JOHN A. OESTERLE, Ph.D.
College of St. Thomas, St. Paul, Minnesota

LOGIC--------------^he Art of Defining

and Reasoning

PRENTICE-HALL, INC.

NEW YORK

1952

Mt. Angel Abbey Library

BOO?

Copyright, 1952, by PRENTICE-HALL, INC., 70 Fifth Avenue, New
York. All rights reserved. No part of this book may be reproduced,
by mimeograph or any other means, without permission in writing
from the publishers. Printed in the United States of America.

L. C. Cat, Card No.: 52-11408

PREFACE

rT'lhe aim of this book is to present the basic doctrine of logic
for an introductory course. The book is based upon the
Organon of Aristotle, in which the fundamental doctrine of logic is
given in its proper order. The text also relies upon the great com­
mentators on Aristotle, especially St. Thomas Aquinas and St. Albert
the Great. Dependence upon these authors is evident throughout the
book. Contemporary authors on logic have been consulted as well.
So far as possible, the doctrine of logic is presented in ordinary
language, with many examples. Some of the technical terminology
of logic has been sanctioned so completely by time and use that it has
become a necessary part of the vocabulary of a logic text. In other
respects, points are presented more flexibly and informally. In
general, only essential matter is included in the text in order to
concentrate on points that should be covered in any introductory
course in logic. The workbook form has been adopted to insure at
least a minimum amount of exercise work in developing the art of
logical thinking.
The division of logic according to the three acts of the intellect is
based upon the Commentary of St. Thomas Aquinas on Aristotle’s
Posterior Analytics, Lesson I. Part One of the book is almost ex­
clusively material logic. Definition is the most important topic in
this first act of the intellect, for it manifests the simple object most
perfectly. The predicables and the categories are treated, which,
though somewhat difficult for an introductory course, are indispensable
for understanding definition properly.
Part Two, the logic of the act of composition or division, is primarily
formal logic. In general, the order of Aristotle’s On Interpretation
is followed. It is here that the consideration of the complex object
begins. An emphasis has been placed on supposition as a property
of the parts of a proposition, since the notion of supposition is fre­
quently neglected, or is erroneously considered in the logic of the first
act of the intellect. Modal propositions are mentioned briefly, but
opposition of modal propositions is omitted because of its difficulty
for an elementary course.

VI

PREFACE

Part Three, the logic of the third act of the intellect, concerns the
act of reasoning, by which we proceed discursively from one thing to
another so as to arrive fully at a knowledge of the complex object.
This part of logic, even in an introductory textbook, should be
treated from the standpoint of both formal and material logic.
Consequently, after the usual presentation of the syllogism and
induction on the part of form, there is a summary of argumentation on
the part of matter. In this way, it is possible to indicate, at least,
the nature of demonstrative reasoning, dialectical reasoning, rhetorical
and poetic argumentation. The final chapter, on sophistical reason­
ing, treats defective reasoning on the part of matter. All of these
topics can be developed more fully, if time permits, by reference to the
appropriate places in the Organon of Aristotle.
There is no reference throughout this text to what is called “sym­
bolic” logic. This absence of reference does not imply that symbolic
logic is not important or should be ignored; the contrary is rather
the case. However, in approaching logic, it is important, first, to have
a sound understanding of logic itself, apart from any mathematical
approach to logic, which is a distinct and posterior consideration.
Furthermore, symbolic logic cannot perform the role that traditional
logic, the logic basic to the human mind, fulfills. Symbolic logic
is the appropriate instrument for the experimental method of science,
in so far as experimental science is mathematical. Traditional logic,
logic in the unqualified sense, is the method of philosophy and of
knowledge generally. It is important, therefore, in an introductory
course in logic, to begin with the fundamental notions and correct
order of logic itself.
Two brief excerpts have been added in the Appendix. The first
is from Lesson I of the Commentary of St. Thomas Aquinas on
Aristotle’s Posterior Analytics. This excerpt gives the order and parts
of logic in a comprehensive glance. The second is Chapter One of
Aristotle’s On Interpretation, with the first three lessons of the Com­
mentary of St. Thomas. This excerpt contains some important
doctrine on notions introductory to the second act of the intellect.
It can also be used as a model for the reading, outlining, and analyzing
of an important text. In going through this Commentary, one can
learn how to read an important text both critically and in an orderly
manner.
I am greatly indebted to my colleagues in the Department of
Philosophy at the College of St. Thomas for assistance and encourage­
ment in preparing this book. They have tried out portions of the text
in mimeograph form in class and have helped me to make necessary
alterations and corrections. I am also indebted to my wife, who

PREFACE

VÜ

translated the portion from Aristotle’s On Interpretation as well as
the St. Thomas Commentary, and who assisted me in the editing of
the manuscript.
J. A. O.

TABLE OF CONTENTS

Preface

V

xiii

Introduction

PART ONE:
THE FIRST ACT OF THE INTELLECT

1. Words, Concepts, andSigns

3

2. The Predicables

11

3. Distinctions Preliminary tothe Categories

17

4. The Categories

23

5. Division

33

6. Definition

41

ix

X

TABLE OF CONTENTS

PART TWO:
THE SECOND ACT OF THE INTELLECT

7. Truth and Falsity

51

8. The Proposition

55

9. Divisions of the Proposition

63

10. Supposition

71

11. Opposition of Propositions

79

12. Obversion of Propositions

89

13. Conversion of Propositions

95

14. The Compound Proposition

105

PART THREE:
THE THIRD ACT OF THE INTELLECT

15. Argumentation

113

16. The Syllogism

117

17. Principles and Rules of the Syllogism

125

18. Reduction of Syllogisms to the FirstFigure

145

19. The Abbreviated Syllogism

153

xi

table of contents

20. The Compound Syllogism

161

21. Induction

169

22. Argumentation Materially Considered

175

23. Sophistical Reasoning

191

APPENDIX

Commentary of St. Thomas Aquinas, Lesson I, on Aristotle’s
Posterior Analytics.
Excerpt from Aristotle’s On Interpretation, Chapter One,
with Commentary of St. Thomas Aquinas, Lessons I, II,
and III.

Introduction

MEANING AND DIVISION OF LOGIC

HAT is logic and why should we study logic? We might
begin our answer to this question by observing that every­
one naturally desires to know. This self-evident statement simply
means that a human being is so constituted that he cannot help wanting
to know. A human being is a knowing being.
But what kind of knowing? We know in various ways. For ex­
ample, I know that a dinner is cooking by smelling it. I know that a
man is in a chair by looking at him. I know what New York looks
like by remembering my visit there a year ago. In a more complex
way than in any of the preceding examples, I know that sooner or later
I shall die; even more, I know that every man dies and why every man
must die.
What kind of knowing do we mean, then, when we say that everyone
naturally desires to know? In the sense that every human being is
so constituted that he cannot help wanting to know, every kind of
knowing is included. But if we take the statement to mean the kind of
knowing with which a human being is distinctively concerned, then the
statement applies properly to the last kind of knowing. The last kind
of knowing is reasoned knowing.
What do we mean by reasoned knowing? It is that kind of knowing
by which we find out why this or that is so. Thus, if someone asks me
why every man must die—why every man is mortal—I have to give
him some reason for accepting the statement as true. In brief, I have
to prove it. This kind of knowing is distinctively human knowing,
for we do not go about proving to horses or cows or even apes that they,
too, must die, although it is just as true that they die as it is that human
beings die.
All human beings, then, in varying degrees, want to know why things
are so. An evident sign of this is that even as children we frequently
ask for the why of things. We are insatiably curious. This universal
xiii

W

xiv

INTRODUCTION

wonder of human beings is never entirely smothered, although we often
disregard its promptings. As the ancient Greeks declared, wonder is
the starting point of knowledge. Wonder is the starting point in the
sense that we wonder what can be the explanation or cause of the things
that we are continually observing. It is only when we do know the
cause of a thing that our wonder ceases about that thing, for only by
knowing the cause is our wonder fully satisfied.
Now logic is nothing else than the art that guides us in coming to
know something previously unknown to us. Logic, then, is an instru­
ment for helping us to find out why things are as they are. An axe is
an instrument for cutting down a tree. A sharp axe is an efficient in­
strument for cutting down a tree. The power of thinking is an
instrument for knowing the why and wherefore of things, but thinking
sharpened by skill in logic is an efficient instrument for scientific know­
ing. We thus have at least a preliminary answer to what logic is and
why we should study it. If every human being wants to know, in
some degree, and if logic is an indispensable means of obtaining
knowledge more easily, more surely, and more efficiently, then the
study of logic is of use to every human being.
Let us now investigate in greater detail what logic is about and how
we reason in a logical way. Suppose that you were walking down
a street on a wintry day after a heavy snowfall. The sun is out
and shining brightly. You notice the shining of the sun in particular
because your eyes are bothered by the reflection of the sun on the snow.
The thought might occur to you how much the snow reflects the light
of the sun. This thought, in turn, might call your attention to the
whiteness of the snow. You would recognize at once that the whiteness
of the snow was the reason for the bright reflection of the snow in your
eyes.
In this very ordinary example, you have informally gone through a
reasoning process. You started with the statement Snow reflects light.
You proceeded almost immediately to give the reason why snow reflects (
light, namely, Snow is white. The first statement follows from the
second statement, and the two statements can be put down in the
following order:
Snow is white.
Therefore, snow reflects light.

The word “therefore” indicates that the second statement follows as a
conclusion from the first. Now if you analyze these two statements, you
will notice that there is a third statement implicity contained in
them, a statement containing the words “white” and “light.” This

XV

INTRODUCTION

third statement would read: White reflects light. You would then
have three statements, appearing in the following order:
White reflects light.
Snow is white.
Therefore, snow reflects light.

This full argument is called a syllogism. It is a movement of our
power of reasoning that grasps the truth of a conclusion by seeing the
truth and connection of the two propositions leading to the conclusion.
Logic guides us in knowing how to construct an argument like this, a
kind of knowing, as we shall see, that is demonstrative knowledge.
But to know what a syllogism is, and how to construct a syllogism,
we have to know the parts of a syllogism, just as we have to know the
different parts of a house in order to build a house.
The most immediate parts of a syllogism are the propositions of
which it is composed. Logic will help us understand what propositions
are, and what their relation is to each other, so that from them we
can make good arguments, or syllogisms, and thus demonstrate what
we know.
There are, however, other parts of a syllogism besides propositions.
Words, which signify concepts, also make up a syllogism; for instance,
“snow,” “light,” and “white” were parts of the syllogism given above.
Words, in fact, are parts of propositions as well as parts of syllogisms.
The words “snow” and “white” are parts of the proposition Snow is
white. “Snow” and “white” are also parts of the syllogism given
above, but they are parts of a syllogism differently from the way in
which they are parts of a proposition, as we shall see later.
The syllogism given above was chosen deliberately to bring out the
need of knowing the parts of a proposition before knowing the whole
proposition; it also brings out the need of knowing the parts of a
syllogism before knowing the whole syllogism. Clearly we have to
know what various words mean before we put them into propositions,
and we have to know whether propositions are true before we can con­
struct a sound argument out of them. Thus, in the given syllogism,
we have to know what “snow” means and what “white” means—we
have to be able to define the words—before we can determine whether
the proposition is true or not. And then, before we can give a full
syllogism, we must further know the structure of a proposition, and how
to determine when a proposition is true. Finally, in giving the full
syllogism, we have to know how to relate propositions to each other and
infer a conclusion from them.
We can now see the extent of an elementary course in logic. There

xvi

INTRODUCTION

are three main topics to be considered: (1) definition, (2) proposition,
and (3) syllogism. Each of these belongs to a different act of the human
intellect.
Definition is known by the act of simple apprehension. The act of
simple apprehension is the way in which we grasp a simple object,
such as man or dog or horse. This is the first act of the human intellect,
and we express these simple notions by definitions. We must know
such simple objects first before we can combine simple objects into the
complex structure of a proposition. In short, we must know the defini­
tions of dog and animal before we can combine them into the propo­
sition Every dog is an animal.
The proposition (also called an enunciation) is known by the in­
tellectual act of composition and division of terms, in which truth or
falsity appears. If we combine or compose two terms, as in Every
dog is an animal, we have an affirmative proposition. If we divide
or deny two terms of each other, as in No horses are dogs, we have a
negative proposition.
The syllogism is known by the act of reasoning, in which we proceed
from one thing to another. More specifically, by knowing two propo­
sitions as true and as related in a certain way to each other, we reason
to a third proposition concluding from them. Thus, by knowing Every
mammal is an animal and Every cow is a mammal, we arrive at the
reasoned knowledge Every cow is an animal.
Let us recall here that we originally spoke of logic as the art that
guides us in coming to know the unknown. There are, actually, only
two kinds of unknown objects: a simple object, such as man, and a
complex object, such as artistic man. Let us relate these two kinds
of unknown objects to the three acts of the intellect listed above.
As we have seen, a simple object is made known by the first act of
the intellect, which we called simple apprehension. The principal
means of knowing a simple object is by defining it. A sign that we
know the simple object man is the definition that we give of man.
Since the purpose of the first act of the intellect is to arrive at defi­
nitions, this act is guided by the part of logic that we call the art of
defining.
A complex object is made known by means of argumentation. But
argumentation requires two additional acts of the intellect: the act
of composition or division and the act of reasoning. Hence, the
second act of the intellect combines the simple objects that have been
made known by the first act of the intellect in definition. It combines
them by affirming one simple object of another; it divides them by
denying one of the other. If such a combination or division is not
self-evident, then it must be manifested by argumentation, and because

xvii

INTRODUCTION

of this, a third act of the intellect is necessary. The third act is the
reasoning process by which we proceed from propositions made known
by the second act of the intellect to a conclusion following from these
propositions.
From this discussion we can now give a definition of logic and the
principal divisions of logic. Logic is the art that directs the three acts
of the intellect. The division of logic can be outlined as follows:
Object
Simple

Made Known By
Definition

Complex

Argumentation

Acts of the Intellect
Simple Apprehension
[Composition or Division
[Reasoning

Logic
(Part One)
(Part Two)
(Part Three)

FORMAL AND MATERIAL LOGIC

The division of logic into formal and material logic need not be con­
sidered to any great extent in a beginning course. The division is
constantly presupposed in such a course, however, and we shall there­
fore examine it briefly.
In the broad meaning of the word, the form of logic is concerned
with the order that reason puts into its acts of knowing. The acts of
knowing (which we have listed above as simple apprehension, composi­
tion or division, and reasoning) constitute the matter of logic.
But when we talk about formal logic and material logic, we are
using a narrower meaning of the words form and matter. In this
narrower meaning, both formal and material logic refer to the order
that reason puts into its acts of knowing. In so far as this order in
the acts of knowing refers to the manner of signifying, we have formal
logic. In so far as this order in the acts of knowing refers to the
things signified, we have material logic.
Let us employ an example to bring out more concretely the tra­
ditional division of formal and material logic. We shall use the
syllogism, in which the distinction is revealed most fully and clearly.
Formal logic deals with the manner of ordering terms and propo­
sitions in a syllogism. We can signify this in the following way:
Every B is C.
Every A is B.
Therefore, every A is C.

