparent. " Term " has a grammatical associa-
tion and generally denotes a word, while' concept
denotes always an idea of some kind. In logic,
however, a term is any word or words that con-
stitute a subject of thought. Concept denotes the
subject of thought without suggesting so distinctly
the word by which it is named. But it is the idea
or subject of thought that is the important fact,
and this may be expressed either by a single
word, or by any combination of them that denotes
a single idea. For instance, " the Queen of Eng-
land," "the elderly gentleman in the box," are as
much terms in logic as the single words " man,"
" tree," " house," etc. Consequently a " Term "
in logic may even be a whole clause or phrase,
provided that this is a mere adjunct of a cen-
tral concept which it designs to make more
definite.

II. DIVISION OF TERMS. — The classifica-
tion of terms is various, inasmuch as there are
many points of view from which to consider them.

CLASSIFICATION OF TERMS OR CONCEPTS 19

But each division may cover all the terms used in
discourse or having importance.

i st. Categorematic and Syncategorematic
Terms. — This division is based upon the distinc-
tion between what is essential and what is not
essential to the formation of a proposition.

1. Categorematic terms are those which can
stand as the subject or predicate of a proposition.
They are of three kinds : (a) substantive, as
" horse," " animal," " government ; " (b) adjectival,
as " true," "generous," " pertinent," and (c) verbal,
as " shine," " rule," " assert."

2. Syncategorematic terms are such as cannot
stand alone as subject or predicate of a proposi-
tion. They are of two kinds : (a) modal, as " veri-
ly," "amiably," "considerately," or all adverbs,
and (b) relational, as "in," "by," "to," "and,"
" through," or prepositions and conjunctions.

zd. Singular and General Terms. — This divi-
sion is based upon the distinction between Individ-
ual and Class Wholes, or the number of objects to
be denoted by a term. Accordingly, terms in this
classification are distinguished by their form of
extension, a property to be considered farther on.

i. Singular Terms are those which apply in the
same sense only to a single object, real or imag-
inary. Proper names are good illustrations, as
" Europe," " Plato," " Paris," though any term not
a proper name but denoting only a single whole,
will also be singular, as " the first man," " the
highest good," and possibly " time," " space," etc.
A combination of terms, such as " The present
Secretary of State," " The King of Spain," " The

2O LOGIC AND ARGUMENT

Superintendent of Public Buildings," etc., will also
be singular, when it refers only to one specific
person or thing. Even expressions, like " this
table," referring to an individual case in view, or
" the street running diagonally across the city of
A," etc., are singular terms. Some seem to have
thought that terms like "water," "stone," " ice,"
" mercury," " iron," may sometimes be singular,
as being similar to "space," "time," "universe,"
but I should treat them as abstract whenever used
to denote the quality or qualities which make the
kind of thing denoted by them. Oneness of kind
is not the only or distinctive feature of singular
terms, but individuality, or singularity, as repre-
senting a concrete individual whole.

2. General Terms are those which can apply, in
the same sense, to each individual in an indefinite
number of objects, real or imaginary, and of the
same kind. They are, therefore, terms represent-
ing class wholes, as singular terms represent indi-
vidual wholes. Illustrations of general terms are
such as "man," "vertebrate," "animal," " trees,"
" figures," " bipeds," etc. In these instances the
terms denote more than one object and apply to
all of the same kind. Their meaning is important
in the interpretation of what are called universal
propositions.

3d. Collective and Distributive Terms This

division is based upon the distinction between ag-
gregate wholes of the same kind and class terms.
It partly coincides with the division into singular
and general terms, the latter always being distrib-
utive.

CLASSIFICATION OF TERMS OR CONCEPTS 21

1. Collective Terms are those which apply to an
aggregate whole of individuals, usually similar in
kind and constituting together a totality that is
spoken of as if it were an individual. Thus,
"army," "forest," "crowd," " nation," " family,"
" regiment," are collective terms because they de-
note composite or aggregate wholes.

2. Distributive Terms are those which apply to
each individual in a class, or to a single individual.
For example, " man," " vertebrate," " quadruped,"
" book," " Germans," are distributive terms. It
will be remarked also that they are general terms.
But even singular terms are distributive, as " Bis-
marck," " Pitt," etc. Consequently, " distributive"
expresses individual denotive power as distinct
from composite, while singular and general dis-
tinguish between one and more than one object
of thought, whether collective or distributive.
Hence we find the division between singular and
general terms crossing between that of collective
and distributive. Thus some singular names or
terms are collective, as " The Vatican Library,"
"The 72d Regiment," "The French nation,"
while also all collective terms not singular and
applicable to an indefinite number of similar ag-
gregates are general and therefore are distributive
at the same time that they are collective. But
they are not distributive in the same sense that
they are collective.

It is important also to keep clear the distinction
between class wholes and collective wholes, or the
distinction between distributive and the collective
functions of the same or different terms. They

22 LOGIC AND ARGUMENT

are often confused so as to call a term denoting a
class a collective term. But the radical difference
is that, besides denoting more than one, collective
terms name a whole spoken of as one object,
while class or general terms denote both more
than one and apply to each individual in the class.
Collective terms do not apply to the units com-
posing the aggregate. The relation between the
two divisions may be summarized in the follow-
ing tabular form :

Terms

or Terms

i Distributive only <- it »• ) Singula

General j Collective and fSistributive [ CollecUve ^ GeSera

4th. Concrete and Abstract Terms.— It is much
more difficult to define concrete and abstract
terms satisfactorily, because the current and tra-
ditional accounts of them show less agreement
than in the previous cases. But the general dis-
tinction is based upon the difference between any-
thing considered alone, and out of relation to its
individual subject. There are also terms that
have both a concrete and an abstract signification.

i. Concrete Terms are those which stand for a
thing thought and used as a subject of properties,
or for an attribute thought and used as an attri-
bute, but in each case conceived independently
and alone. This definition provides for two
kinds, certain nouns and all adjectives. Thus
" Parthenon," " Lincoln," " Charter Oak," and
" wise," " noble," " clear," etc., are concrete terms
or conceptions.

CLASSIFICATION OF TERMS OR CONCEPTS 23

2. Abstract Terms are those which represent an
attribute conceived apart from the subject to
which it belongs, and treated as if it were a sub-
ject itself. Thus, " righteousness," " ability," " vir-
tue," "purity," " redness," are abstract concepts
or terms. These are used as nouns and can be-
come subjects of propositions, while the attributes
they express can only be predicates.

3. Subdivisions. — Some terms are only concrete,
some are only abstract, and some may be either
concrete or abstract. This fact gives rise to the
distinction between ///r^ and mixed terms. Then,
as concrete terms may be either substantives or
adjectives, we may recognize two kinds of this
class and two kinds of the abstract. The follow-
ing table or outline with illustrations will indicate
what is meant while it explains the definitions :

( ( r j Substantive=Singular Nouns, e.g., Homer.

p ete"1 Attributive= Adjectives, e.?., Pure.

Terms •( lre ' 1 Au_f_.,rt 1 Static= Adjectival Nouns, e.g.. Sweetness.
act" 1 Dynamic = Verbal Nouns, e.g., Distillation.
(_ Mixed = Concrete and Abstract, e.g., Government, Religion, etc.

Certain kinds of terms are omitted from the
illustrations in this outline. They are such gen-
eral terms as "man," "tree," "animal," " build-
ing," etc. The reason for this omission is that
some writers treat them as concrete. But this is
due to a conception of the concrete which is not
the logical one and which will come up for con-
sideration in a moment. I regard them, however,
as both concrete and abstract, and hence as belong-
ing to the mixed class along with "government,"
" religion," etc., and for the same reason. All

24 LOGIC AND ARGUMENT

general terms, in fact, may be treated as abstracts,
though it may not be true that all abstract terms
are general. But general terms are abstract when
they stand only for the common properties of the
individuals composing the class, and concrete
when they denote the individuals as such. Thus,
in the use of a distinction still to be explained,
general terms are abstract when they are taken in
their intension or to denote the qualities expressed
by them, and concrete when they are taken in
their extension or to denote the number of individ-
uals in the class.

4. The Popular Distinction. — The popular con-
ception of concrete terms is that of sensible ob-
jects, and of abstract terms as that of non-sensible
things. This notion coincides with the difference
between material and immaterial things. From
this point of view "man," "tree," "Plato," "Bis-
marck," " nation," " white," " round," " heavy,"
would all be concrete, and "thought," "emotion,"
"spirit," "government," "religion," "generous,"
"sincere," etc., would be abstract. But while this
distinction may do very well for the purpose of
indicating the difficulties involved in imparting
our ideas of non-sensible things, it does not serve
the purposes of clear logical thinking. The com-
mon mind may find it easier to deal with tangible
or sensible things, but the propositions and beliefs
we form have as much to do with the non-sensible
as the sensible, and hence the distinction for logic
between the concrete and the abstract must be
between facts conceived as self-sufficient and facts
conceived out of relation to their subject, and not

CLASSIFICATION OF TERMS OR CONCEPTS 25

between the representable or picturable and the
non-representable or unpicturable. Errors in ar-
gument do not occur from the confusion of the
intangible with the tangible, but from the illegiti-
mate transition from a fact out of relation to its
subject, or vice versa, and hence it is this distinc-
tion which logic must keep in view.

5th. Positive and Negative Terms. — This divi-
sion is based upon the distinction between terms
that imply the presence and those that imply the
absence of an attribute. From the position of
grammatical form in connection with meaning we
may recognize also Privative and Nego-positive
terms or concepts, as will be further explained,
but considering " terms " and " concepts " as
identical we may reduce the four forms to two,
and divide each of the two into pure and mixed.
This may be represented after the definition of
each.

1. Positive Terms are those which signify the
presence or possession of certain qualities de-
noted by the word ; for example, " good," " pure,"
"excellence," "metal," " organic," " human," etc.,
are positive terms. They are positive grammat-
ically and logically, or both in form and matter.

2. Negative Terms are those which denote the
absence of certain given qualities ; as " inorganic,"
"insincere," "imperfect," "headless," "unnatu-
ral," etc. These are negative in both form and
matter. The usual symbols of negative terms
are in, tin, less, dis, a or an, anti, mis, sometimes
de, and non, and not.

3. Privative Terms are those which signify the

26 LOGIC AND ARGUMENT

absence of a quality or qualities once possessed
or belonging normally to the object named. Thus
"deaf," "dead," "dumb," "blind," "dark," etc.,
are privative terms. They are positive in form
and negative in matter or meaning.

4. Nego-positive Terms are those which denote
the presence of a positive quality though ex-
pressed in a negative manner ; as " inhuman,"
" disagreeable," " infamous," " inconvenience,"
" displeasure," " invaluable," etc. They are nega-
tive in form and positive in matter. They can,
in most cases at least, be distinguished from nega-
tive conceptions or terms, pure and simple, by
substituting their positive equivalents. Thus
" unhappiness" and "invaluable" have their
equivalents in the positive terms " misery " and
"costly." Some terms may be interpreted in
either a negative or a nego-positive sense, ac-
cording as we choose to use them. Thus " un-
certain," " unhealthy," " unpleasant," " indistinct,"
may be conceived as the negatives of " certain,"
" healthy," " pleasant," " distinct," or, as the
nego-positive equivalents of "doubtful," "sickly,"
"painful," "obscure."

5. Summarized Divisions. — The last remark
shows that there may be a grammatical difference
in the form of terms, but no logical difference in
meaning or matter. It will be possible, therefore,
to reduce the fourfold division of terms as here
defined and based partly upon grammatical and
partly upon logical principles, to two classes,
based only upon logical principles. They will be
viewed wholly from the standpoint of concepts,

CLASSIFICATION OF TERMS OR CONCEPTS 2^

which are logical in their implication, and not
from that of terms, which have a grammatical
association. Hence we may ultimately reduce all
concepts, or terms in meaning, to two classes, the
positive and negative, making the privative nega-
tive and the nego-positive, positive, though for
the sake of clearness calling attention to their
mixed character from the standpoint of gramma-
tical structure as compared with their meaning.
This is only to say that the grammatical and the
logical criteria of the nature of terms are not
always coterminous. Each taken alone will give
us two divisions, positive and negative, but when
terms come to be arranged under these divisions
some that would be positive grammatically would
be negative logically, and some that would be
negative grammatically would be positive logi-
cally. We may, therefore, outline in tabular form
the various ways of classifying and defining terms
or concepts as just discussed.

(Positive = Positive in both form and matter.
Negative = Negative in both form and matter.
Privative = Positive in form but negative in matter.
Nego-positive = Negative in form but positive in matter.

f Positive = Grammatical and Logical forms cotermi-
Pure -1 nous.

| Negative = Grammatical and Logical forms cotermi-

nous.

Terms or

f Privative = Grammatically positive and Logically

Mixed -I negative.

] Nego-positive = Grammatically negative and Logi-
cally positive.

f Positive -| Dimple = £ure Positive
Concepts •(

Negative •} Simple = Pure negative.
I ° "( Complex = Privative.

2g . LOGIC AND ARGUMENT

6. Infinitated Terms. — There is a form of con-
ception which is called " infinitated." This term
is applied to such conceptions because it refers
to that use of them which denotes the thought of
all other things than those expressed by the cor-
responding positive term. It avails to divide
all possible objects of thought into two classes.
These classes may be called the positive and the
negative, as above. The negative may be called
the infinitated concepts. The usual symbol of such
terms is non and not, as " non-moral," "non-ma-
terial," " not-animal," " not-tree," etc. They are
not always, if ever, recognized as rhetorically ele-
gant, but are valuable often to make clear the
really negative, or infinitatively negative nature
of the idea in mind. Thus " tree " and " not-tree "
will together comprise all objects of thought and
in some logical processes, as dichotomous division,
obversion and contraversion, to be considered
later, it is important to have this fact known.
Every term then, conceived or expressed by the
qualification non or not, and denoting the whole
universe of objects excluded from the positive
concept is an infinitated conception. Even such
terms as "not-just," "not-good," "non-moral,"
or perhaps all negative terms, can be conceived in
an infinitated sense, and sometimes are so. But
in common usage negative adjectival or attribu-
tive concepts are applied to the same general kind
of subject as the positive, and no reference is
made or understood to objects outside this par-
ticular limit. Thus, " not-just " would be con-
fined to the universe of actions, this being divided

CLASSIFICATION OF TERMS OR CONCEPTS 29

into "just "and "not-just actions," other things
than actions not being implied or included in " not-
just," and the infinitation not extending beyond
the negative facts within the concept " action."
The source of equivocation from this may be dis-
cussed again. But the wider meaning of infinita-
tion is clearer when applied to substantive terms.
6th. Absolute and Relative Terms — This di-
vision is based upon the distinction between in-
dependence and dependence on other terms for
meaning. In its narrower import the distinction
is not very important for practical logic, though
the wider use of it, largely, if not wholly coincid-
ing with that between Concrete and Abstract con-
cepts, has very great value. Assuming the latter
as sufficiently considered, we may be content with
a very brief account of the former.

1. Absolute Terms are those in which the proper-
ties or qualities expressed are intrinsic to the in-
dividual subject and do not represent a mere rela-
tion to any other subject or being. Thus " man,"
" tree," "earth," "star," " book," may be consid-
ered as absolute terms. They do not imply any
necessary correlatives to complete their meaning.
The things which they denote may exist in all
sorts of relations, but it may not be necessary to
think of these relations in order to obtain an ad-
equate idea of what the term means. Quite the
contrary terms is true of relative.

2. Relative Terms are those whose distinctive
meaning is derived from the relation expressed
to some other individual object. Thus " father,"
"son," "parent," "master," "servant," " mon-

30 LOGIC AND ARGUMENT

arch," " subject," etc., are relative terms. Each
term suggests a relation to others as the distinc-
tive meaning of the word. Thus " father " is a
" man," but a man in a certain relation, and the
term is intended to express that relation, which
may not be a quality necessary for recognition of
the individual as such. We see in this way that
relative terms suggest the thought of other indi-
viduals with the relation involved as a part of the
term's meaning, while absolute terms suggest only
the qualities in the subject without a relation to
others being necessarily involved.

CHAPTER III
THE CONTENT OF TERMS

i. INTRODUCTION.— Every term or concept
has a content. This content is its meaning. As
a term it is simply a word, a sound, a vocable, but
it stands for something. It is a name for a thing,
a fact, a quality or any circumstance about which
consciousness or knowledge can be occupied. As
a concept it is an idea which contains a reference
to the same that is denoted by a word. The mean-
ing or content is simply the character or charac-
ters which a term names or implies, or which an
idea represents.

But the meaning, material content and ways of
viewing a term are rich and various. All of them
have a quantity and a quality import ; that is, a
reference to number and a reference to properties.
These characteristics bear an important relation
to the laws of thought and the art of discourse.
Different principles have to be considered in treat-
ing of these two aspects in which terms may be
taken, especially when we come to treat of propo-
sitions. But at present we are limited to their im-
portance in terms.

The aspects under which concepts have always
31

LOGIC AND ARGUMENT

been considered by students of logic have been
expressed by the \.&m predicables, borrowed from
Aristotle, and expressing the nature of the " predi-
cates "or attributes possessed by terms. They
are the most general conceptions under which the
meaning of terms can be described and have been
given as five in number. I hope to show that
they are reducible to four, with a subdivision of
two of them which has an interest outside of the
mere quantity and quality import of terms. But
I shall first give the old table of predicables, fol-
lowing it with a new one.

OLD TABLE. NEW TABLE.

Genus (yivot) = Genus. Genus = Genus.

Species (et&x) = Species. Species . = Species.

Differentia (Suwfropa) = Difference. Conferentia = Identity.

Proprium (iti&v) = Property. Differentia — Difference.

Accidens (<ni>i/3<:/3»i<co«) = Accident.

To the new table I might add Essentia and Ac-
cidentia, or Essence and Accident, but I regard
them as subdivisions of Conferentia and Dif-
ferentia. The new table, however, enables us to
classify the " predicables," or ways of looking at
terms, according to their quantitative and their
qualitative meaning. The Genus and the Species
are names for that view of concepts which regards
them in their quantitative power or meaning, and
Conferentia and Differentia, in their qualitative
power or meaning. This will be made clearer in
the discussion. The following outline will show
their relations to each other and to Essentia and
Accidentia.

THE CONTENT OF TERMS 33

f Quantitative j Genus.
(Extension). { Species.

Content of Terms. 4 \ Conferentia. \ Essentia.

Qualitative ' 1 Accident*

| • ^' UtJ.ll till 1 \ ^ I

(Intension). 1 , F

[Differentia. {%£££

II. EXPLANATION OF THE PREDICABLES.

— Before we enter upon the discussion of the
analysis of terms or concepts, which is a process
of determining the nature and range of their
meaning, it will be necessary to define and explain
the meaning of the predicables, and to show the
relation which they bear to each other. They all
refer to the content of conceptions, and, as indi-
cated, are reducible to two general ways of con-
ceiving the meaning of terms ; namely, their num.
ber significance, which is called their extension, and
their attribute significance which is called their
intension. Each of these properties of terms must
be taken up in its order.

ist. Extension. — The extension of a term is
that property by which it denotes the number of
objects expressed by it. This extension does not
imply any definite number of objects, but names
only the quantitative capacity of a term. The prop-
erty is best illustrated by class wholes or general
terms, as " man," " Caucasian," " animal," though
singular terms have it, but in a less degree. Terms
which compare a wider and narrower meaning
indicate most clearly what is meant by the prop-
erty, as " man " and " biped." " Man " denotes rela-
tively fewer individuals than " biped " and there-
3

LOGIC AND ARGUMENT

fore has less extension, or denotes a less number.
This gives rise to two forms of expressing the
relative differences in extension or quantitative
import of terms. They are Genus and Species.

1. Genus. — Genus is a term which expresses the
power of a class or general concept to include in
it a narrower class of individuals or a number of
individuals not grouped in classes. More briefly,
genus describes every term which denotes a class
whole of any kind. Thus " man " is a genus con-
cept, because it is a name which applies to the
various classes or individuals of the race included
under it. " Substance " is a genus, because it
includes under it iron, clay, brass, gold, silver,
water, etc.

2. Species. — Species is a term which denotes
either a narrower class or an individual compre-
hended in a genus or wider class. It has less
quantitative meaning than genus. Thus " Cauca-
sian " is a species of " man," " iron," of " metal,"
a " triangle," of "figure," etc. According to the
definition also " Plato," " Burke," and all similar
singular terms will be a species of "man." It will
be apparent that the term has a somewhat differ-
ent meaning from that which we often find in
Natural History. It is the same with the term
genus. But the doctrine of evolution shows a
tendency to break down the fixed and definite
conception of them current in science previous to
it, and hence they have become both of them more
elastic. This tendency therefore approaches more
and more the logical and relative conception of the
two terms. This requires a brief consideration.

THE CONTENT OF TERMS 35

3. Relation of Genus and Species. — The illustra-
tions suggest the fact that genus and species are
purely relative terms. Thus we find that " metal "
is a genus compared with "iron," "gold," "sil-
ver," etc., which are its species, but is a species
when compared with "matter," or "substance,"
which are its genera. To make this more general,
we notice that a term is always a genus in relation
to a narrower extension, and a species in relation
to a wider extension. We may thus proceed in
either direction until we reach the limits of farther
progress, as "existence," "substance," "being,"
"vertebrate," "man," "American," "Lincoln."
Here in this example, all intermediate terms be-
tween the two extremes are either genera or
species, according as they are conceived in rela-
tion to a higher or a lower order ; according as they
include a lower, or are included in a higher class.
Thus "American" is a genus to " Lincoln," and
a species to "man," etc. But "the two extremes
cannot be viewed in this twofold relation. " Ex-
istence " is a genus, but not a species, and " Lin-
coln " is a species and not a genus. The former
is not a species, because it cannot be brought
under a wider class of objects, and the latter is
not a genus because it cannot be divided into
lower species or individuals. All singular terms
are species and not genera, and are called the
infiina species, or lowest species. They are always
individuals.

On the other hand the highest genus, because
not a species, is called the sum mum genus or genus
generalissimum. It is represented by some such

^6 LOGIC AND ARGUMENT

term as "existence," "thing," "something," "ul-
timate reality," " the absolute," or even " being "
in its widest sense, but in all cases must be thought
as a single concept. It is thus worthy of remark
that there is in reality but one summum genus,
while there may be an indefinite number of infima
species. All intermediate terms between these ex-
tremes are sometimes called subalterns, as being
either genera or species, according to the relation
in which they are viewed.

An important fact also to remark is that genus
and species represent concepts in a certain rela-
tion of agreement with each other. The genus al-
ways includes the species, and each species includes
a part of the genus, while the species mutually
exclude each other ; that is, the terms denoting
them are always opposed to each other.

It will be necessary to notice again and a little
more fully the use of the terms genus and species
in Natural History. A species is there " a class of
plants or animals supposed to have descended
from common parents, and to be the narrowest
class possessing a fixed form ; a genus is the next
higher class." This is Jevons's definition, but he
does not illustrate it. Perhaps we could say that,
in Natural History, the term "tree " would repre-
sent a genus, and "oak," "elm," "maple," etc.,
would represent z. species, while " red-oak," " white-
oak," "black-oak," etc., would be varieties. But
the peculiar use of the term species here is that it
is supposed to be fixed, and not relative as in
logic, where, as we have seen, any but the summum
genus and the infima species may be either a genus

THE CONTENT OF TERMS 37

or a species, according to its relation to a higher
or lower order. In natural history, however,
species is supposed to represent certain fixed
characters and relations to a common progenitor.
But the acceptance of the doctrine of evolution
prevents the drawing of any such determinate
line of distinction, except arbitrarily. In this doc-
trine, founded upon the variability of " species,"
the conception becomes elastic and indistinct, de-
noting only certain characteristics different from
the genus. Hence the change approximates the
logical import, and may ultimately make them
identical.

2d. Intension. — The intension of a term is its
power to denote qualities. Every term not only
implies a certain number of things, whether sin-
gular or general, but it also stands for certain
qualities or properties which belong to the thing
named. For instance, the term " man " is not
only a name for a certain indefinite number of in-
dividuals to which the word applies, but it is also
a name for the group of qualities or attributes
which constitute these individuals. It denotes a
certain form, stature, habits, intelligence, moral
character, etc. These qualities make the individ-
ual man. The intension of the term is only a
name for the qualities for which the term stands.
They are also called the properties, attributes,
characteristics of that to which they belong.
Every term names or implies at least a certain
number of them, as " mountain," " horse," "vir-
tue," "religion," "car," "metal," "whiteness,"
" Bucephalus." Hence this power to denote qual-

38 LOGIC AND ARGUMENT

ities in a term is called its qualitative power or
intension, which in common English is its func-
tion to indicate or imply the properties possessed
by the thing named. In the arrangement of
things and events according to genera and species
it is found to be necessary to distinguish these
properties into two kinds, which I shall call the
Conferentia and the Differentia. This shows a dis-
tinction between the kinds of intension or proper-
ties expressed by concepts. Each must be defined
and examined in its order.

i. Conferentia. — Conferentia is the name for
the common qualities expressed by a general or
class term. Thus the concept " tree," considered
in respect of its intension alone, or the properties
denoted by it, represents those common, some-
times called universal, qualities found in all the
individuals of the class : for instance, its woody
structure, truncated form, possession of leaves
and branches, capacity for growth, etc. Another
illustration, as " Americans," shows vertebrate
structure, complexion, stature, citizenship or birth-
place, etc., are the common facts expressed by the
term. Conferentia thus names the qualities that
make the class, and is only a technical term for
what are called the common or universal proper-
ties of the group of individuals expressed by gen-
eral terms. Essence or essential properties are
expressions sometimes used for the same fact.
But as I propose to distinguish between what is
universal or conferential as a fact from what may
sometimes be called essential, I shall not make the
terms exactly equivalent.

THE CONTENT OF TERMS 39

The term " conferentia " is synonymous with
one meaning of the term "genus " ; namely, that
in which it is contrasted with differentia. There
are two pairs of contrasts in which the term
" genus " appears. One is " genus and species,"
in which the former includes the latter, and the
other is the "genus and differentia," in which the
former excludes the latter. In the comparison of
genus with species, genus denotes the class with
a, larger number of individuals than the species,
and represents the extension of a concept. In the
comparison of genus and differentia, genus denotes
the common qualities of the class which are dis-
tinct from the differences between the individuals
in it. This equivocal use of the term can be pre-
vented by limiting the word genus to the exten-
sion of the class, and conferentia to the intension
or common qualities.

2. Differentia. — Differentia, or difference, is the
name for the property or properties which dis-
tinguish one species from another, or, if we like,
the species from the genus. Thus two-footedness
or bipedality is the quality which distinguishes
man from the quadrupeds. Or better, the form of
the leaves is a differentia of the oak compared
with the ash tree ; the black skin the difference
between the negro and the Caucasian ; mathema-
tical formula and purposes, the differentia of al-
gebra compared with poetry, etc. Whatever dis-
tinguishes one object from another can be called
the differentia. It is some characteristic in addi-
tion to the common qualities and determines the
species or individual under the genus.

4o LOGIC AND ARGUMENT

3. Relation between Conferentia and Differentia. —
The first thing to be remarked about the proper-
ties expressed by these terms is that the distinction
between them cannot be drawn in Singular terms.
They apply only to General terms which comprise
either more than one species or more than one in-
dividual. In an individual or singular concept
the properties are all on the same level. Only in
general terms compared with the species under
them can we observe the distinction between con-
ferentia and differentia.

The second fact to be observed is that confer-
entia and differentia always exclude each other.
The conferentia is never a differentia, and the
differentia is never a conferentia in the same re-
lation. Thus feathers are a differentia between
birds and horses, and never a conferentia of these
two species. Otherwise they would have the same
name to denote them.

But the third fact is that, although they never
represent the same property in the genus and
species, they may still refer to the same property
in a class, provided that we consider the different
relation in which it may be viewed. Thus the
property which expresses the difference between
one species and another may itself be common to
all the members of the species in which it is found.
Thus "two-footedness " may be the differentia of
man as a species compared with the horse, but the
conferentia of men as a genus compared with " Cau-
casian : " black skin is the difference between the
" negro and the Caucasian," but the conferentia of
the negro race. Consequently conferentia and

THE CONTENT OK TERMS 41

differentia are relative terms. They are names
for the difference between the properties that de-
termine a concept as a genus and those that de-
termine it as a species.

4. Essentia and Accidentia. — Essentia and Acci-
dentia are technical terms for Essence and Ac-
cident, or essential and accidental properties re-
spectively. " Essential " has generally been used
to denote the same as the common properties, or
what I have called the conferentia, but " acciden-
tal " has never been used to denote the differen-
tia. Hence the difference between essence and
accidents has not meant the same as the difference
between the conferentia and the differentia. Es-
sence or essential has been equivocal, now denot-
ing the conferential as distinct from the differen-
tial, and again the essential or more permanent as
distinct from the accidental, casual or variable.
But as the distinction between the permanent and
the variable does not necessarily coincide with
the universal and the particular, or the common
and the different, it will be best to use conferentia
for what is actually universal, whether it be essen-
tial or accidental, and limit the essential to those
properties which the mind selects as the more im-
portant qualities of the subject. This will enable
us to divide both the conferentia and differentia
into the essential and the accidental. Thus the
essence or essentia will denote not only what is
common to the class, but also in addition those
common properties which are necessary to the
subject or class, while there may be properties
that are common or universal, but not necessary

42 LOGIC AND ARGUMENT

to the class and hence called casual or accidental.
For instance, risibility, or concha-shaped ears, or
the comparative shortness of the little finger may
be universal or conferential characteristics of
man, and yet not essential to him. The concept
man might be retained though he lost his risibil-
ity, the present shape of his ears, or the shortness
of the little finger. Accidental properties are,
therefore, those which are treated as non-essential
to the subject of them and are divided by logicians
into the universal and the casual, which is a recog-
nition that the distinction between essence and
accident does not coincide with that between con-
ferentia and differentia. The distinction, how-
ever, between essence and accident is not so nec-
essary for logic as is that between conferentia and
differentia. The latter is the true basis for all
classifications and divisions, while that between
essence and accident has probably only an ethical
value. But the relation between the two pairs
of contrast is illustrated in the tabular outline of
properties in extension and intension, in which
essentia and accidentia are found as divisions of
both conferentia and differentia. The nature and
functions of the latter and their relation to the
determination of the genus and species are repre-
sented in the following summarized outline.

In this table the letters of the alphabet repre-
sent the qualities that make up the individuals, as
A B C D are the qualities constituting " Socrates,"
etc. But ABC are common or conferential to
" Socrates " and " Solon," A B F to "Pitt" and
" Porson," while D is the differentia of " Socrates "

THE CONTENT OF TERMS

compared with the others, E of "Solon," etc.
ABC being common to " Socrates " and " Solon,"
may be treated as the qualities for which the term
" Greek " may stand, while A B F being cemmon or
conferential to " Pitt " and " Porson" may be repre-
sented by the term " English." But here C is the
differentia of " Greek " as compared with " Eng-
lish," while A B is common or conferential to both,
and may be represented by " man." We have
then in the scheme an illustration of the relation
both of genus to species and conferentia to differ-
entia, as well as the relation of the two pairs of
distinction to each other. Conferentia and dif-
ferentia become the names of the q'ualities by
which we form the genus and the species.

Man . .

Greek. . . «

Socrates .

Solon .

English..

Porson .

3d. Relation between Extension and Intension.

Extension we have tound to denote the number,

44 LOGIC AND ARGUMENT

though indefinite, of the objects denoted by a
term, and intension the qualities expressed or im-
plied by it. We find also that every term has the
property both of extension and intension. Now
the intension always represents a certain quantity
of attributes, so that we are enabled to express
a relation between the quantity of extension and
the quantity of intension expressed by a term ;
that is, the number of objects denoted by it and
the number of qualities, though only in relation to
a wider genus or a narrower species. Thus " tree "
includes mathematically (extensively) all the in-
dividuals under " oak," " elm," " ash," " pine," etc.,
and also denotes the conferentia or common qual-
ities of all these individuals. But " oak " repre-
sents a smaller number of individuals than " tree,"
while it also denotes a larger number of properties,
at least one property more than " tree." Hence
its intension is larger than tree, while its exten-
sion is smaller. A similar illustration can be found
in comparing any genus and species : as " quad-
ruped " and " horse." " Quadruped " denotes more
individuals than horse, but fewer qualities. It
can stand only for the conferentia of all four-
footed animals, possibly only one property, and
does not indicate the differentia. The species
"horse" in this case contains all the conferentia
of "quadruped," and something more, the differ-
entia ; but it denotes fewer individuals. Hence
we can say that the extension of " quadruped " is
greater, and that of " horse " is less, while the inten-
sion of " quadruped " is less and that of " horse "
is greater. The result of this is that we can

THE CONTENT OF TERMS 45

formulate this relation in a law. It is that the ex-
tension increases as the intension decreases, and vice
versa, or extension and intension vary in an inverse
ratio to each other. We may symbolize this rela-
tion by a diagram as follows :

V A 7

wlXy

Y Y

A EUROPEAN l\

/' \ ' ~f \

/ --

/ MAN _ \ / PLATO \

Extension. Intension. Extension and Intension.

FIG. I. FIG. II. FIG. III.

In Fig. I. the base of the pyramid represents the
largest extension, which decreases until it reaches
its minimum in " Plato." Fig. II. reverses the
order of terms, but still uses the base of the pyra-
mid to represent the largest quantity, in this case
of intension, which decreases until it reaches its
relative minimum in the term " man." Fig. III.
shows the inverse ratio of both properties, the
bases and apices being arranged to suit this
fact.

This formula has its qualifications. In the first
place it may apply only in the majority of cases,
and it is not a necessary law, except for inter-
mediate classes between individuals and remoter
genera. In the second place, no mathematical
relation between extension and intension can be
determined either absolutely or relatively be-

46 LOGIC AND ARGUMENT

tween different species, or different genera. The
law applies only in the relation between genus
and species.

III. ANALYSIS OF CONCEPTS — This is a
process of unfolding the meaning and implications
of terms. That is to say, it involves the recogni-
tion and statement of what is found in their quanti-
tative and qualitative import. We have found that
the content of terms consists in the particular ideas
they express, and these ideas are their capacity to
denote number of some kind and their capacity
to denote properties of the things named. Hence
analysis is only the conscious statement of all that
is involved in their number and property power.
There are three forms of this analysis. They are
Definition, Division, and Partition. Each of these
processes requires separate explanation.

ist. Definition. — Definition is that process of
analysis which states the conferentia and differentia
ofa term orconcept. It is commonly called the anal-
ysis of the genus and differentia, but previous dis-
cussion shows why we use the term "conferentia"
instead of "genus." It is, of course, the term for
the genus that is named in the definition, but it is
not taken in its mathematical or extensive, but
purely in its intensive sense to denote the confer-
entia or general qualities expressed by the term.
An illustration of definition would be : " A horse
is a domestic quadruped, used exclusively for the
purpose of drawing vehicles or performing definite
services in the form of work or pleasure." This is
necessarily a little indefinite, but it names the
genus "domestic quadruped" denoting the con-

THE CONTENT OF TERMS 47

ferentia, and the specific qualities which may be
taken as the differentia. Taking " rational " as a
differentia, we might define " man " as a " rational
animal," the term "animal " referring to the con-
ferentia.