As we shall see later, this is a formally correct syllogism.
Now let us consider the syllogism in the following way:
Every animal is a living being.
Every cow is an animal.
Therefore, every cow is a living being.

xviii

INTRODUCTION

This is also a formally correct syllogism. The use of words, however,
brings out the matter of the syllogism, matter in the sense of the things
signified, which material logic considers. But material logic does not
consist in merely applying the form of logic; it considers certain de­
terminations on the part of the things signified. Thus, sometimes the
things signified—the logical matter—will give a necessary conclusion,
as in the syllogism given on page xvii. At other times, however, the
things signified will give only a probable conclusion, as in the follow­
ing example:
Every mother loves her child.
Susan is a mother.
Therefore, Susan loves her child.

The determination of a syllogism as necessary, or the determination
of a syllogism as probable, is made on the part of material logic, even
though the syllogism remains the same formally.
From all this it follows that formal and material logic, as we now
understand this division, are not to be regarded as two aspects of
logic that can be totally isolated from each other. We cannot, for
example, suppose that an introductory course in logic is only formal
logic. Any course in logic must include both formal and material
logic, although one aspect may be emphasized more than the other.
A purely formal logic, then, is not possible.
Thus, in the syllogism that we have expressed formally above, the
symbols, A, B, and C still imply matter, or things signified, to the
extent that the symbol A has to be some object that can stand as the sub­
ject of the conclusion of the syllogism, the symbol B has to signify
some object that can stand as the middle term of the syllogism, and
the symbol C has to signify some object that can stand as the predicate
of the conclusion. Furthermore, as we shall see later, the symbol C
has to signify an object more universal than B, and B an object more
universal than A.
Introductory logic, consequently, is not purely formal logic. It is
both formal and material logic, since we cannot ignore either part al­
together. We do, however, in some places emphasize formal logic and
in other places material logic. Part One of the text is almost ex­
clusively material logic, for in the first act of the intellect there is little
order or arrangement in manner of signifying that we can introduce
into a treatment of the simple object. Part Two, concerning the act
of composition or division, and Part Three, concerning the act of
reasoning, emphasize the formal part of logic in an introductory course.

Part One
THE FIRST ACT OF THE INTELLECT

Chapter One

WORDS, CONCEPTS, AND SIGNS

X A /E shall begin with some general observations, drawn from
* ’ psychology, on the way in which human beings know
things. We shall summarize only the few points on human knowing
necessary for logic.
Experience teaches us that we know in two distinct ways. As we
mentioned in the Introduction, we know things through our senses,
internal and external. We also know things through our intellect,
and experience teaches us that our intellect attains something that our
senses do not attain. By our senses we know the colors and sounds and
the sizes and shapes of things; from our sense knowledge of things our
intellect arrives at a knowledge of what those things are—the natures of
the things. We do not sense the natures of things; we sense only
material, singular characteristics of things. For example, we know
by our senses the appearance of a person, his color, his size and his
shape. We know intellectually the kind of person he is—that he is of
honest character or that he is a prudent man.
We recognize also from experience that our intellectual knowledge is
abstractive. We abstract when we make a separation. Intellectual
abstraction, or separation, consists in leaving aside whatever is material
and singular, retaining only the nature of the thing, as we abstract man
from James. Whereas our sense knowing directs us to material,
singular things (for example, the color of this man), our intellect di­
rects us to the natures of these things, which, by abstraction, are
known as universals (for example, the nature of man).
In sense knowing we have images; in intellectual knowing we
have concepts. Through images we know material, singular things.
Through concepts we know directly the universal nature of material,
singular things. Indirectly, we can refer our concept to the singular
thing known by the senses.
With these preliminary points about human knowing summarized
3

4

WORDS, CONCEPTS, AND SIGNS

from psychology, we can now consider the role of words and concepts
in logic.
NECESSITY OF CONSIDERING WORDS IN LOGIC

A word is an articulate sound that signifies a concept. As a physical
object, a word is a material thing, which can be sensed, but its mean­
ing, that is, what the word signifies, is intellectual. Words thus stand
for things or objects as they are conceived by the intellect. Conse­
quently, a word such as “man” stands for the concept that I have of a
human being. We speak words or write words to express the concepts
that we have of various things.
It is necessary, therefore, that logic consider words, since without
words we could not express the things we conceive. Logic, of course,
is primarily concerned with things as they are conceived by the intellect.
But since we express our concepts most perfectly by words, logic must
also make use of words as instruments for expressing and communicat­
ing concepts.
THE RELATION BETWEEN WORDS AND CONCEPTS

Since words and concepts are sometimes confused, the following relation
of words and concepts will help to keep them distinct:
One word can mean, or signify, one concept. “Man” signifies the
concept of a human being.
One word, by equivocation, can signify two diverse concepts. The
word “bark” can signify the concept of the sound that dogs make
through their mouths. “Bark” can also signify the outer covering of a
tree.
Two words can signify one and the same concept. The word “God”
in English signifies the concept of a supreme being. The word “Dieu”
in French signifies the same concept of a supreme being.
Let us notice, then, the precise importance of words, without either
exaggerating or diminishing their role in human knowledge and com­
munication. Their importance is found primarily in the function they
have of expressing and communicating our concepts. We should not
exaggerate their importance by equating, and even identifying, them
with concepts, thereby forgetting that their purpose is to express our
conceptions. We should not diminish their importance by supposing
that we can somehow get along without them.
It is true that words cannot achieve the perfection in signifying that
our concepts have. We frequently experience this situation when we
say that we are at a loss for words to express what we mean. Words
have a necessary limitation in their signification because they are

WORDS, CONCEPTS, AND SIGNS

5

sensible, physical things restricted in the manner in which they signify.
Concepts are not restricted in this way because of their immaterial
mode of existence in our minds.
There is, therefore, necessarily some gap between a material means
of signifying, as with words, and an immaterial means of signify­
ing, as with concepts. Because of this incommensurability between
words and concepts, words cannot adequately or perfectly signify
concepts. Words, in fact, arbitrarily signify concepts. The word
“man,” for example, has no necessary connection with the concept we
have of a human being. The word “anthropos” could just as well
signify the concept as indeed it does in Greek.
SIGNS

We referred to signification when we distinguished between words and
concepts. Let us consider signification and signs more specifically,
so that we can understand better what kind of sign a word is and
what kind of sign a concept is. There is an additional reason for con­
sidering signs. A good deal of attention has been given in recent
years to the analysis of signs, usually referred to as semantics, the
study of signs. It would be a matter of ignorance, however, to sup­
pose that an analysis of signs is only a modern development. Treatises
on signification stretch back to St. Augustine, Aristotle, and Plato.
The importance of semantics is thus indicated by the attention
given it in both ancient and modern times. We shall, then, summarize
some of the main points on signification.
THE DEFINITION OF A SIGN

A sign is that which represents something other than itself to a know­
ing power.
This definition indicates that we explain signs in terms of knowing.
How we know, therefore, is more fundamental than how we use signs.
Any attempt, consequently, to establish a sound semantics without a
sound analyses of knowing is certain to be inadequate, if not false. We
cannot give an adequate account of signification without distinguish­
ing the two basic kinds of knowing in man, sense knowing and in­
tellectual knowing. We must keep the role that the image plays in
sense knowing distinct from the role that the concept plays in in­
tellectual knowing.
The definition also reveals the elements of signification: the sign
(that which represents), the thing signified (something other than itself),
and the knowing power. Any sign, then, has to depend both upon
the thing it signifies, that is, what it refers to, and upon the knowing

6

WORDS, CONCEPTS, AND SIGNS

power (sense and intellectual) that uses the sign. A road sign is an
obvious illustration of these elements. The sign itself is expressed in
words: thirty miles per hour. The thing signified is the speed limit.
The knowing power is both the sense power of vision, by which the
sign is seen, and the intellectual power of thinking, by which the
words of the sign are understood. All signification contains these
three distinct elements.
THE DIVISIONS OF A SIGN

From the discussion of the definition of a sign, we can now see that
a sign may be divided in two ways. On the one hand, a sign is re­
lated to the knowing power, and upon this basis we make one division.
On the other hand, a sign is related to the thing signified, and upon
this basis we make the other division.

1. As the sign is related to the knowing power

(a) Formal sign. The formal sign is a sign that functions as a means
of knowing. We therefore speak of a formal sign as an intentional
form, a form through which an object is represented to our knowing
power. Since we have two kinds of knowing powers, sense and intellec­
tual, there is a formal sign through which we know things by sense, the
image, and a formal sign through which we know things by the intellect,
the concept. There are, consequently, only two formal signs: the
image and the concept. They are the interior signs of knowing that
we have.
(&) Instrumental sign. The instrumental sign is an object first
known in itself, unlike the formal sign, which is a pure means of
knowing. The instrumental sign is a sign which must be known first
as an object before we can know that it represents something else.
For example, the red light of a traffic signal, an instrumental sign, must
be first seen and known as an object before we can know what it sig­
nifies, namely, to stop.
The distinction between formal and instrumental signs is a very
important one. Unfortunately, it is a distinction that is often ignored
or confused. The instrumental sign is usually recognized because it
is so obvious, but the formal sign, not being immediately apparent,
is frequently overlooked. The formal sign is interior to the knowing­
power, and for this reason is less familiar and less obvious than the
instrumental sign, which is exterior to the knowing power. The formal
sign might be compared to a pair of glasses through which we see, but of
which we are not usually aware, although we are seeing by means of

L

_I
—
1

S8
i

Í5
1

? Í5 1

*

•

-~— *
-« — —
>
t

WORDS, CONCEPTS, AND SIGNS

7

them. The instrumental sign, for example, an arrow, must be known
first as an object before it functions as a sign.
This distinction between the formal and the instrumental sign helps
us to see the distinction between concepts and words. All words are
instrumental signs, for we must first know the word before we know
the meaning of the word. All concepts are formal signs, leading us
directly to the knowledge of things themselves. By understanding
concepts as formal signs, we see that concepts are never the objects of
our intellectual knowing, except indirectly, but only the means by which
we know things. Now, just as all instrumental signs presuppose formal
signs (for we cannot know any instrumental sign, such as an arrow,
except through an image, which is a formal sign), so all words, as in­
strumental signs, depend upon concepts, as formal signs, for their mean­
ing or significance.
An important consequence follows from this. We have just seen
that words must depend upon concepts for their meaning; words there­
fore cannot immediately and directly signify things. The word “dog”
does not directly signify a real animal; it signifies directly both the
image and concept we have of a real animal.
This first division of the sign gives us only two kinds of sign, for­
mal and instrumental. All signs, however, can be classified within
this division. We shall now go on to the second division of the
sign, under which all signs can be classified again, but in a different
way.

lí — j

—j

2. As the sign is related to the thing signified
(«) Natural sign. A sign is called “natural” because there is a
natural relation between the sign and the thing it signifies. A natural
sign is causally related to the thing it signifies. Hence a natural sign
has the same signification for all men. For example, smoke is a
natural sign of fire.
(&) Conventional sign. A sign is called “conventional” when the re­
lation between the sign and the thing signified is made deliberately
and arbitrarily by the human will. The conventional sign, because it
signifies arbitrarily, requires agreement as to what it is to represent,
this agreement usually being sanctioned by legal or social authority.
The traffic light is an example of a conventional sign.
A word is a conventional sign, with the dictionary as the authority
for the imposition of a given meaning. As we have seen, a word
arbitrarily (that is, conventionally) signifies a concept; a concept, how­
ever, naturally signifies a thing. We thus have another way of
distinguishing words from concepts: words are conventional signs and

8

WORDS, CONCEPTS, AND SIGNS

concepts are natural signs. Thus, the word “tree” conventionally
signifies the concept that is a natural sign o£ a certain kind of plant.
We can illustrate this by the following diagram:
signifies by
signifies
convention
naturally
Word ------------- > Concept ---------- > Thing

(c) Customary sign. A sign is called “customary” when the relation
between the sign and the thing known is made by association through
tradition or custom. The customary sign is a kind of mean between
the natural sign and the conventional sign, and for this reason it is
sometimes difficult to distinguish the customary sign from the other
two kinds. Like a natural sign, a customary sign may have some
natural basis for the signification. But the basis for the signification
will not be purely natural, and hence, like the conventional sign, the
customary sign has also a voluntary basis for the signification. As the
word “customary” suggests, the distinctive characteristic of the custom­
ary sign is the custom or tradition underlying the signification, as, for
example, in religious signs and symbols. The tipping of a hat is a
customary sign of courtesy shown to people.
QUESTIONS —CHAPTER ONE

1. What are the two distinct kinds of human knowing? Illustrate with ex­
amples drawn from experience.
2. What is the meaning of the statement that our intellectual knowledge is
abstractive?
3. Why does logic consider words? Are words the primary concern of logic?
4. Specify the different ways in which words and concepts are related. Use
original examples.
5. In what does the importance of words consist?
6. Why is there an incommensurability between words, or any written and
spoken symbols, and concepts?
7. What does “semantics” mean?
8. Give the definition of a sign.
9. What are the elements of signification?
10. Upon what basis is the first division of a sign made? Upon what basis is
the second division made?
11. Distinguish between a formal sign and an instrumental sign.
12. Explain the distinction between words and concepts in terms of formal
and instrumental signs.
13. Must a word always directly signify a concept? Explain.
14. What is a natural sign? Give five examples.
15. What is a conventional sign? Give five examples.
16. What is a customary sign? Give five examples.