The essential purpose of a definition is to make
clear and definite the meaning of a term or con-
cept, giving it limits, or circumscribing the field
of ideas which it represents. But the word "defi-
nition " is often taken in a broad sense to denote
any method of indicating limits of this kind, and
hence we may recognize three forms of it in com-
mon parlance : (a) Etymological Definition, which
is nothing more than giving the root derivation of
a term ; (b) Descriptive Definition, which is any
statement of fact about a term or object not
equivalent to it, and is not a true or accurate defi-
nition of it, and (c) Logical Definition, which is the
proper meaning of the term " Definition" in logic.
The peculiar nature of this process is that it
makes the subject and predicate of the proposition
identical, in which the definition is given. The
rules which regulate correct logical definition are
as follow :

1. A definition should state the essential attri-
butes of the species defined.

2. A definition must not contain the name or
word defined. Otherwise the definition is called
a circulus in definiendo.

3. The definition must be exactly equivalent to
the species defined.

4. A definition should not be expressed in ob-
scure, figurative, or ambiguous language.

48 LOGIC AND ARGUMENT

5. A definition must not be negative when it can
be affirmative.

2d. Division. — Division is an analysis of the
extension of a term or concept, or the separation of
a genus into its species. Thus we are said to
divide the genus " tree " when we name the species
under it, as "oak," "elm," "ash," etc., and these
again into narrower species. But in determining
the nature of the process, and in regulating
its correct form, three things must be taken
into account : (i) The Principle of Division, (2)
The Kinds of Division, and (3) The Rules for
Division.

1. The Principle of Division. — This is called the
Fundamentum Divisionis, or principle which shall de-
termine the method of legitimate analysis for ex-
tension. It asserts that every logical division must
be carried out upon some principle which will be
some quality whose differences in kind may serve
for distinguishing the species under the genus.
Thus in dividing the genus "man " I may take color
as the principle of division, and determine the
species by the differences in kind of color, as
"white man," "black man," " red man," etc., or
" Caucasian," " Negro," " Indian," etc. Or I might
take language as the principle of division, and
divide "man " into " Aryan," " Semitic," " Turan-
ian," etc.

2. The Kinds of ZVw/V//.— There are, of course,
forms of false and forms of true division. The
latter are the only cases to which any technical
names have been given. One of the false forms is
called Cross Division. This is the form in which

THE CONTENT OF TERMS 49

more than one principle of division has been em-
ployed, so that the species given overlap each
other. Thus a case of " cross division " would be
the separation of " books " into the species, " dic-
tionaries" and " large books," " useful books," "old
books," etc. " Dictionaries" and "large books" or
"useful books" overlap. Each species must exclude
all others. The forms of definition which are tech-
nically recognized are two, Dichotomy and what I
shall call Polytomy.

(a) Dichotomy. — Dichotomy is that form of di-
vision which separates a genus into two species
with reference to the presence or absence of a
given quality. The two terms representing the
species become thus, one of them a positive and
the other a negative term. This is the simplest
and surest mode of making the division exhaust-
ive. Thus we may divide " animals " into " ver-
tebrate " and " invertebrate " ; " Europeans " into
" Germans " and " non-Germans " ; " cities " into
" large " and " not-large " (or perhaps small) ; or
" climate " into " temperate " and " intemperate."
This can be carried on indefinitely with either term
of the dichotomy.

(b) Polytomy. — Polytomy or manifold division is
that form of it which separates the genus into
species according to the presence of positive qual-
ities alone. Several or many species are usually
necessary to exhaust the genus. An illustration
would be the division of " quadruped " into
" horses," " dogs," " cattle," " sheep," etc., though
it may not be strictly scientific. A more accurate
instance is the following :

5°

LOGIC AND ARGUMENT

Figures . .

Plane.

Rectilinear

Curvilinear

f Rectilinear

( Trilateral.
< Quadrilateral.
( Multilateral.

f Circular.
I Elliptic,
j Parabolic.
(_ Hyperbolic.

I Tetrahedral.
•< Pentahedral,
f Sextahedral, etc.

Solid.

f Spherical.
I „ ... Conical.

I Cumlmear-j Cylindrical.
Paraboloidal.

In this instance, we observe that the principle
of division may change for each independent
class, but not for those that stand as species
under the same genus. Moreover, in all such di-
vision the genus in relation to the species is said
to be super or dinate, a species in relation to a genus
is said to be subordinate, and a species in relation
to a species is said to be co-ordinate. Thus " Fig-
ures " is superordinate to " Plane," " Plane " is
subordinate to" Figures," and " Plane" is co-ordi-
nate with " Solid."

3. The Rules of Division. — A rule of division
represents the condition under which the process
shall be carried out and so regulates the manner
of doing it. Hamilton enumerates seven rules,
but Jevons reduces them to three, which are all
that are necessary for practical purposes. They
are as follows :

(a) Every division should be governed by a
single division.

THE CONTENT OF TERMS 51

(b) The constituent species should exhaust the
genus.

3d. Partition. — Partition is an analysis of the
intension of a term or concept without regard to
the relation between genus and species, or that
between conferentia and differentia. It unfolds
the qualitative meaning of a term, or separates a
whole into its parts. It is simply a process of
describing an object by its qualities or the parts
constituting it. There are two kinds : (i) Mathe-
matical or Quantitative Partition, and (2) Logical
or Qualitative Partition.

1. Mathematical Partition. — Mathematical par-
tition is the analysis of a whole into its parts as
expressed in terms of space or time. This means
that it looks at things as space or time wholes.
Thus " house," " tree," " Germany," are space
Wholes, as being objects which occupy space, and
" age," " life" (in one of its senses), " the civil
war," etc., are time wholes. Mathematical parti-
tion when applied to them divides them into the
separate parts which make the whole. Thus
" tree " would be mathematically partitioned into
"roots," "trunk," "branches," and "leaves;"
"house," into "walls," "doors," "windows,"
"rooms," "roof," etc.; "age," into "infancy,"
" childhood," " maturity," " old age," etc. No re-
gard here is paid to genus and species.

2. Logical Partition. — Logical partition is the
analysis of a whole into its properties, relations,
etc. Thus " tree " would be logically partitioned

«J2 LOGIC AND ARGUMENT

into " color," " hardness," " shape," " growth,"
" utility," etc., or, to put it more systematically,
into material and economic qualities with their
subdivisions. "Man" may be partitioned into
animal and rational properties each with their
subdivisions. There is here no reference to genus
and species, except as classification of the prop-
erties is involved. This process furnishes the
aspects in which a concept may be viewed, and
enables us to examine the whole content of an
idea, concept, or object without distinction of
attributes, though they may be systematically
viewed at the same time.

3. Rules of Partition, — Partition is sometimes
considered as a kind of Division, and is treated
as that form of it which separates a whole into its
component attributes instead of its component
species. This is a legitimate view of it, though it
is treated co-ordinately with division here in order
to emphasize the use of it for the purpose of fur-
nishing the distinct aspects of a theme in dis-
course which are not so easily illustrated by
division into species. The principles which regu-
late it are much the same, though practical
purposes are served by the mention of only a few
of the more important ones.

(a) The analysis of the intension should be ex-
haustive.

(b) The properties considered should be classi-
fied and distinguished according to the principles
of division.

EXPLANATORY DISCOURSE

I. INTRODUCTION — We have found what the
logical processes are which represent the analysis
of a conception or theme into its parts or meaning,
and we have now to examine the application of
them to discourse and more especially to outline
the principles which regulate the constructive
processes of thought expression. All discourse,
whether literary or explanatory or both combined,
is most satisfactory to the mind when it is syste-
matic and orderly. The impression produced
upon the mind by such discourse is more distinct
when it follows definite principles and purposes.
Its efficiency in both the aesthetic and the logical
field is greatest when it is systematic. The ex-
planatory stage, however, is but the preliminary
step toward confirmation, which will have to be
discussed somewhat later. But at present we
have to examine how the expression of ideas with-
out proof can be systematized, and to show what
methods are necessary to that end.

There are two general processes involved in
explanation. They are Analysis and Synthesis, as I
have named them. Less technically, the two proc-
esses may be called the discovery of the parts of
53

LOGIC AND ARGUMENT

a complex idea, and the arrangement of them to
give a clear conception of them as wholes.
5 II. ANALYSIS OF THEMES.— The analysis
of a conception or theme must precede and con-
dition the orderly synthesis or composition of ma-
terials to make complete discourse. It consists
of the several processes of Definition, Division,
and Partition. But these must be applied, not for
their own account, but with reference to some
other end than themselves. Hence the special
way of treating any given theme, in so far as these
processes are concerned, will vary with the sub-
ject-matter and its complexity. But nevertheless
some general rules and conceptions can be fol-
lowed in all cases.

The analysis of a theme is simply the selection
of all the parts, incidents, attributes, relations, and
classes expressed by it. The great object of the
process is to indicate the compass of the subject
and to determine the right order of procedure in
dealing with it. It may be briefly defined as the
process of skeletonizing a subject. This is a process
of mapping out the divisions and topics calculated
to give a clear and exhaustive treatment of a
theme. The order of procedure must be that of
Definition, Division, and Partition. The functions
served by all three of these methods are those of
indicating clearly the limitations under which the
explanation is to be taken. They bring thought
and expression down to definite and circumscribed
limits. The manner in which such a skeleton is
to be used will depend upon the tastes and object
of the writer. First it may be used merely to pre-

EXPLANATORY DISCOURSE 55

pare the order of treatment to be given a theme,
without being embodied as a skeleton in the body
of the discourse. Second, it may be incorporated
with the introduction as an index to the reader of
what the logical conception of the whole is to be.
The first form leaves to the reader the discovery
of the outline. This often has its advantages
where the object is merely to have system without
producing the impression that the discussion is
for the sake of the system alone. Third, the out-
line may be distributed throughout the treatise or
discourse, especially where we are dealing with
the student mind, partly for the purpose of train-
ing in habits of logical and systematic conception
and thinking, and partly to aid in the clearer com-
prehension of the subject. But in all cases of ex-
planatory discourse, as here considered, whether
the outline be embodied in the discourse or not, it
should have a place in the writer's mind.

In suggesting rules for practice, however, it is
important to keep in view the kind of discourse to
which they are meant to apply. I have intended
the process of applied analysis to be limited to
what I have called explanatory as distinct from
literary discourse. Literary prose I have intended
to be a sphere of expression, not designed to con-
vince or instruct the reason as its main object,
but, like poetry, to be governed by (esthetic rules
and ends. Of course, both poetry and literary
prose may combine logical with aesthetic objects,
and when they do must be governed in the same
proportion by logical principles. But I am here
laying down rules to apply only to what I have

tj6 LOGIC AND ARGUMENT

chosen to call explanatory discourse, which has
for its chief object to impart or communicate ideas
for the instruction of the intellect, and either does
not consider aesthetic taste at all or makes this of
secondary importance so far as that end is con-
cerned. The term explanatory discourse, there-
fore, stands for that form of it which is exclusively
employed with logical processes and logical ob-
jects. The rules for literary or aesthetic discourse
may be wholly different. Of them I do not pro-
pose to treat. Outline and skeleton analysis
may not be necessary in aesthetic literature pure
and simple, but only when combined with the log-
ical and explanatory. But for the latter this proc-
ess is essential for clearness, effectiveness, and
comprehension, and more especially for the com-
munication of systematic ideas, which is its object.
All rules of procedure here adopted, therefore,
will leave the student free to accept any laws of
literary taste that aesthetics require. We are here
concerned only with that expression of thought
that aims to reproduce the rational order which
the mind finds by reflection on the world and phe-
nomena. This order represents the unity of log-
ical relations, involving the proper selection of
ideas, topics, and marshalling of material for the
purpose of influencing conviction.

i st. Application and Use of Definition The

first step in explanatory discourse is definition.
The nature of this process has already been indi-
cated and it only remains to show how it is to be
used and what its functions are in systematic
thought and expression.

EXPLANATORY DISCOURSE 57

As explanation is the systematic arrangement
of the facts involved in a theme, the first duty on
the part of a writer is to define his subject. The
definition must include a clear idea of the term or
terms in the theme, and of the proposition when
the theme is so comprehensive. Thus if the sub-
ject of a descriptive discourse is " Houses," the
first thing to do will be to define the general
term " house." The definition may be made to
include the historical and etymological meaning
of the term itself, but should terminate in the
logical statement of the conferentia and differen-
tia denoted by it in order that it may not want in
clearness. If the theme be a proposition, both
terms or all terms in it may be subjected to the
same process, and the meaning of the proposition
of the whole determined. So much for the first
step.

The function of definition is to give limitations
to the discourse and to aid the comprehension of
those for whom the communication of ideas is in-
tended. It brings to specific notice the proper-
ties expressed by a term, and makes clear the
most essential qualities involved in its meaning.
It thus conveys an idea, definite and clear, to the
person receiving the information communicated,
and more especially indicates the facts, things, or
qualities not to be considered in the use of the
term. This latter function is what is meant by
giving an idea or term limitations. Apart from
definition it might mean anything. But this proc-
ess shuts out, at least by implication, all that the
thing is not, and also distinguishes, in what it is,

58 LOGIC AND ARGUMENT

between the essential and the unessential marks
constituting an object. Thus if I am asked to
discourse upon the theme " Man," my first task
must be to indicate, at least in the most general
way, for what the term man essentially stands. I
may say that " Man is that genus of organized be-
ings which show the attributes of rationality,"
etc., or that he is "that species of biped which
exhibits certain peculiar mental and moral habits
of life," etc. The distinctive qualities, of course,
would have to be named. But the process would
bring out the aspects of man and his nature which
were to come under consideration in the discourse.
Besides, it decides the compass and range of the
discussion, showing just what conception and
facts are to be considered in the theme. Ideas
thus have definiteness and clearness.

It is not necessary to indicate in the outline of
a theme that the process of definition is going to
be followed. This may be done in text-books and
theses designed for a certain kind of instruction.
But the main thing in all cases is the application
of the process as the necessary means of orienta-
tion in a subject ; that is, the necessary means of
making clear the general nature and scope of the
subject. It may be applied at every step in the
development of a theme.

2d. The Application and Use of Division

Division was found to be the analysis of a con-
ception or theme into its species or kinds, as
" man," into Caucasian, Negro, Malay, etc. In
discourse this process is to be applied to the de-
termination of the general parts of the subject,

EXPLANATORY DISCOURSE 59

though in certain kinds of discourse Partition will
take its place. But in most, if not all, themes it
will have a function to perform. Thus if the sub-
ject be "Books," the mode of division for the dis-
course will depend upon the aspect of the subject
to be considered, and the topics for chapters or
sections selected accordingly. If "books" are
to be discussed from the point of view of their
subject-matter, they might be divided into philo-
sophic, scientific, literary, religious, etc., as repre-
senting the distinct kinds to be treated separately.
If the theme is to be considered in respect of their
form, the division might be folios, quartos, octavos,
duodecimos, etc. If the question concerns their
relation to civilization the divisions might be scien-
tific books, political books, artistic books, religious
books, etc. In all, they are classified and discussed
with reference to some principle of division that
determines the point of view to be considered. If
again, for instance, the theme be " Protection,"
we could divide it into chapters on Protection of
Manufacturers, Protection of Agriculture, Protec-
tion of Trade, Protection of Labor, etc. Or in
another form, if the question is as to methods, it
can be divided into Revenue Protection, Bounty
Protection, Prohibition of Imports, etc. In all
these cases separate applications of the main prin-
ciple are concerned and require separate treat-
ment.

The chief function of division is to reserve for
distinct discussion those special aspects of a sub-
ject which are not immediately recognizable in
the general definition, but are found in the differ-

60 LOGIC AND ARGUMENT

ences that mark the species. Definition states
what characterizes the whole class without regard
to species, and so deals with the essential inten-
sion of a conception. Division, on the other
hand, dealing with the extension, recognizes the
differences characterizing the species under the
genus. Thus, in the subject of protection, the form
of it denoted by bounties involves certain inci
dents and influences not noticeable in its appli-
cation in revenues. Hence the reservation of this
form of it for separate treatment offers an oppor-
tunity to discuss this aspect of it wholly distinct
from the incidents common to every kind of pro-
tection.

3d. The Application and Use of Partition. —
The chief function of Partition is the presentation
of the aspects of a theme. As already shown, it
is the division of a concept into its attributes,
implications, and relations, and so the analysis
of its intension. This is only an application of
the principles of division to the properties and
relations of a thing instead of its species, and af-
fords an opportunity to systematize discourse in
regard to the implications of a theme. Certain in-
cidents can be made to centre about a given attri-
bute or relation that might otherwise be scattered
about through the discussion without relevancy or
proper order. Partition thus presents a system of
topics distinct from species as centres of gravitation
for relevant matters of interest to that aspect.
Thus if the theme be " House," I may partition it
into origin, style, utility, etc., or foundation, walls,
floors, windows, etc., and discuss the appropriate

EXPLANATORY DISCOURSE 6 1

incidents connected with each aspect. Or again,
if the theme be " Protection," it may be partitioned
into history, administration, effects, etc., or mo-
tives, application, results, etc. " Books " might be
partitioned into such topics as form, size, style of
print, binding, cost, utility, etc. Each topic can be
made the subject of a section or chapter, accord-
ing to the purpose of the writer.

4th. Methods of Applying Analysis — The one
great object of analysis is clearness and system-
atization of thought and discourse. But it can be
carried out in a way to make discourse too mechan-
ical and to bury the thought in a mass of outline.
A proper mean should be used in the process.
There are three ways in which topical analysis can
be applied: (i) We may outline the whole subject
in the introduction and omit farther express anal-
ysis from the body of the discourse, using only so
much as is necessary for the chaptering. This will
avoid all mechanical appearances in the discussion.

(2) We may distribute the outline throughout the
discourse so that each chapter and section will
represent a distinct recognition of the separate
topics treated. Whether mechanical or not, this
will be necessary for certain kinds of discourse.

(3) We may make the analysis of a theme and fol-
low it without any explicit recognition of it in a
mechanical form, but leaving it to be discovered
by the reader, if necessary. This last method ob-
tains the advantages of systematization and logical
discourse without its mechanical features.

The method of applying the analysis will not
always be the same. (i) It may sometimes be

62 LOGIC AND ARGUMENT

Division alone and (2) sometimes Partition alone.
At others, and perhaps In most cases, it will be best
to apply both Division'and Partition together in
forming the outline. These may be combined in
various ways. Division may determine the topics
for the main parts of the discourse, and Partition
the topics for the subordinate parts. Sometimes
even both may be combined in the main divisions,
according to the degree of importance attaching
to the topics so arranged. This procedure may
violate mechanical correctness, but economy of
analysis may, at times, justify such a departure
from mechanical and logical accuracy. But gen-
erally Partition can be applied to determine the
topics and subdivisions of the subordinate divi-
sions of discourse, as well as often determining
those of the main parts.

III. SYNTHESIS OR COMPOSITION. — Syn-
thesis or Composition is the arrangement of the
matter of thought about the topics which analysis
presents. It requires Proof or Confirmation for
the completion of the process. But this part of it
cannot come under consideration at present, nor
until we have studied the nature of reasoning.
Only so much of the process can be explained here
as concerns the arrangement of ideas to present a
clear idea of the object or theme which is the sub-
ject of discourse. The topics are mere centres of
gravity for the complex matters of thought and so
afford a principle of cohesion for them, and compo-
sition is a process of selecting and arranging the
particulars of knowledge about their appropriate
topics or centres of gravity. We may divide it, for

EXPLANATORY DISCOURSE 63

convenience, into three kinds : (i) Description,
(2) Narration, and (3) Exposition. Description
applies, in the technical meaning given it here, to
space wholes ; Narration, to time wholes ; and Ex-
position, to thought wholes.

It is important to remark that there is no essen-
tial difference between the processes of descrip-
tion, narration, and exposition. The same general
laws govern all of them. The differences con-
nected with them are in the objects or themes
considered, and different terms are applied to the
discourse in order to recognize the differences in
the subordinate features of it. Certain subsidiary
rules apply to discourse on space wholes that do
not apply to time and thought wholes, as they are
here called. The same is true of either of the
latter compared with the others. But the general
process of arranging materials is the same in all
of them, and gives rise to the same laws of pro-
cedure.

i st. Laws of Composition or Synthesis — A
law of Composition is a rule regulating the process
of explanatory discourse so that it will exhibit
the greatest possible clearness and systematiza-
tion. It is simply a condition of right procedure,
and affords a criterion for determining the merits
of the discourse. Such a law represents some idea
according to which the selection and arrangement
of material have to be made.

i. Law of Selection. — The law of selection is
that condition which requires us to distinguish be-
tween the matter that is relevant and that which
is irrelevant to the theme or any part of the theme

64 LOGIC AND ARGUMENT

which is under consideration. It is not all of our
ideas about a given subject that can receive equal
attention or be used with equal freedom. The
selection of ideas and matter of thought pertain-
ing to a subject should be directed with reference
to the manner in which the theme is analyzed.
Much can be neglected altogether, unless the pur-
pose be to deal with every aspect of the subject,
and even then selection must be made to distin-
guish between what pertains to one part and what
pertains to another. Thus if the theme be
" House," I should select the things to be said
about it with reference first to the definition of it,
and second with reference to each aspect of the
general theme chosen for separate treatment. If
I treat the subject as denoting some form of resi-
dence, I should exclude all matters pertaining to
houses for business, names of dynasties, or bodies
of legislators. I should select only matter bear-
ing upon or included within the notion of resi-
dences. Or if the theme be "The Moral Influence
of Art," I should exclude all matter dealing with
mere history of art. In fact, its history in every
aspect might be ignored, unless features of it could
be given relevance to its moral character. Simi-
larly all discussion of execution, finish, and style
could be and ought to be disregarded, and only
the ideas and their embodiment and suggestion
selected for deve-loping the theme. Relevancy is
the distinctive criterion of the process.

2. The Law of Unity. — The law of unity is that
condition of explanatory discourse which regulates
the arrangement of material after it is selected.

EXPLANATORY DISCOURSE 65

Selection determines what is relevant to the gen-
eral theme. The law of unity determines the
arrangement of this matter in its proper relation
to the subordinate topics, so as to give system to
the whole. Besides, it is constructive in its ar-
rangement, while selection only prepares the way
to this unity. Relevancy is also a principle here,
though it is constructive as well as selective. The
order of arrangement for producing unity will vary
with circumstances. Now it may take one order
and now another, depending upon the occasion,
the object, the state of public opinion, and what-
ever is required to make the discourse effective.
Sometimes I may put the most important matter
first, and sometimes the less important, making
the presentation cumulative in its impressiveness.
The discretion of the writer and the nature of the
circumstances must regulate this. But always
relevant arrangement must be the rule of con-
struction. Thus, if I am discussing the subject
of " Protection " and the two subordinate topics
under it, revenue and bounty protection, I should
not arrange facts illustrating one of these topics
under the other, though the facts under both have
also a bearing upon the general theme. But facts
and figures on bounties should be arranged to il-
lustrate the influence of this specific kind of pro-
tection, rather than the general process. Nor
should I confuse with the facts relevant to these
subordinate topics facts that have only a general
significance. Again, if I am explaining the theme
" Cities," I should not confuse matter relevant to
special cities with that which is relevant to the
5

66 LOGIC AND ARGUMENT

general conception. Everything in its place is as
good a logical as it is a domestic maxim.

2d. Forms of Composition — These have al-
ready been named as Description, Narration, and
Exposition, according as they are occupied with
space, time, or thought wholes as themes. We
have also said that essentially they are the same
in method, and only certain interesting differences
in the themes or objects of the discursive treat-
ment can justify separate names for them. The
general laws regulating them, as we have said, are
the same. But the distinction of themes requires
certain modified rules of some importance in the
management of materials, and hence there will be
some convenience in the use of these terms in
spite of essential identity in their content.

i. Description. — Description is that process or
form of explanation which exhibits the properties,
attributes, and relations of spacial objects in their
proper order. Even mental and related phenom-
ena will not be excluded from this definition in-
asmuch as they may be treated as concomitant
properties of spacial wholes. This description,
however, may take two forms, according as it
deals only with spacial relations or only with
properties of a non-spacial character. They cor-
respond to mathematical and logical partition.
Mathematical description exhibits the parts of a
whole not coinciding with each other. For in-
stance, the mathematical description of a " house "
would take in their proper order the separate and
individual parts of the house, such as foundation,
walls, doors, windows, roof, furniture, etc., and

EXPLANATORY DISCOURSE 6^

exhibit their form, structure, functions, etc. Log-
ical description, on the other hand, will exhibit
the properties and functions of an object which
may occupy the same space, arid so are to that ex-
tent independent of that property. For instance,
the logical description of a "house "will repre-
sent its form, size, appearance, artistic character,
cost, use, etc., without regard to mathematical
divisions.

The methods of procedure or rules regulating
the process, in order to meet the demands of the
laws of unity and selection, are much the same,
with slight variation, for both mathematical and
logical description. Both require that the most
important parts or properties be taken first, and
the subordinate matters afterward. But in mathe-
matical description no principle of logical division
can be adopted. The properties and relations
named cannot be grouped, but must be taken, as
it were, in a serial order. In logical description,
however, something of classification can often, if
not always, be adopted, inasmuch as the proper-
ties of a subject can, at least generally, be classi-
fied. Thus in the logical description of a " house,"
I should group together all that is to be said in
regard to form and color, as being both of them
visual properties. If the theme be "man" we
should group together the physical qualities and
not confuse with them any of the mental. Sub-
groups of each of these can also be taken in order
to introduce further order into the description.
This will involve the simultaneous application of
Division and Partition ; of Partition to the sub-

68 LOGIC AND ARGUMENT

ject and of Division to its properties as classified.
In many cases also mathematical and logical par-
tition can be applied at the same time in combi-
nation. Thus by first classifying the properties
of " man " as physical and mental, and if we desire
further to subdivide each group, the physical into
form, size, functions, complexion, etc., and the
mental into intellectual, emotional, and moral, we
might then apply mathematical partition to the
form and size, reserving any other process for
functions and complexion, while logical partition
would apply to the mental properties. Clearness
and convenience must be the guides in each step.
2. Narration. — Narration is that process of ex-
planation which presents a theme in its time rela-
tions, or which exhibits events in their proper
order. It will be seen from this definition that
the process is essentially history, no matter what
the theme may be. This may also have two
kinds : mathematical and logical Narration. Mathe-
matical narration will divide the whole into cer-
tain periods marked by chronological divisions of
importance, and exhibit all events within them in
their order, perhaps with such subordinate chrono-
logical divisions as are necessary or convenient for
clearness. Each period forms a topic about which
relevant and appropriate events shall be grouped.
Thus take the theme " England." First I may de-
cide whether I shall treat the theme geologically
or politically, or in any other way. The time di-
visions are likely to be different in each case.
Taking it politically, I select those dates which
best represent the idea and its development which

EXPLANATORY DISCOURSE 69

I am seeking to elucidate. The usual chronologi-
cal divisions of English history will illustrate this
process. Logical narration will divide a histori-
cal theme and its periods into the various aspects
which constitute them as wholes before narrating
the details. The narration may, at least to some
extent, ignore chronological limitations in this
operation, though applying them to each separate
aspect. Thus taking England again and its gen-
eral history instead of presenting all forms of its
development in their exact chronological position,
I can divide this history for the whole and each
period into political, industrial, religious, scientific,
aesthetic, and moral aspects, and narrate within
these limits the facts and events appropriate to
each topic. This will give the best logical form
and order to the discourse, though there may be
other reasons at times for a chronological order
without these divisions. In pure mathematical
narration the principle must be chronological
order. In pure logical narration the principle
must be logical classification and connection of
events without regard to other events in the same
time. In many instances, however, it is possible
and will be proper and important to combine both
processes. This may be done in various degrees
according as the object of the narration permits
it.

3. Exposition. — Exposition is that process of ex-
planation which exhibits a theme as a logical or
thought whole independent of time or space re-
lations. It is a process that deals largely, if not
wholly, with abstract and general conceptions,

LOGIC AND ARGUMENT

while pure Description and Narration will be oc-
cupied with concrete things, and will consider in-
dividual objects and their qualities without distinc-
tion between the essential and accidental. But
Exposition when dealing with thought wholes
must limit its process to the essential properties
or events brought together. Every general term
or concept can be brought under this process,
which will be a presentation of the theme in re-
spect of its properties and related events accord-
ing to logical partition alone. It will therefore
be a process of exhibiting the nature of the sub-
ject considered. The order of selection will rep-
resent the most important properties or facts
concerned, according to the point of view main-
tained. The themes to which Exposition will be
applied and to which Description and Narration
might not require to be applied, or might not be
possible, are such as "science," "philosophy,"
" history," " religion," " politics," etc. Even more
concrete conceptions, to which Description and
Narration might apply, can be made the subject
of Exposition, such as "man," "quadruped,"
" forest," " army," " the age of iron," " the Re-
naissance," etc. But in its pure form it limits
the process of explanation to the properties and
events constituting an abstract whole, and con-
sists in the arrangement of material about topics
determined by the logical division and partition
of the theme. Such conceptions as " govern-
ment," "poetry," "life," "virtue," are highly ab-
stract, not because they denote intangible things,
but because of their exceedingly general charac-

EXPLANATORY DISCOURSE 71

ter. But every general term, taken as already ex-
plained, may also be an abstract or thought
whole, in that the group of properties denoted by
it has required intellectual as well as sensational
functions to produce them. Exposition is the pro-
cess of unfolding their full content and meaning,
and demands the logical analysis of the theme and
the arrangement of subordinate matter in its due
relation to the appropriate topic.

IV. CONCLUSION.— The only important re-
mark in the conclusion of this subject is that
themes will often be found capable of any or all
three forms of composition. Some conceptions
possess time, space, and thought relations, so that
it is a matter of convenience whether one or the
other of the forms of Composition is used. In
all of them the essential step is the analysis, and
then a perception of the relevancy of the matter
arranged.

CHAPTER V
PROPOSITIONS

I. DEFINITION. — In the expression of our
ideas or thoughts we are accustomed to combine
terms and concepts in a way to express some
definite meaning. Such a combination of terms
is called, in common parlance, a proposition, or
sentence. But for the purposes of Logic we re-
quire to be more accurate in our account of the
matter. Hence a Proposition is any affirmation or
denial of an agreement between two conceptions. For
instance, "Gold is a metal "is a proposition which
expresses an agreement or some measure of iden-
tity between " Gold " and " metal." " Man is not
a quadruped " denies this agreement. Every
proposition consists of two terms : namely, the
Subject and the Predicate, with a connecting ele-
ment in the simplest form, which is called the
Copula. This Copula is some form of the verb
to be, with its usual adjuncts. In such propo-
sitions as " Napoleon ruled France " the copula is
not expressed, but may be said to be implied.
The verb and its object constitute the predicate,
and the meaning of the proposition can be ex-
pressed equally well in the form, " Napoleon was
the ruler of France." The subject is that of
72

PROPOSITIONS 73

which something is affirmed or denied. The
predicate is that which is affirmed or denied of
the subject. The logical subject and predicate
may contain more terms than would be called by
these names in Grammar. They may be repre-
sented by any number of terms, provided they con-
stitute a single concept.

II. DIVISIONS — Propositions may be divided
in a variety of ways, according to the object to be
served by the division. In all instances, however,
Logic requires that the divisions mark a function
that is represented in some of the processes of
reasoning. But in regard to their general import
I shall divide them into Univocal and Equivocal
Propositions. These terms univocal and equivocal
I shall give a definite meaning for the purpose.
They could also be called simple and ambiguous.

ist. Univocal Propositions. — Univocal propo-
sitions are those whose meaning is definite and
clear, and whose form of expression represents the
normal relation of subject and predicate, and do
not imply complementary propositions. They are
further subdivided into several forms.

i. Logico- Grammatical Propositions. — These are
propositions which have common uses and names
in Grammar and Logic. They are sometimes di-
vided into Categorical and Conditional, with a sub-
division of the latter into Hypothetical and Disjunc-
tive. Sometimes Conditional and Hypothetical
propositions are not distinguished at all, and the
Disjunctive are treated as a distinct class of prop-
ositions by themselves. The latter division I
should regard as the better, especially as each

LOGIC AND ARGUMENT

proposition may be said to determine a form of
the syllogism, the Categorical, Hypothetical or Con-
ditional, and the Disjunctive.

A Categorical proposition is one in which a state-
ment or assertion is made without any qualifying
conditions. For instance, " A is B," or " Man is
mortal." The fact in such cases is stated to be
certain or known without doubt. It may be only
an imaginary fact yet, the assertion is in the form
of reality.

A Hypothetical or Conditional proposition is
one in which the assertion is made to depend upon a
supposition of some kind ; as, " If A is B, C is D,"
or "If it rains, the ground will be wet." The first
clause of the conditional proposition is called the
antecedent, the second is called the consequent.
The symbols of such propositions are //, even if,
provided that, although, sometimes when, and any
form of expression denoting a condition, such as
had or were introducing a proposition that is not
a question. There are four forms in which the
conditional proposition can be expressed, two of
which are affirmative, and two of which are neg-
ative. They are as follows :

(a) If A is B, C is D. (b) If A is not B, C is D.
(c) If A is B, C is not D. (d) If A is not B, C is
not D.

A Disjunctive proposition is one which implies
or asserts an alternative in the relation between
the subject and predicate ; as, "A is either B or
C," or "Metals are either hard or soft." The
symbols of the disjunctive proposition are either —
or. They are its symbols, however, only when

PROPOSITIONS

they denote mutual exclusion between the altera-
tives, and not when they denote merely the suffi-
ciency of one or the other of two facts to account
for a phenomenon without excluding the exist-
ence of the alternative circumstance ; as, " Gib-
bon was either very industrious or very talented."
The disjunction, however, when it is complete and
formally correct, means that the connection be-
tween subject and predicate must be only one or
the other of two things. In the proposition A is
either B or C ; the question whether A is B or
whether A is C is indefinite or undecided, but it is
definitely one or the other, and hence the propo-
sition means either that A is B and is not C, or
that A is not B and is C, or that A is C and is not
B, or finally that A is not C and is B. Hence it
means that if A is B it is not C, etc. This is the
reason that it is usually classed as a conditional
proposition. But if it be closely examined it will
be found to contain both categorical and con-
ditional elements. It is categorical in its, form, or
mode of expression, and conditional in its matter,
or meaning. The relation of form and matter in
the three propositions may be summarized as fol-
lows :

Proposit

( Categorical = Assertory in form and matter,
itiuns < Conditional = Hypothetical in form and matter.

(. Disjunctive == Categorical in form, but conditional in matter.