EXERCISE—CHAPTER ONE
Classify the following signs as natural, conventional, or customary:

1- Thunder as a sign of a storm.
2. A cross as a sign of Christianity.

3. The word “horse” as a sign of the concept of
a certain animal.
4. A ruler as a sign of a measure of length.
5. The concept of flower as a sign of a certain
kind of plant.

6. A ring as a sign of marriage.

7. Bowing as a sign of respect.
8. Footprints as a sign of a living being.

9. A clock as a sign of time.
10. A number as a sign of quantity.

11. Flowers as a sign of love.
12. A frown as a sign of irritation.

13. The blowing of a whistle as a sign of a foul
in a game.
14. Complexion as a sign of health.

15. A copyright as a sign of ownership.

16. Shaking hands as a sign of friendship.
17. Fever as a sign of illness.
18. A question mark as a sign of a question.
19. Frost as a sign of cold weather.
20. 32° Fahrenheit as a sign of freezing.
logic: the art of defining and reasoning,

9

copyright,

1952,

by prentice-hall, inc.

Chapter Two
THE PREDICABLES

E have just finished considering words and concepts, their
place and role in logic, the distinction between them,
and their relation to each other. The treatment of words and con­
cepts is a natural beginning for the logic of the first act of the in­
tellect, since logic aims to order our concepts as they are expressed
by words. We have also considered signs, for the notion of significa­
tion helps to clarify the distinction between words and concepts.
Now the logic of the first act of the intellect is concerned with a
simple object, such as man or dog. This first part of logic is ordered
primarily to definition, since we know a simple object completely
when we can define it. To define an object, we must be able to say
something about that object. To say something about an object is to
predicate something of it. The predicables, then, are simply the dif­
ferent ways in which we can say something about an object. For
example, we can say “animal” of dog, and “brown” of dog.
We need to know what the predicables are so that we shall be able
to make good definitions. A predicable, however, is included under
the notion of the universal, and, therefore, to understand what a
predicable is, we shall consider the universal first.

W

THE UNIVERSAL

The general meaning of “universal” is something common to many
things. For example, we speak of universal suffrage, meaning the
participation of many in the right to vote. We speak of universal
military training. We speak of the generosity of Americans, in the
sense of a trait found universally in Americans. In this broad mean­
ing, universal is taken as opposed to the singular, which is restricted
to only one thing.
We use words both as universal and singular. The word “man,”
11

12

THE PREDICABLES

for example, signifies our concept of human nature as it is common
to all individual men. We get this universal notion of man by ab­
stracting it from the individual men in which it is found. The word
“Paul,” on the other hand, expresses something singular—the word
“Paul” is proper to an individual. (It does not matter that many
individuals might be named “Paul.” In each instance “Paul” ex­
presses something singular, and we add middle and last names to bring
out the individuality.) We express the equivalent of the distinction
between the universal and the singular in grammar by speaking of
common nouns and proper nouns.
Now when we speak of the predicables as universals we are using a
restricted meaning of the word “universal.” The “universal” we are
going to consider now is a nature as it can be found in many indi­
viduals. The mind sees that a nature can be found in many and the
mind then forms the relation of one nature to many individuals—the
relation of universality. This kind of universal is called the logical
universal. The logical universal, therefore, is a relation made by our
mind and added to the nature which we have abstracted from singulars.
Let us consider this matter again in the following way. As we have
seen, we abstract a nature from its singulars or inferiors. For ex­
ample, we abstract the nature of man from individual men. To this
nature as abstracted we can add explicitly the relation this nature has
to the inferiors under it. This relation of a nature to its inferiors
is a logical universal. The relation of the nature of man to the indi­
viduals included under it is the relation of species. Species is one of
the predicables, for in virtue of this relation of man to individual men
we can predicate man of individual men. All predicables follow
from the relation of a nature to its inferiors.
NOTION AND DIVISION OF PREDICABLE

We shall now consider the predicables directly and in detail. The
predicables are the ways in which a universal can be said of its in­
feriors, that is, the kinds of connection there can be between a uni­
versal and the inferiors or subjects in which it is found.
There are five predicables. We shall see that there are five by
considering the predicables according to the essential and accidental
connections that the logical universal has with its inferiors. An es­
sential connection occurs when the universal is intrinsic to the nature
of its inferiors. For example, the universal animal is of the very nature
of dog, and therefore intrinsic to dog. An accidental connection
occurs when a universal is extrinsic to the nature of its inferiors. For
example, color is something extrinsic to the nature of dog.

THE PREDICABLES

13

The kinds of essential connection
1. Genus. Genus is the universal that can be said of many that
differ specifically. It answers the question What is it? However, the
predicable genus answers this question incompletely, because the genus
expresses only part of the essence or nature. For example, “animal”
is a genus when said of man and dog. It expresses only part of the
essence of man or of dog.
2. Species. Species is the universal said of many that differ in num­
ber. It also answers the question What is it? But the predicable
species answers this question completely; that is to say, it expresses
the whole essence. For example, “man” is a species when said of Paul
or James or John.
3. Difference. Difference is the universal said of many that differ
even in species. It answers the question Of what quality is the essence?
The predicable difference distinguishes one species from another within
the same genus. Thus, if we ask of what quality man’s essence is, to
distinguish man from any other species in the genus of animal, we
answer “rational,” and by this we designate the specific difference.
The kinds of accidental connection

1. Property. Property is the universal said of a species as that which
belongs only, necessarily, and always to that species and to every in­
dividual of that species. A property is convertible or interchangeable
with the species of which it is a property. For example, “grammatical”
is said of man as a property. We can convert the property with the
species by saying that wherever there is a man there is the property of
being grammatical, and wherever there is a grammatical being there
is a man.
Property is sometimes understood in a looser sense when it is used
to designate merely that which belongs to a species always, but does
not belong only to it. In logic we use property in the strict sense,
as we havez defined it above.
2. Accident. Accident is the universal said of a species as that which
belongs contingently to that species and to the individuals of that
species. An accident is a characteristic that can come to be or dis­
appear without destruction of the species in which it is found. For
example, “white” is said of man as an accident. The color white does
not necessarily characterize man, nor is it found always in man, nor
does it belong only to man.
As we shall see later, definitions are stated in terms of these
predicables.

14

THE PREDICABLES

QUESTIONS---- CHAPTER TWO

1. What is the general meaning of “universal”? Give an original example
of something universal in this sense.
2. What is a logical universal?
3. What is the common notion of the predicables? 4. What predicables have an essential connection? Define each of them and
give an original example of each.
5. What predicables have an accidental connection? Define each of them
and give an original example of each. .
6. Why are the predicables studied in logic?

EXERCISE-CHAPTER TWO

State which predicable the second word expresses in relation to the first.
------------------------------------- 1. Robin—bird
------------------------------------- 2. Man—artistic
------------------------------------- 3. Paul—man
----------------------------------

4. James—white

------------------------------------- 5. Snow—white
----------------------------------

6. Logic—art

---------------------------------- - 7. Man—rational
------------------

8. Horse—brown

----------- —--------------------9. Justice—virtue
---------------------------------- 10. Man—biped
---------------------------------- . 11. Fido—dog

-— ------------------------------12. Flower—red
-------------------------------- _ 13. Lily—flower
---------------------------------- 14. Blue—color
------------------------------------ 15. Brute—irrational

— ---------- — --------------- 16. Man—tool-making
--------------- ——.----------- 17. Cow—animal
---------------------------------- 18. Swan—white

— -------------------------------- 19. Elephant—heavy
----------------------------------- 20. Tree—plant

logic: the art of defining and reasoning,

15

copyright,

1952,

by prentice-hall, inc.

Chapter ‘Three
DISTINCTIONS PRELIMINARY TO
)

I
1

THE CATEGORIES

'T'HE categories, which we shall consider in the next chapter,
are the most universal genera under which all things can be
ordered. However, before we can treat the categories we must con­
sider certain distinctions which we need in order to understand the
categories. These preliminary distinctions are traditionally called the
“antepredicaments.” “Predicaments” is another name for the cate­
gories. The antepredicaments therefore designate certain distinctions
and considerations which have to be taken up in advance of the pre­
dicaments, or categories.
We shall consider three distinctions which serve as conditions
needed for determining the categories.
I. UNIVOCAL, EQUIVOCAL, AND ANALOGOUS NAMES

A univocal name or word is one that is imposed on many things and
signifies the same nature in each. For example, the name “man”
signifies all individual men in so far as each one has the same human
nature, and hence all agree in the same meaning of man. Thus, “man”
is said univocally of Paul, James, John, and so forth. Likewise, the
name “animal” is said univocally of horses, dogs, lions, and so forth,
each of which has the same nature, signified by the word “animal.”
An equivocal name is one that signifies different natures. The name
is common but the natures which it signifies are totally distinct. Thus,
the word “bow” is common to and is said of a weapon and a knot, but
a weapon and a knot are totally distinct things.
An analogous name is one that signifies different natures but is im­
posed primarily on one nature and secondarily on others with reference
to the first. An analogous name is proportionately one, because, al17

18

DISTINCTIONS PRELIMINARY TO THE CATEGORIES

though it is said of distinct natures, it is said with reference to the
nature it primarily signifies. For example, “healthy” is said primarily
of a man or an animal who is healthy, and secondarily of food, which
preserves health, of medicine, which causes health, and of blood, which
is a sign of health.
Sometimes there is difficulty in distinguishing between equivocal
and analogous names. It may be of help to note that when a name is
equivocal, there is only an accidental and arbitrary connection between
the two natures which are signified. But when it is analogous, the
name has been imposed deliberately upon the distinct things to show
some relation or likeness among them, in such a way that the name
refers primarily to one and secondarily to the others. The secondary
meanings exist only because of the primary meaning, just as food
cannot be understood to be healthy except in relation to a man or an
animal, where health is found primarily. Hence the things signified
secondarily are defined in relation to the thing signified primarily.
In relation to the categories, the distinction of univocal, equivocal,
and analogous names is important because only names signifying
univocally are used in the categories.
II. COMPLEX AND INCOMPLEX EXPRESSIONS

A complex expression, which signifies a complex thing, is that which
has two or more natures present at once. “Brown animal” is a complex
expression since it signifies both the essence of brown and the essence
of animal.
An incomplex or simple expression, which signifies a simple thing,
is that which has only one nature, as in “dog,” “color,” “quantity,”
and “science.”
In relation to the categories, this distinction is important because
only incomplex expressions, signifying simple things, can be placed
in the categories. Complex things belong in more than one category,
III. EXISTENCE IN A SUBJECT AND PREDICABLE
OF A SUBJECT

The words “existence in a subject” signify inherence in a subject.
This is the kind of existence an accident has. An accident is that
which exists in a subject, that is, in a substance. A substance is that
which exists in itself. Thus, color is an accident because it exists in
a subject or substance.
The words “predicable of a subject” signify something that can be
said or predicated of a subject. Thus, “animal” is predicable of “dog.”

DISTINCTIONS PRELIMINARY TO THE CATEGORIES

19

As we have seen in the preceding chapter, only something universal
is predicable of a subject.
Now, we can relate “existence in a subject’’ and “predicable of a sub­
ject” to each other in various ways. For example, what is it that both
exists in a subject and is predicable of a subject? It is a universal ac­
cident, for to exist in a subject is to be an accident, and to be predicable
of a subject is to be universal. Whiteness is an example of a uni­
versal accident, for it exists in a subject (in a substance, such as man)
and is also predicable of that subject.
On the other hand, what is it that does not exist in a subject and
is not predicable of a subject? It is a singular substance, for that which
does not exist in a subject is a substance, and that which is not
predicable of a subject is singular. Paul is an example of a singular
substance, for he exists in himself and not in some other subject, and
“Paul” cannot be predicated of something else.
There are still two other relations we can make. What is it that
does exist in a subject but is not predicable of a subject? It is a
singular accident, for that which does exist in a subject is an accident,
and that which is not predicable of a subject is singular. The indi­
vidual height of Paul is a singular accident. On the other hand, what
is it that does not exist in a subject but is predicable of a subject? It
is a universal substance, for that which does not exist in a subject is a
substance, and that which is predicable of a subject is universal. Man
is an example of a universal substance, for man does not exist in a
subject, but can be predicated of a subject—for example, of “Paul.”

Let us summarize these relations in the following order:

Singular substance: It does not exist in a subject and is not predicable
of a subject.
Universal substance: It does not exist in a subject and is predicable
of a subject.
Singular accident: It exists in a subject and is not predicable of a
subject.
Universal accident: It exists in a subject and is predicable of a
subject.

With respect to the categories, these four relations help us to see the
difference between substance and accident, for the categories are made
up of substance and accidents. Likewise, the distinction is drawn be­
tween singular substance and universal substance, also known as first
substance and second substance. Finally, the distinction is made be­
tween singular accident and universal accident.