2. Logico-Qualitative Propositions. — Propositions
may be divided into Affirmative and Negative, ac-
cording as they affirm or deny the agreement be-
tween subject and predicate. This relation is

called or determines what is regarded as their
quality. An affirmative proposition asserts an
agreement between subject and predicate ; as,
"Gold is yellow," or, " Doves are birds." A neg-
ative proposition is one which denies an agreement
between subject and predicate ; as, " Men are not
quadrupeds," or, " Gas is not heavy." The affirm-
ative proposition has no express verbal sign or
symbol. The symbols of the negative proposition
are not, no, and none, the first being attached to
the copula or verb, and the last two to the subject
of the proposition ; as, " No trees are animals," or,
" None of the men was tall."

3. Logico-Quantitative Propositions. — Proposi-
tions are divided according to the quantity ex-
pressed by the subject. The usual division is into
Universal and Particular propositions. This dis-
tinction is generally determined by the question
whether the predicate is affirmed or denied of the
whole or of a part of the subject. Hence it is said
that a Universal proposition is one in which the
predicate is affirmed or denied of the whole of the
subject; as, "All men are mortal," or, " No men
are horses," and a Particular proposition one in
which the predicate is affirmed or denied of apart
of the subject ; as, " Some men are wise," or,
" Some negroes are not white."

But the difficulty with this definition is that
there is a sense in which the predicate is affirmed
or denied of the whole of the subject in the partic-
ular as well as the universal proposition. For the
nature of the subject may include what is known
in grammar as the " logical " subject, which con-

PROPOSITIONS 77

sists of all the terms constituting a complex con-
ception and standing in the relation of " subject"
to the proposition. In this sense the predicate
of a particular proposition is affirmed or denied
of the whole of its logical subject, but of only a part
of the grammatical subject. If, therefore, we could
say that a universal proposition affirms or denies
the predicate of the whole subject, grammatical
and logical, and a particular proposition, of a part of
the grammatical subject only, we should seem to
have avoided the difficulty. But it returns again in
such propositions as "All good men are worthy of
respect," which would be particular according to
the definition : for the predicate is affirmed of
only a part of the grammatical subject.

It would, therefore, be better for the purposes of
definition either to divide propositions into Defi-
nite and Indefinite, or to define universal proposi-
tions as affirming or denying the predicate of the
whole of a definite subject, and particular proposi-
tions of the whole of an indefinite subject. This
is what is actually meant by the two kinds of
propositions, and only technical difficulties in defi-
nition would ever lead to any discussion of the
matter. But with the condition that universal
and particular shall express just this distinction
between definite and indefinite subjects, we may
accept the current division of propositions and in-
terpret the common definitions accordingly.

The signs of the universal proposition, when
formally expressed, are all, every, each, any, and
whole, or words with equivalent import. The
signs of particular propositions are also certain

7 8 LOGIC AND ARGUMENT

adjectives of quantity, such as some, certain, a few,
many, most, or such others as denote at least a part
of a class.

But this twofold division of propositions into
universal and particular is the result of a reduc-
tion from a fivefold division which is frequently
adopted by logicians. Thus propositions are fre-
quently divided, according to quantity, into Uni-
versal, General, Plurative, Particular, and Singular.
The first and the fourth, Universal and Particular,
are the same in definition as those by the same
name in the twofold division, while the other three
may be treated as reducible to one or the other of
these two. This can be shown as follows :

A Singular proposition is one in which the sub-
ject is a singular term, and hence is quantitatively
definite in its subject ; as, " Napoleon was a great
general." Here the predicate is affirmed of the
whole of a definite subject, and hence, according
to the definition, it is possible to treat the singular
proposition as a Universal. This is true, however,
only in the formal laws of the Syllogism, and of
Immediate Inference, but is not applicable in the
process of Opposition, where Singular propositions
must remain such.

A General proposition is one in which the quan-
titative meaning of the subject is ambiguous : as
" Man is intelligent." We cannot tell from the
form of statement whether this proposition means
that, "y4//men are intelligent," or that "Men in
general (normal men) are intelligent." The prop-
osition is capable of either interpretation, and,
according as we think of all or some, when using

PROPOSITIONS 79

it, is universal or particular. Formally, it is only
particular, because it does not expressly assert
a//, but we often supply this conception in thought.
For definite logical purposes all such propositions
ought to be reduced to definite formal expression
to bring out their intentional meaning either as
universal or as particular propositions, before we
are safe in using them in an argument. All such
propositions as the following are general : " Met-
als are useful," " Trees are beautiful," " Religion
is a source of consolation," " Diamonds are brill-
iant," " Paper is cheap," " Governments are neces-
sary."

A Plurative proposition is one in which the
subject is quantified by most or an equivalent
term; as " Most ruminants are horned," and re-
quire mention only because of a peculiar syllo-
gism which is valid in spite of its composition from
particular premises. Plurative propositions are
undoubtedly particular. They, however, affirm
or deny definitely the predicate of more than the
half of the subject, but indefinitely in regard to
which half is meant by the term " most " They
are, therefore, to be classified as particular be-
cause they do not assert the predicate of the
whole of the subject definitely. The following is
a general summary of the reduction of the fivefold
to a twofold division of propositions.

{/ Singular ji
J- General . . . -!
Indefinite. -, urattve ( Particular.
( Particular. . . . )

8o LOGIC AND ARGUMENT

Some caution must be observed as to the mean-
ing of several terms which are ambiguous in de-
fining propositions. Thus the term all is equivo-
cal. It is sometimes used collectively instead of
distributively. Thus in the proposition, " All the
angles of a triangle are equal to two right angles,"
it means, not "all" or each of the angles taken
separately, but collectively. This peculiarity,
however, does not affect the universality of the
proposition.

Again the term "particular " does not denote
an individual or singular subject. It often de-
notes this in common parlance, but this is not its
import in formal logic. Here it means an indefi-
nite part of a whole. This meaning is explicitly
indicated by the use of the term some, which, in
pure particular propositions means some and it
may or may not be all. The predicate is affirmed of
an indefinite part of the subject, and nothing is
either implied or stated about the rest of this
subject, or conception, of which only a part is ex-
pressly indicated in the proposition.
• The quality and quantity of propositions may
be combined in the classification of them, so that
we shall have universal affirmative, universal neg-
ative, particular affirmative, and particular nega-
tive propositions. It has been customary to
denote each of these classes by 'an abbreviated
symbol. The first four vowels of the alphabet
have been chosen for this purpose — A, E, I, and
O. The symbol of the universal affirmative is A ;
of the particular affirmative, I ; of the universal
negative, E ; of the particular negative, O. These

PROPOSITIONS 8 1

letters shall be henceforth used for greater con-
venience to denote their proper propositions. It
may be interesting to remark that A and I occur
in the Latin affirmo, and E and O in the Latin
nego, from which scholastic writers took them for
mnemonic purposes, but the fact has no special
significance.

The following summarizes the result in tabular
form :

f Universal.. j Affirmative = A.

| Negative = E.

Propositions . . <

2d. Equivocal Propositions. — Propositions ob-
tain a double or equivocal meaning in three ways :
First, by the equivocal use of certain terms ;
second, by the inverted position of certain terms
and clauses ; and third, by the double meaning of
the proposition as a whole, even when there is no
ambiguity in any of the terms composing it. The
first and the third of these influences affect propo-
sitions in the same way, giving them that double
import which enables us to speak of an implied
proposition as the complement of the one given.
These may be called Duplex propositions because
they are susceptible of analysis into two distinct
judgments. Those due to the second cause may
be called Inverted propositions. The equivocal
nature of these propositions, however, whether
duplex or inverted, is not so much in their con-
tent or meaning as in regard to their relation to
6

82 LOGIC AND ARGUMENT

certain rules for formal logic. In the processes
of reasoning we are accustomed to treat proposi-
tions according to certain definite rules regarding
their form and meaning. In equivocal proposi-
tions, however, we have either to modify these
rules or to reduce these propositions to their uni-
vocal equivalents before excepting the meaning
in which they occur.

i. Inverted Propositions. — These are of two kinds.
First, those in which the inversion is of the subject
and predicate ; and second, those in which it is of
some relative clause. In regard to the first of these,
an example, such as can frequently be found in
poetry, is, "Full short his journey was," or "Great
is Diana of the Ephesians." In such cases the order
of subject and predicate must be changed before
the proposition can be dealt with according to the
formal rules of reasoning in so far as they are rep-
resented in the ordinary rules of discourse. In
regard to the second class, a part of the subject
may sometimes be mistaken for apart of the pred-
icate, when it is described by a relative clause
standing at the end of the sentence ; as, " No man
is honest who cheats his neighbor," or, " No one is
fit for a king who cannot rule himself." The real
subjects in these propositions are, " No one who
cheats his neighbor," and " No one who cannot
rule himself," so that we cannot follow the rule of
mere spacial position for determining them ; and
hence unless we keep this fact in mind such in-
stances would give trouble in determining the
validity of certain forms of reasoning as will ap-
pear when that subject is discussed.

PROPOSITIONS 83

2. Duplex Propositions. — A duplex proposition
is one which implies a complementary proposition,
and so requires to be analyzed into two distinct
judgments. There are three kinds : Partitive, Ex-
'dusive, and Exceptive. The chief characteristic of
them is that the complementary proposition implied by
them is of the opposite quality of that which is asserted
in the given instance. If the original proposition be
affirmative the complementary proposition is neg-
ative, and vice-versa. This will be important to
keep in mind, because the process of reasoning
will be affected as much by the implied proposition
as by the original, as will be illustrated.

(a) Partitive Propositions. — Partitive proposi-
tions are those whose subjects express a part of a
whole of which the subject of the implied prop-
osition is the complementary part, and are de-
termined by the terms " Few," and the second-
ary uses of "Some" and "Ail-not." The term
" Most " can also be included. " Ail-not," instead
of being the symbol of a universal proposition, is
often conceived as the same as " Not-all," and
hence indicates a particular proposition. For in-
stance, " All metals are not denser than water "
and " All men are not red-haired," may mean " Not
all metals are denser than, water," and "Not all
men are red-haired."

Strictly considered according to form of ex-
pression, the original propositions are E \nform,
but in matter of thought they are I propositions
with O implied. When we say " Not all men are
red-haired," or "All men are not red-haired," the
latter being taken as the equivalent of the former,

84 LOGIC AND ARGUMENT

though formally ambiguous, we mean that "Some
men are red-haired," and " Some men are not red-
haired." Whichever of the two I have in thought,
the other is implied.

The term " Some " is subject to a similar ambi-
guity. It may denote now " some but not all" and
again "some at least, and it may or may not be all."
The latter is the proper meaning for pure particu-
lar propositions, and the former is the meaning for
duplex partitive propositions. Thus the propo-
sitions, " Some metals are precious," especially if,
in speaking, the emphasis be upon the word
"some" may mean that "Some metals are pre-
cious," and at the same time also that " Some
metals are not precious." This occurs when the
term is equivalent to '•''not all" or "only a part!
In such instances it implies its complementary op-
posite, so that it means I and O at the same time.
If the original be I, it implies the simultaneous use
or assumption of O ; and if O, it implies I. The
proper use of the term, however, for pure particu-
lar propositions when considering the usage of for-
mal logic in the processes of argument, is that in
which it denotes " some and it may or may not be
all"

The importance of this will appear in consider-
ing the subject of Opposition. But in actual rea-
soning, or the discourse of actual life, we must be
on the alert for the ambiguity to which the term
is incident, and so be ready to detect the fallacy
which it may occasion.

A third proposition of a partitive and duplex
nature is that introduced by " Few" z.\\& " Most;"

PROPOSITIONS 85

as " Few men can be President," or " Few cities are
as large as Vienna," or again, " Most men are civil-
ized." In these we mean also, that " Most men
cannot be President," or that " Most cities are not
as large as Vienna," and that " Some men (a few)
are not civilized." Such propositions imply a com-
plementary opposite, because the terms "Few "and
" Most " denote a part, but not all. The expression
"a few" is sometimes synonymous with the par-
titive "few," and sometimes synonymous with
the particular "some," a.nd so varies between being
a symbol of partitive and a symbol of pure partic-
ular propositions. But "few" always introduces
a proposition which implies the complementary
opposite, and so has the meaning of I and O to-
gether.

(b) Exclusive Propositions. — Exclusive propo-
sitions are introduced, or have their meaning de-
termined by "on/y," " alone" and" none but." They
are, therefore, those which limit the predicate to
the subject, and are illustrated by such instances
as, " Only Caucasians are white," " Elements alone
are metals," " None but honest men can be
trusted." When we say that " Only elements are
metals," we do not necessarily mean that " All
elements are metals " (for this might not be true),
but that the class " metal " belongs exclusively to
the class " elements," and that it cannot be in any
class excluded from that of "elements." Hence
the meaning of the proposition is brought out
either by its simple converse, or the complement-
ary opposite proposition which it implies. The
exclusive proposition must be reduced to one of

86 LOGIC AND ARGUMENT

these when testing any special case of reasoning.
Thus, " Only Caucasians are white," must be re-
duced either to " All white men are Caucasians,"
or to "All non-Caucasians are not white " when
testing the process of formal reasoning with such
propositions.

(c) Exceptive Propositions. — Exceptive propo-
sitions are those which are introduced by such
terms as " All except" "All but" "All save" etc.
For example, " All except minors are citizens,"
" All the planets except Venus and Mercury are
beyond the Earth's orbit." Such propositions ap-
pear to be universal and simple at the same time.
But they really consist of two propositions, which
may be either both of them universal, or both
particular, or one of them universal and the other
particular. Thus, " All but minors are citizens "
may be resolved into " All persons over twenty-
one years of age are citizens," and " All under
twenty-one years of age are not citizens," or into
" Some men are citizens " and " Some men are not
citizens," or again into "All minors are not citi-
zens," and " Some persons are citizens." The first
two forms of reduction, however, are preferable
as representing a better form of comparison. The
class of exceptive propositions is not so important
for logic as the partitive and exclusive, because
their influence upon fallacies in reasoning is not
so great.

The following tabular resume represents the
divisions of propositions and the form to which
the equivocal forms have to be reduced in order
to be amenable to the rules of logic :

PROPOSITIONS

Univocal
(Simple)

Equivocal
(Complex)

Logico-Grammatical

Quanto-Qualitative

Inverted

Duplex

(" Categorical.
•< Hypothetical.
(.Disjunctive.

'U"-rsa. ]^-f4Ve-

.™^i £?£££"•

Inverted Subject and Predicate.
Inverted Relative Clause.

In order to satisfy the formal laws of logic, the
whole class of equivocal propositions has to be
reduced to univocal judgments.

III. DISTRIBUTION OF TERMS.— What is
called the distribution of terms in propositions
has much importance in determining the legiti-
macy, or at least the intelligibility of our reason-
ing and the assurance that it will be accepted by
others. A better expression would probably be
the quantification of terms, but " distribution " is
the term employed by logicians and it will be
safer to abide by usage. Terms are said to be
distributed or undistributed according as the whole
or only a part of the extension of a concept is
taken into account in the assertion. A distributed
term is one in which something is said about a
definite whole or about the totality of a definite
class. An undistributed term is one in which
something is said only about an indefinite part of
a whole or class. Another way to state it is to
say that distributed term is one in which the con-
ception is definitely quantified, and an undistributed
term is one in which the conception is indefinitely

88 LOGIC AND ARGUMENT

quantified. Now to apply these definitions to the
several propositions, A, E, I, and O.

Thus in proposition A, " All men are bipeds,"
the subject is said to be distributed because the
assertion is definitely about the whole of a class,
or about a definite whole. But the predicate in
the same proposition is said to be undistributed,
because nothing is asserted definitely about the
whole of it or its extension. The proposition does
not affirm that " All men are all the bipeds," but
leaves it free to suppose that there may be other
things included in the class besides " men." Noth-
ing is either said or implied to this effect, and
hence, in so far as this particular assertion is con-
cerned, nothing is known about the question
whether the quantity of the predicate is greater
or equal to that of the subject, so that the quan-
tity is wholly indefinite, though certainly equal to
that of the subject, but indeterminate beyond this.
Fig. IV. will represent graphically this relation,

FIG. IV. FIG. V.

quantitatively expressed, between subject and
predicate, the former being distributed and the
latter undistributed. In proposition I, for ex-
ample, " Some men are negroes," the subject is
not distributed, because it is indefinitely quanti-

PROPOSITIONS 89

fied, or because nothing is said about the whole
class "men." The predicate is undistributed in
this case for the same reason that it is in the A
proposition. The relation here between subject
and predicate is expressed by Figure V. In propo-
sitions E and O the quantification of the subjects
is determined by the same rules as in A and I,
and is equally apparent.

But the quantification of the predicate in E and
C- A is not so easy to make clear in language. No
term is employed to indicate explicitly whether
the whole of the predicate is taken into account,
and we are left either to diagrams to represent
the meaning or to the evident import of the term
"not" and its indication of exclusion. Perhaps
we could even treat this term as the quantifying
one in the case. But in both E and O the predi-
cate is said to be distributed, and this because the
propositions mean to assert that the whole of the
predicate is excluded from the subject. The re-
lation between subject and predicate in proposi-
tion E may be diagrammatically represented by
Figure VI., and in proposition O by Figure VII.

FIG. VI. FIG. VII.

There is another way of representing this rela-
tion in a form for testing the validity of the syllo-

LOGIC AND ARGUMENT

gism in formal reasoning. If we represent the
subject of a proposition by S, the predicate by P,
the affirmative by the sign of equality, the nega-
tive by a cross, the distribution of a term by a
circle around it, and the non-distribution by the
absence of the circle, we can have the relations
indicated as follows : A propositions will be rep-
resented by (s) = P ; E propositions by @ x @ ;
I propositions by S = P, and O propositions by
S x @.

The rules for this quantification may be formu-
lated as follows, two forms of statement being
given for convenience :

Subject. Predicate,

f ,, • . (Affirmative, A Distributed, Undistributed.

Universal ^Negative> E Distributed, Distributed.
Propositions •{

o _.• i ) Affirmative, I Undistributed, Undistributed.

[ ^articular j Negative. O Undistributed, Distributed.

All Universal propositions, A and E, distribute
the subject.

All Particular propositions, I and O do not dis-
tribute the subject.

All Affirmative propositions, A and I, do not
distribute the predicate.

All Negative propositions, E and O, distribute
the predicate.

There are two propositions of a peculiar charac-
ter which require special mention in this connec-
tion. They are Definitions and Exclusive proposi-
tions. In the former the predicate quantitatively
coincides with the subject ; that is, is treated as
identical with it. In this way it appears to be dis-
tributed, although it seems to be a universal af-

PROPOSITIONS 91

firmative. But formally it is not so distributed.
We only know this equivalence between subject
and predicate by first knowing that the proposi-
tion is a definition. The form of expression does
not indicate it invariably or infallibly, and hence
formally definitions have to be treated as A prop-
ositions. When the predicate is considered as
distributed in them, it is only from a knowledge
of its material meaning, and not from the mode
of expression, which is all that formal logic can
recognize.

In exclusive propositions of the form " Only
elements are metals," or " Only the honest de-
serve respect," though apparently A propositions,
the subject is undistributed and the predicate is dis-
tributed. This is the meaning of the term " only."
In the case " Only elements are metals," we do
not say or imply that " All elements are metals,"
though this might be true. But we mean that
" nothing else " can be " metals," or that " all non-
elements are not metals," which is the same in
meaning as " All metals are elements," in which
"metals" is distributed, and hence distributed in
the exclusive proposition.

In this elementary treatise I shall say nothing
about the doctrine of the explicit quantification
of the predicate as advocated by some writers, far-
ther than to say that it adds four new proposi-
tions to our classification. These are U and Y,
affirmative corresponding to A and I, and 17 and o>
(Greek letters), negative, corresponding to E and
O. In U and Y the predicate is said to be dis-
tributed, as in the propositions "All the Cau-

92 LOGIC AND ARGUMENT

casians are all the whites," and " Some elements
are all the metals." In rj and w the predicate is
said not to be distributed, as " No men are some
animals," and " Some metals are not some ele-
ments." Such forms of expression are not fre-
quent enough in practical discourse to treat them
as important.

CHAPTER VI
OPPOSITION

I. MEANING OF OPPOSITION.— Opposition
treats of the relation between the propositions A, E,
I, and O, growing out of their quantity and quality.
It has not to do with the relation between the sub-
ject and predicate, nor with the elements of propo-
sitions as such, but with the propositions as a
whole. The question regarding their consistency
and inconsistency with each other is the proper
one to be considered in thus fixing their relations>
and hence the conditions under which the. truth or
falsity of any one or more propositions can be
maintained when other propositions are asserted.
But Opposition does not undertake to decide what
propositions are necessarily true to start with, but
only what will follow in three of them if the fourth
is supposed to be either true, false, or indetermi-
nate. Some propositions, if true, interfere with the
truth of others, or may also include the truth of
still others, and the falsity of some propositions
likewise interfere with the falsity of others, or
may include the falsity of still others. All four
propositions, assuming, of course, that they con-
tain the same matter, cannot be either true or
false at the same time. Hence the problem of
93

LOGIC AND ARGUMENT

opposition is to determine the conditions and
limitations under which any one or more of these
propositions can be affirmed or denied when cer-
tain others are affirmed or denied.

We have said that, in order to determine the
relations of agreement or disagreement between
these propositions, they must have the same mat-
ter. This means that the subject and predicate
of any given proposition must either be the same
as those of any others compared with it, or must
be capable of comparison with such subject and
predicate through the relation of genus or species.
Thus we cannot determine any relation of consist-
ency or inconsistency between such propositions
as "Iron is hard " and "Water freezes," or even
such as " Iron is hard " and " Iron is useful." We
must have, for the purposes of the purest formal
logic, such propositions as " All metals are ele-
ments," " No metals are elements," " Some metals
are elements," and " Some metals are not ele-
ments." In these alone can we ascertain, in the
simplest way, the formal rules for the relation of
consistency and inconsistency, between proposi-
tions.

The place which Opposition occupies in argu-
mentative discourse is this : It determines the
manner in which we may most effectively prove
or disprove certain propositions, and hence the
conditions under which clear thinking and debat-
ing are to be conducted. To this we shall return
after exhibiting the laws of Opposition.

II. LAWS OF OPPOSITION.— The relations
of consistency and inconsistency between propo-

OPPOSITION 95

sitions can first be illustrated and the laws for those
relations formulated afterward. Thus if we assert
that "All horses are animals," it cannot be true at
the same time that " No horses are animals," or that
" Some horses are not animals." This we express
by saying that if A be true, E and O cannot be true
at the same time. They are both inconsistent with it.
Also again, if it be true that " No men are quadru-
peds," it cannot be true that "All men are quadru-
peds," or that " Some men are quadrupeds." This
we again express by saying that if E be true, A and I
cannot be true at the same time, but are inconsistent
with it. But still farther, if it be false that " All men
are Caucasians," it will be true that " Some men are
not Caucasians," but nothing is determined, one
way or the other, about the proposition " No men
are Caucasians." This last may^ be true as a mat-
ter of fact, but this truth does not follow from the
falsity of the first. Hence, to express the same
matter more formally, if A be false, it follows that
O must be true, but it does not follow that E is
either true or false. It is indeterminate so far as
A is concerned, no matter whether it be true or
false as a fact. On the other hand again, if it be
false that " Some men are not mortal," it must fol-
low that " All men are mortal," and, as we have
shown previously, the negative of this, " No men
are mortal," will be false. This we express by
saying that if O be false, A will be true and E is
false. Similarly, if I be false, E must be true and
A false. In this way we find that if A be true, O
will be false, and if A be false, O will be true ; and
if E be true, I will be false, and if E be false, I will

96 LOGIC AND ARGUMENT

be true ; again, if O be true, A will be false, and if
O be false, A will be true ; and if I be true, E will
be false, and if I be false, E will be true. This
kind of inconsistency between A and O, on the one
hand, and between E and I on the other, we call
contradiction. In the loose sense of the terms, the
words "contradiction" and "contradictory" are
used to express any kind of inconsistency which
prevents two things from being true at the same
time. But as the relation between A and E is
not the same as between A and O or E and I, a
technical meaning has to be given to the term
"contradiction" and another term employed to
express the relation between A and E. In the Con-
tradictories A and O, and E and I there is a mutual
or reciprocal and universal inconsistency which
enables us to say that one or the other must be
either true or false, or that only one of them can
be true or false at the same time. But A and E
are called Contraries, because, although the truth
of A implies the falsity of E, and vice versa, the
truth of E implies the falsity of A, yet the falsity
of either of them does not imply the truth of the
other, but the falsity of either leaves the other
wholly indeterminate.

It remains to determine the relations between
A and I, E and O, and I and O. First, if it be
true that " All men are mortal," it will be also
true that " Some men are mortal ; " if it be true
that " No men are quadrupeds," it will also be true
that " Some men are not quadrupeds." This we
express by saying that if A be true, I must be
true, and if Ebe true, O must be true, because the

OPPOSITION 97

part must be included in the whole. But on the
other hand, if it be true that " Some men are
wise," it does not follow that " All men are wise ; "
or if it be true that " Some men are not wise," it
does not follow that " No men are wise." This
we express by saying that if I be true, A will be
indeterminate, and if O be true, E will be indetermi-
nate. This is because the whole is not included
in the part. But again, if we suppose a proposi-
tion A to be false, it will be found that I will be
indeterminate, and the same with O if E be false.
On the other hand, if I be false, it does not leave
A indeterminate, nor will the falsity of O leave E
indeterminate. On the contrary, the falsity of I
implies the falsity of A, and the falsity of O that
of E. This variable relation is expressed by call-
ing A and I, and E and O, Subalterns. But A in
relation to I, and E in relation to O are each
called Subalternans, while I and O are called Sub-
alternates.

When we compare I and O we find that they are
of the opposite quality and the same quantity.
One is affirmative and the other negative, and in
that respect they are " opposed " to each other.
But the relation of consistency and inconsistency
between them is the reverse of that between A
and E. We found that A and E could not both
be true, but they might both be false at the same
time. In the case of I and O compared, if it be
true that " Some metals are elements," the law of
Contradiction between E and I will make E, " No
metals are elements," false, and by subalternation,
as just explained, O will be indeterminate. That
7

98 LOGIC AND ARGUMENT

is, nothing follows about O from the truth of I,
and also nothing about I from the truth of O.
But if it be false that " Some men are trees," it
follows by contradiction that the proposition " No
men are trees" is true, and by subalternation,
"Some men are not trees" would be true also.
This we express by saying, that if I be false, E
will be true, and by inclusion O will be true, and
by parity of reasoning if O be false, I will be true.
But both cannot be false at the same time, because
this would involve the simultaneous truth of A
and E, but they, I and O, may both be true.
This relation is expressed by calling them Sub-
contraries.

These various relations of the four propositions
can be diagrammatically represented by what is
called the Square of Opposition.

A Contraries E

o „%•

c °^ y ™

£ fy \p c
s \& g

* A, 5

£ ^ -fc

VJ >O <f v>

I Subcontraries O

The rules for regulating or expressing these
relations can be formulated as follows :

1. Of Contradictories, one must be true and the
other false.

2. Of Contraries, only one can be true and both
may be false.

3. Of Subcontraries, only one can be false and
both may be true.

OPPOSITION

4. Of Subalterns, if the subalternans be true, the
subalternate will be true, but if the subalternans
be false, the subalternate will be indeterminate.
On the other hand, if the subalternate be true, the
subalternans will be indeterminate, but if the sub-
alternate be false, the subalternans will be false.

III. SPECIAL CASES.— The rules of Opposi-
tion are laid down for Universal and Particular
propositions, as introduced respectively by All
and Some, or their equivalents. But they have to be
modified for Singular propositions and for a class
which may be called abstract general propositions,
and which may be treated as Singulars. Singular
propositions will have no Contraries and no Sub-
contraries. They can have only Contradictories.
Thus, " Socrates was a man " has only the Con-
tradictory " Socrates was not a man." The form
" Some Socrates," or " Some of Socrates was a
man," is palpably impossible and nonsense, and
anything more universal than itself with the same
subject is equally impossible. That it can only
have a Contradictory and neither Contrary nor
Subcontrary is evident from the attempt to apply
the rules of Opposition to it. If the affirmative
be true, the negative will be false ; if the affirma-
tive be false, the negative will be true ; and vice
versa. This expresses the relation of Contra-
diction.

What I have called abstract general propositions
is illustrated by such as " Charity is a virtue,"
"Science is useful," " Religion is true." Consid-
ered as abstract terms, the subjects in these cases
may be treated practically as Singulars. Hence

I00 LOGIC AND ARGUMENT

the rules for the Opposition of Singular proposi-
tions may also be applied to them.

The importance of these considerations will be
observed at once if we remark that in almost all
ordinary discourse and argument we are dealing
either with concrete Singular propositions or
Abstract general ones. The recognition of this
fact will simplify the methods of treating dis-
course. We should have only to consider the
simple relation of contradiction in the process of
argument.

IV. PRACTICAL APPLICATION OF OPPO-
SITION.— The practical use of Opposition con-
sists in its showing how proof and refutation can
be best accomplished. If an opponent asserts an
A proposition, the proper and easier way to refute
him is to prove O. If O be true, A cannot be true.
A could be equally disproved by the truth of E,
but it is always harder to prove a Universal than
a Particular or a Singular. Any person who as-
serts a universal proposition, either A or E, lays
himself under the obligation to explain away or
disprove every single exception brought against
it. An opponent may thus always restrict himself
to the much easier task of finding instances which
contradict the universality of the statement against
him, but if he takes upon himself to affirm the Con-
trary instead of the Contradictory, he lays himself
open to attack. " Were it to be asserted, for in-
stance, that ' All Christians are more moral than
Pagans,' it would be easy to adduce some ex-
amples showing that 'Some Christians are not
more moral than Pagans,' but it would be absurd

OPPOSITION 101

to suppose that it would be necessary to go to the
contrary extreme, and show that ' No Christians
are more moral than Pagans.' " The error in dis-
proof, however, may lie in certain assumptions
about the relations between the two propositions
after the proper one has been proved. Thus I
may be required to disprove the proposition " All
Indians are moral," and in order to do so I may
maintain, or prove, that " Indians are not civilized."
But here I simply evade the issue. My proposition
neither contradicts the one to be disproved nor is
the contrary of it. Again, it is no disproof of the
assertion that " Cromwell was a usurper," to say
that l< Foreign nations acknowledged his author-
ty," any more than it would be proof of his legiti-
macy to make the same statement. Likewise it
is no disproof of the assertion " A is bad " to say
that " He is religious," any more than it would
prove that a man is white by showing that he is
not black. If I assert that " Governments are
necessary," it is no disproof of it to show that
" Some governments are bad." Many arguments
in refutation, however, are conducted upon just
such logic, assuming an inconsistency where there
is none. But to be pertinent and effective, an
argument in refutation must really contradict, and
the most secure resource for this contradiction is
the assertion of a Particular against a Universal
proposition. But the proof of a Particular against
a Particular proposition will not refute, because,
as we have seen in the Square of Opposition, both
I and O may be true at the same time. The dis-
proof in this case necessitates an appeal to a Uni-

102 LOGIC AND ARGUMENT

versal proposition whatever the disadvantages in
this procedure.

In the process of proof as distinct from refu-
tation, there is no escape from the obligation to
use Universals, no matter whether the proposition
asserted be a Particular or a Universal. The
proof of the Particular must involve some Univer-
sal or Subalternans which includes it, and the
proof of a Universal involves some proposition
more general and inclusive of the one to be estab-
lished. This necessity of resorting to Universals
for proof is the fact that makes proof more diffi-
cult than refutation, which, as we have seen, does
not require to go further than the use of Particular
propositions, save in the case of refuting a Partic-
ular. But there is an alternative here which con-
siderably lightens the task of the debater when
called upon to argue against Particular proposi-
tions. This is the demand for proof of them,
especially when we know, what will be learned in
discussing the syllogism, that Particular proposi-
tions can serve no purpose for further reasoning
of any important kind, and hence are serviceable
only for disproof.

CHAPTER VII
IMMEDIATE INFERENCE

I. DEFINITION.— The term inference in gen-
eral expresses a very comprehensive process that
is difficult to define, because it equally includes
the reasoning to what is possible with what is
certain and necessary. But it is at least the act
of mind which undertakes to connect or to see
new or old ideas upon the basis of those already
known, and takes several forms, the two main ones
going by the name of Deductive and Inductive in-
ference. When it comes to considering immediate
inference, however, the definition is less compre-
hensive and, therefore, much easier. Immediate
inference is simply the deduction of one propo-
sition from another implying it. The process is
usually defined as reasoning without a middle term.
This means that only one proposition is required
for the premise, and that the conclusion is drawn
directly from this one and without comparison
with any other term or proposition. Thus from
the proposition, " The sciences are useful," I can
infer, if " infer " is the right term here, that
" Some useful things are science," or, " What is
not useful is not science." The process may be
nothing but a restatement of the original meaning
103

IO4 LOGIC AND ARGUMENT

in a new form or relation, but it nevertheless has
its use in understanding the various forms of
thought which the mind adopts in its transition
from one form of expression to another, and hence
correct immediate inference serves as a criterion
of the legitimate mode of passing from one propo-
sition to another without introducing new matter.

II. DIVISIONS. — The divisions of Immediate
Inference are based upon the various forms in
which it is possible to state directly the meaning
and implications of a proposition without intro-
ducing new thought or ideas. These forms may
be called, in terms of general usage in logic, Con-
version, Obversion, Contraversion (Contraposition),
Inversion, Contribution, and Antithesis. Each of
these requires separate treatment.

ist. Conversion. — Conversion is the transposi-
tion of subject and predicate, or the process of
immediate inference by which we can infer from
a given proposition another having the predicate
of the original for its subject and the subject of
the original for its predicate. But there are
certain limitations under which this transposition
can take place. For instance, from the propo-
sition, "All horses are animals," we cannot infer
that " All animals are horses ; " nor that " Some
animals are not horses," though this may actually
be a fact. The rules, therefore, which limit the
process of conversion are two :

(a) The quality of the converse must be the
same as that of the convertend.

(b) No term must be distributed in the con-
verse which is not distributed in the convertend.

IMMEDIATE INFERENCE 105

These rules may be abbreviated so as to read :
Do not change the quality of a proposition, and Do
not distribute an undistributed term. We may undis-
tribute a distributed term, but not vice versa. The
Convertend is the proposition to be converted ; the
Converse is the proposition or result after the
process of conversion has been performed.