20

DISTINCTIONS PRELIMINARY TO THE CATEGORIES

QUESTIONS---- CHAPTER THREE

1. Explain univocal, equivocal, and analogous names. Give original examples
of each.
2. What is the difference between an equivocal name and an analogous name?
3. What does “existence in a subject” mean?
4. What does “predicable of a subject” mean?
5. Distinguish between singular substance and universal substance.

EXERCISE—CHAPTER THREE

Classify the following words as univocal, equivocal, or analogous.
1. Student as signifying senior and freshman.
2. Father as signfying God and man.
3. Blue as signifying the color of sky and of
water.

4. Talking as signifying the vocal sounds of
man and parrot.

5. Body as signifying horse or cow.
6. Flower as signifying tulip and rose.
7. Key as signifying an instrument to open a lock
and tonality of scale.
8. Science as signifying ethics and politics.
9. Religious as signifying man and music.
10. Bat as signifying an animal and a club.
11. Plant as signifying a flower and a tree.
12. Color as signifying red and blue.

13. Sound as signifying a noise and a long
channel of water.
14. Sickly as signifying an ailing condition and a
kind of complexion.
15. Pen as signifying a writing instrument and a
small enclosure.
16. Animal as signifying a horse and a dog.

17. Race as signifying a contest and a certain kind
of people.

18. Violet as signifying a flower and a color.
19. Publication as signifying a book and a maga­
zine.
20. Poor as signifying lack of riches and bad
health.
logic: the art of defining and reasoning,

21

copyright,

1952,

by prentice-hall, inc.

Chapter Four

THE CATEGORIES

THE natures of all things can be ordered according to greater
or lesser universality. They can also be placed in genera
that have no genera above them. These ultimate genera are the cate­
gories.
Let us first distinguish between the predicables and the categories.
In the chapter on the predicables we treated the relationship of a
nature to its inferiors, which is the logical universal, and we divided
this logical universal into the five predicables. But the logical uni­
versal presupposes the nature as abstracted from individuals, and it is
this nature we treat when considering the categories. We are, then,
concerned with the real natures of individual things in the categories.
But in logic—as distinct from the treatment of the categories in
metaphysics-—we are concerned with real natures only in so far as
they are capable of orderly arrangement in the categories. The logical
consideration of the categories reduces to this: For any given nature
we ask what its supreme univocal predicate is, that is to say, what its
supreme genus is. For example, what is the supreme univocal predicate
of man? In what supreme genus is man? The supreme univocal
predicate of man is, as we shall see, substance. Man, therefore, is in
the category of substance. Color, however, has not the supreme
univocal predicate of substance, for we cannot say that color is a sub­
stance. It will, therefore, be in some other category.
Hence, in logic, we order all things under their supreme genera.
Within each supreme genus, we then order all things according to
greater or lesser universality. The categories, therefore, are simply
the ordering of all things as genera and species under supreme genera.
Why do we study the categories in logic? There are two prin­
cipal reasons. One reason is that the study of the categories gives us
an orderly grasp of all things. The other reason is that a knowledge
of the categories is useful for definition. Knowing the ultimate genus
23

24

THE CATEGORIES

to which a thing belongs is the first step in coming to know the
proximate genus, which, as we shall see, is necessary for the definition
of a thing.
Certain conditions have to be observed in determining the cate­
gories:
(1) Only real natures belong in the categories; artificial things are
excluded. Furthermore, the categories are not divisions or classi­
fications of words.
(2) Whatever is in a category must be a simple thing. It must be
something whose nature is one.
(3) Whatever is in a category must be signified by a univocal name.
(4) The physical or entitative parts of a thing belong in the cate­
gory in which the whole thing or nature belongs. For example, the
soul, as an entitative part of man, belongs reductively in the category
of substance since man belongs in the category of substance.
THE TEN CATEGORIES

With these preliminary considerations finished, we shall now list the
ten categories, the ten ultimate predicates that can be said of all things,
giving a brief explanation of each category, with examples.
1. Substance

The primary meaning of substance is that it neither exists in a sub­
ject nor is predicable of a subject. This meaning of substance, as we
have seen, applies to first substance. The category of substance, how­
ever, concerns second substance—universal substance—because the
categories are supreme universals or ultimate genera of all things.
Examples of substance, then, are: dog, man, tree.
2. Quantity
Quantity is an accident that makes a substance divisible into con­
stituent parts. Quantity exists in a substance in so far as a substance
is material. Quantity is either discrete, as in numbers: ten, twenty,
thirty (from which arises the science of arithmetic); or continuous,
as in line, surface, plane (from which arises the science of geometry).

3. Quality
Quality is an accident that gives a substance a certain attribute.
For example, whiteness is the quality in virtue of which a substance is
called white. There are four species of quality.

THE CATEGORIES

25

(«) Habit and disposition. A habit is a quality by which a sub­
stance is well or ill disposed. A habit is a firmly established quality,
for example, science or a moral virtue. A disposition is a quality
easily changed, as opinion.
(Z?) Potency or impotency. Potency is the quality that is a proximate
principle of operation. It disposes a substance for operation, as
healthiness, firmness. Impotency is a weak and imperfect form of
potency, as nearsightedness, feeblemindedness.
(c) Sense qualities. These are the qualities which affect the senses,
as sweetness, whiteness.
(d) Figure and form. Figure is the quality that terminates quan­
tity, as straightness, triangularity, curvedness. Form (shape) adds a
certain proportion and beauty to the termination of quantity, which
is manifested especially in artificial things, as in the form of a statue.

4. Relation
Relation is an accident existing in a subject resulting from its refer­
ence to something else, as superiority, smallness, maternity.

5. Action
Action is an accident resulting from the subject’s acting upon
something else, as throwing, striking, making.

6. Passion

Passion is an accident resulting from the subject’s being acted upon,
as being thrown, being struck, being made.
7. When

The “when” of a thing is an accident existing in a subject resulting
from the subject’s being measured by time, as yesterday, Monday, year.
8. Where
The “where” of a thing is an accident existing in a subject resulting
from the subject’s being in a certain place, as here, in the room, in
Europe.

9. Position
Position or posture is an accident existing in a subject resulting
from the subject’s having an order of parts in place, as kneeling,
sitting, reclining.

26

THE CATEGORIES

10. Habit

Habit (as distinct from the habit which is a species of quality)
is an accident resulting from the subject’s wearing clothes or orna­
ments, or having weapons, as the state of being robed, armed, or
shod.
Notice that every category except substance is an accident. The
categories, then, are made up of substance and nine accidents. We
are speaking here of predicamental (categorical) accident, as distinct
from predicable accident, which we treated in Chapter Two.
The predicable accident refers to the logical universal that is said
of its inferiors contingently, as “white” is said of dog. The predicable
accident is therefore opposed to genus, species, difference, and prop­
erty.
The predicamental accident signifies that mode of existence which
is to inhere in another. A quality, for example, is a predicamental
accident because its mode of existence is to exist in a substance.
Predicamental accident, therefore, is opposed to substance.
The question might be raised as to why there are ten categories.
We shall give a brief answer to this question here. The number of the
categories is determined by the diverse ways of predicating, for each
category is the most universal predicate in its genus. We can sum­
marize this in outline form.
A. A predicate can be said of a subject as pertaining to the essence
of the subject. Such a predicate is in the category of substance.
Thus, when I say “Paul is man,” I signify man as second substance,
which pertains to the essence of Paul.
B. A predicate can be said of a subject as it exists in the subject:
1. On the part of matter. We then have the category of quantity,
as in “Paul weighs two hundred pounds.” Two hundred
pounds is a quantity.
2. On the part of form. We then have the category of quality,
as in “Paul is studious.” Studiousness is a quality.
3. As referring the subject to something else. We then have the
category of relation, as in “Paul is superior.” Superiority is a
relation.
C. A predicate can be said of a subject as signifying movement in re­
lation to something outside the subject:
1. When the subject is the principle of movement. We then have
the category of action, as in “Paul is hitting.” Hitting is an
action.
2. When the subject is the term of movement. We then have the

THE CATEGORIES

27

category of passion, as in “Paul is being hit.’’ Being hit is a
passion, or is passive.
D. A predicate can be said of a subject as signifying something taken
from outside the subject:
1. As the predicate signifies an extrinsic measure of the subject:
(¿z) When the predicate is taken on the part of time. We then
have the category of when, as in “Paul arrives today.” “To­
day” signifies when.
(&) When the predicate is taken on the part of place:
(1) As the predicate signifies place simply. We then have
the category of where, as in “Paul is in Europe.” “In
Europe” signifies where.
(2) As the predicate signifies the order of parts in place. We
then have the category of position, as in “Paul is kneel­
ing.” Kneeling is a position.
2. As the predicate does not signify a measure of the subject. The
predicate then signifies the mode of habit in the subject. We
then have the category of habit, as in “Paul is wearing a robe.”
“Wearing a robe" signifies the condition of being clothed. This
is habit in the sense we mean when we speak of a riding habit.
MODES FOLLOWING UPON THE CATEGORIES

We shall add here two modes which follow upon all or most of the
categories. These modes are also known as the postpredicaments, or
certain characteristics which follow upon the predicaments or cate­
gories generally.
1. Opposition

Opposition arises from the distinction and ordering of natures
within the categories. There are four kinds of opposition.
(a) Contradictory opposition. Contradictory opposition is the
fundamental kind of opposition. Strictly it is an opposition between
being and non-being. The notion of contradictory opposition also
extends to the total opposition of any two things as expressed by one
positive name and its corresponding negative, as in man and non-man.
(&) Privative opposition. Privative opposition is the opposition be­
tween the form and the lack of the form in a subject that is capable
of possessing the form. For example, sight and blindness is a privative
opposition with reference to man as a subject.
(c) Contrary opposition. Contrary opposition is an opposition be­
tween two positive things which are extremes of difference within one
and the same genus, each of which excludes the other from the same

28

THE CATEGORIES

subject. Contrary opposition in which no mean can be found is im­
mediate, as in odd and even. Contrary opposition in which there is a
mean is mediate, as in black and white, good and bad.
(d) Relative opposition. Relative opposition is an opposition be­
tween things which mutually refer to each other, as in double and half,
father and son.
2. Priority

Priority means some kind of precedence of one thing over another.
The various kinds of priority can be reduced to two.
(a) Priority of time. This is the kind of priority we usually think
of when we speak of one thing as prior to another. Priority of time
is priority in duration or in existence. Thus, youth is prior to adult­
hood.
(b) Priority of nature. Priority of nature is a priority in causality.
Priority of nature must be distinguished carefully from priority of time.
The priority of a cause to an effect need not involve priority of time.
For example, my hand moving a book is a causal relation. My hand
moving a book has a priority of nature over the book as moved, but
not a priority of time. The movement is simultaneous. Priority of
nature is a priority of perfection.
QUESTIONS---- CHAPTER FOUR

What is the difference between the predicables and the categories?
In what does the logical consideration of the categories consist?
Why are the categories studied in logic?
What conditions have to be observed in determining the categories?
Why are there ten categories?
Explain each category, and give original examples.
What is the difference between predicable accident and predicamental
accident?
8. What is the most fundamental kind of opposition? Why is it the most
fundamental?
9. What is the difference between privative opposition and contrary op­
position?
10. What is the difference between priority of time and priority of nature?

1.
2.
3.
4.
5.
6.
7.

EXERCISE I—CHAPTER FOUR

In which category does each of the following belong?
_______________ 1. Turnip
_______________ 21. Lameness
________________

2. At noon

_______________

3. Philosophy

_______________ 23. Drinking

_:_____________

4. Inequality

_______________ 24. Priority

________________

5. Granite

________________

6. At home

_______________ 22. Mathematics

_______________ 25. Nineteen
26. Wearing a uni­
form

________________ 7. Inability to
spell

_______________ 27. Flower
_______________ 28. In the cell

_______________ 8. Wearing a
mask

_______________ 29. Dentistry
_______________

9. Jumping

_______________ 30. Leaning
_______________ 10. Parenthood
_______________ 31. Stickiness
_______________ 11. Lying down
_______________ 32. Dancing
- _____________ 12. Laying down

33. In the morn­
ing

_______________ 13. Being laid
down

________________ 34. Minority
_______________ 14. At once
_______________ 35. Upright
_______________ 15. Courage
_______________ 36. Inferiority
- _____________ 16. Quart

_______________ 37. Grasshopper
------------------------ 17. Deafness
_______________ 38. On the chair

- ____________ i_ 18. Triangularity
_______________ 39. Equality
________________ 19. Mineral
--------------- ------- 40. Being put on
the spot

------------------------ 20. Surface

logic: the art of defining and reasoning,

29

copyright,

1952,

by prentice-hall, inc.

EXERCISE II—CHAPTER FOUR

State the kind of opposition that the following pairs of words signify.
_ _____________________

1. Human—non-human

....................

2. Human—inhuman

______________________

3. Mother—daughter

______________________

4. True—false

5. Christian—non-Christian

______________________

6. Rich—poor

______________________ - 7. Whole—part
______________________

8. Wit—witless

______________________

9. Logical—illogical

______________________ 10. Teacher—student
______________________ 11. Healthy—sick
______________________

12. Veteran—non-veteran

------------------------------------ 13. Odd—even
______________________ 14. Success—failure
----------------------------------- 15. Priority—posteriority
______________________

16. Life—death

______________________ 17. Whole—half
--------------------------------- - 18. Being—non-being
______________________ 19. Good—bad
---------------------------------- 20. Considerate—inconsiderate

logic: the art of defining and reasoning,

31

copyright,

1952,

by prentice-hall, inc.

Chapter Five

Division
■psIVISION is the distribution of a thing into its parts.
-*^A division is a means of knowing a thing, for when we
divide a thing into its parts we know better and more distinctly the
thing that we are dividing. For example, by dividing sign into
natural, conventional, and customary we know more about the sign
itself through knowing its dividing members. Division as a mode of
knowing can be seen most evidently in outlining, which is simply
an adaptation of division. If we can outline a topic well, we can
be sure of knowing it well. Outlining is therefore a valuable tool
of learning, for by means of it we can reduce a book or a lecture to
a summary of the main points in a logical order.
The immediate purpose of division is for the sake of making a good
definition, which will be treated in the next chapter. The art of
dividing is necessary for definition because, by dividing a genus into
its species, we arrive at a knowledge of the species, and it is of a species
or a nature that we give a definition.
THE RULES OF DIVISION

The rules of division tell us how to make a good division:
1. The dividing parts must be inferior, that is, less universal than that
which is divided.
Obviously, if we are dividing a thing, each dividing member will
have to be less than what we are dividing. The thing we are dividing
will have to be universal (a division of a singular thing would be
physical division, not logical division). The dividing members, con­
sequently, will have to be less universal. The dividing members could
not be singulars, for singulars are the result of an enumeration, not a
division.
33

34

DIVISION

For example, we can divide tree into oak, elm, maple, and so forth.
Tree, as related to oak elm, maple is more universal and therefore
stands as a genus in relation to the different kinds of tree, which are
species of tree.
2. The dividing parts must exhaust or adequately divide a genus.
In Chapter Two, we divided predicable into genus, species, differ­
ence, property, and accident. This is an exhaustive division, for there
are no other possible kinds of connection between a predicate and a
subject. If we divided predicable only into genus and species, we
should not have an exhaustive division of predicable.
A corollary of this rule is that a division must have at least two
dividing parts, for there must be at least two parts to a whole. It
would be a contradiction to have a division with only one dividing­
part.

3. The dividing parts must be formally opposed to each other such
that each part excludes the other.
We examined the different kinds of opposition in the preceding
chapter. We can use any of the four kinds of opposition in making
a division. We can make a division by contradictory opposition by
dividing religion into Christian and non-Christian. Division by con­
tradictory opposition is the most certain and the easiest form of di­
vision. It is a sure and simple way of securing an exhaustive division,
since only two dividing members are possible. In some cases, how­
ever, it is not a very revealing division.
By privative opposition, we can divide man into sane and insane,
the latter signifying the lack of a certain perfection that man ought
to have. By contrary opposition, we can divide number into odd and
even. In distinguishing between privative opposition and contrary
opposition, notice that privative opposition always includes the signifi­
cation of something absent that should be present whereas contrary
opposition always signifies an opposition between two positive things
standing as the extremes within a genus.
Division by relative opposition may be either into parts that
mutually refer to each other, as the division of family into parents and
children, or into parts that merely specify formal differences within a
genus, as the division of flower into rose, tulip, lily, and so forth.

4. One and the same basis must be kept throughout a division.
The basis of division is the foundation or point of view taken in mak­
ing the division. For example, we can divide man into Spanish,
French, German, and so forth, with nationality as the basis of division.

DIVISION

35

So long as we are dividing man according to that basis, we must not
change it. If, while making that division, we included white or black,
we should be shifting the basis of division from nationality to color.
However, nothing prevents our dividing something exhaustively
according to one basis, and then dividing the same thing exhaustively
according to another basis. This is called co-division, and consists in
taking successive bases of division of the same thing. For example, in
Chapter One we gave a co-division of the sign. We first divided
the sign on the basis of the relation of the sign to the knowing power
and so obtained the dividing parts of formal and instrumental. We
then divided the sign according to a different basis of division, namely
the relation of the sign to the thing signified, and so obtained the
dividing parts of natural, conventional, and customary. It is not
necessary to state explicitly the basis of a division, as we did when
dividing the sign; the dividing parts themselves usually reveal the
basis of division.
Subdivision is distinct from both division and co-division. Sub­
division is simply a division made under another division, or a sub­
ordinate division. Thus, we can divide all things into the ten cate­
gories, as we did in the preceding chapter. We can then subdivide
within each category. In a subdivision, the same basis of division as is
in the main division may be kept, or a different basis of division may be
taken.
THE KINDS OF DIVISION

1. Division of a universal whole into its subjective parts

This is a division in which the whole, or that which is being divided,
can be predicated of each of its parts. It is the division most prop­
erly of a genus into its species. For example, we divide animal into
man and brute. Man and brute are the species of animal, and
animal can be predicated of man and brute. This kind of division
is the principal kind. In it, a genus is divided into its species by true
differences.
2. Division of an integral whole into its composing parts

This is a division into parts which, taken together, make up a
whole. It is of two kinds:
(a) Division of a substance into its parts. For example, we divide
man into the composing parts of body and soul, or we can divide man
into the composing parts of arms, feet, and so forth.
(bj Division of a definition into its parts. We define man as

36

DIVISION

rational animal. We can therefore divide man into rational and
animal.
3. Division by name

In this kind of division, we divide a word into its different meanings,
for example, the word “bow” into knot and weapon.
4. Accidental division

There are three kinds of accidental division:
(íz) Division of a subject according to its accidents. For example,
we divide man into white, black, red, yellow.
(b) Division of an accident according to its subjects. We divide
white into man, milk, snow, and so forth, according to the subjects
in which the accident of whiteness exists.
(c) Division of an accident according to its accidents. We can
divide white into sweet and sour.
QUESTIONS---- CHAPTER FIVE

Why is division studied in logic?
Enumerate and explain the rules of division.
Explain the kinds of opposition used in division and give original examples.
Distinguish division, co-division, and subdivision. Illustrate with original
examples.
5. Explain the kinds of division. What is the principal kind?

1.
2.
3.
4.

EXERCISE I—-CHAPTER FIVE
Are the following divisions good or bad? Explain your answers.
1. Book into fiction and non-fiction.

---------------

2. Animal into those that can burrow, those that can fly, and
those that can make sounds.

---------------

3. Plane triangle into scalene, isosceles, and equilateral.

4. Color into red, white, dark, light.

5. Worker into skilled, unskilled.

6. Tree into trunk, roots, limbs.

—.— .........

7. Man into artist, scientist, American.

8. Seal into animal, stamp.

_______ .__

9. Color into soft, loud.

10. Art into music, painting, cooking.

logic: the art of defining and reasoning,

37

copyright,

1952,

by prentice-hall, inc.

EXERCISE II—CHAPTER FIVE
Make a good division of the following topics, carrying the division through
at least two subdivisions. (This may be done in outline form.)
1.

Education

2.

Government

3.

Art

4.

Religion

5.

Quality

6.

Automobile

logic: the art of defining and reasoning,

39

copyright,

1952,

by prentice-hall, inc.

EXERCISE III—CHAPTER FIVE

Outline the following paraphrase of a portion of Aristotle’s Ethics.
Let us consider the position that happiness does not involve pleasure.
There are some who think that no pleasure is good in any sense. There
are others who think that some pleasures are good but most are bad. There
are still others who think that even if all pleasures are good, yet the best
thing cannot be pleasure. Various reasons are given for the view that
pleasure is not good at all. Thus, a temperate man avoids pleasure. Again,
a prudent man pursues what is free from pain, but not what is pleasant.
Then, too, pleasures are an obstacle to thought. (We might note, here, that
thought is speculative or practical, but in either case pleasure is an obstacle
to thought.) There are also reasons for the view that not all pleasures are
good. Thus, some pleasures are really base and objects of reproach. Further,
some pleasures are harmful, either as unhealthy or as emotionally exhausting.
The reason for the view that the best thing cannot be pleasure is that pleasure
is not an end but a process.

40

Chapter Six
DEFINITION

A DEFINITION is that which explains the nature of a thing,
all the points that we have treated so far in logic, defi­
nition most of all manifests the simple object. If we can define a
thing well, we can be sure of knowing a thing well. We shall now,
therefore, give the rules for making a good definition, after which we
shall summarize the kinds of definition.
THE RULES OF DEFINITION

There are four rules of definition, all of which must be observed in
order to obtain a good definition.
1. The definition should be composed of genus and difference.

Genus and difference have been explained in the predicables in
Chapter Two. They are properly found in essential definitions; in
other kinds of definition, at least something must be stated in place
of a genus and in place of a true difference. Consequently, every
good definition states both something common and something dis­
tinctive. For example, in the definition of man as a “rational animal,”
animal is stated as the genus and rational is stated as the difference.
Animal is common to the various kinds of animal while rational differ­
entiates man from all other animals by stating what is proper to man.
2. The definition and the definitum should be convertible.

The definitum is the thing or nature that is being defined. The
definition, strictly speaking, is the explanation of the definitum. Thus,
in the example given above, “man” is the definitum and “rational
animal” is the definition.
When we say that the definition and the definitum must be converti41

42

definition

ble, we mean they can be validly exchanged. If this can be done, then
the definition is a good one. Thus, we can validly convert Man is a
rational animal to A rational animal is man, without in any way
adding to or detracting from the definition.
If we were to say Man is a two-footed animal, we should discover
that we could not validly say, in conversion, A two-footed animal is
man, for two-footed animal includes more things than man, and hence
is a bad definition.
Convertibility is the most direct way to test whether the definition
is good.
3. The definition should signify more clearly than the definitum.

If the purpose of the definition is to manifest the definitum, it is
obvious that the definition must be clearer than the definitum. Con­
sequently, this rule eliminates the use of equivocal names, ambiguous
expressions, obscure words, and negative expressions. Sometimes we
may have to use negative names, but, so far as possible, they should
be eliminated. In particular, the definitum should be excluded from
the definition. We should not define a logician as a logical thinker.
4. The definitum must be universal.

No singular thing can be defined, for the singular is not an object
of scientific knowledge. The definitum must be universal and must
be a species under a genus. Consequently, a supreme genus or category
cannot be defined, for it has no genus above it.
THE KINDS OF DEFINITION

1. Essential definition
An essential, or real, definition is one that gives the essence of the
thing signified by the name. The essential definition is always stated
in terms of genus and true difference, for the genus and true differ­
ence express the essence of a thing.
Rational animal is an example of the real definition of man.
Animal stands as the genus and rational as the true difference.
2. Nominal definition
A nominal definition designates the nature to which the name is
applied but does not specify the essence of the thing through the
genus and true difference. According to this meaning of nominal
definition, anything short of a real or essential definition is a nominal

DEFINITION

43

definition, either because such a definition does not explain a nature
sufficiently or because the thing being defined does not have a nature,
as definitions in grammar and definitions of artificial objects.
(a) Definition by property. A property is a proper accident of a
thing, connected necessarily, only, and always with its nature. Gram­
matical animal is a definition of man by property, since grammatical
is proper to man.
(&) Definition by accident. “Accident” here is understood as com­
mon accident. Common accidents are characteristics that belong to
more than one nature, or are not necessarily connected with a nature,
or are not always present in a nature. A definition by accident usually
has to have two or more common accidents as the difference in order
to satisfy the rule of convertibility in definition. Thus, it would
not be sufficient to define man as a biped animal, although “twofooted” is a common accident of man. We can, however, achieve a
satisfactory accidental definition of man by saying that man is a
featherless, biped animal.
(c) Definition by cause. The causal definition is understood as ap­
plying to extrinsic causes, namely, to the efficient and final causes.
Thus, we can define a human soul as a form created by God for eternal
happiness, in which we specify the efficient cause God and the final
cause eternal happiness. All artificial things are defined by their final
cause or purpose.
A definition by intrinsic causes, namely by material and formal
causes, reduces to an essential definition. Thus, man is that which is
composed of body and rational soul, where body means sensitive,
animated body (which is the same as animal) and where rational soul
reduces to rational; hence, the essential definition of man is rational
animal.
(d) Definition by name. A definition by name or word, or a verbal
definition, explains the meaning of a word, either by etymology, as in
philosophy is the love of wisdom (showing the Greek origin of the
word), or by stating the common meaning of the word, as in the
soul is the principle of life.
QUESTIONS---- CHAPTER SIX

1.
2.
3.
4.
5.

Explain how everything treated in Part One is ordered to definition.
Explain, with original examples, the first two rules of definition.
Why must the definitum be universal?
Explain the difference between essential and nominal definition.
Explain définition by extrinsic causes and by intrinsic causes, giving ex­
amples. What kind of definition is definition by intrinsic cause?

EXERCISE—CHAPTER SIX
Determine whether the following definitions are good or bad. If they
are good, encircle the genus and underline the difference. Specify the
kind of difference: specific difference, property, accident, or extrinsic cause.
If they are bad, give the rule violated.
1. Man is an artistic animal.

2. Revenge is punishment inflicted to satisfy the feelings of the punisher.

3. A grammarian is one who is skilled in grammar.

4. A fish is an aquatic, jawed vertebrate with fins, scales, and gills, and a
heart with one auricle.

5. A knife is an instrument used for cutting.

logic: the art of defining and reasoning,

45

copyright,

1952,

by prentice-hall, inc.

6. George Washington is the first president of the United States.

7. A rectangle is a right-angled parallelogram.

8. Thinking is the manipulation of memory.

9. A hammer is an instrument for driving nails, beating metals, and the
like, consisting of a head, usually of steel, fixed crosswise to a handle.