The forms of conversion are two, according as
the quantity of the Converse is the same or differ-
ent from that of the Convertend. If the quantity
of the converse remains the same as that of the
convertend, the conversion is called Conversio sim-
plex, or Simple Conversion ; if the quantity is
changed (diminished), it is called Conversio per
accidens, or Limited Conversion, usually Conver-
sion by Limitation. We have now to illustrate the
process and to ascertain the extent of its applica-
tion to the several propositions, A, E, I, and O.

i. Proposition A. — Take the proposition, "All
apples are fruit." In this proposition, as already
shown, the predicate is not distributed. This
means that other things also may be contained in
the predicate, or class " fruit," so far as can be
determined by the assertion given. It is, of
course, not known from the assertion itself that
any additional matter is included in the predicate,
but only that the form of expression does not ex-
clude this possibility. Hence, if in transposing
the subject and predicate, we say "All fruits are
apples," we should be asserting more than the
original proposition will admit. In the original
we have said nothing about the whole of the
term "fruit," whether it includes or excludes

I06 LOGIC AND ARGUMENT

other subjects, but only that it includes " apples ; "
and so we cannot be permitted to infer anything
not distinctly said or implied by our premise.
Consequently, we can assert something only of a
part of this predicate in the process of conver-
sion, if we assert anything at all, inasmuch as the
original asserts something only of a part of the
predicate and asserts or implies nothing about the
rest of it. That we may assert something is evi-
dent from the fact that some degree of identity or
connection exists between the subject and predi-
cate in the convertend, and this same relation can
be asserted or inferred in the converse. By lim-
iting our statement, therefore, to the part of the
predicate of which we actually affirm something,
we are able to infer from the original proposition
that " Some fruits are apples." This is evidently
legitimate, and as evidently true if the original
be true. Here the quantity of the proposition is
changed, while its quality remains the same ; that
is, the quantity of the convertend is universal and
its quality affirmative, while the quantity of the
converse is particular and the quality affirmative.
We have, therefore, converted A into I. To con-
vert " All apples are fruit " into " All fruits are
apples," would be to violate the second rule for
conversion. Hence A cannot be converted into
A. To change the quality of the proposition A
in conversion — that is, into either E or O — would
be to violate the first rule for conversion. It is
apparent that we cannot infer an exclusion be-
tween a subject and predicate from an affirmed
connection or identity between them. Hence A

IMMEDIATE INFERENCE 107

cannot be converted into either E or O, and we
have found also that it cannot be converted into
A, but only into /. This fact is expressed by say-
ing that A is not capable of simple, but only of
limited, conversion.

There is at least one apparent exception to this
rule, and perhaps two. This is the case of defini-
tions and exclusive propositions. Definitions are
often considered, at least tacitly, as universal af-
firmatives, and yet they are capable of simple con-
version. The truth is, however, that definitions
are not A propositions in their meaning, but only
in their form of statement. They are materially
U propositions and capable of simple conversion
on that account, but formally we can only apply
limited conversion to them. We must know from
some other fact than their form of statement that
they are definitions in which the predicate is made
convertible or identical with the subject. But
without assuming this material identity we could
know nothing of the virtual distribution of the
predicate, and hence formally definitions have to
be treated as all propositions in A, until we are
told or made to know the intention of the person
using them. Formally considered, therefore, they
can no more be converted than ordinary proposi-
tions into A. Nevertheless, it is important to ob-
serve that in some cases of our actual reasoning
the mind may be correct in its processes on the
ground that the datum is a definition — that is,
subject and predicate are identical or convertible,
although formally ; that is, in its external appear-
ances, the reasoning is fallacious. It would simply

I08 LOGIC AND ARGUMENT

be a case where the real meaning is different from
the formal and apparent meaning of the propo-
sition.

The exclusive proposition, although it may ap-
pear to some people as a universal, is not such.
The subject is not distributed, though the predi-
cate is. The "only" means some, and it may or
may not be all, but certainly nothing else. Hence the
exclusive proposition is, from its distribution of
the predicate and not that of the subject, in fact
but an inverted universal, so that its simple con-
version is but its reduction to an univocal propo-
sition.

2. Proposition /. — The proposition " Some men
are vertebrates " can only be converted into " Some
vertebrates are men," or by simple conversion.
We cannot infer from it that "All vertebrates are
men," for the same reason that we cannot con-
vert A into A. It is because the predicate in the
convertend is undistributed, and must not be dis-
tributed as subject in the converse. It would
seem to be an exception to this that from " Some
men are Caucasians" we maybe supposed to infer
correctly that "All Caucasians are men." But
while this converse may be true, we must not sup-
pose that because any proposition is true we can
infer it from anything else. We simply happen to
know that "All Caucasians are men, "and this fact
\snotf0rmally expressed or implied in the propo-
sition " Some men are Caucasians ; " and as we are
only dealing with formally definite or indefinite as-
sertions, we are not allowed to transgress our rules
simply because we may happen to know that any

IMMEDIATE INFERENCE IOQ

given proposition is true. We must distinguish
between what we can believe and what we may in-
fer. Further again, it would violate the first rule
to convert I into Eor O, for the same reason that
A cannot be converted into E or O. Hence I can
only be converted into I. This is a case of Conversio
simplex, or Simple Conversion, because the quan-
tity and quality, or form, of the converse is the
same as that of the convertend.

3. Proposition E. — The proposition " No books
are pens " can be converted either simply or by
limitation. In this E proposition the predicate is
distributed, and this fact will permit of the distri-
bution of the same term in the converse. Hence
we can infer or assert " No pens are books." By
subalternation from this we can infer " Some
pens are not books." The first of the two cases
is the simple converse, and the second the limited
converse of the original, and can be directly ob-
tained by remembering that a distributed term
can be undistributed, but not vice versa. Hence E
is convertible into either E or O. But O may be
called a weakened converse of E, because E might
as well be inferred.

4. Proposition O. — A peculiar difficulty exists in
particular negative propositions, as will be ap-
parent in the attempt to convert the proposition
" Some men are not Caucasians," which is true,
into " Some Caucasians are not men," which is not
true. Of course it is not the truth or falsity of
the converse that determines whether the conver-
sion is correct or not, but we may safely use a
contradiction between convertend and converse

IIO LOGIC AND ARGUMENT

as evidence of mistake somewhere. But the rea-
son for the error is to be found in the nature of
the original assertion. First, we have found that
the converse must be of the same quality as the
convertend. In this case, therefore, the converse
must be negative. But according to the rule,
negative propositions distribute the predicate.
Hence the subject of the convertend which is not
distributed becomes the predicate of the converse
which is distributed, and so violates the second
rule. Therefore O cannot be converted by the
ordinary method, if at all.

It has been usual, however, to apply what is
called an indirect method called Conversion by Ne-
gation. Take, for example, " Some realities are not
material objects." If we infer that " Some or all
material objects are not realities," we violate the
second rule, because the predicate of the converse
is distributed, while the subject of the convertend,
which becomes the predicate of the converse, is
not distributed. But now if we attach the nega-
tive term "not" to the predicate in the original
we have " Some realities are not-material, or
non-material objects ; " or again, the equivalent,
" Some realities are immaterial objects." The
proposition thus resulting is supposed to be iden-
tical with the first and original instance. But we
observe that it becomes I in this form which we
can convert simply into " Some immaterial objects
are realities," or in the less euphonious form,
" Some not-material objects are realities." This
proposition, then, can be inferred from the origi-
nal, and the process of reaching it has been called

IMMEDIATE INFERENCE III

the indirect one of Negation. The same process
is applicable to any similar propositions. Thus
the instance of " Some elements are not metals "
would become, first, " Some elements are not-met-
als, or non-metals," and then "Some non-metals
are elements," etc.

But it must be observed that the quality of this
so-called converse is affirmative, while that of the
convertend is negative, and hence viewed in this
light the process of conversion by negation is a
violation of the first rule. Besides, we have been
led by it to affirm something positive about non-
material or immaterial objects assumed in the con-
verse, when the convertend merely denies some-
thing about material objects. While this may be
allowable by some other process, it is not permissi-
ble by conversion. The violation of the first rule
decides that matter. Hence we conclude that
proposition O is really not convertible at all, be-
cause the retention of the quality violates the
second rule, and the alteration of the quality vio-
lates the first rule. This is now the general opin-
ion of logicians. Nevertheless, the process de-
scribed as conversion by negation is a legitimate
one, at least formally speaking. But it is in real-
ity a double process : first one of obversion and
then one of conversion, which makes the result
the converse of the obverse of the original. This
makes it what we shall call Contraversion, or the
process commonly called Contraposition.

2d. Obversion. — Obversion is sometimes called
" Immediate Inference by Privative Conception."
This will serve as a good name when the propost-

II2 LOGIC AND ARGUMENT

tions are affirmative, and when a privative term
can be found for the purpose. But when the
proposition is negative, and when a privative term
is not accessible, it is much better to use the term
Obversion. The process consists in negating the
copula and the predicate without converting. Thus
the proposition " All men are mortal " is obverted
by saying, " All men are not not-mortal," or " No
men are not-mortal," or again, as it is sometimes
expressed, " No men are immortal." Here it is
noticeable that Obversion changes the quality of the
proposition in the process from affirmative to neg-
ative, or from negative to affirmative, as the case
may be. The meaning of the original is retained
by virtue of the fact that the two negatives make an
affirmative, but the form of expression appears as
negative, since one of the negatives qualifies the
copula and the other the predicate.

In the negative proposition the obversion is
accomplished simply by connecting the negative
particle with the predicate, which both changes
the quality of the proposition and the character
of the predicate, as in the affirmative. Thus,
" No men are quadrupeds," or " All men are
not quadrupeds," by obversion becomes "All men
are not-quadrupeds," meaning that they are in the
class " non-quadrupeds " from not being in the
class "quadrupeds." This process terminates in
the same result as literally following the rule. To
follow the rule of double negation in this case
the proposition would become " All men are not
not-quadrupeds," and the first two negatives be-
coming superfluous, cancel each other ; so that we

IMMEDIATE INFERENCE 113

have, as in the first case, " All men are not-quad-
rupeds." A negative proposition is, therefore, most
conveniently obverted by transferring the negative
particle to the predicate. In regard to the process
in general it will be found, by following the rule,
to apply to all four propositions — A, E, I, and O.
3d. Contraversion or Contraposition. — Contra-
version or Contraposition consists in the negation
of copula and predicate with conversion. That is, we
first obvert the original and then convert this ob-
verse. It amounts to the same thing to take the
negative of the predicate in the contravertend for
the subject of the contraverse, and deny the con-
nection between it and the subject of the contra-
vertend, if the latter be affirmative, and affirm
the connection if the contravertend be negative.
This can be best explained by an example. Take
the proposition "All men are mortal." By the
very terms of this judgment the class " men " is
wholly included in the class " mortal," as indi-
cated in Fig. IV., and excluded, therefore, from
everything "not-mortal." We can, therefore, af-
firm that " All men are not in the class of those
who are not mortal ; " or, more briefly the obverse,
" All men are not not-mortal." By simple convex
sion from this we get "All not-mortal are not
men." But, again, noticing that the inclusion of
" men " in the class "mortal " excludes those who
are "not-mortal" from "men, "we may as well
affirm that fact directly, and hence from the origi-
nal infer at once from " All men are mortal " that
" All not mortals are not men." We reach the re-
sult in this case without a roundabout process.
8

H4 LOGIC AND ARGUMENT

The same process will apply to propositions in E.
Simply include the negative particle in the sub-
ject of the contraverse and make the latter affirm-
ative. Thus, "All negroes are not Caucasians"
will be contravened by saying "Some not-Cau-
casians are negroes." The transfer of the nega-
tive particle to the term to be used for the subject
of the contravertend has the effect of obversion,
and makes the proposition an A, which must be
converted by limitation into I.

By similar processes we can treat I and O.
But we shall find that I cannot be contravened,
for the same reason that O cannot be converted.
Summarizing results, however, we find that all
propositions except O can be converted ; all can
be obverted, and all except I contravened.

In the practical application of Contraversion
we must be careful about the use of privative, and
especially nego-positive, terms. The result to the
latter in particular, in substitution for the nega-
tion of the predicate, may lead to equivocation,
and therefore to material error in the process.
Thus to contravert " All just acts are expedient "
into " All inexpedient acts are unjust," is to assume
that "unjust" is convertible with " not-just," which
is not necessarily the case. A better illustration
of the contention here made is perhaps the propo-
sition " All human actions are free," in which the
contraverse is " All not-free actions are not hu-
man," instead of " All not-free actions are inhu-
man" Other cases of a like error may not be so
evident, but they are precisely the kind of error
against which we have to guard.

IMMEDIATE INFERENCE 115

4th. Inversion. — Inversion is the process of in-
ferring from one proposition another which shall
contain for its subject the negative of the subject
in the original, and for its predicate the predicate
of the original. The result is accomplished by
alternating the processes of obversion and con-
version, and beginning with either of them and
proceeding until the result is gained. A and E
can be inverted ; I and O cannot. In the case of
the two propositions the result depends upon the
way we begin. Take an A proposition : "All horses
are animals." If we start with conversion, then
obvert, and again try to convert, we shall find that
we have an O proposition for the last process and
we can proceed no farther. But if we first obvert,
then convert, obvert again, then convert, and last-
ly obvert, we shall find the required proposition.
Thus, " All horses are animals " obverted is " All
horses are not not-animals ; " then this converted
gives "All not-animals are not horses ; " obverted
again we have " All not-animals are not-horses,"
and again converted, being an A proposition, be-
comes " Some not-horses are not-animals," and
lastly obverting, we have " Some not-horses are
not animals." The process, however, is not im-
portant in practical logic and does not require to
be more than mentioned.

5th. Contribution. — Contribution is the process
by which what is affixed to the subject as a modifier
may also be affixed to the predicate in the same sense.
It takes two forms, called respectively Immediate
Inference by Added Determinants, and Immediate
Inference by Complex Conceptions. The simplest

H6 LOGIC AND ARGUMENT

illustration of the general process is in mathemat-
ics. Thus if x = a, then x + i = a + i.

1. Inference by Added Determinants. — This con-
sists in merely adding some adjective or similar
term to both subject and predicate. Thus, to " A
house is a dwelling" we can add "A good house
is a good dwelling." But we cannot add different
quantities to both terms, as is implied by using the
superlative degree of an adjective. Thus, while
we can say " Dogs are quadrupeds," we cannot
say "The largest dogs are the largest quadru-
peds." The quantity and quality added must be
the same. This will not always apply to particu-
lar proportions.

2. Inference by Complex Conception. — This con-
sists in the addition of complex phrases and
clauses to both sides ®f the proposition, always
observing the identity of quantity and quality in
both cases. Thus, to " Pigeons are birds" we can
add " Pigeons that live in warm climates are birds
that live in warm climates," etc. But here we
have to be on our guard against the same error as
in Added Determinants. From " Voters are men "
we cannot infer that '•' The majority of voters is
the majority of men."

False inferences by contribution often occur,
even though it be unintentional, in long and com-
plicated cases of discourse, and it requires close
observation to detect them. In simple reasoning
they are not so liable to take place.

6th. Antithesis. — Antithesis isM<? inference from
any given proposition to a complementary opposite. It
is not valid in any proposition except materially in

IMMEDIATE INFERENCE 1 17

definitions, and in duplex propositions. But it is a
very common error to make the inference. Thus,
if we make the assertion that " All good men are
wise," many people think themselves entitled to
infer that " All bad men are not wise." If good-
ness and wisdom are identical, the inference is
correct, because the proposition would practically
be a definition. But we know nothing about such
identity from the proposition. The process as-
sumes the distribution of the predicate when this
is not the case. We must, however, be on our
guard also not to confuse the mere statement of
an antithesis with the inference to it. Thus the
Book of Proverbs often states antitheses, which we
are not obliged to interpret as inferences from one
of the propositions.

CHAPTER VIII
MEDIATE REASONING

I. DEFINITION.— Mediate inference is reason*
ing by means of a middle term. A Middle term is one
which is compared with two others, called Minor
and Major terms, and on the ground of which a
connection or relation, affirmative or negative, can
be established between these two in the conclusion.
This use of a middle term makes it necessary that
there should be more than a single premise in or-
der to effect a conclusion. An illustration of this
form of reasoning is found in the following :

All machines are instruments for applying power.

All locomotives are machines.
.•. All locomotives are instruments for applying
power.

In this process we are supposed to see or dis-
cover the connection between subject and preid-
cate in the conclusion because of their connection
with the middle term, " machines," in the premises.
The reasoning in such cases is usually called
the Syllogism, or Syllogistic Reasoning.

II. DIVISIONS — There are two kinds of syl-
logistic or mediate reasoning, according as the
conclusion is or is not included in the premises.
These are usually called Deductive and Inductive

118

MEDIATE REASONING lip

Reasoning. Deductive reasoning is of that kind
which aims to deduce the conclusion ; that is, to
draw it out of the premises by virtue of its sup-
posed necessary inclusion in them. Inductive rea-
soning is of that kind which aims to induce the
conclusion ; that is, to suppose a new idea or prop-
osition as a probable truth from known facts. In
deductive reasoning the premises make the conclu-
sion necessary, supposing that the formal rules of
the syllogism have been observed ; in inductive
reasoning the conclusion is at most only possible or
probable. In both of them there are two direc-
tions, so to speak, in which the reasoning may
occur. We may start with the premises and dis-
cover the conclusion. This may be technically
called inference. Or we might start with the asser-
tion of a proposition and seek to discover the
grounds upon which it rests ; namely, the pre-
mises. This may be technically called proof. The
former is a progressive, and the latter a regressive,
process. In the one we discover a conclusion
from foregone premises, and in the other we dis-
cover the premises for a foregone conclusion.

III. ELEMENTS OF THE SYLLOGISM.—
Every syllogism must have three propositions and
three terms, and only three of each. This is the
simple rule for the syllogism. The three terms
are called the Major, the Minor, and the Middle
terms. Of the three propositions, two are called
the Premises, and one the Conclusion. Of the pre-
mises, one is called the Major and the other the
Minor. The Major term is the predicate of the
conclusion, and the Minor term the subject of the

120 LOGIC AND ARGUMENT

conclusion. The Middle term is found only in
the premises, and may be either the subject or the
predicate in either of the premises, but must al-
ways be found once in both premises. The Major
Premise contains the Major and Middle Terms :
the Minor Premise, the Minor and Middle terms ;
and the Conclusion, the Minor and Major terms.
Without the express statement of the conclusion
there is no rule for determining, in the actual rea-
soning of practical life, which of the premises is
the major and which the minor. We are at liberty
to choose either of them as a major or minor, and
to try the consequences by the rules of the syllo-
gism. But for the sake of a uniform rule which
shall express the most convenient form in which
reasoning ought to be conducted in order to avoid
obscurity, logicians have agreed to the law that
properly the major premise shall stand first, the
minor premise second, and the conclusion last.
This enables formal discourse and reasoning to
be conducted without misunderstanding as to or-
der and definiteness. But in common discourse
this rule is not always followed. In this the minor
premise may come first, and the major premise
second ; or the conclusion may come first, as often
in the case of proof, and the premises in any order
we please after that. But formal regularity or
uniformity of procedure would require us to adopt
some rule of correct order in which the inclusion
of terms is most easily perceived. The order is,
the major premise first, minor premise next, and
the conclusion last.

It has been usual to employ symbols for the

MEDIATE REASONING 121

several terms of the syllogism in order to illus-
trate more easily the various relations of terms
and propositions in the forms of reasoning. The
letters chosen for this purpose are S, M, and P,
with an additional implication in the use of S and
P, as compared with their previous employment. S
shall stand for the minor term, which is always the
subject of the conclusion, and P for the major term,
which is always the predicate of the conclusion.
They thus stand respectively for the subject and
predicate, as heretofore, but only in the conclusion,
since the minor term, S, is not always the subject
in the premise, nor the major term, P, always the
predicate in the premise. M shall stand for the
middle term, and may be either subject or predicate
in either or both of the premises. The combina-
tion of these terms will represent the premises and
conclusion.

Terms.

M = Middle Term.

S = Minor Term = Subject of Conclusion.

P = Major Term = Predicate of Conclusion.

Propositions.

M is P = Major Premise.
S is M = Minor Premise.
S is P = Conclusion.

IV. RULES FOR THE SYLLOGISM.— The

rules for the construction of the syllogism may be
divided into two classes. First, those affecting

122 LOGIC AND ARGUMENT

the subject-matter of the propositions and the
syllogism as a whole. Second, those affecting
the quantity and quality of the propositions. We
do not investigate here how these rules came to
be adopted, as the reasons for them would take
us farther than an elementary treatise will allow.
Hence we simply state the results with the pur-
pose of using the rules to test the valid and in-
valid forms of reasoning.

i st. Rules Affecting the Subject-Matter of the
Syllogism.

1. Every syllogism must have three terms, and
only three terms.

2. Every syllogism must have three proposi-
tions, and only three propositions.

3. No term in the premises of the syllogism
should be ambiguous.

An ambiguous term is equivalent to the use of
four terms in the syllogism. Although it con-
forms in appearance to the rule, its double mean-
ing makes it include the fourth term.

ad. Rules Affecting the Quantity and Quality
of Propositions.

4. The middle term must be distributed at least
once in the premises.

5. No term must be distributed in the conclu-
sion which was not distributed in the premises.

6. No conclusion can be drawn when both
premises are negative.

7. No conclusion can be drawn when both
premises are particular.

8. No universal conclusion can be drawn when
one of the premises is particular ; or if one of the

MEDIATE REASONING 123

premises be particular, the conclusion must be-
particular.

9. No affirmative conclusion can be drawn
when one of the premises is negative ; or if one of
the premises be negative the conclusion must be
negative.

In the construction of every syllogism we must
have reference to two things : first, the quantity
and quality of the propositions, and second, the
position of the middle term. These conditions
give rise to what are called the Moods and the
Figures of the syllogism.

V. MOODS OF THE SYLLOGISM.— The Mood
of a syllogism is that characteristic of it which is
determined by the quantity and quality of its propo-
sitions. The Mood can never be separated from
the Figure in practical reasoning, but it is not
determined by the same characteristics. Every
syllogism, as we have seen, must contain three
propositions and only three. But there are four
forms of propositions (eight in case of quantify-
ing the predicate) to be considered, from which
three have to be chosen and combined in various
ways. Thus all three propositions, major premise,
minor premise, and conclusion may be A propo-
sitions, or one an A or I proposition, one E and
the other an E or O, etc. With the four propo-
sitions, therefore, the conceivable Moods will
represent all possible combinations, either of the
same or different quantity and quality. When the
combinations are completed we find them to be
sixty-four in number. They appear in the follow-
ing table :

124

LOGIC AND ARGUMENT

AAA AEA AIA AOA EAA EEA EIA EGA

AAE AEE AIE AOE EAE EEE EIE EOE

AAI AEI All AOI EAT EEI EII EOI

AAO AEO AIO AGO BAG EEO ElO EGO

IAA IEA IIA

IAE IEE HE

IAI IEI III

IAO IEG IIO

IOA OAA OEA OIA OOA

IOE OAE GEE OIE OOE

IOI OAI OEI Oil OOI

IOO OAO OEO OIO OOO

But these are not all valid forms of reasoning.
Some of them violate one rule, some another, and
some even two rules. For example, EEA violates
rule 6, and IIA violates rule 8, and IOA rules 8
and 9. By applying the several rules, including.
6, 7, 8, and 9, to this table we are enabled to re-
ject all but tivelve of these Moods, as violating one
or the other of these rules, and as not possibly
valid in any case. The twelve Moods remain as
possibly valid, though they must first be tested by
rules 4 and 5 before they can be accepted, and it
will be found that some of them are valid in one
Figure of the syllogism and not in another, while
one of them will be found to be invalid in all of
them. This is IEO. The possible Moods, how-
ever, remaining after applying the last four rules
to the whole table are as follows :

AAA

AAI

All

AEE

AEO

AOO

EAE IAI
EAO (IEO)
EIO

OAO

MEDIATE REASONING 125

These remain to be tested in the four Figures, so
that there will be forty-eight forms still to consider.

VI. FIGURES OF THE SYLLOGISM.— The
Figure of a syllogism is that characteristic of it
which is determined by the position of the middle
term. As there are two propositions, each with a
subject and predicate, in the premises of every
syllogism, there are four possible positions for
the middle term. It may be the subject of both,
the predicate of both, the subject of the major
and predicate of the minor, or the predicate of
the major and the subject of the minor premise.
These positions and the several Figures are rep-
resented in the following diagram :

FIG. I. FIG. II. FIG. III. FIG. IV.

M = P P = M M=P P=M

S = M S = M M = S M = S
S := P S = P S = P S-P

The twelve possible Moods have to be tested
in each of these Figures before we know the con-
ditions under which they are valid at all. By
applying the rules for the distribution of terms
and the limitations upon correct reasoning, as
determined by rules 4 and 5, we find that some of
the twelve moods are valid in each Figure and
some are not. Thus we have an illustration of
this method in the mood AAA for all the Figures.

FIG. I. FIG. II. FIG. III. FIG. IV.

A (g)=P A (P)=M A (M)=P A (P) = M

A (S}=M A (|)=M A ®=S A © = S

A (S)-P A (D=P A (S)=P A (S) = P

VALID. INVALID. INVALID. INVALID.

126 LOGIC AND ARGUMENT

In the first Figure the rules for distribution are
satisfied, and AAA is valid. But in the second
Figure the middle term is not distributed in either
premise, and the fallacy is called Undistributed or
Illicit Middle, In the third Figure the minor
term is not distributed in the minor premise, but
is distributed in the conclusion. This gives an
Illicit Minor. In the fourth Figure the same fal-
lacy is committed, and hence AAA is valid in
only one Figure. By applying the same test to all
the twelve Moods in the four Figures we have
the following as the valid and the invalid Moods
in each Figure. A line is drawn across those that
are invalid.

AAA

AAI A** AAI AAI

All *** All Arrt

AEE AEE AEE

AEO A66 AEO
AGO

EAE EAE

EAO EAO EAO EAO

EIO EIO EIO EIO

IAI IAI

OAO OAO OAO

Six Moods are valid in each Figure and six are
invalid, so that we have in this representation a
measure of the combination of propositions and
forms of reasoning that are legitimate.

MEDIATE REASONING 127

If we observe this list we shall notice that the
First Figure is the only one which will give a uni-
versal affirmative conclusion, and it is the only one
which will give conclusions in all four propositions,
A, E, I, and O. The Second Figure gives only
negative conclusions, and the Third Figure gives
only particular conclusions. The Fourth Figure
has never been regarded as important enough in
argument, being so little used, to receive any at-
tention from logicians, though it gives conclusions
in E, I, and O. We have only to mutate or trans-
pose the premises of the Fourth Figure in order
to produce the First Figure.

VII. REDUCTION OF MOODS AND FIGURES.
— The First Figure of the syllogism is the most
natural form for most of our reasoning, at least
when we are not engaged in the process of dis-
proof. Consequently, looking at the perplexing
number of Moods and Figures that are valid, the
old logicians sought to reduce the various Moods
in the other Figures into the valid forms of the
First. The process is a rather complicated one
and has no practical importance, and is impossi-
ble, directly, in the Moods AOO of the Second
Figure, and OAO of the Third Figure. But
without going through the scholastic method of
reduction, and without guaranteeing that the
method of reduction here indicated will result al-
ways in valid equivalents after the process has
been accomplished, I may suggest a few simple
rules for the reduction of the Moods in one Figure
to those of another. The whole process can be
effected by the proper adjustment of conversion and

128 LOGIC AND ARGUMENT

mutation of premises. Thus, convert the major
premise of the First Figure, and we obtain a syllo-
gism of the Second Figure. Convert the major
of the Second and we obtain the First Figure.
Mutate the premises in either the First or Fourth
Figure and we obtain the other, etc.

VIII. PRACTICAL IMPORTANCE OF THE
FIGURES. — There is some difference between the
various Figures in regard to their practical value.
In the first place, they cannot all be applied to at-
tain the same result, the Second Figure giving no
affirmative, and the Third Figure no universal con-
clusion. The First Figure is the most natural and
the most usual form of reasoning, and is regarded
by logicians as the Figure best adapted to proof,
especially as it will give all four propositions, A, E,
I, and O, in its conclusion, and is the only one in
which universal affirmatives are possible, which
represent the most important forms of conviction.
Again, the First Figure being the most natural
and the most usual form of reasoning, it is inter-
esting to remark that argument is not possible in
it with a particular major premise, or a negative
minor premise. Hence, the rule that we are liable
to fallacy unless our major premise is universal, a
fact which is true for all the Figures except IAI
in Figs. III. and IV., and OAO in Fig. III. As
these two Moods are perhaps never used in prac-
tical life, and the Figures very seldom, we can
dismiss them and accept the rules as practically
universal. In an argument, therefore, involving
proof, we must see that our premises are universal
if we wish to establish a universal conclusion.

MEDIATE REASONING 129

The Second Figure is best adapted to disproof,
or refutation. It is so adapted, partly because
one of the premises must be negative, and chiefly
because of the nature of the comparison which
can be instituted between the subject and predi-
cate. It is evident that two things which cannot
agree in their predicate cannot agree with each
other. In the First Figure a disagreement be-
tween the subject of one and the predicate of the
other premise leads to fallacy. Hence, in order to
disprove an assertion, we have only to show that
one instance, or more, included in the general
statement, does not agree with the predicate, and
we have the contradictory established. For in-
stance, if the assertion is made that " All forms
of government are beneficial," it is evident by
subalternation that " Despotic governments (some
governments) are beneficial," though the assertor
may not consciously recognize the fact when he
makes the statement. Hence, the opponent may
assert and prove (by the First Figure, EAE)
that " Despotic governments are not beneficial."
This last proposition will be the minor premise of
a syllogism of which the major premise is the
first proposition. This would give the conclusion,
" Despotisms are not forms of government," a
conclusion which contradicts what is implied by
the subalternate of " All governments are benefi-
cial," and so contradicts the original assertion.
The affirmative will thus either have to give up
his allegation or show that " Despotisms are not
forms of government," and thus admit the possi-
bility that they are not beneficial without suppos-
9

130 LOGIC AND ARGUMENT

ing the contradiction indicated. The former posi-
tion accepts the refutation ; the latter has to
meet an equivocation in the use of terms which is
at least almost as fatal as a contradiction.

The Third Figure is adapted to the proof of
exceptions to universals, and so may use its result
for the disproof of some universal assertion.
Suppose someone asserts that " No philosophers
are wise." The easiest disproof of this, as we
have seen, lies in the proof of the contradictory I.
We have then only to take some syllogism in the
Third Figure with this proposition as its conclu-
sion ; as follows :

Plato, Kant, etc., were wise.
Plato, Kant, etc., were philosophers.
.*. Some philosophers were wise.

Here we both prove that " Some philosophers
are wise," and disprove the universal negative of
the same proposition, assuming, of course, that
our premises are true.

The Fourth Figure is not regarded by logicians
as having any practical value.

CHAPTER IX

SIMPLE AND COMPLEX FORMS OF CATEGOR-
ICAL REASONING

I. CLASSIFICATION OF FORMS.— The syl-
logism as it has been explained was the simple
syllogism of three propositions. All arguments
can be reduced to this simple form, but while this
is the fact much of our reasoning takes on a more
complex form. Some propositions may be omit-
ted in formal and explicit expression, though in-
cluded in the thought of the reasoner, and in
other cases, while the premises of the main argu-
ment are explicitly stated, they are complicated
with various propositions, stated or implied, that
are intended to prove them instead of merely as-
serting them. This introduces at least implied
syllogisms into the discourse, which are subordi-
nated to the main purpose. These two circum-
stances give rise to two divisions of the syllogism.
They are the Complete and Incomplete, each with
the subdivisions Simple and Complex. The com-
plete syllogism represents an explicit statement
of all that is involved in the mental process.'
This may not often occur in ordinary discourse,
and when it does it is not likely to follow the
formal expression which has been explained in the

132 LOGIC AND ARGUMENT

Moods and Figures. The usual mode of argu-
ment is either to state the facts, leaving the
hearer to draw the inference, or to state only one
of the premises, leaving the other to be under-
stood. But where it is necessary to be clear and
explicit we formulate the argument into complete
syllogisms of some form. They may all be classi-
fied as follows :

Syllogisms

1 , f Simple = Ordinary form,
-ompiete.. | Complex = Prosyllogism and Episyllog

I Simple = Enthymeme

Incomplete •{ , . c. ,

Epicheirema.jS.ngl.

Complex = \

I- I Sorites \ Progressive.

lbontes \ Regressive.

II. EXPOSITION. — The classification has
shown us one simple and two complex forms of
reasoning to be considered that have not been
noticed. They are all reducible to the rules and
form of the simple complete syllogism.

ist. Prosyllogism and Episyllogism. — The
Prosyllogism and Episyllogism consists of two
syllogisms, the conclusion of the first being a pre-
mise in the second. The following are illustra-
tions, the one abstract and the other concrete :

A is B Men are vertebrates.

C is A Europeans are men.

.'. C is B .•. Europeans are vertebrates.

D is C Italians are Europeans.

.•. D is B .*, Italians are vertebrates.

FORMS OF CATEGORICAL REASONING 133

2d. Enthymeme. — An Enthymeme is an incom-
plete syllogism in which one of the premises, or
the conclusion, may be omitted. If the major
premise be omitted, the enthymeme is of the first
order ; if the minor premise be omitted, the enthy-
meme is of the second order ; and if the conclu-
sion be omitted, the enthymeme is of the third
order. The signs of it are such words as indicate
that a reason is given for the truth of the prop-
osition asserted. These words are for, because,
since, inasmuch as, and in the conclusion, therefore,
consequently, etc. As an illustration we have the
propositions : " The air must have weight, be-
cause it is a material substance." The conclusion
in this instance is the statement, " The air must
have weight." If we were stating a mere fact not
looking to any further result, it might not require
proof, but we often desire to support an assertion
by reasons that will show its truth apart from
mere acceptance on authority. In the above in-
stance, the major premise is omitted, and is "All
material substances have weight." When reduced,
the enthymeme becomes a simple complete syllo-
gism.

There are forms of the enthymeme in which the
signs are not expressed, but which have to be de-
termined by the evident relation of the thoughts
stated. The definite and explicit use of the signs
often give a stilted and formal appearance to dis-
course, and hence rhetorical reasons may be sus-
tained for omitting them. The intended, or at
least the implicit, reasoning in such cases must be
discovered from the actual dependence logically

134 LOGIC AND ARGUMENT

of one thought upon another. Hence, in much of
the discourse that does not formally profess to be
reasoning we shall find that process tacitly indi-
cated, and it must be adjudged accordingly.

3d. Epicheirema. — An epicheirema is a syllo-
gism in which one or both of the premises is sup-
ported by a reason which implies an imperfectly
expressed syllogism ; in other words, it is a syllo-
gism in which one or both of the premises is an
enthymeme of the first or of the second order.
The epicheirema may be single or double. It is
single when only one of the premises is an enthy-
meme ; it is double when both premises are en-
thymemes. Following are illustrations :

Single.
A is B ; for it is P. Vice is odious, for it

depraves.

C is A. Avarice is a vice.

.'. C is B. .-. Avarice is odious.

Double.

A is B ; for it is P. Man is rational be-

cause he has a
mind.

C is A, for it is Q. Europeans are men,

because they are
civilized.

.*. C is 8. .'.Europeans have

minds.

The single epicheirema when reduced to a
complete form -becomes a prosyllogism and epi-
syllogism, or two syllogisms. The double epi-

FORMS OF CATEGORICAL REASONING 135

cheirema, when completed, becomes three syllo-
gisms, representing two prosyllogisms and two
episyllogisms, one of the three being both a pro-
syllogism and an episyllogism, the former in rela-
tion to the following and the latter in relation to
the preceding syllogism. An illustration of this
is the following :

( Whatever has a mind is rational
ind< Man has a mind.
( .'. Man is rational.

Man is rational, for he has a mi

Europea
.'. Europe

( Whatever is civilized is man.
ans are men, for they are civilized •< Europeans are civilized.