10. Man is a living being capable of spontaneous movement and rapid
motor response to stimulation.

46

REVIEW QUESTIONS---- PART ONE

In Part One of logic there is a certain amount of important doctrine. The
following questions are designed to bring out the most important points that
should be known. Answers to these questions are needed for the material
in Part Two and Part Three.
Introduction
1. What is logic?
2. Of what use is the study of logic?
3. What is a simple object?
4. What is a complex object?
5. What are the three acts of the intellect? Explain them.
6. What do formal logic and material logic have in common?
7. How is formal logic distinguished from material logic?
Chapter One
8. What is a word?
9. Why does logic consider words?
10. Distinguish between words and concepts.
11. Define the sign.
12. What are the bases for the divisions of the sign?
13. What is the difference between natural and conventional signs?
14. Is a word a natural or conventional sign? Why?
15. Is a concept a natural or conventional sign? Why?
Chapter Two
16. What is a universal?
17. What is a singular?
18. What is a logical universal?
19. What is a predicable?
20. Define genus; species; specific difference; property; accident.
21. Which of the predicables have an essential connection with their inferiors?
22. Which of the predicables have an accidental connection with their in­
feriors?
23. What question does the predicable “genus” answer?
24. What question does the predicable “species” answer?
25. What question does the predicable “specific difference” answer?
Chapter Three
26. Define univocal name; equivocal name; analogous name.
ÏI. Why is an analogous name said to be proportionately one?
28. What does existence in a subject mean?
29. What does predicable of a subject mean?
30. What is a singular substance? a universal substance?
31. What is a singular accident? a universal accident?
Chapter Four
32. What is a category?
33. What is the purpose of studying the categories?
34. What four conditions have to be observed in determining the categories?
35. Name and explain each of the categories.
36. Name two kinds of quantity and give an example of each.
37. Name the four species of quality and give an example of each.
47

38. What is the difference between predicable accident and predicamental
accident?
39. What is contradictory opposition? Give an example.
40. What is privative opposition? Give an example.
41. What is contrary opposition? Give an example.
42. What is the difference between immediate and mediate contrary op­
position?
43. What is relative opposition? Give an example.
44. What is meant by priority}
45. What is the difference between priority of time and priority of nature?
Chapter Five
46. What is division?
47. How does division help us to know a thing?
48. What are the rules for a good division? Illustrate each rule.
49. What are the different kinds of division? Give examples.
50. What is the difference between subjective parts and composing parts?
Chapter Six
51. What is definition?
52. What is the importance of definition?
53. What are the rules for a good definition?
54. What is a definitum?
55. What is the difference between a real and a nominal definition?
56. What are the different kinds of nominal definition?

Part Two

THE SECOND ACT OF

THE

INTELLECT-

COMPOSITION AND DIVISION

■J
■I
■I
PI
PI
PI

Chapter Seven

TRUTH AND FALSITY

I Á/E have already referred, in the Introduction, to the second
’ * act of the intellect as the act of composition and division.
The second act of the intellect combines or divides the simple objects
that have been made known by the first act of the intellect. By the
act of composition, we combine one simple object with another, as in
Man is artistic. By the act of division, we deny one simple object of
another, as in Wealth is not happiness. This composition and division
of simple objects is not a mere juxtaposition of words, but an actual
affirmation and denial. This affirmation or this denial is the “complex
object” that specifies the second operation of the mind. The complex
object distinguishes the second operation from the first, which is speci­
fied by the simple object.
By this second act of composition or division, we form propositions.
Let us notice that we must first form a proposition in the mind before
we can make a judgment. In a judgment, we assert that a composition
or a division conforms to reality. The judgment will be true if the
composition or division conforms, false if it does not. A judgment by
our intellect presupposes that we have something to judge, namely, a
composition or division of simple objects. We exercise judgment, then,
on some composition or division of simple objects, and it is in this
way that truth and falsity are in the second act of the intellect.
Let us examine what we mean by truth as we are using it here, for we
use the word in more than one sense.
Speaking most generally, we say that our intellect seeks to know
truth. Our intellect is made for truth, just as our sense of hearing is
made for hearing sound. This is what we mean when we say that
the true is the good of the intellect. Truth, then, implies some rela­
tion between an intellect and something known. Things, however,
can be related to the intellect in two ways.
In the first way, things are related to the intellect as measuring the
51

52

TRUTH AND FALSITY

intellect. A measure is a standard to which we compare other things.
When what I know corresponds to things, what I know is measured
by those things. My knowledge is then speculatively true. Speculative
here is not meant in the popular sense of “theorizing from conjectures
without sufficient evidence.” Speculative truth is the conformity of the
intellect to things, and speculative falsity is the lack of such conformity.
Speculative truth is also called formal truth. For example, the propo­
sition that a square has four sides is true because it conforms to reality,
whereas the proposition that a square has three sides is false because
it does not conform to reality.
The same conformity of intellect to thing occurs less perfectly in the
first operation of the intellect, and also in what is called the truth of
the senses. Thus, when we say that truth is found in the senses, we
mean that our sense powers conform, in their knowing, to things in
reality. For example, I see the color of a flower and what I see con­
forms to reality. However, my eye does not know this conformity,
for the knowledge of this conformity requires intellectual under­
standing.
In the second way, a reverse relation occurs between things and the
intellect, namely when things are related to the intellect as measured.
by the intellect. We are now considering the intellect as it knows
in a practical way. In practical knowledge, our intellect is the cause
of things, whereas in speculative knowledge, things are the cause of our
knowledge.
Thus, the work of the artist is called true in so far as it conforms
to the idea in the mind of the artist and as it attains the nature of the
art. A work of art is called false in so far as it departs from this con­
formity. For example, an artificial object that is poorly designed
for sitting cannot be truly called a chair.
Just as the artificial object is measured by the idea in the mind of
the artist, so all natural objects are measured by the idea in the divine
intellect. This conformity of natural objects to the divine intellect is
called transcendental truth. Transcendental truth, then, is the
truth that follows upon all being, and is therefore convertible with
being.
When we speak of truth and falsity in logic, we are not speaking of
practical truth and falsity. Logic is not concerned with the truth of
making or with the truth of doing, the two divisions of practical truth,
since logic is an instrument to aid us in arriving at truth in our
knowledge of things. Logic is not concerned with transcendental
truth, the truth convertible with being, for the study of the truth that
is convertible with being belongs to metaphysics. Logic, finally, is
not concerned with moral truth and falsity, that is, with telling a truth

TRUTH AND FALSITY

53

and telling a lie. The conformity in moral truth is between speech and
thought, not between thought and thing.
Logic is concerned only with speculative truth, in which our intellect
knows the conformity between a proposition we form and things ex­
isting outside our intellect. By knowing this relation between thought
and thing, we are able to judge the composition or division of simple
objects that we have made as true or false.
QUESTIONS---- CHAPTER SEVEN

1.
2.
3.
4.
5.
6.
7.
8.

What do we mean by the act of composition and the act of division?
Explain the ways in which things are related to an intellect.
What is speculative truth?
What is practical truth?
What do we mean by truth of the senses'}
What do we mean by transcendental truth}
What do we mean by moral truth}
With what kind of truth are we concerned in logic?

n i iiïiiïi:

Chapter Eight

THE PROPOSITION

A PROPOSITION is a composite expression that signifies
-by
*
•¿
indicating the true or the false.
We have spoken of truth and falsity in the preceding chapter. Let
us note here that truth or falsity is said to be in a proposition as a
sign of true or false understanding. Truth or falsity, however, is in
the mind as in a subject. Truth, finally, is in the thing as in a cause
of the truth which is in the mind. Thus, because this dog is white,
my knowledge that this dog is white is true, and the proposition by
which I signify that knowledge is true. Hence we speak of the
proposition as that which “signifies by indicating the true or the
false.”
A composite expression is an orderly group of words. The proposi­
tion is one kind of composite expression. Let us examine the meaning
of “composite expression” so as to understand better what a propo­
sition is.
*
A composite expression is a whole whose parts signify something
separately. This distinguishes a composite expression from a simple
word, which signifies a simple object, as man, tree, dog, and so forth.
A composite expression extends from a definition to full argumentation.
Composite expression is divided into perfect and imperfect.
A perfect composite expression generates a complete meaning in the
mind of the hearer. An imperfect composite expression fails to gen­
erate a complete meaning in the mind of the hearer; it leaves one in
suspense because of the incompleteness of meaning, as in while men are
fighting.
There are five kinds of perfect composite expression: deprecatives,
imperatives, interrogatives, vocatives, and enunciatives. A deprecative
* “Composite expression” is used here to stand tor oratio in Latin and logos in
Greek, which would be better translated as “speech” except for difficulties of its use
in English.
55

56

THE PROPOSITION

expression is a prayer (as, Give us this day our daily bread.). An im­
perative is a command (as, Stand up!). An interrogative is a question
(as, Who is coming?). A vocative is an appeal (as, O, dear friend!).
An enunciative is an enunciation or a proposition (as, Man is wise.).
We now see the full meaning of the definition of a proposition as a
composite expression that signifies by indicating the true or the false.
The proposition is, first of all, a perfect composite expression, and
therefore has a complete meaning by itself. The proposition is dis­
tinguished from other kinds of perfect composite expression by its
indication of the true or the false. We shall thus keep the proposition
distinct from such other composite expressions as commands or prayers.
The other kinds of composite expression are treated in rhetoric and
grammar.
We have spoken of the proposition as indicating the true or the
false. A proposition indicates the true or the false in so far as it
predicates something of a subject. We predicate something of a
subject either by affirming the predicate, as in Man is wise, or by deny­
ing the predicate, as in Man is not wise.
The elements of a proposition are the noun and the verb, out of
which a proposition is formed in words. From the standpoint of
logic, we include the pronoun and the adjective under the noun, and
the participle under the verb.
A noun is defined as a vocal sound that signifies by convention,
without time, and no part of which is significant separately. “Vocal
sound” is stated as the genus, by which the noun is distinguished from
all sounds that are not vocal, that is, sounds not involving some
imagination. “Signifies” differentiates the noun from various non­
significant vocal sounds, such as nonsense syllables. “By convention”
differentiates the noun from vocal sounds that signify naturally, such
as the groans of a sick person and the vocal sounds of animals. “With­
out time” differentiates the noun from the verb in so far as what the
noun signifies is not measured by time. “No part of which is signifi­
cant separately” differentiates the noun from a composite expression,
such as wise man, in which the parts signify something separately.
A verb is a vocal sound that signifies with time and is always a
sign of those things predicated of another. In this definition of the
verb, only that which distinguishes the verb from the noun is given;
otherwise the definition of the verb is the same as that of the noun.
Notice that the verb signifies with time. Since motion, which consists
of action and passion, is measured first and principally by time, the
verb, which signifies action or passion, signifies with time. The
verb is also a sign of the attribution of a predicate to a subject, either
when signifying the predicate itself, as in Paul is (meaning, Paul

THE PROPOSITION

57

exists), or when uniting the predicate to the subject, as in Paul is
wise.
The noun and the verb, therefore, are the necessary elements of a
proposition. We cannot express a proposition in words without at
least a noun and a verb. There are times, it is true, when we seem
to use only one word to express a proposition. For example, if
someone asks me, “Who is studying in the room?” I can answer simply,
“Paul.” However, it is clear that I am merely using a short-cut ex­
pression that means, in the context of the question, “Paul is studying.”
Similarly, “Yes” can signify an affirmative proposition in answer to a
question, and “No” can signify a negative proposition. Thus, if
someone asks me, “Are you tired?” I can answer, No,” as a short-cut
expression for “I am not tired.”
We also speak of the subject, predicate, and copula in a proposition.
In the proposition Man is wise, man is used as a subject, as that of which
something is predicated. Wise is used as a predicate, as that which is
predicated of an inferior. Is is used as a copula, as a sign of the join­
ing of the predicate to the subject. The subject and the predicate
are the matter of the proposition. The copula is the form of the
proposition.
We shall see in the following chapters that it is frequently useful
to put propositions into what is called “logical form.” The logical
form of a proposition is the explicit expression of the subject, predicate,
and copula as distinct parts of the proposition, as in Man (subject)
is (copula) artistic (predicate). Sometimes propositions will have to be
restated in logical form to bring out the parts of the proposition more
clearly. The proposition Paul walks can be stated more explicitly,
in logical form, as Paul is one who walks.
QUESTIONS---- CHAPTER EIGHT

1.
2.
3.
4.
5.
6.
7.
8.

Define proposition.
What do we mean by a “composite expression”?
Distinguish between perfect and imperfect composite expression.
Explain the different kinds of perfect composite expression. Give examples
of each.
What do we mean by speaking of the proposition as “indicating” the true
or the false?
Define noun. Explain the parts of the definition.
Define verb. Explain the parts of the definition,
What is the “logical form” of a proposition?

EXERCISE I—CHAPTER EIGHT
In the following composite expressions, write “Yes” if the composite ex­
pression is a proposition, “No” if it is not. In those that are propositions,
underline the subject once, the predicate twice, and encircle the copula.
1. I should like to meet your friend.

2. No dogs allowed.

3. Students are serious.

4. Some men are tenors.
5. A question is an interrogative expression.
6. Come into the room for a moment.
7. Every composer is a musician.

8. When will the class be over?

9.

The prohibition against smoking is a new regulation.

10. Soldiers are not cowards.

11. Have exact fare ready when entering car.

12. No sophomore is eligible for scholarships.
13. I wonder whether I was nominated.
14. He who fights for his country is patriotic.

15. Some citizens are non-voters.
16. Forgive our faults.

17. No non-graduates are able to apply.

18. I am available.
19. Consider the moral, I pray.

20. He who thinks he is wise is not wise.
logic: the art of defining and reasoning,

59

copyright,

1952, BY

prentice-hall, inc.

EXERCISE II—CHAPTER EIGHT

In the following propositions, write “Yes” if the proposition is in logical
form, “No” if not. Re-write in logical form those that are not.
1. No dog is a cat.

B)
Bl
Bl
Bl
Bl

2. Every good logician is able to reason correctly.
3. Man dies.

4. Some fruit is sour.
5. Every good man comes to the aid of his party.
6. No American advocates the overthrowing of his government.