/ .'. Europeans are men.
ans are rational.

4th. Sorites. — A sorites is so called because the
propositions constituting it form what is regarded
as a " chain," or a continuous series, of premises
from which a conclusion is drawn at the end of
the series, but not before. It consists of enthy-
memes of the third order, as the epicheirema con-
sists of enthymemes of the first and second order.
When completed, therefore, the sorites also forms
a prosyllogism and an episyllogism, or a number
of them. To complete it we have only to supply
the omitted conclusion. The form of the sorites
is twofold, Progressive and Regressive. The fol-
lowing are illustrations :

Progressive Series.

A is B. Bucephalus is a horse.

B is C. A horse is a quadruped.

C is D. A quadruped is an animal.

D is E. An animal is an organism.

.*. A is E. .*. Bucephalus is an organism.

136 LOGIC AND ARGUMENT

Regressive Series.

A is B. An animal is an organism.

C is A. A quadruped is an animal.

D is C. A horse is a quadruped.

E is D. Bucephalus is a horse.

.-. E is B. /. Bucephalus is an organism.

The difference between the progressive and the
regressive sorites is only one of form in statement,
not in the form of reasoning. The sorites may
also be divided into the constructive and the de-
structive. It is constructive when the conclusion
is affirmative j destructive when the conclusion is
negative. The above illustrations are of the con-
structive form and represent the propositions as
all of them universal affirmative, hence of the
Mood AAA. But there are two more constructive
Moods, AAI and All, and three destructive Moods,
EAE, EAO, and EIO, all six being of the First
Figure.

The rules for the valid forms of the sorites
should be stated, because the number of cases in
which this mode of reasoning is legitimate is ex-
ceedingly limited. Any number of premises may
be used, but the quantity and quality of the prop-
ositions constituting them are under strict limi-
tations. The rules regulating their construction,
therefore, are two, and are as follows :

1. Only one premise can be negative, and this
must be the prime major.

2. Only one premise can be particular, and this
must be the final minor.

Since the sorites is an incomplete prosyllogism

FORMS OF CATEGORICAL REASONING 137

and episyllogism, there are intermediate major and
minor premises. The prime major, therefore, will
be the last premise in the progressive, and the first
premise in the regressive, series. The final minor
will be the first premise in the progressive and
the last in the regressive series. If any other
premise than the prime major be negative, the
Mood being AEE, there will be a fallacy of illicit
major, and if any other premise than the final
minor be particular, the Mood being IAI, there
will be a fallacy of illicit or undistributed middle.

CHAPTER X
HYPOTHETICAL REASONING

I. NATURE AND DIVISIONS.— We have al-
ready seen that there are three kinds of proposi-
tions which correspond to as many kinds of rea-
soning. These propositions are the Categorical,
Hypothetical, and Disjunctive, and the forms of
reasoning go by the same name. A categorical
syllogism is one in which all the propositions are
categorical. A hypothetical syllogism is one in
which one or more of the premises are hypotheti-
cal. The main object of the latter is to secure a
conditional conclusion, if not in its form of state-
ment, certainly in its subject-matter. In categori-
cal propositions and syllogisms we usually mean to
assume or to assert the truth of our premises, and
if our formal reasoning be correct we can accept
the conclusion as a true proposition. But often
we wish first to bring out, if only conditionally,
the truth upon which a proposition rests, so as
to see if the connection between this conclusion
and the major premise be admitted. The whole
question will then depend upon the manner of
treating the minor premise. This has the advan-
tage of getting the major premise admitted with-
out the formal procedure of proof, and the minor
premise is usually more easily proved than the
138

HYPOTHETICAL REASONING 139

major. Consequently, one is made to see more
clearly the force of the argument or reasoning by
removing the question of the material truth of the
major premise and concentrating attention upon
the relation between the conclusion and its condi-
tions, so that we know clearly what we have first
to deny if we do not wish to accept it.

The divisions of hypothetical reasoning are
Simple and Dilemmatic. Simple hypothetical rea-
soning is further divided into Constructive and
Destructive. Dilemmatic reasoning is also divided
into Constructive and Destructive, and each of these
into Simple and Complex. The following table out-
lines these divisions :

/ ^- , i J Constructive.
( SlmP'e- (Destructive.

Hypothetical Syllogisms .A . Constructi ve i Simple.

( Dilemmatic 1 Complex.

1 Destructive]^.

II. SIMPLE HYPOTHETICAL SYLLOGISMS.

— The simple hypothetical syllogism is a form of
reasoning in which either one or both premises
are single hypothetical propositions. Most fre-
quently it is the major premise alone that is con-
ditional, while the minor premise and conclusion
are thus categorical. The proposition called
hypothetical, and regarded as single, really con-
sists of two propositions, one of which is depen-
dent upon the other. That part of it which ex-
presses the condition is called the antecedent, and
that part which depends upon their condition is
called the consequent. The condition is indicated
by some such terms as if, supposing, granted that,
provided that, although, had, were, etc. The con-

140 LOGIC AND ARGUMENT

sequent has no sign. But an illustration of the
hypothetical proposition is " If the sea is rough, it
is dangerous," of which the first part is the ante-
cedent, and the second part is the consequent.

The minor premise either categorically or hypo-
thetically affirms or denies one or the other of
the two terms in the major premise, and as this
must always be a hypothetical proposition, antece-
dent or consequent may be either affirmed or de-
nied. This gives four forms, or Moods, to be
considered, two of which are valid and two invalid
modes of reasoning. The two valid Moods are
called the modus ponens, or Constructive, and the
modus tollens, or Destructive hypothetical syllo-
gisms. The modus ponens means that if the an-
tecedent be affirmed categorically in the minor
premise, the consequent must be affirmed categori-
cally, or follows as a categorical conclusion. The
only effect of a hypothetical minor premise is to
make the conclusion hypothetical. The modus
tollens means that if the consequent be denied, the
antecedent must be denied. The two forms are
illustrated by the following :

Modus Ponens.

If A is B, C is D. If Iron is impure, it is brittle.

A is B. or Iron is impure.

.-. C is D. .-. Iron is brittle.

Modus Tollens.

If A is B, C is D. If the sun shines, it is light.

C is not D. or It is not light.
.-. A is not B. .-. The sun does not shine.

HYPOTHETICAL REASONING 14!

The rule, therefore, for the valid forms of hy-
pothetical reasoning is that either the antecedent
must be affirmed or the consequent denied. The gene-
ral reason for this will appear in the reduction of
hypothetical syllogisms.

The two false Moods are illustrated as follows :

1st Form.

If A is B, C is D. If it rains, it is cloudy.

C is D. or It is cloudy.

.. A is B. .-. It rains.

2d Form.

If A is B, C is D. If Gold were cheap, it would

be useful.

A is not B. Gold not cheap.

•. C is not D. .-. Gold is not useful.

The first of these is the fallacy of affirming the
consequent, and the second, the fallacy of denying
the antecedent. The general rule is that affirming
the consequent or denying the antecedent causes a fal-
lacy. The reason that affirming the consequent
leads to a fallacy is the fact that the condition
mentioned in the major premise may not be the
only one determining the consequent. Some other
condition of it might be true also, and affirming
the consequent would involve this also, but there
is no way of determining what it is. It might be
true, for instance, that " If it is not raining, it is
cloudy," and if affirmation of the consequent en-
tailed the antecedent, we could as well conclude

142 LOGIC AND ARGUMENT

that "It is not raining," or that " It is raining,"
two contradictory conclusions from the same
premise. Hence, we have no right to draw any
inference whatever. A concrete illustration will
make this still clearer. If a man's character be ava-
ricious, he will refuse to give money for charity ;
but it does not follow that every person who re-
fuses to give money for charity is avaricious, as
can be seen by the impossibility of simple con-
version in this proposition. There may be many
proper reasons other than avariciousness leading
him to refuse ; he may have no money, he may
feel that it would do more harm than good, or he
may have some better object in view. No infer-
ence therefore can be drawn from the affirmation
of the consequent.

In the case of denying the antecedent the fal-
lacy is due to the same causes as in the first case.
The antecedent is not the only possible condition
of the consequent, and hence the denial of it will
not prevent the consequent from being a fact ex-
isting by virtue of dependence upon other condi-
tions. It is apparent in the concrete illustration
given that other qualities besides cheapness might
make gold useful, and therefore the absence of
this quality would not remove the usefulness of
the metal.

Difficulties and exceptions to this dictum appear
in many cases, such as :

If fire is hot, it will burn.
Fire is not hot.
.-. It will not burn.

HYPOTHETICAL REASONING 143

But in such instances the apparent correctness
of the reasoning depends upon other characteris-
tics than the form of statement, which is all that
formal logic can recognize. The meaning of the
major premise in all such cases is either that of a
definition making subject and predicate convert-
ible, or that of an exclusive proposition making
the syllogism, when the major premise is convert-
ed from the exclusive to a universal proposition,
a simple modus tollens, one denying the consequent.
In practical reasoning, therefore, we should be on
the alert for instances which appear to be valid
and yet appear equally to violate the formal rules,
but which when interpreted rightly conform to
them.

One important observation must be made in
order to determine when we are affirming and
when denying either term of the hypothetical
proposition. We found that either the antecedent
or the consequent, or both antecedent and conse-
quent may be negative, as :

(a) If A is B, C is not D.

(b) If A is not B, C is D.

In all such cases the minor premise must be
negative in order to affirm, and affirmative in
order to deny a term, antecedent or consequent,
that is negative.

III. DILEMMATIC REASONING. — The di-
lemma differs from the simple hypothetical syllo-
gism, not in the form of reasoning, but only in the
fact that either the minor premise, or both minor

144 LOGIC AND ARGUMENT

premise and the conclusion may be disjunctive
propositions, and in the fact that the major pre-
mise consists of two hypothetical propositions.
The first form of it is the simple constructive di-
lemma :

If A is B, C is D ; and if E is F, C is D.
Either A is B, or E is F.
.-.Cis D.

We observe in this and all similar cases that
the consequent is the same for both antecedents.
This gives as its distinctive mark a categorical con-
clusion. A concrete illustration is the following :

"If a science furnishes useful facts, it is worthy
of being cultivated ; and if the study of it exer-
cises the reasoning powers, it is worthy of being
cultivated ; but a science either furnishes useful
facts, or its study exercises the reasoning powers ;
therefore it is worthy of being cultivated."

The second form is the complex constrtictive di-
lemma :

If A is B, C is D ; and if E is F, G is H.
Either A is B, or E is F.
.-. Either C is D, or G is H.

In this instance the consequents are not the
same, and this results in a disjunctive conclusion
which is the distinctive mark of the complex con-
structive dilemma. The following is a concrete
illustration :

" If a statesman who sees his former opinions
to be wrong does not alter his course, he is guilty
of deceit ; if he does alter his course, he is open

HYPOTHETICAL REASONING 145

to the charge of inconsistency ; but he either
does not alter his course, or he does alter it when
he remarks a change of opinions ; therefore he is
either guilty of deceit, or is open to the charge of
inconsistency."

The destructive dilemma also takes two forms, the
simple and complex. The conclusion is again
categorical in the former and disjunctive in the
latter. The following is the form of the simple
destructive dilemma :

If A is B, C is D ; and if E is F, C is D.
But C is not D.
.-. Neither A is B, nor E is F.

A concrete illustration is : " If it rains, the
river rises ; and if the tide flows, the river rises ;
but the river does not rise, and therefore it neither
rains nor does the tide flow."

The complex destructive dilemma takes the fol-
lowing form :

If A is B, C is D ; and if E is F, G is H.
Either C is not D, or G is not H.
.•. Either A is not B, or E is not F.

The concrete example is: "If this man were
wise, he would not speak irreverently of Scripture
in jest ; and if he were good, he would not speak
irreverently in earnest ; but he either speaks of
it irreverently in jest, or he does it in earnest ;
therefore he is either not wise, or not good."

The fallacies in the dilemma are the same as in
the simple hypothetical syllogism, and arise from

146 LOGIC AND ARGUMENT

the attempt to draw a conclusion after affirming
the consequent or denying the antecedent.

IV. REDUCTION OF HYPOTHETICAL TO
CATEGORICAL REASONING. — The form of
statement and the language of the rules in hypo-
thetical reasoning do not betray the fact that it
can be reduced to categorical form, but this is
the fact, and it shows a simpler conception of the
general process than might be imagined from the
division into the three types. It enables us also
to see the Moods and Figures in categorical syllo-
gism to which the Moods of the hypothetical syl-
logism are equivalent. In all cases, therefore, of
hypothetical reasoning, which we wish to reduce
to the categorical form, we have only to regard
the antecedent of the hypothetical proposition as the
subject of the categorical, and the consequent of the
hypothetical proposition as the predicate of the categor-
ical. In some cases this change is a very simple
one ; in others it can be effected only by a circum-
locution. The following is an illustration of this
reduction in the simpler form :

Hypothetical.

If iron is impure, it is brittle.
Iron is impure.
.'. Iron is brittle.

Categorical.

Impure iron is brittle.
Iron is impure.
/. Iron is brittle.

HYPOTHETICAL REASONING 147

Where we have to supply a circumlocution, such
phrases as " the case of" or "the circumstances that'
must be used, as in the following instance :

Hypothetical.

If Aristotle is right, slavery is a legitimate

institution.

Slavery is not legitimate.
.•. Aristotle is not right.

Categorical.

The case of Aristotle being right on slavery is a
case of slavery being a legitimate institution.
Slavery is not legitimate.
.*. Slavery is a case of Aristotle not being right.

If now we look at the first instance of the hypo-
thetical syllogism reduced to the categorical, we
shall discover that it is equivalent to AAA of the
First Figure in the categorical. This is a case of
affirming the antecedent and is valid, as also AAA
of the First Figure always is. But if we affirm the
consequent in any case we affirm the predicate of
the categorical proposition, according to the rule
for the reduction, and hence we obtain AAA of
the Second Figure in the categorical syllogism,
which is an error of illicit or undistributed middle.
But if in the minor premise we deny the ante-
cedent, we have a case of AEE of the First Figure,
which, as we have before seen, is a fallacy of illicit
major. If we deny the consequent, we have a case of
AEE of the Second Figure, which is valid. Hence,

148 LOGIC AND ARGUMENT

when the four forms of hypothetical syllogism are
reduced to the categorical, assuming the major
premise to be affirmative, we have four Moods in
the categorical syllogism representing the reason-
ing in the hypothetical. These are AAA, affirm-
ative Moods, of the both Figures, and AEE, neg-
ative Moods, of the both Figures, only one in
each case being valid. If the maj,or premise of
the hypothetical syllogism be n-egative, we may
also have the forms EAE of both the First and
Second Figures. If the minor premise be particu-
lar, according as it is affirmative or negative, we
may have the Moods All, AOO, and EIO of both
Figures.

CHAPTER XI
DISJUNCTIVE REASONING

I. NATURE OF DISJUNCTIVE REASONING.

— A disjunctive syllogism is one which is deter-
mined by the presence of a disjunctive proposition
in the major premise, and in the conclusion also
when the disjunction in the major premise con-
tains more than two terms. A disjunctive propo-
sition we have already learned to be one which
contains alternative predicates for the subject in
which either and or are used to denote a choice
between two terms. Wherever "either — or " is
found in such propositions, the expression means
that only one of two things can be affirmed of the
subject, and that the other or others must be de-
nied. Thus, when we say that " The weather is
either clear or cloudy," we mean that it is one, it
cannot be the other. It is this kind of propo-
sition that determines the nature of the disjunc-
tive syllogism and the manner of drawing its in-
ferences.

But there is an ambiguity in the use of the ex-
pression " either — or." One of these uses implies
a contradiction or mutual exclusion between the
terms of the disjunction. This is the proper log-
ical use of the expression in defining disjunctive
149

150 LOGIC AND ARGUMENT

propositions. The second meaning of the expres-
sion is that either term of the apparent disjunction
may have an affirmative connection with the subject
without implying that the other is negative, or that
at least one of them is true, though both may be.
This is illustrated in the proposition, " Gibbon
was either very talented or very industrious."
Here we mean that at least one of these qualities
must be present in the subject, in order to explain
certain facts. Such cases, however, are not true
disjunctive propositions, as they have to be con-
ceived for disjunctive reasoning. They give rise
to what is called the fallacy of incomplete disjunction,
a form of petitio principii, or begging the question,
considered from the point of view of correct dis-
junctive propositions. The true disjunctive prop-
osition must use " either — or" to denote reciprocal
exclusion between their predicates. The proper
way, therefore, to test whether a proposition is
materially, as it may be formally, disjunctive is to
convert it into its equivalent hypothetical propo-
sitions, and see if the consequent necessarily fol-
lows in both cases. Thus, in the proposition " A
is either B or C," we have a case which can be re-
solved into " If A is B, it is not C," and " If A is
not B, it is C." If we find that both propositions
are true in this result, we may safely assume that
the disjunction is materially what it is formally.
Otherwise, while the formal reasoning may be
correct, the material conclusion may be false,
owing to the incomplete disjunction in the major
premise. There is no formal fallacy in disjunctive
reasoning. The reason for this will be seen when

DISJUNCTIVE REASONING 151

discussing its reduction to the other forms. But
one important fact must be noted, and it is that
when we say " A is either B or C," we mean both
" if A is B, it is not C " and " if it is not B, it is C,"
etc. This brings out the formal exclusion ex-
pressed by the expression " either — or."

II. FORMS OF DISJUNCTIVE REASONING.
— There are two forms of disjunctive reasoning,
called the modus ponendo fattens and the modus tollen-
do ponens. The meaning of the first is that if we
affirm one of the alternatives we must deny the other,
and of the second, that if we deny one of the alter-
natives we must affirm the other. An illustration of
each is the following :

Modus Ponendo Tollens.

A is either B or C. Oak trees are either tall

or short.

A is B. Oak trees are tall.

.*. A is not C. .*. Oak trees are not short

If we said " A is C," the conclusion would be
" A is not B ; " or that " Oak trees are short," it
would be " Oak trees are not tall."

Modus Tollendo Ponens.

A is either B or C. The air is either cool or

warm.

A is not B. The air is not cool.

.•. A is C. .'. The air is warm.

The case of incomplete disjunction can be illus-
trated as follows :

152 LOGIC AND ARGUMENT

Gibbon either had great talents or he was very

industrious.
He had great talents.
.*. He was not very industrious.

There is no error in the process of reasoning in
this latter instance, but only in the assumption
that the disjunction in the major premise repre-
sents a contradiction or mutual exclusion between
the predicates.

III. REDUCTION OF DISJUNCTIVE SYLLO-
GISMS.— We have found earlier in this treatise
that a disjunctive proposition is categorical in its
form, but hypothetical in its meaning. Proceed-
ing upon this fact, we can give it hypothetical ex-
pression, and then, if need be, categorical expres-
sion without disjunctive form, so that we should
have but one set of principles to which all formal
reasoning can be reduced. But if a disjunctive
proposition can be reduced to a hypothetical one,
as the alternative predicates, implying the connec-
tion of one and the exclusion of the other from
the subject, enables us to do, we have a simple
illustration of this reduction in the following syl-
logisms :

Disjunctive. Hypothetical.

A is either B or C. If A is B, it is not C.

A is B. A is B.

/. A is not C. /. A is not C.

The Moods which this process will ultimately
represent will depend upon whether the minor

DISJUNCTIVE REASONING 153

premise of the disjunctive syllogism be affirmative
or negative, or whether we state the hypothetical
equivalent of the major premise in an affirmative
or negative form. This can be worked out for
each case without illustration here.

One peculiarity in the disjunctive syllogism
makes it appear to violate certain rules already laid
down about legitimate reasoning. We notice that
in disjunctive syllogisms we may have a negative
conclusion when both premises are affirmative,
or an affirmative conclusion when one of the pre-
mises is negative. This is shown in the illustra-
tions which exhibit the two forms of this syllogism,
where there is a negative conclusion in the modus
Ponendo tollens, and an affirmative one in the modus
tollendo ponens. But this exception is only appar-
ent. The major premise of a disjunctive syllo-
gism actually contains or implies two propositions
when we come to state its meaning ; perhaps even
four. " A is either B or C " means that " If A is
B, it is not C ;" that " If A is not B, it is C ;"
that " If A is C, it is not B ; " and that " If A is
not C, it is B." This will show that what appears
as an affirmative proposition really implies a nega-
tive by virtue of the contradiction expressed in
the disjunction, and the implication that the two
or more predicates cannot be affirmed of the sub-
ject at the same time. This is apparent when the
major premise of the disjunctive is converted into
the major premise of the hypothetical syllogism.
Here if the form " A is either B or C " is reduced
to the hypothetical " If A is B, it is not C," we
have a negative proposition for the major premise

154 LOGIC AND ARGUMENT

of the hypothetical syllogism, and its categorical
form, so that the modus ponendo tollens of the dis-
junctive will become the modus ponens of the hypo-
thetical, and EAE of the categorical syllogism,
which gives a negative proposition for its conclu-
sion. By a similar process we could explain why
it seems that an affirmative conclusion can be
drawn when one of the premises is negative. In
this we see that the modus ponendo tollens of the
disjunctive becomes EAE of the First Figure in
the categorical syllogism, and the modus tollendo
ponens AAA of the First Figure in the categori-
cal. It is thus the complex character of the dis-
junctive proposition that causes the apparent
exception, but its real conformity to the regular
rule for reasoning.

CHAPTER XII
FALLACIES

I. DEFINITION AND DIVISIONS The term

" fallacy " is derived from the Latin fallo, denot-
ing deception, and comes to mean illusion, or
error. But in Logic " fallacy " must be dis-
tinguished from illusion, in its psychological sense.
An illusion, even perhaps in all cases, is a false
interpretation or construction of the data of sense-
perception ; a fallacy is an error in reasoning.
This latter term, however, is often applied to
those errors which are liable to occur in the in-
terpretation of ambiguous propositions, made so
by the displacement of a word or phrase, or by
the vocal accent. This is illustrated in the so-
called semi-logical fallacies of Accent and Amphi-
bology, both giving rise to different meanings in a
proposition. But in the true logical sense these
errors are not fallacies, but rhetorical illusions.
They may give rise to fallacies in reasoning by
rendering the data uncertain and equivocal, but
they are not errors in the reasoning itself. They
are simply errors of interpretation and expres-
sion.

The fallacies with which logic deals may be
divided into Formal and Material, They are all
155

156 LOGIC AND ARGUMENT

errors in the inference or transition of the mind
from one proposition to another. But a formal
fallacy is an error that arises from a violation of
the formal laws of the syllogism. It is incident
to the form or statement of some proposition in
relation to another, or, as it is often called, a fal-
lacy in dictione or in voce. It arises out of an error
in the distribution of terms and in reasoning from
premises forbidden by rules six and nine. On
the other hand, a material fallacy is one which is
due to some peculiarity in the subject-matter of
the reasoning, and hence arises independently of
the form of statement ; that is, independently of the
quantity and quality of the propositions, and so is
said to be extra dictionem. The formal reasoning
may be correct enough, but owing to some error
in the material elements of the process the con-
clusion may be vitiated, as in the ambiguity of
terms, the assumption of actually false premises,
or the assumption of matter not found in the
premises. The formal fallacies can be detected
by anyone who can understand merely the formal
laws of reasoning, but material fallacies require
that the reasoner be familiar with the subject-
matter of the discourse or argument. In Political
Economy, for instance, anyone familiar with
formal reasoning could detect formal fallacies
without knowing anything about the subject it-
self, but in order to discover material fallacies
he must know enough about the subject and
laws of Political Economy to recognize equivo-
cal terms, false propositions and material in the
conclusion transcending the premises.

FALLACIES 157

II. FORMAL FALLACIES — Formal fallacies
have been sufficiently defined as determined by
the nature of the premises and errors in distribu-
tion. Their classification remains to be briefly
considered.

i st. Illicit Process of the Middle Term —
This fallacy grows out of the failure to have the
middle term distributed at least once in the prem-
ises. It is illustrated as follows :

Some Pennsylvanians are Americans. I M = P

All Philadelphians are Pennsylvanians. A (s) = M

.'. Some Philadelphians are Americans. I S = P

2d. Illicit Process of the Major Term — The

illicit major is due to the distribution of the major
term in the conclusion when it is not distributed
in the premise. Following is an illustration :

All men are carnivorous. A (M) = P

Some animals are not men. O S x (M)

. *. Some animals are not carnivorous. 0 S x (P)

3d. Illicit Process of the Minor Term — The

illicit minor arises from the distribution of the
minor term in the conclusion when it is not dis-
tributed in the premise. Following is an illus-
tration :

No Caucasians are negroes. E (M) x (p)

All Caucasians are mortal. A (M) — S

No mortals are negroes. E (5) x P

4th. Illicit Process with Negative Premises. —
The fallacy in this instance is not due to an error
in the distribution of terms, but to the attempt to

158 LOGIC AND ARGUMENT

reason to what is not implicitly or explicitly in-
cluded in any of its parts in the premises. Illicit
distribution is a partial transgression of the prem-
ises quantitatively considered, while the present
fallacy is a total transgression of them, and so must
be illustrated in another way in addition to the ex-
hibition of distribution. Following is an illus-
tration :

No men are quadrupeds. E (M) x (?)
No ruminants are men. E (M) xf?)

FIG. VIII.

Either one of the
diagrams in this in-

i i stance will represent

V J the possible relations

^- of subjects and predi-
cates. But there is
nothing specifically
saidor implied thatwill
enable us to say wheth-
er "ruminants" are
included in " quadru-
peds " or excluded from them. Consequently, we
can infer neither an affirmative nor a negative
exclusion.

5th. Illicit Process with Mixed Premises and
Conclusions — This is the fallacy of drawing a

FALLACIES

'59

negative conclusion from affirmative premises and
an affirmative conclusion when one of the prem-
ises is negative. The mode of illustrating it or
representing it by diagrams will be somewhat sim-
ilar to that of negative premises, and also like it can-
not be represented by the method of distribution.

The fallacy of particular premises and that of
drawing a universal conclusion when one of the
premises is particular, are instances of illicit dis-
tribution of terms either of the middle, major,
or minor.

III. MATERIAL FALLACIES — Material fal-
lacies have been defined as errors growing out of
the subject-matter of the conceptions and propo-
sitions constituting a syllogism. They can all be
reduced, with only the apparent exception of the
petitio principii, to what is called the fallacy of
Quaternio Terminorurn, or Four Terms. We found
in one of the rules regulating the formation of the
syllogism that it must have three and only three
terms. Four terms make it impossible to reason,
because they introduce matter that prevents com-
parison by a middle term. In some form or other
all the material fallacies reduce to this one type of
four terms. This introduction of new matter may
be either in the premises or in the conclusion. It
may be introduced into the premises in two forms,
and into the conclusion in two forms. First, the
middle term may have a different meaning in each
premise. This makes it equivocal and equivalent
to the use of four terms. Second, the major and
minor terms may each or either of them have a
different meaning in the premise from that in the

l6o LOGIC AND ARGUMENT

conclusion. This again gives a double significa-
tion to them, which is equivalent to four terms.
But this form of four terms, which is due to a
double meaning of the words, may be called
Equivocation, the first class of material fallacies.
Third, the error may grow out of assuming a prem-
ise or premises which may be false, or require to
be proved. Fourth, we may assume new matter
without equivocation in the conclusion when the
premises are true or not disputed. In both of
these assumptions we take something for granted,
which should either be proved or shown to be con-
tained in the premises. These two forms of fal-
lacy may be called Presumption, as indicating some
form of assumption that vitiates the conclusion,
either as false because one or both of the premises
are false, or as not contained materially within
them. The two general material fallacies, there-
fore, will be Equivocation and Presumption. We
shall consider them in their order.

i st. Fallacies of Equivocation. — Fallacies of
Equivocation are due to the use of ambiguous
terms, which often conceal their equivocal mean-
ing even when the mind sees that there is some-
thing wrong with the conclusion. But there are
two forms of equivocation which are based upon
a certain quantitative import in terms on the one
hand, and a certain qualitative import on the other.
One of these deals with equivocations between
Collective and Distributive terms and proposi-
tions, and the other with equivocations between
Abstract and Concrete terms and propositions.
The first of them divides into Fallacies of Com-

FALLACIES l6l

position and Division, and the second into Fallacies
of Accident, which represent three specific forms.

i. Composition and Division. — These fallacies
arise from the confusion of collective and distribu-
tive terms or propositions with each other. When
the major premise is distributive and the minor
premise collective, the fallacy in the conclusion is
called one of Composition. When the major prem-
ise is collective and the minor premise is distrib-
utive, the fallacy is one of Division. To put the
matter in another form, to argue from a distrib-
utive to a collective use of a term is to commit
the fallacy of composition ; to argue from the
collective to the distributive is to commit the fal-
lacy of division. The following are illustrations
of the fallacy of Composition :

All the angles of a triangle are less than two
right angles.

A, B, C together are the angles of a triangle.
/. A, B, C together are less than two right angles.

In the major premise of this syllogism the prop-
osition is true if taken to mean that each angle is
less than two right angles, but we have attempted
to argue from this truth to the supposed case that
the same angles taken together are less than two
right angles, which is false. A similar case is the
following :

Thirteen and seventeen are prime numbers.
Thirty is thirteen and seventeen.

.-. Thirty is a prime number.

In the major premise " thirteen " and " seven-
teen " are each prime numbers ; in the minor

1 62 LOGIC AND ARGUMENT

premise they are together equal to thirty. Hence,
we are trying to argue from the distributive to
the collective in the conclusion, " Thirty is a
prime number," which is false.

Again, if we were to argue that, because " All
the peers derived their title from the crown," and
" The House of Parliament consisted of all the
peers," therefore, " The House of Parliament de-
rived its title from the crown," we should be com-
mitting the fallacy of composition. So also we
cannot argue from the truth of the individual in-
cidents of a story, as having independently oc-
curred, to the truth of the narrative as a whole, or
collectively taken.

Illustrations of the fallacy of Division are the
following :

All the angles of a triangle are equal to two

right angles.

A is an angle of a triangle.
.*. A is equal to two right angles.

In this instance the major premise is true col-
lectively ; that is, the proposition is true on the
assumption that the phrase " All the angles "
means "All the angles together." But the minor
premise is distributive, and hence also the con-
clusion, which asserts, falsely, of course, what is
true only of a collective term in the major prem-
ise. Another illustration exhibits the same fact :

The Germans are a nation.
Bismarck and Stein are Germans.
.'. Bismarck and Stein are a nation.

FALLACIES 163

It would be a similar fallacy to argue from the
fact that Congress had voted for a subsidy, that

Mr. A , a member of Congress, had voted for

it. So it would be to argue that every individual
house made a city, because a collection of them,
including these individual instances, made a city.
The individual items of expense in a bill need not
be large because the aggregate is large.

2. Fallacies of Accident. — The fallacies of Acci-
dent arise from equivocations in terms expressing
different totals of attributes or qualities. Here
we have to do with the various attribute meanings
of conceptions. For instance, the term " chair "
means now a piece of furniture, and again the
presiding officer of an assembly; or "paper" is
now a kind of substance, and again the sheets of
that substance used for printing the news. Now if
we argue from one of these meanings to the other,
we commit some kind of a fallacy of Accident.
This term comes from its application in the classi-
fication of ideas. We found in dealing with the
predicables and with Genus and Species that we
required certain terms to express the common and
certain terms to express the distinctive qualities of
things. These were conferentia and differentia.
Essentia or Essence, and Accidentia or Accident,
express the same ideas. Conferentia denotes the
common or essential, and differential, the distin-
guishing or differential, sometimes the accidental
properties of things. This difference in the mean-
ing of terms, some standing for only conferentia
or common properties, making them abstract, as in
all general abstract terms, and others standing for

164 LOGIC AND ARGUMENT

both the conferentia and the differentia, making
them concrete, as in all singular terms and the ex-
tensive use of general terms — this difference often
gives rise to the equivocal use of certain terms, and
a confusion of their abstract with their concrete use,
or, as is sometimes said, their general with their
particular application. Hence, if we undertake to
argue from conferentia or essence (abstract) to
differentia or accident (concrete), or vice versa,
we commit some fallacy of Accident. This takes
three forms : Simple Accident, Converse Accident, and
Specific Accident.

(a) Simple Accident. — The following is an instance
of Simple Accident in which we argue from what is
true in general to a special case. It is a very old
illustration :

What you bought yesterday you eat to-day.
You bought raw meat yesterday.
/. You eat raw meat to-day.

A better illustration is the following, in which
the argument is from the abstract to the concrete,
or from what is true of the essential qualities un-
der certain conditions, to what is supposed to be
true in a particular form and without these con-
ditions :

Intoxicating liquors are dangerous.
A glass of wine is an intoxicating liquor.
/. A glass of wine is dangerous.

Here the major premise represents what is true,
not in all forms and quantities of liquor, but only
in regard to their essential characteristics, while

FALLACIES 165

the conclusion asserts the same predicate of a
special and small quantity of liquor. In both in-
stances the argument is from the general to the
special case.

(b) Converse Accident. — As illustrations of Con-
verse Accident we may take the following :

Loyalty to the government is the duty of the
citizen.

Loyalty to Charles I. was loyalty to the govern-
ment.

.•. Loyalty to Charles I. was the duty of the citi-
zen.

Here we may find the equivocation either in the
middle or the minor terms. The " loyalty to
the government" may be of different kinds, or
the " loyalty to Charles I." may be different in the
minor premise from what it is in the conclusion.
The latter supposition makes the case clearer, and
we find that it represents reasoning from the
purely personal loyalty of the minor premise to
political loyalty, including an implied personal
loyalty which might be impossible even if desired
by the citizen. Perhaps a better illustration is
the following :

Grape juice does not intoxicate.
Wine is grape juice.
/. Wine does not intoxicate.

Here we plainly argue from the special form of
"grape juice "to a more general form in which
only the essential qualities of the original are to
be found. It would be a similar fallacy to argue

1 66 LOGIC AND ARGUMENT

from the contemptible character of one reformer
in a particular cause to the conclusion that all re-
formers are bad.

(c) Specific Accident. — The case of Specific Acci-
dent is illustrated by the following syllogism in
which the meaning of the terms that are equivocal
represents the difference between two species rather
than the difference between genus and species, or
vice versa :

The end of life is its perfection.
Death is the end of life.
.-. Death is its perfection.

The term "end " is used in this instance with two
distinct meanings, one of them denoting a terminus,
and the other a. purpose, though both are expressed
by the same sound. This is simple equivocation,
and has usually been called the fallacy of Ambig-
uous Middle, but it can be ranked with those of
accident by remembering that we argue in it from
one accident in a term to another accident in the
same term. This will enable us also to see that
the same fallacy is possible with the major and
minor terms. Another illustration of the same
fallacy is the following :

All criminal actions are punishable by law.

Prosecutions for theft are criminal actions.

.-. Prosecutions for theft are punishable by law.

In the major premise "criminal actions " means
conduct that is wrong or unjust, and in the minor
premise the same phrase means only a suit at law,
which is not necessarily bad conduct. Hence,

FALLACIES l6j

there is an equivocation in the argument, which
reasons from an accident of the term in one case
to an accident of a different kind in the other.

(d) Rules for Fallacies of Accident. — The sim-
plest rules for the detection of the various fallacies
of accident may be formulated as follows, when
they depend upon the middle term :

I The major premi

Simple Accident . . •( The minor premi
I The conclusion f

The major premise true in a general sense,
ise true in a specific sense,
false.

1 The major premise true in a specific sense.
Converse Accident •< The minor premise true in a generic sense.
| The conclusion false.

("The major premise true in any sense different from
| the minor.
Specific Accident. . -j The minor premise true in any sense different from the

major.
I The conclusion false.

When the fallacy turns upon the minor and major
terms, the rules have to be expressed in a slightly
different form.

Simple Accident = Substitution in the conclu-
sion of a specific minor or
major that is general in
the premise.

Converse Accident = Substitution in the conclu-
sion of a general minor or
major that is specific in
the premise.

Specific Accident = Substitution in the conclu-
sion of one specific minor
or major for another spe-
cific meaning of the same
term in the premise.

l68 LOGIC AND ARGUMENT

zd. Fallacies of Presumption. — Fallacies of
Presumption, as already defined, are those of either
taking something for granted in the premises
which ought to be proved, or of assuming new
and irrelevant matter in the conclusion. They
may accordingly be divided into two kinds : the
Petitio Principii, or Assumption of the Principle,
and the Fallacia Consequents, or Inconsequence ;
also generally called Non Sequitur. The former
is usually charged when, the formal reasoning
being correct, the conclusion is seen to follow
from the premises, but is not accepted because
one or both of the premises are denied ; the latter
is charged when the premises are admissible, and,
the formal reasoning being correct, the conclu-
sion is seen to be either false or not included in
them.

i. Petitio Principii. — The common name for this
is Begging the Question, but it is here called As-
sumption of the Principle or general truth which
is used for proof. It means that the proposition
to be proved is in some way simply assumed with-
out proof. We divide it into two forms, the Peti-
tio Argumenti, or Begging the Question, and
Ignoratio Elenchi, or Evading the Issue. Each of
these is divisible into two forms, and will be dis-
cussed in the proper place.

(a) Petitio Argumenti. — This is here technically
called Begging the Question, and means that the
proof of any proposition is so assumed as to in-
clude the proposition under dispute. This as-
sumption may be of a proposition more general
than the conclusion, or really identical with it.

FALLACIES 169

This circumstance gives rise to two forms of the
Petitio Argumenti ; namely, the assumptio non pro-
bata, and the circulus in probando.

The assumptio nonprobata occurs when the prop-
osition or propositions assumed to prove a given
assertion can be questioned by those whom we
may be endeavoring to convince. Suppose, for
instance, that we have asserted the proposition
that " Church and State should be united," and
we were asked to prove it. To satisfy this de-
mand we should be obliged to find a major and
minor premise, or a series of arguments, in which
the asserted proposition is included as a conclu-
sion. The syllogism summarizing the process
would stand as follows :

Good institutions should be united.
Church and State are good institutions.
.•. Church and State should be united.

In this argument, if the minor premise be ad-
mitted and no formal fallacy chargeable, there is
no way to escape the conclusion but to deny the
truth or the universality of the major premise,
thus implying that the question is begged or as-
sumed in the effort to prove it. It might be true
that most good institutions should be united, but
the exception of "church and state" might be the
very instance that prevents my right to assume a
universal major premise containing it.

It is not merely the failure to prove one's prem-
ises that constitutes the fallacy of begging the
question. This failure must be one which occurs
when proof is needed or demanded, and this is

lyo LOGIC AND ARGUMENT

when the premise in turn is treated as a conclu-
sion to another argument. Hence, the begging of
the question occurs only when the attempt to
prove a proposition involves the assumption of it
in a premise that the hearer or opponent does not
admit. It is, perhaps, most frequent when trying
to convince another of a given assertion, although
it may also occur whenever we are trying to
prove to our own minds a conclusion without as-
suring ourselves sufficiently of the stability of the
premises upon which the conclusion rests. But it
is most frequent in arguments with others, be-
cause the one condition of proof or conviction in
such cases is that the opponent, reader, or friend
admit the principle upon which the conclusion is
to be established, while the subject himself may
not require proof at all for his conviction, as he
already accepts the proposition. But we cannot
prove to another a truth with premises that he does
not admit. He simply charges begging the ques-
tion because he is not obliged to admit in the con-
clusion what he does not admit in the premises.

Moreover, a proposition in the conclusion may
be true, and yet not be proved by the premises.
The advantage of proving any proposition lies in
making it a special case included under a general
law or class of unquestioned character, so that
when a person has admitted the larger, he must
perforce admit the smaller. But there are in-
stances in which we may dispute the universality
of a principle or premise either to show that the
conclusion may, so far as we know, be an excep-
tion, or to assert that it has not been proved by

FALLACIES iyi

such a process, however true the proposition to
be proved may be in reality. This means that we
may even charge a begging of the question when
we admit the conclusion, if the premise does not
contain it,' and can be disputed. Suppose we as-
sert that " All cattle have cloven feet," and are
asked to prove it. The syllogism purporting to
meet this demand may stand as follows :

All ruminants are cloven-footed.
All cattle are ruminants.
/. All cattle are cloven-footed.

Now, though we admit the last proposition to be
true as a matter of fact, yet we can say that it is
not proved, and the question is begged by the
major premise, if this is not universally true, but
is assumed to be so for the sake of the argument.
It is one thing to perceive the truth of a propo-
sition, and it is another to prove it by a superior
premise or condition. The charge of begging of the
question, then, may be made, not only when the con-
clusion is denied, but also when it is not proved.

The circulus in probando is a species of begging
the question which consists of what is called
"arguing in a circle," or in assuming as proof of a
proposition that proposition itself. Thus, it would
be arguing in a circle to say that " Man is wise
because he is intelligent and prudent ; " for " in-
telligence and prudence " are considered the same
as " wisdom." So also would it be to argue that
the "Weather is warm, because it is summer, and
it is summer, because the weather is warm," and
" Men never practise excess, because they are not

172 LOGIC AND ARGUMENT

guilty of immoderate habits." Jevons gives the
following illustration : " Consciousness must be
immediate cognition of an object ; for I cannot
be said really to know a thing unless my mind has
been affected by the thing itself." Here " to know "
and " immediate cognition " are identical in mean-
ing and cannot be used to prove each other. The
difference between this fallacy and the assumptio
non probata, as explained and illustrated, is that
the " circulus in probando" assumes an identical
proposition as proof, while the former assumes a
more general one including or intending to include
the conclusion.

The fallacy of reasoning in a circle occurs
mostly in long arguments where it can be commit-
ted without ready detection. In such cases as are
given above, the fallacy is perfectly obvious. But
when it occurs in a long discourse it may be com-
mitted without easy discovery. It is likely to be
occasioned by the use of synonyms which are
taken to express more than the conception involved
when they really do not. It is difficult to give
any formal expression to this circumstance with-
out resorting to complex syllogisms for examples.
But if in the following case A and C are really
identical in meaning, though apparently not so,
we shall have a circulus in probando.

A is B. Bimana are rational.

C is A. Men are bimana.

.'. C is B. .-. Men-are rational.

Usually, however, the form is much more likely
to take the form of a prosyllogism and an episyl-

FALLACIES 173

logism in which we arrive at some proposition for
proof which is absolutely identical with the propo-
sition to be proved. The following example illus-
trates this fact :

C is B. The months of the earth's aphelion

are warm.

A is C. The season from June to Septem-

ber is the months of the earth's
aphelion.

.•. A is B. The season from June to Septem-

ber is warm.

C is A. Summer is the season from June

to September.
/. C is B. .-. Summer is warm.

Here the term " summer " and " the months of
the earth's aphelion " are absolutely identical in
meaning, though concealed in the terms by which
the propositions are expressed. It is therefore a
case of reasoning in a circle.

(b) Ignoratio Elenchi. — This fallacy is properly
defined as an evasion of the issue. It is sometimes
called irrelevant conclusion, but this is equally ap-
plicable to the non sequitur, while the ignoratio
elenchi is more properly an evasion of the issue,
or a disregarding of the question to be proved.
It also takes two forms, which are : Evasio ad Dic-
tionem, or Evasion of Proof, and Evasio ad Contra-
dictionem or Evasion of the Disproof.

The evasio dictionem is committed when we un-
dertake to prove a proposition which we falsely
assume to be identical with the real proposition at
issue. Thus, if we announce the issue to be that

174 LOGIC AND ARGUMENT

"Church and State should be united," and prove
only that " Church and State are good institu-
tions," we have evaded the issue. An illustration
of the process and of the manner in which the
evasion is committed is the following :

Ad rent.

Good institutions should be united.
Church and State are good institutions.
.-. Church and State should be united.

Non ad rem.

Social organizations are good institutions.
Church and State are social organizations.
.-.Church and State are good institutions.

The error in this instance lies in the assumption
that the proof of the proposition " Church and
State are good institutions " includes also the
proposition " Church and State should be united."

There are several forms of this evasion which
are legitimate for the purpose of convincing an
opponent or the persons to whom we are appeal-
ing, but which are nevertheless not arguments
directed to the issue by itself, and hence are
treated as evasions of the question. The argu-
ment directed correctly to the issue is called the
argumentum ad rem. The reasoning which ignores
it, which I shall call the argumentum ad personam
and which nevertheless may be useful for influ-
encing an opponent, is divided into five forms :
the argumentum ad judicium, argumentum ad popu-
lum, argumentum ad hominem, argumentum ad vere-
cundiam, and argumentum ad ignorantiam. These
may be briefly defined and illustrated.

FALLACIES

175

The argumentum ad judicium is an appeal to
general or universal consent and is consequently
based upon the common judgments of mankind.
It is used to establish a case where we suppose
difficulties in getting facts to support the real
issue. Thus, if we are asked to prove the exist-
ence of matter, the merits of democracy, or the
truth of Ptolemaic astronomy, we may appeal to
the universal belief of mankind as the ground
upon which these convictions rest. The major
premise would be "Whatever universal consent
attests is true," etc., and the minor premise would
be the conformity of the special case to this con-
dition, and hence the conclusion. But it evades
the issue because the question is not what men
believe in the premises, but what the facts are.

The argumentum ad populum is an appeal to
public opinion, or to the passions and prejudices
of the people rather than to their intelligence.
Thus, if the issue be the justice of protection or
free trade, we may appeal to the interests and
political passions of men rather than to reason
and fact.

The argumentum ad hominem is an appeal to the
practice, profession, or principles of the person to
whom or against whom an argument is directed.
It is an effective method of silencing an opponent,
but it is not an ad rem argument and does not
prove the issue.

The argumentum ad verecundiam is an appeal to
authority, or body of accepted doctrines. It is
valid for producing conviction when the author-
ity is accepted by the persons to whom the appeal

176 LOGIC AND ARGUMENT

is addressed, but it is not ad rem proof, and when
not accepted by anyone is still more glaring as an
ignoratio clenchi.

The argument ad ignorantiam is an appeal to a
man's ignorance in order to produce conviction
upon the ground of his inability to dispute the case.

These several forms of argumenta are essen-
tially the same in their principles and import, and
though they do not accomplish real proof, and to
that extent evade the issue, yet they have the
legitimate use of driving a man to define his
position and to clear up the implied contradictions
involved in the application of the ad hominem
argument against him. An excellent illustration
of both the legitimate and the illegitimate use of
this form of argument is found in the story of
Zeno and his argument against the possibility of
motion. He maintained that, if motion be pos-
sible, a body must move either where it is or
where it is not. He said that it could not move
where it is, because it must be at rest to be in any
given point. Then it could not move where it is
not, because it is not there to move. Therefore,
it could not move at all. Tradition has it, says
De Morgan, that Zeno called in a physician to set
a dislocated shoulder, and the physician badgered
the patient by turning his argument about motion
upon the philosopher to prove that his shoulder
was not hurt. He argued that the shoulder must
be put out of its place either where it was or
where it was not, etc. This is an excellent case
of the ad hominem appeal. It admirably exposes
the philosopher's plight in his contention about

FALLACIES 177

motion, but it neither proves nor disproves the
possibility of motion. Nor is it a refutation of
the assertion which is imputed in the story that
the philosopher's shoulder was out of place. It
only establishes a contradiction between his phil-
osophic denial of motion and his present belief
about the dislocation of his shoulder, a belief
which implied the assertion of motion. The philos-
opher would only have to say either that this was
not a case of motion, or that his shoulder was not
displaced in order to recover his consistency and
to indicate that his argument was not overthrown,
while admitting that the physician's reasoning was
correct. But he would have to yield something,
hence he must either explain the contradiction or
give up one of the alternatives. This is the value
of the ad hominem argument.

The second form of the ignoratio clenchi, name-
ly, the evasio contradictionis, remains to be consid-
ered. This means the evasion of the contradiction
or disproof of an assertion. An illustration of
this evasion is the following : Suppose that one
man asserts that " A is not a thief," and produces
his argument therefor, while it is the duty of an
opponent to refute this assertion. What he ought
to prove is that "A is a thief; " but if he only
proves or tries to prove that "A is a rogue," he
completely evades the issue. The whole case is
illustrated as follows :

Proof. Disproof. Ignoratio Elenchi.

.'. A is not a thief. .-. A is a thief. .-. A is a rogue.

178 LOGIC AND ARGUMENT

Here the opponent assumes that if he can only
prove that " A is a rogue," he has won his case
against the affirmative, when, in fact, he assumes
the identity between this and the proposition "A
is a thief," which is the contradictory. But he
thus begs the question while he evades the issue,
which is not that " A is not a rogue," but that " A
is not a thief," " rogue " and " thief " being differ-
ent things, so that he might be a rogue and yet
not a thief.

2. Non Sequitur. — The fallacy is that of False
Consequent. It arises in connection with the con-
clusion and not in connection with the premises.
It therefore consists in the introduction of new mat-
ter into the conclusion, matter that is not contained
in the premises. There is no special necessity
for subdividing it into distinct forms, except that
one class has received a separate name for the
sake of particular convenience, and perhaps be-
cause of its frequent occurrence. If we must
distinguish between kinds at all, which could be
made as numerous as the classes of everything, it
must be into the non sequitur simplex, and the
non causa, pro causa, false cause, or post hoc fallacy,
whose dictum is post hoc, ergo propter hoc. The
simplest form in which this fallacy may occur can
be illustrated in the following :

All men are rational.
Socrates is a man.
.*. Socrates is noble.

It is evident that this conclusion cannot follow
from the premises. The major term is not " no-

FALLACIES 179

ble," but " rational," and hence the former cannot
follow. De Morgan gives a good illustration that
is a little more complex :

Episcopacy is of Scripture origin.

The Church of England is the only Episcopal

church in England.
.\ The church established is the church that ought

to be supported.

Nothing here is said in the premises about "sup-
porting the church," and hence cannot be inferred
in the conclusion. This non sequitur closely re-
sembles the formal fallacies of illicit minor and
illicit major, but a wide difference nevertheless is
marked in the fact that in the former the addition
in the conclusion is new quantity, while in the lat-
ter it is new quality ; that is, new subject-matter.

The fallacy of False Cause, or the post hoc fal-
lacy, is the most important form of non sequitur to
be considered. It consists in arguing/rom a mere
co-existence or sequence, a coincidence to causal or
necessary connection. Thus, to argue that a change
of weather was due to the occurrence of a new
moon because they coincided, once we may say,
would be to commit this fallacy ; or to attrib-
ute a pestilence to the appearance of a comet, a
death in the family to an eclipse of the sun, good
luck to carrying a bone in one's pocket — all these
are cases of confusing cause with coincidence. The
phrase post hoc, ergo propter hoc, meaning " after
a fact, therefore because of it," describes this
fallacy exactly. If we have observed a large
number of such coincidences under various and

180 LOGIC AND ARGUMENT

changing circumstances and conditions, we may
be justified in suspecting a causal connection, but
the coincidence is no proof of it, especially if it
be either a single one or between phenomena that
betray no intrinsic characteristics of necessary
connection. This latter remark is true of even con-
stant co-existences and sequences. We cannot in-
fer that night is the cause of day on the ground
of their constant conjunction. The idea of neces-
sary or causal connection is not contained in that
of merely actual connection, and it is a non scquitur
to include this new matter in the conclusion when
the premises express nothing more than co-exist-
ence or sequence. Thus, if I argue from the coin-
cidence between' the existence of a protective tariff
and the fall in price of iron, I commit this fallacy,
because I assume that there are no other possible
causes of reduction in price. Similarly with any
other such coincidence in which the conclusion
contains new and different matter from the prem-
ises.

IV. GENERAL OBSERVATIONS.— It is im-
portant to remark that the errors in reasoning are
capable of being looked at from different points
of view, and hence are so interconnected that
what may be one fallacy in one interpretation of
the premises may be adjudged a different fallacy
with another interpretation of the premises.
Thus, to take the case of the non sequitur which
we have just been discussing, we may reduce it in
some cases to a petitio principii. For instance, we
have said that to argue from the sequence of
night and day to a causal connection was to commit

FALLACIES l8l

the post hoc fallacy. This is true if we look only at
the material difference between what is here only
a minor premise and the conclusion. But being
merely an enthymeme, if we supply the major
premise we have :

All immediate antecedents of day are its cause.
Night is the immediate antecedent of day.
.*. Night is the cause of day.

Here if the major premise be true the conclu-
sion may follow, but a dispute on the truth of this
premise reduces the argument to a petitio principii.
Hence, what may be charged as a non sequitur in
relation to the minor premise, may be viewed as a
petitio principii in relation to the major premise.
This will always be true of enthymemes when we
observe that the conclusion is not contained in
the stated premise.

A similar reduction can be made of the falla-
cies of accident. Take the following example :

Pine wood is good for lumber.
Matches are pine wood.
. Matches are good for lumber.

Here we have a fallacy of Simple Accident, due
to arguing from the general to the special case,
or from the abstract to the concrete. But calling
it a fallacy of accident depends upon the question
whether we admit the premises and do not ad-
mit the conclusion. We may, however, question
the major premise in this case, or even the
minor. We are tempted to admit the major prem-
ise because we know that " pine wood is good

1 82 LOGIC AND ARGUMENT

for lumber," but we forget, perhaps, to observe
the qualifications under which it is true. It
should be noticed that the statement carefully
omits to say either " All pine wood," or " All
forms of pine wood," and hence expresses what is
only abstractly true ; that is, true of " pine wood"
as a substance, and seeing this we may not notice
the trap into which we fall until the conclusion is
announced, which is palpably false. If this major
premise be considered as universally true at all, it
is only in the abstract sense that the quality of
pine wood fits it for the purpose of lumber, but
the minor premise has to do with pine wood in a
special concrete form, and an equivocation arises
which we may call a fallacy of accident, assuming
that formally the reasoning is correct.

But we may dispute the truth of the major pre-
mise, if we like, as not being true in the concrete
sense in which it ought to be true if the argument
is to be valid, and hence we could charge the fal-
lacy of begging the question by thus raising a doubt
about the first condition of the argument. Again,
we may maintain that the proposition, as true, is
really a particular proposition ; that, taken as
true, it can only mean " Some pine wood is good
for lumber," and in this interpretation we should
have IAA of the First Figure, which represents
the fallacy of illicit middle. Hence, according to
the way we look at the propositions in this in-
stance, we may have any one of three fallacies,
simple accident, petitio principii, or illicit middle. A
similar treatment of the fallacies of Composition
and Division could be made, but it suffices to

FALLACIES 183

show what the principle is in the previous in-
stances.

Another important remark in this connection is
that it is not necessary to put an argument into
the form of a syllogism in all cases in order to
discover what the fallacy is, if any. We have only
to observe the quantity of the propositions serv-
ing as premises and conclusion, the relation be-
tween premises and conclusion, and the manner in
which one term is substituted for another. In
actual discourse the arguments are most fre-
quently expressed either in the form of enthy-
memes, or in a manner to effectually conceal the
syllogistic figures and moods, so that we are left
entirely to depend upon the resources just men-
tioned for the detection of fallacies. Moreover,
since the construction of enthymemes into com-
plete syllogisms leaves us practically free to put
them into either the First or Second Figures at
pleasure, the first of these being formally valid
in nearly all cases so reconstructed, we have
always to allow for this as the possible meaning
of the debater, and so look for material fallacies
if we refuse to accept the conclusion. But when
any doubt exists about the case, the only recourse
is to throw the argument into syllogistic form.

Another important observation to make is the
fact that the imputation of a fallacy in the reason-
ing does not necessarily imply that the proposition
in the conclusion is a false one. The fallacy is
not a reason for the falsity of a proposition, but is
only an explanation of the failure to prove it. In
some cases the reasoning may be valid and the con-

184 LOGIC AND ARGUMENT

elusion false, or the reasoning fallacious and the
conclusion be true, as a proposition. Reasoning
avails only, when valid, to show the connection of
the conclusion with the premises, and all of these
may be either true or false without affecting the
reasoning process. All that the existence of a
fallacy, which is a violation of the rules for legiti-
mate transition from term to term or proposition
to proposition, can establish is a mistake in the
mode of proving a statement, not the truth or
falsity of it, except relative to the same quality
in the premises. It is the perceived falsity of a
statement that often leads us to question the
validity of its deduction, but we cannot suppose
that the process of reasoning determines either
the truth or falsity of a proposition. It only
settles whether it is implied by the premises, and
its truth stands or falls with the same character
in the statements from which the deduction is
attempted.

CHAPTER XIII
INDUCTIVE REASONING

I. GENERAL NATURE OF INDUCTIVE
REASONING. — Inductive inference has been dis-
tinguished from deductive reasoning ever since
Logic was founded, but it has not always suc-
ceeded in keeping its meaning perfectly clear. It
is important therefore that we should briefly ex-
plain the various uses of the term. This can be
done by assuming the two divisions of Induction,
which are commonly accepted. They are Perfect
Induction and Imperfect Induction.

i st. Perfect Induction. — Perfect Induction is
an enumeration of the particulars that form a class.
It is the process which characterized the method
of Socrates in reaching definitions. An example
of it is the following : Mercury revolves on its
axis ; so do Venus, the Earth, Mars, Jupiter,
Saturn, and Neptune. But these being all of the
planets, we can say, "All the planets revolve on
their axes." This appears to be in the form of
reasoning, but in reality it is not reasoning. It
should be called simply Generalization. All the
individuals that constitute the class are simply
enumerated, so that the generalized expression is
but an economical device for avoiding the specific
185

1 86 LOGIC AND ARGUMENT

mention of the individual cases. We do not in-
clude in this process more than is indicated in the
premises, and, besides, it is not one of reasoning,
which Induction, as here considered, should be.

2d. Imperfect Induction. — Imperfect Induc-
tion is the process by -which the conclusion extends be-
ypnd the data upon which it is based, as Generaliza-
tion does not go beyond it. If we had reasoned
from the observed fact of four planets revolving
around their axes, that all of them did so, we
should have an inductive inference, because we
infer some facts not observed. This is the true
Inductive reasoning. Again, if I observe in a
number of cases that a certain kind of cloud has
been accompanied by a hail-storm, and infer that
this will always follow this particular kind of
cloud, I have performed an Inductive inference.

3d. Definition of Inductive Reasoning. — There
have been several ways of defining this process.
It has been usual to contrast it with Deduction.
Now, deduction is often said to be reasoning from
general to particular truths, from the containing
to the contained truth, or from cause to effect.
Induction, therefore, by contrast is defined as rea-
soning from the particular to the general, from
the contained to the containing, or from effect
to cause. Sometimes induction is said to be rea-
soning from the known to the unknown. This
would be making deduction, by contrast, reasoning
from the unknown to the known, which is absurd.
The former ways of representing it are much the
better.

But there is still a better way of comparing

INDUCTIVE REASONING 187

them. Deduction, we saw, is reasoning in which
the conclusion is contained in the premises. This
is the ground of its certitude, and we commit a
fallacy whenever we go beyond the premises, as
shown by the laws of the distribution of terms.
In contrast with this, then, we may call inductive
reasoning the process by which we go beyond the
premises in the conclusion. This is illustrated
in such examples as have already been given for
imperfect induction. To repeat examples, how-
ever, if we observe that red sunsets are frequently
followed by clear days, we may infer that the
same coincidence will occur in the future ; or if
we observe that the dew falls upon clear nights,
and that clear nights are accompanied by a
peculiar radiation of heat, we may infer a causal
connection between this radiation of heat and the
falling of the dew. Good illustrations also of this
inference are Copernicus's discovery of the earth's
motion around the sun, Kepler's law of planetary
motion, Newton's theory of gravitation, the undu-
lative theory of light from the eclipse of the satel-
lites of Jupiter, etc.

The process here is to start from certain given
facts and to infer some other probable fact more
general or connected with them. In this we see
the process of going beyond the premises. There
are, of course, certain conditions which regulate
the legitimacy of this procedure, just as there are
conditions determining deduction. They are that
the conclusion shall represent the same general
kind as the premises, with a possibility of acci-
dental differences. But it goes beyond the prem-

1 88 LOGIC AND ARGUMENT

ises in so far as known facts are concerned. This
can be shown best by studying the formal process.
II. FORMAL PROCESS IN INDUCTION. —
We found that we could give formal expression
to deductive reasoning in the Moods and Figures
of the syllogism. The same can be done, to a
limited extent at least, in induction. It is usual
to state the forms for induction in the Second and
Third Figures. It may be possible to do it in all
the Figures, but we do not require in this work to
develop the formal process in all its possibilities.
Hence, we shall take those forms which most
clearly exhibit both the probability of the infer-
ence and its passage beyond the premises. We
take one in the Second Figure :

A Magnets attract iron.
A Loadstones attract iron.
A .-. Loadstones are magnets.

• In deductive reasoning this would be a formal
fallacy of undistributed middle, but if we simply
mean to suppose from the common attribute of
attraction for iron that the two classes of substance
are the same, and hold the idea as a probability
merely, we are entitled to regard it as inductively
legitimate. This is to say that the agreement of
the two subjects in this particular suggests that
they are of the same kind in general. The same
kind of reasoning can be illustrated in the Third
Figure :

A, B, C attract iron.

A, B, C are magnets.
/. All Magnets attract iron.

INDUCTIVE REASONING 189

Here we have, deductively, a fallacy of illicit
minor, but inductively an inference that what
proves true in certain known cases or particulars
will prove true of the whole class. The inference
or hypothesis here has only a degree of proba-
bility, and is not a necessary one as in deduction.
The term hypothesis or supposition expresses ex-
actly what this inductive inference is, and indi-
cates how it is that we go beyond the premises
or actually known facts, to what has some degree
of possibility or probability. Thus, to illustrate
again, if we find that two or three gases are com-
pressible into liquids under certain degrees of
temperature and pressure, we may well suppose it
possible or probable, and to that extent rational,
that other gases are compressible under some
similar conditions. The supposition may require
verification or proof before the mind is satisfied,
but we make an hypothesis which is the inference
to what is possible or probable, this varying in
degree according to the nature and number of the
facts upon which it is based.

It will be necessary to illustrate inductive rea-
soning by concrete examples which do not repre-
sent the formal process to which they can be re-
duced. For instance, it was observed that there
were disturbances in the movements of certain
planets which could not be accounted for by
known causes. From what was known about
causes and their effects in general it was inferred
that there was some undiscovered planet which
would account for the disturbance. This unknown
planet, not being included in the premises of the

I go LOGIC AND ARGUMENT

reasoning, is thus the object of an inductive in-
ference. It is a conjectured cause of a known
effect, and only awaited verification, as it received
this by the experiments of Leverrier and Adams>
in order to become an assured object of knowl-
edge. Again, it was observed that the specific
gravity of nitrogen taken from the air is greater
than nitrogen taken from all other sources. It
was inferred from this that there must be some
other substance to account for this difference.
Finally, argon was discovered. Still, again, I ob-
serve the rise in price of certain stocks. I may
infer several causes of it, but if I know the circum-
stances well enough, I may infer the probability,
for instance, that some agreement is maturing be-
tween rival companies. I may notice again that
frequently the appearance of a rainbow is followed
by clear weather, and hence may infer from ob-
servation in any particular case the re-occurrence
of the same clear weather. In all of these in-
stances my reasoning is from some specific facts
to a general rule comprehending more than the
special cases.

III. INDUCTIVE FALLACIES — It is not easy
to indicate the inductive fallacies, if it be even
possible, in the formal process of induction. In
deduction they consist of violating the laws of the
quantification of terms ; that is, in going beyond
the premises and endeavoring at the same time
to retain the same certitude in the conclusion as
was supposed in the premises. But induction per-
mits us to transcend the premises, quantitatively at
least, and there can hardly be any formal fallacies

INDUCTIVE REASONING 19 1

in this, unless we except the case of negative
premises. But all this is a matter for more ad-
vanced logic to determine. It is certain, how-
ever, that in respect to the subject-matter of the
conclusion in inductive reasoning there are some
very definite limitations upon the right to tran-
scend the premises. We cannot infer anything we
please from any premises we please. We must
conform to certain definite rules or principles.
Any violation of them will be a fallacy. These
rules are the same as those for material fallacies
in deduction, so that the fallacies of induction,
whether they are ever formal or not, are at least
material ; that is, they occur whenever equivoca-
tion and presumption are committed. There are,
then, two simple rules which should not be vio-
lated, (i) The subject-matter in the conclusion
should be of the same general kind as in the prem-
ises. (2) The facts constituting the premises
must be accepted and must not be fictitious.

CHAPTER XIV
PROOF AND ARGUMENTATION

I. INTRODUCTION Description, Explana-
tion, and Exposition were examined as processes
by which we endeavor to narrate facts and thoughts
in a systematic and orderly manner. They are
designed to give an intelligible and methodical
conception of the data that are connected with a
particular theme. But they are not designed to
convince the mind. They may incidentally do
this, but it is not their primary object to create
conviction. They are occupied with the forma-
tion and presentation of clear conceptions, syste-
matic and methodical discourse, which does as
much to make ideas intelligible as it does to please
the sense of order. But Proof and Argumenta-
tion go beyond this. They endeavor to convince,
to remove doubt, to give belief and knowledge to
the intellect. It will be necessary to examine its
nature and its kinds.

i st. Nature of Proof. — Proof is defined as a
method of producing conviction ; that is, of creat-
ing assent to propositions. This assent takes two
forms : Belief \ or probable truth ; and Knowledge,
or certain truth. Whenever any proposition is as-
serted or made the subject of argument, the ob-
192

PROOF AND ARGUMENTATION

193

ject is to show whether it be true or false. The
general method of argumentation is the same for
both sides. But the proposition at the outset is
supposed not to represent any conviction in favor
of or against itself, but to be balanced between
belief and disbelief, or certitude and denial. The
problem is to influence the judgment so that it
will decide in favor of or against the proposition.
Proof or Confirmation is the process of determin-
ing the conviction one way or the other, and of
removing the balance or doubt so that some de-
gree of assent or denial, whether of belief or
knowledge, will follow as a consequence. The
process is effected in various ways as the kinds
of proof will show.

One important point in the nature of proof
must not be neglected. It is somewhat different
from inference, though it is reasoning. Inference
properly proceeds from premises to conclusion ;
proof proceeds from conclusion to premises.
Proof assumes that a proposition is first asserted
or stated and then established. In inference the
premises are given and the conclusion is found,
but in proof the conclusion is given and the
premises found for establishing it. This is clearly
illustrated by the process of debating where the
issue is first defined and then proved. We state
our proposition as a fact, and then, assuming that
it is doubted by others, proceed to find the prem-
ises, or propositions, which include it and which
enforce conviction upon the doubter. Proof is,
therefore, technically speaking, a process the re-
verse of inference, though it succeeds in establish-
13

LOGIC AND ARGUMENT

ing the same fact, inference being the process for
finding it.

2<3. Kinds of Proof. — The kinds of proof or
argumentation assume two general forms, Direct
and Indirect, and each of these may be subdivided
into two forms. Direct proof or argumentation
consists in the attempt to establish a given propo-
sition ; indirect proof consists in refuting objec-
tions to it. Each of these may be divided into
deductive and inductive argumentation, and as the
method of arranging the data for proof or dis-
proof is the same in both the direct and the in-
direct forms of it, there will be little necessity for
dwelling at any length on these general divisions.
It will suffice to illustrate direct and indirect
proof.

A case of direct proof is found deductively in
the proposition demonstrating that the angles of
a triangle are equal to two right angles, or infer-
ring that the ancestors of land crabs were once
marine crabs from the existence of intermediate
and amphibious species. Here consistent and
pertinent matter is mentioned in which the con-
clusion is contained, or which suggests it as prob-
able. A case of indirect proof of the same propo-
sitions would be the reductio ad absurdum of the
contradictory proposition of the first instance,
and a removal of apparent contradictions in the
second instance. Thus, if to disprove the marine
ancestry of land crabs it be asserted that the one
is physiologically constructed to live in water and
the other is not, we should effectively remove the
force of this objection to the original assertion

PROOF AND ARGUMENTATION

'95

by showing that to-day there are species of ani-
mals which are born and live for a period in the
water, and afterward live on land. This is a case
of indirect proof by removing objections.

The general method of deductive proof is ex-
plained in the discussion of deductive reasoning.
All that remains to be remarked here is that it is
to be resorted to whenever we wish to give certi-
tude to the proposition asserted. In choosing our
premises and facts, therefore, we must be careful
to select those which really include the conclu-
sions. Any other procedure will involve one of the
formal or material fallacies. Thus, if the thesis
to be proven is that " The punishment of Socrates
was unjust," my premises must be stated so as to
include this as an instance. I can assume that the
punishment of innocent men is unjust, and then
prove that Socrates was an innocent and right-
eous man. But if my major premise be "Most
wise men should be exempt from punishment,"
the proof would be impossible. The proof, there-
fore, when demonstration is to be attained, must
represent the conclusion as clearly comprehended
in the premises.

In inductive proof this requirement is not im-
perative. The conclusion is only probable and
represents a preference in this respect over the
alternative course. Hence, it is sufficient to show
that the conclusion is enough like or connected
with other facts to be probably included in them
in regard to the matter at issue. Thus, if I find a
man dishonest in a certain number of transactions,
I may expect to find him so in the future or in

196 LOGIC AND ARGUMENT

other transactions. This is not a necessary con-
sequence, but only a probable one. In an argu-
ment, therefore, we must be careful to distinguish
between this kind of proof and the deductive
process. We must see that we are not confusing
the inductive with the deductive proof. Other-
wise we are liable to a charge of fallacy. If we
recognize that our proof is inductive, the argu-
ment against us must be inductive, unless the con-
tradictory of our proposition can be deductively
proved, in which case inductive evidence of our
thesis is impossible.