I. Not every proposition has logical form.
8. He who is in trouble deserves sympathy.
9. I am human.

Bl
■1
I»
BW
■I
II

10. Comforting are the words of a friend.
----------- .--- 11. All those who have voted have done their duty.
--------------- 12. Automobiles are expensive.
--------------- 13. A friend in need is a friend indeed.
--------------- 14. Not all who have answered have answered correctly.
--------------- 15. Every sale that is successful sells the company.
--------------- 16. Great books become lasting possessions.
logic: the art of defining and reasoning,

61

copyright,

1952, BY

prentice-hall, inc.

Divisions OF

T
I.

THE PROPOSITION.

HE different kinds of proposition are obtained by divid­
ing the proposition according to various bases of division.

ACCORDING TO UNITY

The unity of a proposition is determined by the unity of the com­
position made by the mind in forming a proposition. This unity may
be simple or complex.
The categorical proposition is simply one because it signifies one
composition in the intellect, as in Man is mortal. It is composed
simply of subject, predicate, and copula.
The compound proposition is one by conjunction, because it signifies
more than one composition in the intellect, as in Ij horses are animals,
then horses have sensation. The compound proposition is composed
of categorical propositions.
The categorical proposition and the compound proposition differ
according to the kind of copula each has and according to the kind
of parts each has. The copula of the categorical proposition is a verb.
The copula of the compound proposition is some connective, such as
ij, then, and, neither, or, and so forth. The parts of the categorical
proposition are the subject, predicate, and verb copula. The parts of
the compound proposition are categorical propositions united by vari­
ous connectives.
II. ACCORDING TO

QUALITY

The division of a proposition according to quality is a division into its
species—into affirmative and negative propositions. This is a division
of the proposition into species because affirmative and negative propo­
sitions differ in their very manner of combining the predicate with the
subject.
63

64

DIVISIONS OF THE PROPOSITION

An affirmative proposition is a proposition in which the predicate is
united with the subject, as in Man is wise. The verb copula must be
affirmative.
A negative proposition is one in which the predicate is separated from
the subject, as in Man is not wise. The verb copula must then be
negative.
The distinction between affirmative and negative propositions is
undoubtedly clear enough, but sometimes it is not immediately evi­
dent whether a proposition is really affirmative or negative in form.
The following suggestions will help to make the distinction accurately.
Compound propositions are always affirmative. This is because the
copula in the compound proposition is a connective and not a verb.
The connective copulas of the compound proposition must combine the
parts of the compound proposition; that is, they must join together
categorical propositions. For example, the compound proposition
If it is not cloudy, then it is not raining is an affirmative compound
proposition because of the connectives if and then, even though the
parts of the compound proposition (the categorical propositions)
have negative verb copulas.
In categorical propositions, the verb copula determines whether the
proposition is affirmative or negative. Some propositions may con­
tain more than one verb, but it is only the verb copula that determines
the quality of the proposition. Thus, the proposition Students who
are not seniors are eligible is an affirmative proposition because the verb
are functions as the copula of the proposition and is affirmative.
Negated subjects and negated predicates will not make the propo­
sition negative in quality unless the verb copula itself is negative.
The proposition Non-seniors are ineligible is an affirmative proposition
even though both the subject and the predicate are negative words.
III. ACCORDING TO QUANTITY

This division of the proposition is taken according to the quantity of
the subject of the proposition.
When the subject of a proposition is a singular, the proposition is
singular, as in Paul is wise or in This man is wise. Notice that the
singular in logic means “this one and no other.” It does not mean the
grammatically singular, as opposed to the grammatically plural. The
proposition Every man is wise is grammatically singular but not
logically singular. ,
When the subject of a proposition is a universal name, then some­
thing can be predicated of the subject in three ways: universally,
particularly, and indefinitely. In the proposition Every man is wise

DIVISIONS OF THE PROPOSITION

Bl
bi
B|
Bl
B|

65

the predicate wise is said of every man, thus making the proposition
universal. In the proposition some man is wise the predicate wise
is said of some man, thus making the proposition particular. Notice
that the subject of the particular proposition is the vague individual
(some man), which is to be kept distinct, however, from the subject of
a singular proposition (this man). In the proposition Man is wise the
predicate wise is said of man without any quantitative modifier, thus
making it an indefinite proposition with respect to quantity.
The use of a negation affects the quantity of a proposition as well
as the quality. We have already seen that the proposition Every man
is wise is a universal affirmative proposition. A negation placed before
such a proposition has the effect of changing both its quality and
quantity. Thus, Not every man is wise is negative because the not
changes the copula from affirmative to negative; the proposition is
also particular because the not denies the every and therefore changes it
to the particular. Hence, Not every man is wise is equivalent to say­
ing Some man is not wise. For the same reason, a proposition such as
All books are not interesting, despite its appearance, is particular and
negative in meaning.
IV. ACCORDING TO THE MATTER OF THE PROPOSITION

Bl
Bl
Bl
Bl
Bl
Bl
Bl

The division of the proposition according to the matter indicates the
relation of the predicate to the subject.
A proposition has necessary matter when the predicate is in the sub­
ject per se, that is, when the predicate belongs to the essence of the
subject and is therefore related necessarily to the subject. The proposi­
tion Man is grammatical has necessary matter because the predicate
grammatical is necessarily connected with the essence of man.
A proposition has impossible matter when the predicate is per se
repugnant to the subject, that is, when the subject and the predicate
are incompatible with each other. The proposition Dogs are immortal
has impossible matter because the predicate immortal cannot belong
to the subject dogs.
A proposition has contingent matter when the predicate is neither
per se in the subject nor per se repugnant to the subject, that is, when
the predicate is such that it may or may not belong to the subject.
The proposition Man is white has contingent matter because the
predicate white may or may not be in the subject man. In other
words, there is no necessary relation between the subject and the
predicate in a proposition having contingent matter.

66

DIVISIONS OF THE PROPOSITION

V. ACCORDING AS THE MODE OF COMPOSITION IS

EXPRESSED OR NOT

This is a division of the proposition according to whether or not the
modality of a proposition is explicitly expressed.
A simple proposition (also called de inesse) is a proposition that
does not express explicitly the mode of the composition in the proposi­
tion.
A modal proposition is one in which the verb copula is affected by a
sign indicating in what mode the predicate belongs or does not belong
to the subject. There are four modes that can be expressed in a
proposition: necessity, impossibility, possibility, and contingency.
Consider the proposition Man is grammatical. Although, as we
saw in the preceding section, this proposition has necessary matter,
nevertheless it does not express explicitly the modality of the proposi­
tion, that is, it does not state that man necessarily is grammatical.
Consequently, Man is grammatical is a simple, or non-modal, proposi­
tion.
A proposition becomes modal, therefore, when one of the four
modes is explicitly expressed in it. Man is necessarily grammatical
is a modal proposition because the mode of necessity is explicitly ex­
pressed.
In order to understand the structure of the modal proposition, we
distinguish the dictum from the mode. The dictum of a modal
proposition is the composition of predicate and subject. The mode
is the manner or modality of that composition. Thus, in the modal
proposition Man is necessarily grammatical, the composition man is
grammatical is the dictum and necessarily is the mode.
In terms of this distinction, the modal proposition is defined as
a proposition that modifies its dictum. Thus, the mode in the modal
proposition modifies the composition of the dictum, as necessarily
modifies, through the verb, the composition man is grammatical.
A modal proposition can be expressed in grammatically different
ways. We can say Man is contingently white or It is contingent that
man is white or That man is white is contingent. These propositions
differ only grammatically. So far as logic is concerned, all are
equally modal propositions, and they are all the same modal propo­
sition.
A modal proposition
*
is made negative by negating the mode. The
quality of the modal proposition is not affected by the quality of the
dictum. Thus, the modal proposition It is not contingent that man is
grammatical is a negative modal proposition because the mode is

DIVISIONS OF THE PROPOSITION

67

negated, even though the dictum remains affirmative. The dictum, of
course, can also be negative in a negative modal proposition, as in
It is not possible that man is not grammatical. The modal propo­
sition It is possible that man not be white is affirmative even though
the dictum is negative.
QUESTIONS---- CHAPTER NINE

1. What are the various bases of division for determining the kinds of
propositions?
2. Distinguish between a categorical proposition and a compound proposition.
3. Why are compound propositions always affirmative?
4. When is a proposition universal? When particular?
5. What is an indefinite proposition?
6. Is the proposition Every dog is an animal logically singular? Explain.
7. When does a proposition have necessary matter? impossible matter? con­
tingent matter?
8. Distinguish the dictum from the mode in a modal proposition.

EXERCISE I—CHAPTER NINE
Classify the following propositions as categorical or compound. If cate­
gorical, classify as affirmative or negative; universal, particular, singular, or
indefinite.
1. Some men are not handsome.

______________________

2. Man is artistic.
3. Some books that are not entertaining are non­
fiction.

______________________

4. Every dog has his day.
5. Not every proposition is universal.
6. If labor is scarce then labor is expensive.
7. This book is uninteresting.

______________________

8. Man is irrational.

9. Students either pass or fail courses.
_________________ ,____ 10. No science is opinion.

EXERCISE II—CHAPTER NINE

In the above exercise, turn the following into true modal propositions:
1.

2.

8.

10.

n
ri

logic: the art of defining and reasoning,

69

copyright,

1952, BY

prentice-hall, inc.

Chapter Ten
SUPPOSITIOR

SUPPOSITION concerns the use of words within a proposition, the use of words as subjects and predicates of propo­
sitions. Supposition, therefore, is a property of the parts of the
proposition; more specifically, it is a property of the extremes of the
proposition, the subject and the predicate.
Let us first distinguish between signification and supposition, for these
two are often confused. The signification of a word is, as we have
seen, the meaning of a word. A word signifies conventionally the con­
cept we have of a thing. The supposition of a word presupposes the
signification of a word, for we cannot tell how to use words in propo­
sitions unless we know’ what the words mean. We must know, then,
what words signify before we can use them to stand as the subject or
predicate of a proposition.
Let us take, for example, the word “man.” The signification of the
word “man” is the meaning of the word, that is, the concept that the
word conventionally signifies; the concept, in turn, is a natural sign
of the nature of man. The signification of “man” is the same whether
the word is within a proposition or outside of a proposition.
The supposition of “man” does not arise until we make use of the
word in a proposition^ as in Man is artistic. In Man is artistic the word
“man” is used so as to have a certain connection with the other words
in the proposition. More specifically, it stands as the subject of the
proposition. Consequently, the supposition of “man” adds nothing to
the signification of the term. The supposition merely makes use of the
meaning of “man” in a proposition.
Hence, the question of the supposition of terms in a proposition
reduces to the following. Given the signification of "man,” can it then
be used (can it “suppose”) as the subject of a proposition? Is the
signification of the word capable of standing, in relation to the copula,
as the logical subject?
71

72

SUPPOSITION

DEFINITION OF SUPPOSITION

With this preliminary clarification, we can now define supposition as
the use of a u’ord for an extreme of a proposition according to the
requirement of the copula.
By the phrase “the use of a word for an extreme of a proposition, ”
we mean the substitution of the word for a subject or a predicate of
a proposition. In the proposition Man is artistic, “man” stands for the
logical subject, and “artistic” stands for the logical predicate.
By the phrase “according to the requirement of the copula,” we
mean that the supposition of words as subjects and predicates depends
upon the kind of existence that the copula is signifying, namely, past,
present, or future. Let us notice, however, that in some propositions
the copula signifies an existence independent of time. For example,
in the proposition Every man is mortal, the copula is signifies an ex­
istence independent of time in the sense that the copula does not limit
the time to any given period—the past only, the present only, or the
future only—but signifies, rather, an eternal existence. Whenever a
proposition has a universal subject that signifies a nature, such a
subject will always satisfy the requirement of the copula, since a
nature as such does not have past, present, or future.
When, however, the copula of a proposition signifies a definite-period
of time, then the words standing as the subject must signify something
that has an actual existence in time in agreement with the time
signified by the copula. For example, in the proposition George
Washington was a president of the United States, the words “George
Washington” can suppose as the logical subject, since the words signify
someone existing at the time demanded by the copula.
But if I were to form the proposition George Washington will be
a president of the United States, I should then have a proposition in
which the words “George Washington” do not suppose as the subject
of a proposition, for the copula demands the future existence of some­
one, but the words “George Washington” are intended to refer to
someone who existed in the past. Such a proposition is an example
of what is called a “proposition with a non-supposing subject.” Such
a proposition will always be a false proposition, though not a “mean­
ingless proposition,” as it sometimes has been called. A non-supposing
subject occurs in a proposition, therefore, when the copula signifies
a time of existence at which the subject could not exist.

SUPPOSITION

73

THE KINDS OF SUPPOSITION

There are two kinds of supposition: proper and improper.
Improper supposition is the use of a word in a proposition as it
signifies in a metaphorical sense. For example, in The lion of the
tribe of Juda conquers, “lion,” standing as the subject of the propo­
sition, signifies Christ metaphorically.
Proper supposition is the use of a word in a proposition as it signifies
in a literal sense. For example, in Every lion is an animal, “lion,”
standing as the subject of the proposition, signifies literally a certain
kind of animal. Proper supposition is divided further into material,
simple, and personal supposition.
Material supposition is the use of a word to represent itself, as in
“Running” is a verb, “Tree” is a noun, and “Country” is a word of
two syllables. In material supposition, we merely consider the matter
of a word—the appearance of the word in sound or writing—without
explicitly considering the form of the word, that is, its meaning.
Simple supposition is the use of a word to signify the nature of
something as it is in our intellect, as in Man is a species. In simple
supposition, we use a word to signify a nature conceived in the mind,
without reference to the existence it has in actual individuals. In
the proposition Man is a species, “man” is used to signify human na­
ture as such, and does not include in its signification the individuals
(Paul, James, John) in whom the nature of man actually exists.
Personal supposition is the use of a word to signify both the nature
and the individuals in which the nature is found, as in Man is an
animal. A word used with personal supposition signifies immediately
the nature itself and mediately the individuals of that nature. In the
proposition Man is an animal, “man” is used to signify immediately
human nature and mediately Paul, who, being a man, is also animal.
Notice carefully the distinction between simple and personal suppo­
sition. Simple supposition is the use of a word to signify a nature
conceived apart from the existence of the nature in individuals. Per­
sonal supposition is the use of a word to signify the real existence of
a nature in individuals. When we examine later the opposition of
propositions, and the syllogism, we shall see that it is necessary to
keep the same supposition of words in order to avoid fallacies.
DISTRIBUTION OF THE SUBJECT AND PREDICATE

IN PROPOSITIONS

The distribution of the subject and the predicate in a proposition refers
to the supposition of a universal name in a proposition. Distribution

74

SUPPOSITION

is a question of whether the supposition of a universal name includes
all the individuals under it, or only some. A universal name is dis­
tributed if it refers to all the individuals. It is undistributed if it
refers only to some of the individuals. The question of distribution,
therefore, does not properly arise in the case of a singular word.
There are four rules governing the distribution of words in a propo­
sition.