II. PROCESS OF PROOF OR ARGUMENT.
— There is always a definite order of events in
the proper presentation of proof. We have to
remember that the object is to convince, and not
merely to please. But to effect this end we should
not plunge into a debate without knowing what
both the nature and the compass of the issue is.
The presentation of arguments is the final stage
of the process in producing conviction. The first
thing is to make the issue clear. Then we have
to show how much ground it covers. Finally, we
have to present the proofs. These three proc-
esses may be called Definition, Division c- Analysis,
and Probation. Each will come up in order for
treatment.

i st. Definition. — In an argument definition is the
process of determining the nature of the issue or
thesis to be proved or disproved. The thesis will
be some proposition for or against which argu-
ments are to be produced. But before the argu-
ments can be seen to have pertinency we must

PROOF AND ARGUMENTATION

I97

know exactly what is to be proved or disputed.
Propositions are often equivocal, and only careful
definition can make clear what is to be defended or
opposed. Thus, in the simple proposition " Man
is mortal," there may be a doubt about the issue.
Whether the predicate " mortal " is to be affirmed
or denied of the subject will depend as much
upon what we mean by the subject " man " as upon
the nature of the predicate. The issue here is the
connection between the subject and predicate. If
we define " man " as the particular animal organ-
ism which we know as having certain qualities,
our proposition will mean one thing. If we define
the term as the abstract subject of consciousness
without reference to the animal organism, our
proposition will mean another. Again, if " man "
means the race of individual organisms, the prop-
osition will mean still another thing. Our argu-
ments must be different for each aspect of the
question. It is so with every thesis. Take again
the proposition " Protection is beneficial to the
country." Here the first duty in determining
what the issue under debate may be, is to define
carefully what is meant by "protection." There
is the etymological import of the term, which
would be rejected here as not indicating specifi-
cally enough what was meant. Then there is the
broad conception of prevention of any kind of in-
jury to citizens, which would define the object of
all civil laws. This might not be the issue in-
tended. Then there is lastly the economic policy
of taxing certain imports for the benefit of the
producer. This conception would indicate the

198 LOGIC AND ARGUMENT

issue usually understood by such a proposition
This illustrates a definition of the subject. But
the predicate equally demands definition in many,
if not all, cases. We must make clear what we
mean by " beneficial to the country." We must
indicate whether the issue regards economic or
moral benefits, or both. The arguments will be
very much affected by this distinction. But in all
cases we must make the issue clear by definition
in order to prepare the mind for estimating the
pertinence of the argument, as well as for enabling
the debater himself to select pertinent and valid
proofs. The rules for determining the definition
have been given already in their proper place.

2d. Analysis. — Analysis or division is the proc-
ess of showing how many specific and different
aspects of an issue are involved in it and which
can be separated for distinct treatment. The
process recognizes a classification and logical or-
der for the several arguments to be produced. It
may also be defined as the process of supplying
the topics for the discourse or argument. Suppose
we have the thesis " Literature civilizes man."
The analysis into topics may extend to both the
subject and the predicate. We simply apply the
principles of division to each term in order to
determine the several topics or aspects of the
issue.

The importance of this process after definition
is that it enables the debater to discuss a part of
his theme at a time, and not expose the whole of
it to attacks that may be based upon its general
and abstract meaning. Thus, if we divide " liter-

PROOF AND ARGUMENTATION 199

ature " into its various form to speil " scientific
philosophic, historical, etc., or other forms, we can
select one division at a time for probation, in
which it may be easier to establish the claim as-
serted than in some other case, and in this way
we can produce at least a presumption in favor of
others. Hence, in trying to show that " Literature
civilizes man," we can divide the subject first into
a series of topics. Thus, we could have the prop-
osition " Polite literature civilizes man," and again
subdivide " polite literature " into prose and
poetry, and each of these into its further subdi-
visions, so as to bring out the merits and influence
of each in the process of civilization. Then we
could proceed to show that " Scientific literature
civilizes man," and also resort to various subdi-
visions here. But the nature of the influence of
scientific thought is different from that of polite
literature. It affects the interests and character
of men in a different way. Hence, it is convenient
to separate the treatment of the one aspect of
the issue from the other. It will be the same
with the other two divisions, " philosophic" and
" historical literature." Similarly a series of top-
ics may be deduced from an analysis of the predi-
cate. We may divide the civilizing process into
" the elevation of artistic literary taste," " the re-
finement of manners," " the extension of knowl-
edge," " the improvement of morals," etc. All of
these maybe regarded as processes in civilization,
and we have to show that literature either in its
parts or as a whole does or does not accomplish
these results. In this way we give a variety of as-

200 LOGIC AND ARGUMENT

pects to the issue, and prepare the mind to esti-
mate it more clearly while the discourse may be
more logical and effective.

The process just illustrated is that of division.
But a thesis or subject may be analyzed into topics
by partition. This process has already been ex-
plained. It names the properties connected by a
conception or theme. Hence, we may supply the
aspects of an issue in argument by partition either
of subject and predicate, or the proposition as a
whole, as well as by division. Thus, if we have the
thesis " Monarchy is the best form of government,"
we may analyze the issue by partition so as to
show what has to be sustained or disproven in the
following manner. For the thesis we might fix on
the several characteristics that define monarchy
as a government : (i) The simplicity of mon-
archy ; (2) The efficiency of monarchy ; (3) The
venerable nature of its power ; (4) The influence
of monarchy upon science and art, etc., to almost
any extent we might please. Against the thesis
we might produce counter characteristics : (i)
The irresponsibility of its power ; (2) The ten.
dency to nepotism ; (3) Its historical habit of in-
terfering with human liberty ; (4) Its inadjusta-
bility to social and economic progress, etc.

All themes or issues can be analyzed in this
way, and the value of the process is simply that
which has already been indicated ; namely, the dis-
tinction and logical classification of arguments so
as to aid the mind in the formation of its convic-
tions and the systematization of its ideas. The
next process is Probation.

PROOF AND ARGUMENTATION 2OI

3d. Probation. — Probation is the process of
proof, the statement and arrangement of facts and
truths which will establish belief or knowledge in
regard to the proposition at issue, or the contrary.
The thesis or issue is the proposition to be proved
or disproved. The truths which prove or dis-
prove it are the known facts and principles which
may constitute the premises, and the thesis will
be the conclusion. These determining truths may
be axioms, postulates, proved propositions, or any
truth or fact which the person to whom the pro-
bation is presented may accept. Their accept-
ance is the condition of their proving or disprov-
ing anything. We must observe, therefore, that
probation, as here discussed, is a material as well
as a formal process. The object in proof is, not
merely to have correct reasoning, but also to have
correct and true propositions. We must, there-
fore, enunciate some facts or principles accepted
by the person to whom the probation is presented,
and then bring the thesis or issue under it in such
a way as to enforce conviction, or at least make it
the most probable alternative. As thus defined,
however, there are two general types of this pro-
bation which we may consider. They are the
Deductive and the Inductive arguments.

i. Deductive Arguments. — These are arguments
that endeavor to give perfect certitude to the
proposition affirmed or denied. I give an illus-
tration of its method from mathematics. Suppose
I am asked to prove that the sum of the angles of
a triangle is equal to two right angles. If now I
can show either by observation or proof that the

202

LOGIC AND ARGUMENT

sum of the angles of a triangle is equal to some
quantity which is known or admitted immediately
to be equal to two right angles, I can then draw
the conclusion desired. The demand and the
attempt to give proof assumes that the proposi-
tion cannot be immediately seen to be true, at least
in the special concrete case. Hence, I try to find
some known truth in which the concrete case is
evidently included. I first construct my triangle
as follows :

The thing to be proved is the assertion that
a + b 4- c = two right angles. Now we know by
construction that c + d + e = two right angles.
The triangle is also by construction a right-angled
triangle, so that c is a right angle and also d + e
make a right angle. By drawing the line, separat-
ing d and e, parallel with the hypothenuse of the
triangle, we make b = d and a = e, according to a
proposition in geometry here assumed. The ar-
gument then takes the following form :

c + d + e — two right angles.
a+b + c = c + d + e.
.•.a + b + c = two right angles.

He who admits the two premises must thus
admit the proposition which was to be proved. It
is the same with any other proposition, such as

PROOF AND ARGUMENTATION 203

" Democracy is the proper form of government."
If it is to be proved, its identity or inclusion in
some other admitted proposition must be seen ;
that is, we must see that it follows from some
other known fact.

There are no special subdivisions of this form of
argument except the categorical, the hypothetical,
and the disjunctive syllogism. These have already
been explained, and it remains only to mention
certain advantages which one or two of them may
have over others. The disjunctive syllogism has
the value of confining the issue when the debater
is careful to observe the demand for complete dis-
junction. The hypothetical argument has the ad-
vantage of getting the conclusion admitted on the
condition that the minor premise is proved. It
designs, therefore, to limit the duty of proof to
the minor premise by getting consideration for
the major premise without committing the affirm-
ative to a categorical assertion of it. It is the
connection between it and the conclusion that is
to be gained with a reservation for the minor
premise which has probably to be proved, and
which, as representing a simple matter of fact,
may be easy of proof. Hence, there are situations
in which these forms of argument are preferable
to the categorical ; but the debater must use his
own insight as to the proper emergencies for the
application of them. Disproof, of course, employs
the same method, and only tries to establish a con-
trary or contradictory proposition.

2. Inductive Arguments. — There are arguments
that endeavor to show why the conclusion is

204 LOGIC AND ARGUMENT

preferable to any other supposition. They should
always be recognized as such by the person pre-
senting them, if he wishes to escape the charge of
certain formal and material fallacies. The in-
ductive argument consists in the statement of the
facts which suggest the rationality of the conclu-
sion. Suppose the thesis is to maintain that the
earth moves around the sun. When Copernicus
advanced this doctrine he had only an inductive
argument to favor it. This consisted in a few
simple facts which his theory would explain, but
which did not appear to necessitate it. They
were first the facts that night and day and the
seasons were as consistent with his conception as
with the Ptolemaic, while the apparent retrograde
motions of the heavenly bodies were more simply
explained by his than by the opposing doctrine.
In the course of time the case was taken as proved,
but at first all that could be asserted was that
some facts suggested it and made it possible or
probable. Or again, A is bitten by a cobra, and
the inference is that he will die. Now, if I can
assume as certain that all who are bitten by the
cobra must die, the reasoning would be deductive.
But it may be that all my knowledge in the case
is limited to the fact that some who have been
bitten by the cobra die. Instead, therefore, of
having deductive proof, I have only the inductive.
It will stand as follows :

Some (X. Y. Z.) bitten by the cobra die.
A is bitten by the cobra.
.'. A will die.

PROOF AND ARGUMENTATION 2O$

Here the conclusion can only be probable in so
far as the premises are concerned, and the man
who relies upon this method of proof escapes the
necessity of proving the universality of the major
premise, and requires only to show a sufficient
number of actual facts either easily provable or
readily admitted in order to give at least some
possibility to the thesis to be established, pro-
vided, of course, that he observes the material
conditions for inference of any kind. Many prop-
ositions, perhaps, are capable only of inductive
proof, and the proper sagacity must be shown in
deciding this matter.

III. CLASSIFICATION AND ARRANGE-
MENT OF ARGUMENTS The deductive and

inductive arguments which have been discussed
assume various forms according to the purpose
which they are made to serve. But they are not
classified according to the form of the reasoning.
They are considered from the kind of force or
cogency which they represent in producing con-
viction. As to the arrangement of them, there
must be some conception of the special situation
before any rules can be laid down absolutely
about it. The general principle is that the order
of arguments must depend upon the state of the
mind or minds addressed and the order of de-
pendence in the proofs. Hence, we may lay down
two general rules which determine the order of
stating arguments, and which will be considered
after classifying the kinds of arguments.

ist. Forms of Argument. — Here we have to
do, not with merely formal processes, but with

206 LOGIC AND ARGUMENT

certain material aspects and relations of facts and
truths which give rise to interest and conviction.
They may be classified as follows :

1. Analytic Arguments. — These are merely the
analysis and presentation of what the very con-
ception of the thesis* and its terms involves. It
partakes usually of the nature, or at least the cer-
titude, of deduction, and also of definition. Rather
it represents an analysis of all that is implied in
the contents of definition. For instance, suppose
the issue is " Protection is inexpedient." After
defining protection as a tax" on goods not pro-
duced by a country in order to encourage such
production, it may be seen that such a tax in-
volves in its very conception a discrimination
against unprotected consumers, and therefore in-
expedient or even unjust. This conclusion is the
result of mere analysis, or inference from the con-
ceptions in the thesis as premises.

2. Synthetic Arguments. — Analytic arguments are
of the nature of deductions or inferences from the
ideas contained in or implied by the thesis itself.
But synthetic arguments are of the nature of re-
gressive proof, going back to premises containing
the thesis as a conclusion. It is thus a process of
finding a truth containing the proposition to be
proved, and enough more usually to make it true,
whatever we may think of the proposition at
stake. Thus, in the thesis " Protection is inex-
pedient," we should seek the assertion of some
general and unquestionable truth, such as " Any
policy which favors one class at the expense of
another is inexpedient." This is a major premise

PROOF AND ARGUMENTATION 207

which will gain easy admission, or impose a heavy
task upon an opponent to refute it, and hence it
leaves the affirmative the easier task of proving
that the minor premise is contained in it as the
necessary link in the chain leading to the conclu-
sion. The synthetic feature in it is the fact that
the thesis seems to be or is a necessary conse-
quence of two or more independent, or apparently
independent, truths. It is deductive in its nature,
as it has been illustrated ; but it is not deductive
in the sense that it starts from definition and mere-
ly shows that the proposition is a consequence of
that definition, but it is deductive only in the
sense that it necessarily follows from two prem-
ises mediated by the third term and is included
in them. But the synthetic argument involves the
difficulty of making good the assertion of truths
that contain something more comprehensive than
the particular conclusion at issue. It is possible
also to give the synthetic argument an inductive
character. It becomes so according to the nature
of the premises.

3. Argument from Antecedent Possibility. — This
argument is sometimes called antecedent proba-
bility, but antecedent possibility is better. It
means the argument which shows that there is
nothing opposed to the supposition under discus-
sion. It may be considered a form of indirect
argument. It proves that it is not against reason
to suppose the apriori possibility of the proposi-
tion, and leaves to other positive evidence the
proof of the proposition as a fact. Suppose the
issue is whether there is any immaterial substance

208 LOGIC AND ARGUMENT

or not. It is an antecedent possibility to show
that the conception of such a rea'ity does not
contradict any known reality. It is not the slight-
est evidence of the fact. No such immaterial
reality may exist as a fact. But it is no reason to
deny it that there is no positive evidence for it.
Hence, wherever there is a tendency to deny the
existence of something on the ground of the want
of evidence, it is a defence of its possibility to show
that no facts stand in the way of supposing it, so
that positive belief or conviction only awaits evi-
dence. In regard to the particular instance be-
fore us, this argument for antecedent possibility
consists in showing that the known facts, or the
limits of positive knowledge only extend to the
denial of evidence for immaterial substance, and
not to the denial of its existence. The error, of
course, in assuming the latter on the ground of
the former, has its counter error in the assumption
of its existence because it cannot be positively de-
nied. But we must be as careful to avoid this use
of the argument as we are desirous of impeaching
the opposite side for committing the counter
error. We must be careful to show that the ar-
gument is only indirect, and not direct.

One form of this argument for antecedent pos-
sibility is the so-called argument from Analogy,
which is based upon the resemblance of relations
rather than upon the resemblance of properties be-
tween things. For instance, the argument from
the habitation of the earth to the habitation of
other planets is one of analogy ; or again, from
the metamorphosis of the butterfly to immortality.

PROOF AND ARGUMENTATION 209

These arguments are often taken for real ones,
but in so far as they are arguments at all they are
only indirect and of a weak kind even at that. In
fact, it might be possible to maintain that the
chief, if not the only, function of analogy is to de-
fine a conception or issue. But there are probably
uses of it where it avails to establish an antece-
dent possibility, though it can do no more than
this.

4. Argument from Circumstantial Evidence.

This is a form of inductive and synthetic proof,
and is that form of argument which endeavors
to prove a thesis by the presence of certain signs
or incidents which suggest it. For instance, I
have to show that light has velocity. If I can
point to the phenomenon or fact that there is a
difference of time in the observation of the
eclipses of certain satellites, determined by the
position of the earth in its orbit, I may safel'y
maintain that my thesis has some probability.
If I can collect a number of concurrent facts, I
strengthen that probability. A still better in-
stance is the following : A man is charged with
murder. We wish to prove the accusation. We
find certain characteristics in the boot-tracks go-
ing away from the murdered person. If we find
that the boots of the accused correspond exactly
to these characteristics, we have at least presump-
tive evidence of his guilt. If, further, we find that
the accused possesses bullets or slugs like those
found in the body of the murdered person, we
have corroborative circumstantial evidence. Un-
less this can be of a large and cumulative amount
14

210 LOGIC AND ARGUMENT

or of a particular quality, it does not suffice for
demonstrative proof, but only establishes a certain
degree of probability. It is simply an argument
from certain signs, marks, characteristics, coinci-
dences, etc., to the probability that a given thesis
is true. Whenever we argue from any given at-
tribute or phenomenon to an unknown cause, we
in fact employ the argument from circumstantial
evidence, though the phrase is usually limited to
legal situations and problems, where the data
from which the inference is drawn are not usually,
if ever, attributes of anything, but events and
facts apparently independent of the thing to be
proved.

5. Personal Argument. — This argument may be
regarded as a form of circumstantial evidence,
though it is not what we should call the ad rem
argument, but what I should technically call the
argumentum ad personam. So far as the real issue
is concerned, this class of arguments is comprised
in that which I have called the evasio dictionis, and
includes the argumentum ad judicium, argumentum
ad populum, argumentum ad hominem, etc. These,
we have shown, may be legitimate if they are di-
rected to produce conviction, but not tor proving the
truth. In debate or argumentative discourse the
first object is to produce conviction ; that is, agree-
ment or disagreement in regard to the issue, and
the material truth must then depend upon other
processes than mere reasoning. In order that one
side or the other may thus establish this result, it
is necessary that each shall be allowed to present
a form of argument that involves the other in the

PROOF AND ARGUMENTATION 211

conclusion which the latter denies. This is a way
of indicating that the truth lies on the side of
consistency, only it does not finally decide upon
which side the consistency lies. If, for instance,
the issue is " The appointing power of the execu-
tive should be increased," and the affirmative
quotes A as an authority in his favor, it is perfect-
ly pertinent for the negative to quote in reply the
same authority for facts which contradict this con-
clusion. This is an ad hominem argument against
the affirmative, and requires either the abandon-
ment of his authority or the acceptance of the
negative's conclusion. In the appeal to universal
consent, or to the convictions of the audience,
there is the effort to present facts with some pre-
sumptive weight in the conclusion to be sustained.
It is the same with the argumentum ad verecundiam.
But the authority to which appeal is made in this
case must be recognized by the opponent.

6. Argument from Testimony. — This is a form of
argument based upon the credibility of a witness
to real or alleged facts. The facts are circum-
stantial evidence of the thesis, and the character
of the witness is the measure of the weight at-
taching to his testimony on the facts. " The de-
gree of weight to be attributed to testimony is
always to be estimated by this view of the nature
of testimony — that it is a sign, implying the facts
to which it testifies as more or less necessary
conditions of its having been given. Whenever,
therefore, occasions or motives exist in the case
for giving the testimony other than the truth, the
credibility of the witness will be so far impaired.

212 LOGIC AND ARGUMENT

We are thus to judge of the credibility of histor-
ians. The historian of a sect or of a party must
be received as a credible witness only so far as it
may appear that truth was the condition of his
speaking as he does. All admissions against his
own sect or party, unless made as baits or lures,
wil-1 be received as honest testimony. If these
qualifications are wanting, there is nothing on
which testimony can rest." But where honesty
and candor, as well as good judgment, exist, the
facts attested will have all the weight of these
qualities, though this may not be so great as in
the case that the facts are personally known by
the disputants.

This argument from testimony takes two forms :
(i) Testimony in regard to facts, and (2) Testi-
mony representing matters of opinion. The latter
involves the results of judgment and inference, and
the former does not go beyond matters of per-
ception, in which more people are competent to
pronounce than in matters involving interpreta-
tion and inference. The second form is some-
times called "expert evidence." It me:;:
accept the judgment of qualified men where com-
mon experience is not a guide.

2d. Arrangement of Arguments. — The general
principles which regulate the order of stating the
arguments are two. They are : (i) The state of
the mind addressed ; (2) The dependence of the
arguments upon each other.

" If the mind addressed be already in a state of
belief, and the object of the discourse is to con-
firm and strengthen it, then the weaker arguments

PROOF AND ARGUMENTATION 213

may generally need to be placed first, and the
stronger ones last. But if there be an opposing
belief to be set aside, it will be better to advance
the stronger first, in order to overthrow opposi-
tion at once. The weaker may follow, which will
confirm when they would be of no avail in the
first assault. In order to leave a strong impres-
sion, however, some of the stronger arguments
may be reserved for the close ; or what is equiva-
lent, the arguments may be recapitulated in the
reverse order."

When it comes to the consideration of the sec-
ond principle, which disregards the state of mind
addressed, we have an order that may not repre-
sent the order of strength in producing convic-
tion, but an order in which the strength itself may
be affected by what goes before. The succeeding
arguments are supposed to receive additional
weight from the cogency of the preceding. Other
things being equal, therefore we have the follow-
ing rules :

(1) Deductive should precede inductive proofs.
This assumes that they are both applicable to the
issue. In case that only one of them is possible,
this rule does not apply, and in case that the state
of mind is already one of belief, the order should be
reversed. Those also who maintain that induc-
tion conditions deduction might adopt the reverse
of this order.

(2) Analytic proofs should precede the syn-
thetic and all others. The reason for this rule is
that the analytic argument naturally follows the
process of definition, and prepares the way for

214 LOGIC AND ARGUMENT

the reference to general principles or particular
facts antecedent to the proposition stating the
issue, while the analytic argument does not go be-
hind the conceptions which define this issue.

(3) Antecedent possibility arguments should
precede the inductive arguments generally and
those from circumstantial evidence in particular.
If any presumption against the possibility of the
thesis exists, the first thing is to get that out of
the way, and the mind is then receptive for the
others.

But there are no hard-and-fast rules to be fol-
lowed for every thesis. The judgment of the
debater must be used first to gauge the situation
and to adopt the best arrangement to suit it with
a general reference to the rules just mentioned.
The debater must decide in each particular case
both the state of mind addressed and the pro-
priety of using the cumulative method of argu-
ment. In all cases, however, no matter what the
technical name given to the kind of argument, the
cumulative argument has great value and weight.
This is the successive presentation of arguments
that grow in cogency and power, and the order
will depend somewhat upon circumstances. The
order here will be first antecedent possibility,
testimony, circumstantial evidence, personal argu-
ment, and deduction. This procedure must or
ought to be concluded by a recapitulation which
sums up in outline all the arguments that have
been presented. Just as definition introduces dis-
course, recapitulation should close it.

QUESTIONS AND EXAMPLES

CHAPTER I

INTRODUCTION

1. Define Logic, and show when it is a science and
when an art.

2. Define Rhetoric, and show its relation to Logic.

3. Explain the various meanings of the term " law,"
and more especially its usage in Logic.

4. What is the meaning of the term " thought ? "

5. Name the prelogical processes.

6. Define the logical processes, and state the common
characteristic of all of them. What is the distinction
between perceiving and apperceiving ?

7. What is the name of the two kinds of Conceptions,
and what do they mean ?

8. Define Judgment and Reasoning, and distinguish
between them.

9. What are the divisions of Idea-expression ?

10. Define a " theme," and the processes of Explana-
tion and Confirmation.

11. What is meant by " analysis " and "synthesis"
in Discourse ?

CHAPTER II

1. What is a Term or Concept ?

2. What are Categorematic and Syncategorematic

Terms ?

215

2l6 LOGIC AND ARGUMENT

3. Define and distinguish between Singular and Gen-
eral Terms.

4. Define and distinguish between Collective and Dis-
tributive Terms ; also between Concrete and Abstract
Terms.

5. What is the popular meaning of Abstract and Con-
crete Terms, and how is it distinguished from the logical
and technical meaning ?

6. In the following list of Terms select the various
kinds of them, and explain why they are such, stating
whether they are pure or mixed :

Act,

Beauty,

Man,

Ability,

Presidency,

Action,

Timeliness,

Virtue,

Excellence,

Wisdom,

Agency,

Plato,

Solitude,

Dexterity,

Government,

Agent,

Library,

Introduction,

Art,

Production,

Warmth,

Science,

Truth,

Stone,

Paper,

Society,

Personality,

Wood,

Army,

House,

Sun,

Washington,

Chair,

Nation,

Sweetness,

Some,

Bible,

History,

Koran,

Prime Minister.

7. Explain the uses of Terms in the following propo-
sitions and passages :

(a) The inhabitants of Germany constitute a

nation.

(b) " All men find their own in all men's good,

And all men join in noble brotherhood "

(f) All standing armies are dangerous to the

state.

(d) Non omnis moriar (i.e., I shall not all die).

(e) All the men cannot lift this weight.
(/) Virtue brings its own reward.

(g) Society is an organism.

(h) All of the regiment was put to flight.

(z) Duty cannot be evaded when the nation is-
sues a call to arms for the defence of its
dignity and humanity. Justice and right
must be secured, even if the people cannot
form a united resistance to an enemy. All

QUESTIONS AND EXAMPLES 217

the moral forces and interests of the com-
munity ought to be arrayed with the gov-
ernment in such an emergency, and when
the country's chief ruler issues his com-
mand for action and obedience.
8. Select and explain the various uses of the following

Terms, Positive, Negative, Privitive, and Nego-posi-

tive :

Tree,

Animal,

Deaf,

Inhuman,

Inconclusive,

Insensible,

Ignorant,

Peerlesi,

Perfect,

('nartistic,

Useful.

Impure,

Defect,

Decarnate,

Inconvenient,

Blind.

Clean,

Cold,

Dislike,

Imperishable,

Pure,

Bitter,

Naked,

Inordinate,

Uncontrollable.

9. Define and explain Infinitated, Absolute, and Rel-
ative Terms.

CHAPTER III

1. What is meant by the Predicables?

2. What is meant by the Quantity and Quality, or Ex-
tension and Intension of Terms ?

3. Define Genus and Species. What is the relation
between them ?

4. Explain the meaning of Conferentia and Differ-
entia, and show their relation to each other.

5. Explain the meaning of Essentia and Accidentia.

6. What is the relation between Extension and In-
tension ?

7. What is the analysis of Concepts ? Name its forms.

8. Explain and illustrate the processes of Definition,
Division, and Partition. What are the rules for each ?

9 Give a logical definition for each of the following
concepts :

Biped, Nation, Diet, Spirit, Water, Honor,

House, Mind, Republic, Action, Religion, Imagination,

Club, Money, Matter, Spectacle, Science, Government,

Flood. Politics, Poetry, Picture, Heat, Gravitation.

2l8 LOGIC AND ARGUMENT

10. Examine the following definitions :

(a) A chair is a thing on which men sit.

(b) Ink is a black liquid.

(d) An animal is a thing which increases in size.

(e) A nation is a collective body of men.

(f) A triangle is a figure which is formed by the

intersection of three straight lines.

(g) Death is the opposite of life.

(h) A king is one who exercises regal functions.
(/) A gentleman is a man who has no visible

means of subsistence.
(_/) Man is a rational animal of the highest form

of development.
(k) Science is the study of phenomena with a

view to scientific knowledge.
(/) Religion is a theory of divine government.
(/«) Faith is the substance of things hoped for,

the evidence of things not seen.
(«) Legislatures are bodies of law-makers.
(o) Members of the solar system are anything

over which the sun exercises an influence.
(/)) Socialism is a theory of government.

11. Apply Logical Division to the following Concepts :

Tree, Religion, Matter, Quadrupeds, Vertebrates,

Stones, House, Machines, Organisms, Literature,

Science, Books, Vegetables, Churches, Employment,

Poetry, Laws, Substance, Mammals, Societies.

12. Divide "man" according to color, language,
and religion ; " government" according to constitution,
territory, and race ; " houses " according to form, ar-
chitecture, use, and history ; "vegetables " according to
structural form, use, habitat, and history ; " language "
according to form, geographical distribution ; " matter'1
according to density, structure, and use; "books" ac-
cording to form, subject, binding, price, age, and utility.

QUESTIONS AND EXAMPLES 219

13. Divide each of the following concepts according
to two distinct principles of division :

Law, Occupations, Metals, Religion, History,

Society, Triangle, Liquids, Instruments, Animals.

14. Analyze the following concepts by partition :

Metal, Picture, Cathedral, Knowledge, Religion, Ink,

Iron, Stone, Honor, Money, Literature, Book,

Plant, House, Water, Virtue, Production, Ice,

German, Diamond, Vertebrate, Sensation, Gravitation, Wheat.

15. Apply Partition to the following abstract concep-
tions so as to exhibit their qualities either of action or
passion :

Politeness, Beauty, Comity, Manliness, Courtesy,
Wisdom, Justice, Credulity, Purity, Confidence,

Generosity, Penitence, Patriotism, Genius, Spirituality.

CHAPTER IV

1. Define Analysis of a theme in Discourse. What
processes constitute it ?

2. What is the place of Definition in Explanatory
Discourse ?

3. What are the uses of Division and Partition in the
same ?

4. How is Analysis to be applied ?

5. Define Synthesis in Discourse.

6. What are the laws that regulate Synthesis or Com-
position?

7. Define each of the three forms of Composition.

8. Describe the following subjects or themes accord-
ing to the various classes of attributes suggested by Par-
tition :

The Zodiac ; America ; Boston ; Mont Blanc ; Web-
ster's Dictionary ; a tree ; a locomotive ; an electric

220 LOGIC AND ARGUMENT

telegraph ; a book ; a diamond ; the yErieid ; Paradise
Lost; Dante's Inferno ; England; The character of Na-
poleon ; Bismarck ; Ohio ; United States ; Atlantic
Ocean ; a statesman ; a philosopher ; a poet ; a laborer ;
Raphael's Madonna ; a legislature.

The elephant ; quadrupeds ; a manufactory ; store ;
true manhood ; genius ; politeness ; a horse-race ;
plants ; electricity ; commerce ; inflation of the cur-
rency ; candor ; temporal power of the Pope ; civiliza-
tion of the present century ; a winter landscape ; the
medieval Church ; the government of England ; the
Roman religion ; Christianity ; commerce ; Greek art ;
political institutions.

9. Apply Narration to the following themes with
analysis :

The Crusades ; the American Revolution ; the Amer-
ican Constitution ; the progress of Art ; the battle of
Gettysburg ; the French Revolution ; the Life of Glad-
stone, of Bismarck, of Pitt ; the glacial epoch ; the
formation of habit ; the growth of a plant ; a boat-race ;
a game of ball ; a railway collision ; the rise of chival-
ry ; the slave trade ; the history of Protection, of Free-
trade ; the growth of intelligence ; currency problems
in the United States ; growth of the Speaker's power in
Congress ; American architecture, etc.

10. Apply Exposition to the following themes with
analysis :

Government ; religion ; science ; property ; politics ;
virtue ; dress ; rhetoric ; manners ; society ; art ; music ;
painting ; sculpture ; personality ; the Church ; archi-
tecture ; the Papacy ; protestantism ; the social con-
tract ; the Constitution ; the Declaration of Indepen-
dence ; justice; commerce; business; law; literature;
currency ; magnanimity ; self-reliance ; poverty ; civil-
ization ; democracy ; empire.

QUESTIONS AND EXAMPLES 221

CHAPTER V

1 . Define a Proposition and distinguish between Univ-
ocal and Equivocal Propositions. Illustrate.

2. Define and illustrate each of the Logico-Grammati-
cal Propositions.

3. What are the symbols of each of these propositions,
and how distinguish them in respect to form and matter ?

4. Define and illustrate both the Logico-Qualitative
and the Logico-Quantitative Propositions.

5. How do we reduce the five-fold division of proposi-
tions into the two-fold ?

6. State, define, and illustrate the divisions of Equivo-
cal Propositions.

7. What are the symbols for each of the Equivocal
Propositions, and how reduce them to the Univocal
form ?

8. What is meant by the Distribution of terms ? What
is the distribution of terms in Definitions and Exclusive
Propositions ?

9. Examine the following propositions and resolve
them into their proper forms for definite logical use :

(a) Man is rational.

(b) All men are not wise.

(d) Man alone is not obedient to his instincts.

(e) Few elements are metals.
(/) Most men are Caucasians.

(g) Only those substances which are not subject

to gravity are immaterial.
(h) All persons except criminals and foreigners

are not allowed to vote.

222 LOGIC AND ARGUMENT

CHAPTER VI

1. What is meant by the Opposition of Propositions ?

2. How do we treat singular and abstract proposi-
tions ?

3. If we assume the falsity of any one of the four
propositions, A, E, I, and O, what follows in regard to
the others ?

4. How may we disprove propositions, and which is
the better form of disproof ?

5. What are the laws of Opposition ?

6. Select pairs of the following propositions and ar-
range them so as to show all the various relations illus-
trated by them :

(a) All metals are elements.

(b) Some metals are not elements.

(d) Some metals are elements.

(e) Most metals are elements.

(f) All metals are not elements.

(g) Not all metals are elements.
(h) Only metals are elements.
(0 Few metals are elements.

7. Examine the relation expressed by the following
propositions :

(a) One man says that all men are wise and an-

other that they are all ignorant.

(b) Free trade lowers prices and protection does

not.

dent, and the other that B will be elected
president.

(d) Mr. X asserts that not a nail was made in

this country before 1861. E says that so
far from this statement of X being true that
in 1856 there were 2,645 nail-machines in

QUESTIONS AND EXAMPLES 223

operation in this country with an output of
86,462 tons, and in 1859 as many as 4,686,-
207 pounds of nails were exported.

(e) Will the educated woman marry ? So queried
one of our alumnae in a recent magazine
article in which the object was to show that
she would not. The review roll of our
alumnae shows that of 76 ladies who grad-
uated in our classes, 32 have already mar-
ried.

(/) The policy which he now says would have
been infamous he was then proposing to
adopt.

(g) If the appreciation of gold has been the
cause of the extraordinary fall in prices,
why have ivory and whalebone not fallen
in price, but on the contrary have steadily
risen in price during the last decade ?

CHAPTER VII

1. What is the meaning of inference? Of immediate
inference ? Of mediate inference ?

2. Name the divisions of immediate inference.

3. What are the rules for conversion ? What is
meant by Convertend and Converse ?

4. What propositions can be converted and what not,
and why ?

5. Why cannot proposition I be contraverted ?

6. Why are Definitions and Exclusive propositions
real or apparent exceptions to these rules ?

7. What is the technical meaning of the exclusive
particle ?

8. What is meant by Conversion by Negation ?

9. What are the rules for Obversion and Contraver-
sion ?

224 LOGIC AND ARGUMENT

10. How do we obvert negative propositions ?

11. Define and illustrate inference by Contribution.

12. What is the difference between the two kinds of
Contribution ?

13. Define and explain Antithesis.

14. State the logical process by which we pass from
each of the following propositions to the succeeding
one :

(a) All oaks are trees.

(b) No oaks are not trees.

(d) All not-trees are not-oaks.

(e) All not-trees are not oaks.
(/) All oaks are not not-trees.
(g) All oaks are trees.

(h) All not-trees are not oaks.
(/) All not-trees are not-oaks.
(j) Some not-oaks are not-trees.
(k) Some not-oaks are not trees.
(/) Some oaks are trees, (a)
(m) Some trees are oaks.
(«) No trees are oaks.
(o) All trees are oaks.

15. Apply the various processes of immediate infer-
ence to the following propositions :

(a) Every man is a biped.

(b) Some books are dictionaries.

(d) No triangle has one side equal to the sum

of the other two.

(e) " Every consciousness of relation is not cog-

nition."

(/) Perfect happiness is impossible.
(g) A stitch in time saves nine.
(//) None think the great unhappy but the great.
(*') Few are wise enough to.be virtuous.
(j) No one is free who does not control himself.

QUESTIONS AND EXAMPLES 225

(k) Good orators are not always good statesmen.

(/) Some inorganic substances do not contain
carbon.

(m) Only the brave deserve the fair.

(«) All men are not born equal.

(<?) No one is a hero to his valet.

(P) Uneasy lies the head that wears a crown.

(g) He jests at scars who never felt a wound.

(r) Better late than never.

(s) Every mistake is not culpable.

(t) I shall not all die. (Non omnis mortar.)

(u) Fain would I climb but that I fear to fall.

(v) Great is Diana of the Ephesians.

(TV) Not many of the metals are brittle.

(x) Talents are often misused.

(y) Some books are to be read only in part.

(z) Two blacks will not make a white.

(a) Not one of the Greeks at Thermopylae es-
caped.

(b1) Nothing is praiseworthy but virtue.

(d1) There is none good but one.

(e) All that glitters is not gold.

(f) He can't be wrong whose life is in the right.
(g') Philosophers in many instances do not es-
cape equivocation.

16. State the relation, if any, between the following
propositions as indicated by the figures in parentheses at
the end of each proposition :

(i.) Good men are wise.

(2.) Unwise men are not good (i).

(3.) Some wise men are good (i).

(4.) No good men are unwise (i), (2).

(5.) Some unwise men are not good (2), (3), (4).

(6.) Some good men are wise (i), (2), (3).

(7.) No good men are wise (i), (3), (4), (6).

(8.) Some good men are not wise (i), (3), (6), (7).
15

226

(9.) No unwise men are good (i), (4), (5), (8).
(10.) No wise men are good (i), (2), (6), (7), (8).

17. What is the logical relation, if any, between the
two following propositions : "A false balance is an
abomination to the Lord, but a just weight is his de-
light."

18. State the relation between the following three
propositions : " The voluntary muscles are all striped,
and the unstriped are all involuntary, but a few of the
involuntary muscles are striped."

19. Can we logically infer that cold contracts bodies
because heat expands them ?

CHAPTER VIII

1. Define mediate reasoning with its divisions.

2. Name and define the elements of the syllogism.

3. What are the chief rules for the syllogism ?

4. Define what is meant by the Mood and the Figure
of the syllogism.

5. Show by the rules what Moods must be rejected
from the whole sixty-four on the ground of being fal-
lacious in all cases.

6. What kind of conclusion can be drawn from the
following premises, AA, EA, IA, AE, OA, El ?

7. What is meant by a weakened conclusion ?

8. Show in what Figures the following premises
give valid conclusion : AA, AE, IA, EA, AO, El,
AI, OA.

9. Why must the major premise of the first Figure
be universal ?

10. Why must one of the premises in the second Fig-
ure be negative ?

1 1. Show that O cannot stand as either premise in the
first Figure, as major premise in the second Figure, and
as minor premise in the third Figure.

QUESTIONS AND EXAMPLES

227

12. What fallacy will be committed by having A as a
conclusion in any figure but the first?

13. What fallacy is committed when the minor pre-
mise is negative in the first and third Figures ?

14. If one premise be O, what must the other be ?

15. Why cannot the premises be IE ?

16. Why can no universal conclusion be drawn in the
third Figure ?

r 17. Could you reason with affirmative propositions in
the second Figure if one of the premises is a definition ?

1 8. How can you treat premises in IE in order to get
a valid conclusion ?

19. If my conclusion be O, what are my premises ?

20. If the minor premise be affirmative, what moods
will give a valid conclusion ?

21. State the Moods and Figures of the following syl-
logisms, and name those which are valid and those
which are invalid :

(a) Some M is P. (6) All P is M. (c) All S is M.

No S is M. No M is S. No P is M.

.'. Some P is not S. .'. No P is S. .'. Some S is not P.

(rf) No M is P. (e) Some P is M. (/) All P is M.

All M is S. All S is P. Some M is not S.

.'. Some S is not P. .'. Some S is M. .'. Some P is not S.

(g] Some M is not S.
Some P is not S.

22 . With E as a middle term, form a syllogism with
C as the predicate of the conclusion.

23. How can you reduce one Figure of the syllogism
to another ?

24. What is the value of each Figure of the syllogism ?

25. Examine the following syllogisms :

(a) All feathered animals are vertebrates.
No reptiles are feathered animals.

/. Some reptiles are not vertebrates.

(b) All vices are reprehensible.
Emulation is not reprehensible.

/. Emulation is not a vice.

228 LOGIC AND ARGUMENT

All Caucasians are rational beings.
.'. All Caucasians are men.

(d) All vices are reprehensible.
Emulation is not a vice.

. \ Emulation is not reprehensible.

(e) Some men are wise.

All philosophers are men.

. '. Some philosophers are wise.

(/) Some animals are quadrupeds.

All trees are not quadrupeds.
.'. Some trees are not animals.
(g) Only citizens are voters.

ABC are voters.
.'.ABC are citizens.
(h) Some statesmen are wise.

Some good men are statesmen.
.'. Some good men are wise.
(/) Some plants are deciduous.

No trees are plants.
.'. Some trees are not deciduous.
26. Deduce conclusions, stating Moods and Figures,
from the following premises :

(a) All planets are heavenly bodies.

No planets are self-luminous.
(6>) All Europeans are Caucasians.
All Caucasians are white.

All carnivora are devoid of claws.

(d) Some animals are quadrupeds.
All quadrupeds are vertebrates.

(e) Oak trees are evergreen.
Pine trees are evergreen.

{/) Some Americans are not white.
All white persons are Caucasian.

QUESTIONS AND EXAMPLES

CHAPTER IX

229

1. Define each form of simple and complex syllogism
or reasoning.

2. How can the enthymeme be completed to form a
syllogism ?

3. What are the conditions of a valid sorites ?

(a) Europeans are Caucasians because they are

white.

(b) We cannot know what is false because knowl-

edge cannot be deceptive.

not deliver the message.

(d) A is B because it is C.

(e) A is B because C is B.

E is A because C is A.
Eis A.

(/) A manor cannot begin at this day, because a
court baron cannot now be founded.

CHAPTER X

1. What is the difference between categorical and
hypothetical reasoning ?

2. Define each kind of hypothetical reasoning.

3. Give the rules for valid hypothetical reasoning.

4. To what in the categorical syllogism are the moods
of hypothetical reasoning equivalent ?

5. What characterizes simple and complex dilemmatic
reasoning ?

6. How can hypothetical reasoning be reduced to
categorical ?

7. Examine the following instances of hypothetical
reasoning, state the moods and convert into categorical
syllogisms :

230 LOGIC AND ARGUMENT

(a) If education is necessary it will be popular.
It is popular, and therefore will be neces-
sary.

(&) Rain has fallen if the ground is wet ; but the
ground is not wet ; and therefore rain has
not fallen.

government might be improved ; but the
citizens will not change their character,
and hence no improvement in their gov-
ernment can be expected.

(d) If rain has fallen the ground is wet ; but rain

has not fallen, and therefore the ground is
not wet.

(e) If the weather is cloudy it will not be warm :

but it is warm, and therefore is not cloudy.

(f) If food is not scarce the wants of the com-

munity are satisfied ; but food is not scarce
and hence the wants of the community
are satisfied.

(g) The ground is wet if rain has fallen ; the

ground is wet ; therefore rain has fallen.

(k] If citizens do not obey the law, they will not
retain their freedom ; but they obey the
law and hence retain their freedom.

(*) If the ground is wet rain has fallen. But
rain has fallen ; therefore the ground is
wet.

(/) If a man cannot make progress toward per-
fection, he must be a brute ; but no man
is a brute, and therefore is capable of such
progress.

(k) If two and two make five in some other
planet, Mill's opinion about the matter is
correct ; but they do not make five in any
place, and hence Mill is wrong.

QUESTIONS AND EXAMPLES

CHAPTER XI

231

1. Define and illustrate disjunctive reasoning.

2. Explain the uses of the symbols of disjunctive prop-
ositions.

3. Name and define the two moods of disjunctive
reasoning.

4. Upon what does incomplete disjunction depend ?

5. What fallacy characterizes disjunctive reasoning ?

6. Examine the following instances of disjunctive rea-
soning, and resolve into both hypothetical and categori-
cal syllogisms:

(a) Criminals are either good or bad.
They are bad.

They are not good.

(b) The weather will be either clear or warm.
It will not be warm.

It will be clear.

A is C.

(d) Aristotle was either very talented or very in-

dustrious.

He was very industrious.
He was not very talented.

CHAPTER XII

1. Give the definition and divisions of the several
kinds of fallacy.

2. What determines the existence of formal fallacies ?

3. How do we classify the material fallacies ?

4. Define and distinguish between the two kinds of
fallacy based upon equivocation.

5. Define and illustrate the fallacies tf petitio principii
and non sequitur.

232 LOGIC AND ARGUMENT

6. What are the legitimate uses of the argumcnta ad
jndicium, ad populum, etc ?

7. Explain several points of view from which fallacious
reasoning can be considered.

CHAPTER XIII

1. Define inductive reasoning. Distinguish between
Perfect and Imperfect Induction.

2. How do you distinguish between Deduction and
Induction ?

3. What is the difference between the formal process
in the two kinds of reasoning ?

4. What are the rules for inductive reasoning ?

CHAPTER XIV

1. Define what is meant by proof and its two kinds.

2. What is the difference between proof and infer-
ence ?

3. What is the difference between direct and indirect
proof ?

4. Name and define the various processes involved
in proof.

5. How should arguments be classified in logical dis-
course ?

6. What is meant by analytic and synthetic argu-
ments?

7. Explain the nature of Personal Arguments.

8. What should be the arrangement of arguments ?

9. Apply argumentation with analysis to the following
themes, choosing according to conviction or conven-
ience whether it shall be proof or disproof :

The benefits of the Crusades. The execution of
Charles the First. The punishment of Socrates. The
policy of protection. The policy of free trade. The

QUESTIONS AND EXAMPLES

233

merits of the classics. Co-education. The freedom of
the press. College athletics. The benefits or evils of
feudalism. The character of Aaron Burr. The ban-
ishment of Napoleon. The execution of the Due
d'Enghien. The Hispano-American war. Civil-service
reform. Universal suffrage. States rights. The Pel-
oponnesian war. Lynch law. Strikes. Boycotting.
The necessity of labor unions. Free education. Trusts.
Political bosses.

The instructor may find it best to supply subjects of
current interest.

PRACTICAL EXERCISES

DEDUCTIVE

1. Personal deformity is an affliction of nature.
Disgrace is not an affliction of nature.
Therefore personal deformity is not a disgrace.

2. None but animals are quadrupeds.
Horses are quadrupeds.
Therefore horses are animals.

3. All roses are beautiful.
Lilies are not roses.
Therefore lilies are not beautiful.

4. Every book is liable to error.
Every book is a human production.

Therefore all human productions are liable to error.

5. All paper is useful ; and as all that is useful to men
is a source of comfort to them, therefore, all paper is a
source of comfort to them.

6. Some statesmen are also authors ; for such are
Burke, Macaulay, Gladstone, Lord Russell, etc.

7. Some philosophers are logicians.

No logicians are ignorant of the works of Aristotle.
Therefore some philosophers are not ignorant of
the works of Aristotle.

234 LOGIC AND ARGUMENT

8. No persons destitute of imagination are true
poets.

Some persons destitute of imagination are good

logicians.
Therefore some true poets are not good logicians.

9. If Caesar was a tyrant he deserved to die.
Caesar was not a tyrant.

Therefore he did not deserve to die.

10. Good is the object of moral approbation. The
highest good is, therefore, the ultimate object of such
approbation.

11. If it stops raining the weather will be colder.
The weather will be colder.

Therefore it will stop raining.

12. It is doubtful whether Caesar will come forth to-
day or not.

For he is superstitious grown of late.

13. Every man should be moderate ; for excess will
Cause disease.

14. All Parisians are Frenchmen.
No Chinese are Parisians.

Therefore some Chinese are not Frenchmen.

15. Some men are not virtuous.
All Americans are men.

Therefore some Americans are not virtuous.

16. Blessed are the merciful ; for they shall obtain
mercy.

17. As almost all the organs of the body have a known
use, the spleen must have some use.

1 8. Some of the inhabitants of the globe are more civ-
ilized than others.

No savages are more civilized than others.
Therefore, some savages are not inhabitants of
the globe.

19. Cogito ergo sum (I think, therefore, I am).

20. He must be a Mohammedan, for all Mohamme-
dans hold these opinions.

QUESTIONS AND EXAMPLES 235

21. He must be a Christian, for only Christians hold
these opinions.

22. Logic is either a science or an art.
It is a science.

Therefore, it is not an art.

23. No idle person can be a successful writer of his-
tory ; therefore, Hume, Macaulay, Hallam, and Grote
must have been industrious.

24. Every moral man obeys the law ; every citizen
does not do so, and therefore is not moral.

25. This explosion must have been occasioned by
gunpowder ; for only gunpowder had a sufficient force.

26. Rational beings are accountable for their conduct ;
brutes not being rational are exempt from responsibility.

27. All valid syllogisms have three terms.
This syllogism has three terms.
Therefore, this syllogism is valid.

28. All syllogisms are valid that have three terms.
This syllogism has three terms.
Therefore, this syllogism is valid.

29. Comets are heavy matter : for otherwise they
would not obey gravitation.

30. A charitable man has no merit in relieving dis-
tress, because he merely does what is pleasing to him-
self.

31. If the government enacts such a law it must either
adopt socialism or go into bankruptcy. But it will not
enact such a law, and hence there is no danger of either
socialism or bankruptcy.

32. None but savages were in America when it was
discovered.

The Hottentots were savages.
Therefore, they were in America when it was dis-
covered.

33. None but despots possess absolute power.
The Czar of Russia is a despot.
Therefore, he possesses absolute power.

236 LOGIC AND ARGUMENT

34. Bacon was a great philosopher and statesman,
and he was also a lawyer ; we may infer that any lawyer
may be a great philosopher and statesman.

35. Mathematical studies undoubtedly improve the
reasoning powers ; but as logic is not a mathematical
study we may conclude that it does not improve our rea-
soning powers.

36. If a man cannot obey the law he must be either a
machine or a demon ; but no man is either of these, and
hence he must be able to obey the law.

37. Whatever tends to draw the mind from pursuits
of a low nature deserves to be promoted. Classical
learning does this, since it gives us a taste for intellectual
enjoyments : therefore, it deserves to be promoted.

38. If virtue is involuntary, vice is involuntary.
Vice is voluntary.

Therefore, virtue is voluntary.

39. All civilized people are inhabitants of the temper-
ate zones. Few Indians are civilized, and therefore few
Indians are inhabitants of the temperate zones.

40. If pain is severe it will be brief, and if it last long
it will be slight ; it is either severe or it lasts long, and
therefore will be either brief or slight.

41. Some who are truly wise are not learned ; but the
virtuous alone are truly wise ; the learned, therefore,
are not always virtuous.

FORMAL AND MATERIAL

42. The Americans are a nation, and as the citizens
of New York City are Americans, they must be a nation.

43. The right should be enforced by law. Hence,
since the exercise of the suffrage is a right, it should be
enforced by law.

44. Napoleon was not a great emperor ; for though
he would have been great had he succeeded in retaining
power, he did not do so.

QUESTIONS AND EXAMPLES 237

45. Seven and nine are odd numbers.
Sixteen is seven and nine.
Therefore sixteen is an odd number.

46. If capital punishment involves cruelty to its vic-
tims it ought to be abolished in favor of some other pen-
alty ; if it does no good to society it should also be
abolished. But it either involves cruelty to its victims
or does no good to society, and hence it ought to be
abolished.

47. The Reformers were strongly opposed to the papal
supremacy, and as Mr. B. was a reformer, because he
favored better politics, he was opposed to the papal
supremacy.

48. Knowledge is of no use to anyone in preventing
him from committing crime ; for we hear every day of
frauds and forgeries which would have never been com-
mitted had not the person learned to read and write.

49. Wealth is valuable ; value is purchasing power ;
purchasing power is the product of labor, and the prod-
uct of labor is property ; therefore, wealth is property.

50. Every rule has exceptions ; this is a rule, and
therefore has exceptions ; therefore, there are some rules
that have no exceptions.

51. All who think this man innocent think he should
not be punished ; you think he should not be punished ;
therefore, you think him innocent.

52. All who think this man innocent think he should
not be punished ; you think he should be punished ;
therefore, you do not think him innocent.

53. The end of punishment is either the protection of
society or the reformation of the criminal. Capital pun-
ishment ought, therefore, to be abolished, because it
neither prevents crimes of violence, nor protects society,
nor does it reform the criminal.

54. Haste makes waste, and waste makes want. A
man, therefore, never loses by delay.

55. Only the virtuous are truly noble ; some who are

238 LOGIC AND ARGUMENT

called noble are not virtuous ; therefore, some who are
called noble are not truly noble.

56. All equilateral triangles are equiangular, and
therefore, all equiangular triangles are equilateral.

57. For those bent on cultivating their minds by dili-
gent study the incitement of academic honors is unnec-
essary ; and it is ineffectual for the idle and such as are
indifferent to mental improvement ; therefore, the in-
citement of academic honors is either unnecessary or
ineffectual.

58. Logic, as it was cultivated by the schoolmen,
proved a fruitless study ; therefore, logic as it is culti-
vated to-day must be a fruitless study.

59. A, B, C, D, and E are the only German students
that I know ; they are all men of considerable intellect-
ual attainments, and consequently I may infer that all
German students are men of considerable intellectual
attainments.

60. Repentance is a good quality ; wicked men abound
in repentance, and therefore abound in what is good.

61. Warm countries alone produce wine. Spain is a
warm country, and therefore produces wine.

62. It is an intensely cold climate that is sufficient to
freeze mercury ; the climate of Siberia is sufficient to
freeze it, and hence must be intensely cold.

63. No designing person ought to be trusted ; engrav-
ers are, by profession, designing persons or designers;
therefore, they ought not to be trusted.

64. I will not do this act because it is unjust ; I know
it is unjust because my conscience tells me so, and my
conscience tells me so because the act is wrong.

65. Is a stone a body ? Yes. Then is not an animal
a body ? Yes. Are you an animal ? I think so. Ergo,
you are a stone, being a body.

66. If ye were Abraham's children ye would do the
works of Abraham. — John viii, 39.

67. He that is of God heareth God's words ; ye there-

QUESTIONS AND EXAMPLES 239

fore hear them not, because ye are not of God.—JoAn
viii, 47.

68. His imbecility of character might have been in-
ferred from his proneness to favorites ; for all weak
princes have this failing.

69. He is brave who conquers his passions ; he who
resists temptation conquers his passions ; so that he who
resists temptation is brave.

70. Suicide is not always to be condemned ; for it is
but voluntary death, and this has been gladly embraced
by many of the greatest heroes of antiquity.

71. All that glitters is not gold; tinsel glitters and
therefore is not gold.

72. Meat and drink are the necessaries of life. The
revenues of the king were spent on meat and drink, and
were therefore spent on the necessaries of life.

73. Nothing but the express-train carries the mail,
and as the last train was the express, it must have car-
ried the mail.

74. Theft is a crime ; theft was encouraged by the
laws of Sparta ; therefore, the laws of Sparta encour-
aged crime.

75. Since all gold is a metal, the most rare of all
masses of gold must be the most rare of all the
metals.

76. He who calls you a man speaks truly ; he who
calls you a fool calls you a man ; therefore, he who calls
you a fool speaks truly.

77. Protective laws should be abolished, for they are
injurious if they produce scarcity, and they are useless
if they do not.

78. Detention of property implies at least possession;
for detention is natural possession.

79. Profit is interpreted or defined to be advantage ;
to take profit then is to take advantage. It is wrong to
take advantage of one's neighbor, and therefore it is
wrong to take profit.

240 LOGIC AND ARGUMENT

80. Peel's remission of taxes was beneficial ; the taxes
remitted by Peel were indirect, and therefore the re-
mission of indirect taxes is beneficial.

8r. Some poisons are vegetable ; not poisons are use-
ful drugs, and therefore some useful drugs are not vege-
table.

82. Whosoever intentionally kills another should suf-
fer death ; a soldier, therefore, who kills his enemy
should suffer death.

83. Few towns in the country have 500,000 inhabi-
tants, and since all such towns ought to have three repre-
sentatives in Congress, it is evident that few towns
should have three representatives.

84. If Bacon's opinion be right it is improper to stock
a new colony with criminals from prison ; but this course
we must allow to be proper if the method of colonizing
New South Wales be a wise one. If this be wise, there-
fore, Bacon's opinion is not right.

85. The people of the country are suffering from fam-
ine, and as A, B, and C are people of the country,
they must be suffering from the famine.

86. You are not what I am ; I am a man ; therefore,
you are not a man.

87. Gold and silver are wealth ; and therefore the
diminution of the gold and silver of a country by expor-
tation is a diminution of the wealth of the country.

88. The holder of some shares in a lottery is sure to
gain a prize, and as I am the holder of some shares in a
lottery I am sure to gain a prize.

89. A monopoly of the sugar-refining business is bene-
ficial to sugar refiners ; and of the corn trade to corn
growers ; and of the silk manufacturers to the silk weav-
ers ; of labor to the laborers. Now, all these classes of
man make up the community. Therefore, a system of
restriction upon competition is beneficial to the com-
munity.

90. Over-credulous persons should never be believed,

QUESTIONS AND EXAMPLES 241

and as the ancient historians were in many instances
over-credulous they ought never to be believed.

91. That is unfortunate ; you insolently assert that you
are a Darwinian, while the truth is that you are a poet.

92. Every incident in the narrative is probable, and
hence the narrative may be believed, since it is probable.

93. If a substance is solid it possesses elasticity, and
so also it does if it be liquid or gaseous ; but all sub-
stances are either solid, liquid or gaseous ; therefore,
all substances possess elasticity.

94. Who is most hungry eats most ; who eats least is
most hungry ; therefore, who eats least eats most.

95. If the elixir of life is of any value those who take
it will improve in health ; now, my friend who has been
taking it has improved in health, and therefore the elixir
is of value.

96. What produces intoxication should be prohib-
ited ; the use of intoxicating liquors causes intoxica-
tion ; therefore, the use of spirituous liquors should be
prohibited.

97. When we hear that all the righteous people are
happy, it is hard to avoid exclaiming, what ! are all the
unhappy persons we see thought to be unrighteous ?

98. Italy is a Catholic country, and abounds in beg-
gars ; France is also a Catholic country, and therefore
abounds in beggars.

99. If it be fated that you recover from your present
disease, you will recover, whether you call in a doctor
or not ; again, if it be fated that you do not recover
from your present disease, you will not recover, whether
you call in a doctor or not. But one or the other of
these contradictories is fated, and therefore it can be of
no service to call in a doctor.

100. All the trees in the park make a thick shade ;
this oak tree is one of them, and therefore makes a thick
shade.

101. All visible bodies shine by their own or by re-

242 LOGIC AND ARGUMENT

fleeted light. The moon does not shine by its own ;
therefore, it shines by reflected light ; but the sun shines
by its own ; therefore, it cannot shine by reflected light.

102. The two propositions, " Aristotle is Living," and
" Aristotle is Dead," are both intelligible propositions ;
they are both of them true or both of them false, because
all intelligible propositions must be either true or false.

103. I am charged with absenteeism from my post,
and on that ground I am accused of ignorance in regard
to the proper duties of my office. But my accuser him-
self, who was my predecessor in the same office, was
not longer than five days in the country of which he was
the chief officer.

104. Every law is either useless or it occasions hurt to
some person ; now, a law that is useless ought to be
abolished ; and so ought every law that occasions hurt ;
therefore, every law ought to be abolished.

105. Does a grain of millet when dropped on the floor
make a sound? No. Does a bushel of millet make any
sound under the same circumstances ? Yes. Is there
not a determinate proportion between the bushel and
the grain ? There is. There must, therefore, be the
same proportion between the sonorousness of the two.
If one grain be not sonorous, neither can ten thousand
grains be so.

106. Injustice is more profitable than justice, because
those who do unjust acts gain more than the just.

107. Ruminant animals are those who have cloven
feet, and they usually have horns ; the extinct animal
which left this foot-print had a cloven foot ; therefore, it
was a ruminant animal and had horns. Again, as no
beasts of prey are ruminant animals, it cannot have been
a beast of prey.

108. Happiness signifies a gratified state of all the
faculties. The gratification of faculty is produced by
exercise. To be agreeable that exercise must be pro-
portionate to the power of the faculty ; if it is insuffi-

QUESTIONS AND EXAMPLES

243

cient discontent arises, and its excess produces weari-
ness. Hence, to have complete felicity is to have all
the faculties exerted in the ratio of their several develop-
ments.

109. I am offered a sum of money to assist this person
in gaining the office he desires ; to assist a person is to
do him good, and no rule of morality forbids the doing
of good ; therefore, no rule of morality forbids my re-
ceiving the sum of money for assisting this person to
obtain office.

no. We must either gratify our vicious propensities
or resist them ; the former course will involve us in sin
and misery ; the latter requires self-denial. Therefore,
we must either fall into sin or practise self-denial.

111. 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 fluid.

112. Every moral aim requires the rational means of
attaining it ; these means are the establishment of laws ;
and as happiness is the moral aim of man it follows that
the attainment of it requires the establishment of laws.

113. The several species of brutes were created to
prey upon each other, and consequently the human
species was created to prey upon them.

114. If any objection can be urged to justify a change
of established laws, no laws could be reasonably main-
tained ; but some laws can be reasonably maintained ;
therefore, no objection that can be urged will justify a
change of established laws.

115. Riches are for spending, and spending for honor
and good actions. Therefore, extraordinary expense
must be limited by the worth of the occasion.

116. If our rulers could be trusted always to look to
the best interests of their subjects, monarchy would be
the best form of government. But they cannot be
trusted ; therefore, monarchy is not the best form of
government.

244 LOGIC AND ARGUMENT

117. The good is pleasure, for it results from the due
performance of proper functions ; but the good" is a
state of consciousness ; therefore, the good is a state of
consciousness which results from the due performance
of proper functions.

1 1 8. He who bears arms at the command of the mag-
istrate does what is lawful for a Christian ; the Swiss in
the French service and the British in the American ser-
vice bore arms at the command of the magistrate ;
therefore, they did what is lawful for a Christian.

119. No soldiers should be brought into the field who
are not well qualified to perform their duty ; none but
veterans are well qualified to perform their part ; there-
fore, none but veterans should be brought into the field.

1 20. Improbable events happen almost every day,
but what happens almost every day is a very probable
event ; therefore, improbable events are very probable
events.

121. The object of war is durable peace; therefore,
soldiers are the best peace-makers.

122. Confidence in promises is essential to human in-
tercourse and commerce ; for without it the greatest part
of our conduct would proceed upon chance. But there
can be no confidence in promises if man were not
obliged to perform them ; the obligation, therefore, to
perform promises is essential to the same ends and in
the same degree.

123. The minimum visibile is the least magnitude
which can be seen ; no part of it alone is visible, and
yet all the parts of it must affect the mind in order that it
may be visible ; therefore, every part of it must affect
the mind without being visible.

124. He who believes himself to be always in the right
in his opinion lays claim to infallibility ; you always be-
lieve yourself to be in the right in your opinion ; there-
fore, you lay claim to infallibility.

125. If the light is not refracted near the surface of

QUESTIONS AND EXAMPLES

245

the moon there cannot be any twilight there ; but if the
moon has no atmosphere, light is not refracted near its
surface ; therefore, if the moon has no atmosphere it
cannot have any twilight.

126. What you say is that virtue is the power of at-
taining good? Yes. And you would say that goods
are such as health and wealth, and the possession of gold
and silver, and having office and honor in the state —
these are what you call goods ? Yes, all these. Then,
according to Meno, who is the hereditary friend of the
great king, virtue is the power of getting silver and gold.

MISCELLANEOUS

INDUCTIVE AND DEDUCTIVE

127. Geometry contemplates figures. Figure is the
termination of magnitude ; but extension in the abstract
has no definite determinate magnitude ; whence it fol-
lows clearly that it can have no figure, and consequently
is not the object of Geometry.

128. The newly discovered painting must be a Ru-
bens ; for the conception, the drawing, the tone and tints
are precisely those seen in the authentic works of that
master.

129. In nine counties, in which the population is from
100 to 150 per square mile, the births to loo marriages
are 396 ; in sixteen counties, with a population of 15010
200 per square mile, the births are 39010 100 marriages.
Therefore, the number of births per marriage is in-
versely related to the density of population, and contra-
dicts Malthus's theory of population.

130. " Cramming" for examination is detrimental
rather than otherwise ; for I have noticed that, no matter
what the subject is, I invariably write a poor paper when
I " cram," and a good one when I do not.

246 LOGIC AND ARGUMENT

131. If the earth were of equal density throughout it
would be about 2>£ times as dense as water; but it is
about 5X times as dense; therefore, the earth must be
of unequal density.

132. The great famine in Ireland began in 1845, and
increased until it reached a climax in 1848. During this
time agrarian crime increased very rapidly until, in
1848, it was more than three times as great as in 1845.
After this it decreased with the return of better crops,
until, in 1851, it was only fifty per cent, more than it
was in 1845. It is evident from this that a close relation
of cause and effect exists between famine and agrarian
crime.

133. "Now that which does not make a man worse,
how can it make a man's life worse ? But neither through
ignorance, nor having the knowledge but not the power
to guard against or correct these things, is it possible
that the nature of the universe has overlooked them ;
nor is it possible that it has made so great a mistake,
either through want of power or want of skill, that good
and evil should happen indiscriminately to the good and
the bad. But death certainly, and honor and dishonor,
pain and pleasure — all these things happen equally to
good men and bad, being things which make us neither
nor worse. Therefore, they are neither good nor evil."
— Marcus Aurelius.

134. If the majority of those who use public houses
are prepared to close them legislation is unnecessary ;
but if they are not prepared for such a measure, then to
force it on them by outside pressure is both dangerous
and unjust.

135. On May 27, 1875, a remarkable shower of small
pieces of hay occurred at Monkstown, near Dublin.
They appeared floating down from a great height. A
similar shower occurred a few days earlier in Denbigh-
shire. From this and many similar facts we conclude
that the distribution of organisms over continents and

QUESTIONS AND EXAMPLES 247

islands separated by the ocean has been effected by the
agency of natural forces.

136. The influence of heat in changing the level of the
ground upon which the Temple of Jupiter Serapis stands
might be inferred from several circumstances. In the
first place, there are numerous hot springs in the vicinity,
and when we reflect on the dates of the principal oscilla-
tions of level this conclusion is made much more prob-
able. Thus, before the Christian era, when Vesuvius
was regarded as a spent volcano, the ground upon which
the temple stood was several feet above water. But
after the eruption of Vesuvius in 79 B.C. the temple was
sinking. Subsequently, Vesuvius became dormant, and
the foundations of the temple began rising. Again
Vesuvius became active and has remained so ever
since. During this time the temple has been subsiding
again, so far as we know its history.

137. This person may reasonably be supposed to have
committed the theft, for he can give no satisfactory
account of himself on the night of the alleged offence ;
moreover, he is a person of bad character, and being
poor is liable to a temptation to steal.

138. Don't you think the possession of gold is good ?
Yes, said Ctesippus, and the more the better, and to
have money everywhere and always is a good. Cer-
tainly, a great good, he said. And you admit that gold
is a good ? I have admitted that, he replied. And
ought not a man have gold everywhere and always, and
as much as possible in himself, and may not he be
deemed the happiest of men who has three talents of
gold in his stomach, and a talent in his head, and a
stater of gold in his eye. — Plato's Dialogues.

139. It has been found that linnets when shut up and
educated with singing larks— the skylark, woodlark, or
titlark— will adhere entirely to the songs of these larks
instead of the natural song of the linnets. We may in-
fer, therefore, that birds learn to sing by imitation, and

248 LOGIC AND ARGUMENT

that their songs are no more innate than language is in
man.

140. The policy of protection was immediately fol-
lowed by a great increase in prosperity and wealth of
the country, and hence we may infer that the result was
due to its connection with the enactment of the protec-
tive law. In reply, however, we are told that before the
passage of the law the loss by fire in Chicago in one year
was $200,000,000, but was only $3,000,000 for the year
after its passage, so great was the effect of this act.

141. A man that hath no virtue in himself envieth
virtue in others ; for men's minds will either feed upon
their own good or upon others' evil, and who wanteth the
one will prey upon the other.

142. Five years ago a first-class pair of nickel-plated
steel skates, with the necessary clamps to fasten them to
the boot or shoe, cost $15. To day, precisely the same
article, and with an equal finish and completeness, can
be obtained for $4. Three years ago a second grade
of nickel-plated steel skates cost $4. The same article
can be produced to-day for $1.50. The decline of
seventy per cent, in five years, and of sixty per cent, in
three years shows just how protection cheapens prices.

143. "'By open discrimination, or by secret rates,
drawbacks, and rebates, a few railway managers may
subject to their will every business in which transporta-
tion is a large element of cost, as absolutely as any ori-
ental despot ever controlled the property of his subjects.
No civilized community has ever known any body of
rulers with such power to distribute at pleasure, among
its mercantile classes, prosperity or adversity, wealth
or ruin. That this is no abstract or remote danger to
society is plain to any man who will look at the condi-
tion of trade and of mercantile morals in the United
States to-day.' How vivid ! But how absurd ! how un-
true ! Our commercial morals are equal to the highest
in the world."

QUESTIONS AND EXAMPLES 249

144. We observe very frequently that very poor hand-
writing characterizes the manuscripts of able men, while
the best handwriting is as frequent with those who do
little mental work when compared with those whose pen-
manship is poor. We may infer, therefore, that poor
penmanship is caused by the influence of severe mental
occupation.

145. Since there is no harm or evil to the elements
themselves in their continual changes into one another,
a man should have no'apprehension about the dissolution
of all elements. For it is according to nature, and
nothing is evil that is according to nature.— Marcus
Aurelius.

146. " Mr. Gladstone, however, commits himself to
the principle that ' all protection is bad.' If this has
been his belief ever since he became an advocate of free
trade, his conscience must have received many and
severe wounds, as session after session, while Chancellor
of the Exchequer, he carried through Parliament a
bounty — may I not say a direct protection ?— of ^180,000
to a line of steamers running between England and the
United States — a protection that began six years before
free trade was proclaimed, and was continued nearly
twenty years after."

UC SOUTHERN

A'- '•••null HI in 1 1|
000 085 248

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