1. Every universal proposition distributes the subject
A universal proposition is one whose subject is modified by some
universal sign; hence, the subject of a universal proposition is dis­
tributed, that is, the subject supposes universally. Examples: Every
man is an animal and No man is a stone.
It is well to distinguish here between a subject that supposes uni­
versally and one that supposes collectively. A subject that supposes
universally stands for each and every individual under it, as in Every
man is an animal, because the universal subject is distributed to all the
individuals included under it. A subject that supposes collectively
stands for a group of individuals taken, not individually and separately,
but together as an aggregate whole, as in The apostles were twelve in
number.
Notice in this connection that the universal proposition is better
expressed in the form Every man is an animal than in the form All men
are animals. The use of every with a singular verb expresses the dis­
tribution of a universal word to each and every singular included under
it. The use of all with a plural verb does not express this distribution
so clearly. In English the word all has a certain ambiguity that has
misled some logicians in their analysis of propositions, especially those
who interpret the universal as a class of objects. The first meaning
of the word all is “the whole of,” referring to the amount of, as when
we say “All the wheat. . . .” The second meaning of all is “the
whole number or sum of,” as in “All the apostles were twelve.” It
is only in its third meaning that all designates the distribution of a
universal name to each and every singular included under it, as in
All men are animals. The use of all for the distribution of a uni­
versal name is not incorrect but we should avoid its ambiguity by
understanding it only in its third meaning, when it is used as a sign
of universality.

SUPPOSITION

75

2. Every particular proposition has an undistributed subject
A particular proposition is one whose subject is modified by a sign
denoting particularity. Examples: Some man is wise (Some men are
wise) and Some man is not wise (Some men are not wise).
An indefinite proposition, formally considered, should be treated as
having an undistributed subject. For example, the proposition Man
is wise is sufficiently verified by a particular instance, and hence the
subject man is taken as undistributed.

3. Every negative proposition distributes its predicate

A proposition is negative when the copula is negative. The nega­
tive copula always makes the predicate universal in distribution, for
the predicate of a negative proposition is universally separated from
its subject. For this reason the predicate of every negative proposition
is distributed. Examples: No cat is a dog and Some man is not
honest.
4. Every affirmative proposition has an undistributed predicate

A proposition is affirmative when the copula is affirmative. The
affirmative copula always makes the predicate undistributed, or par­
ticular. The reason for this is that the predicate, as predicate, is
more universal than the subject. Since it is taken as more universal
than the subject, it cannot be predicated in its full universality, for
it cannot be identified with the subject. Consequently, the predicate
has to be reduced from universality to particularity to be identified
with the subject. For example, in the proposition Every tulip is a
flower, flower is more universal than tulip. Therefore, we cannot
predicate flower universally of tulip: Every tulip is (every) flower.
Consequently, we must reduce the universality of flower and predicate
it only as a particular, or as undistributed: Every tulip is (some) flower.
Now we can see why the fourth rule of distribution says that every
affirmative proposition has an undistributed predicate.
Examples of affirmative propositions with undistributed predicates
are: Every oak is a tree and Some weed is poisonous.

76

SUPPOSITION

QUESTIONS---- CHAPTER TEN

Distinguish between supposition and signification.
Explain how supposition is a property of the parts of a proposition.
Define supposition.
What kinds of existence does a copula signify?
When does the subject of a proposition not have supposition?
What are the kinds of supposition?
What is the difference between material, simple, and personal supposition?
Give examples of each.
8. What do we mean by the distribution of the subject and the predicate in
a proposition?
9. What are the four rules of distribution? Illustrate each rule with ex­
amples.
10. What is the difference between a subject that supposes universally and a
subject that supposes collectively?

1.
2.
3.
4.
5.
6.
7.

EXERCISE—CHAPTER TEN

Classify the subjects and predicates of the following propositions as dis­
tributed or undistributed. Put “D” for “distributed” or “U” for “un­
distributed” above each subject and predicate.
1. Every flower is a plant.
2. No horse is a dog.
3. Some man is courageous.
4. Animals are wild.
5. Some music is not beautiful.
6. Not every lion is tame.

7. All sports are contests.
8. Some books are nonfiction.
9. Some freshman studies logic.

10. Corruption is universal.
11. Every non-veteran is ineligible.

12. Each man dies.
13. All fruit is not sweet.
14. Any book is interesting.
15. Not everyone who passes the test is acceptable.
16. No logician makes fallacies.

17. Man contemplates.
18. Some non-freshman takes logic.

19. Every instrument is useful.
20. Some non-veterans are not non-graduates.
lOGIC: THE ART OF DEFINING AND REASONING.
77

COPYRIGHT, 1952, BY PRENTICE-HALL, INC.

Chapter Eleven

OPPOSITION OF PROPOSITIONS

rT"'HE opposition of propositions is a property of the whole
proposition, as distinct from supposition, which is a prop­
erty of the parts of the proposition. We are now concerned with the
relation of one proposition, as a whole, to another proposition.
Opposition is defined as the affirmation and negation of the same
predicate in regard to the same subject. For example, the propositions
Every man is wise and No man is wise are opposed because the same
predicate wise in one proposition is affirmed of the same subject of
which it is denied in the other proposition. Every man is happy and
No man is wise are not in opposition because the predicates are differ­
ent.
Even when the same words are used as the subject and predicate of
propositions, we must be sure that the words have the same signification
and the same supposition. By “same signification’’ we mean that the
words must signify univocally and not equivocally. The two propo­
sitions Every pen is large and No pen is large are not in opposition
if the word “pen” signifies a writing instrument in the first proposition
and a small enclosure for animals in the second proposition.
By “same supposition” we mean that the words standing as the sub­
ject or predicate in the propositions must remain within the same genus
of supposition. For example, two propositions will not be in oppo­
sition if the subject of one is used in proper supposition and the subject
of the other is used in improper or metaphorical supposition. Thus,
we sometimes speak of human beings metaphorically as angels, and
hence might say Some human beings are angels. Such a proposition,
however, would not be in opposition to No human beings are angels
if we used “angels” properly in this proposition to stand for purely
spiritual creatures.

79

80

OPPOSITION OF PROPOSITIONS

THE DIVISION OF OPPOSITION

This division is based upon the division of the proposition into its
species—into affirmative and negative propositions.
1. Contradictory opposition

Contradictory opposition of propositions consists in removing an
affirmation in one proposition by a negation in the other. Contra­
dictory opposition is an opposition in truth and falsity; that is, contra­
dictory propositions cannot both be true at the same time, nor both be
false at the same time. For example, the affirmative proposition Every
man is wise is contradicted by the negative proposition Not every man
is wise, or Some man is not wise. Likewise, the negative proposition
No man is wise is contradicted by the affirmative proposition Some
man is wise.
Propositions with universal names as subjects are in contradictory
opposition when they differ both in quality (affirmative and negative)
and in quantity (universal and particular). Propositions with singular
names as subjects are in contradictory opposition when they differ in
quality even though no difference in quantity is possible. The propo­
sition John is handsome is contradicted by the proposition John is not
handsome.
2. Contrary opposition
Contrary opposition of propositions consists of a difference in quality
and an agreement in universal quantity. Contrary opposition is an
opposition in truth, but not in falsity. Hence, contrary propositions
cannot both be true, although they can both be false, at the same time.
The proposition Every man is wise is contrary to No man is wise.
Hence, if it is true that every man is wise, then it would have to be
false that no man is wise. On the other hand, if it is true that no man
is wise, then it would have to be false that every man is wise. How­
ever, contrary propositions may both be false, but this can be de­
termined only by referring to the matter of the propositions.

3. Sub-contrary opposition
Sub-contrary opposition of propositions consists of a difference in
quality and an agreement in particular quantity. Sub-contrary op­
position is an opposition in falsity, but not in truth. Hence, sub­
contrary propositions cannot both be false, although they can both be
true, at the same time.
The proposition Some man is wise is in sub-contrary opposition with
Some man is not wise. Hence, if it is false that some man is wise, then
it would have to be true that some man is not wise; or if it is false

*■■■

OPPOSITION OF PROPOSITIONS

81

■ SSS

££ S

EE

S B B F.

that some man is not wise, then it would have to be true that some
man is wise. However, sub-contrary propositions may both be true at
the same time, but this can be determined only by referring to the
matter of the propositions.
It is clear from the definition of the different kinds of opposition
that contradiction is the strongest or greatest kind of opposition of
propositions. In contradictory opposition, one proposition simply
destroys or denies the other, for the opposition of contradiction is a
complete opposition of truth and falsity, of affirmative and negative
and of universal and particular. Contrary opposition while having an
opposition of quality and an opposition of truth, nevertheless has agree­
ment in universal quantity and can also have agreement in falsity.
Sub-contrary opposition also has an opposition in quality, but it has
agreement in particular quantity and can have agreement in truth.
Sub-contrary opposition, however, departs from the definition of
opposition, which requires affirmation and negation of the same
predicate of the same subject. The subject of a particular affirmative
proposition may not stand for the same thing that the subject of a
particular negative proposition stands for. This is because the subject
of a particular proposition is not taken for somè determinate singular,
but indeterminately for any, and hence the two subjects of a particular
proposition may not stand for the same thing. For example, in Some
man is wise and Some man is not wise the “Some man” may not be the
same in both propositions. Opposition is thus verified less and less as
we proceed from contradictory to contrary to sub-contrary opposition.
In addition to these three kinds of opposition, we shall also consider
here the relation of propositions known as “subalternation.” Sub­
alternation of propositions is a relation in which two propositions agree
in quality but differ in quantity. Thus, the proposition Some man is
wise is subalternated to Every man is wise. Likewise, the proposition
Some man is not wise is subalternated to No man is wise. In sub­
alternation, if the universal proposition is true, the subalternated
proposition under it is true. Thus, if it is true that every man is wise,
then it would have to be true that some man is wise. However, if we
only know that the particular proposition is true, we cannot know that
the universal proposition has to be true. For example, if we know
it is true that some man is just, we cannot determine from this alone
that it is true that every man is just.
It must be emphasized, however, that the relation of subalternation
is not a relation of opposition. The opposition of propositions is
based upon the division of propositions into affirmative and negative.
In subalternation, there is no opposition of affirmation and negation,
for propositions in subalternation agree in quality, that is, they are
either both affirmative or both negative. Furthermore, they do not

82

OPPOSITION OF PROPOSITIONS

differ in truth or falsity, but are either both true or both false. Sub­
alternation of propositions, nevertheless, is treated with opposition in
order to complete a study of the relations between propositions. And
in subalternation as well as in opposition, the terms in the proposition
must retain the same signification and the same supposition; otherwise
the various relations of truth and falsity will not validly hold.
Let us now try to simplify and summarize this material on opposition
and subalternation. We shall do this by using the Square of Op­
position, a graphic device that makes the different relations of propo­
sitions concrete.

The letters A, E, I, O symbolize the different kinds of propositions.
The letter A stands for the universal affirmative, the letter E for the
universal negative, the letter I for the particular affirmative, and the
letter O for the particular negative proposition.
The lines in the square represent the following relations. The
diagonal lines AO and El represent the contradictories. The line AE
represents the contraries. The line IO represents the sub-contraries.
The parallel lines Al and EO represent the relations of subalternation.
RULES FOR TRUTH AND FALSITY

The rules for truth and falsity on the Square of Opposition can be
summarized as follows. These rules follow from the definitions of the
kinds of opposition and from the definition of subalternation.
1. Contradictories
Contradictories cannot l^e true at the same time or false at the same
time. In contradictory propositions, whenever one proposition is true,

* The Square of Opposition is a device for seeing the relations between propo­
sitions that do not have a singular name as a subject.

OPPOSITION OF PROPOSITIONS

83

the other proposition is false; and whenever one proposition is false,
the other is true.

2. Contraries
Contraries cannot be true at the same time. In contrary proposi­
tions, whenever one proposition is true, the other is false. However,
when one proposition is false, the other may be true or may be false,
that is to say, the second proposition may be either. Since we cannot
tell from the formal relation of contrariety whether the second propo­
sition is true or false, we say that it is “unknown.” Hence, whenever
one proposition is false, the other is unknown.

3. Sub-contraries

Sub-contraries cannot be false at the same time. In sub-contrary
propositions, whenever one proposition is false, the other is true. How­
ever, when one proposition is true, the other may be true or may be
false. Hence, in sub-contrary relation of propositions, whenever one
proposition is true, the other is unknown.
4. Subalternates
Whenever the universal is true the particular is true, and whenever
the particular is false the universal is false. In the relation of sub­
alternation, whenever a universal affirmative proposition is true, the
particular affirmative proposition under it is true. Similarly, when­
ever the universal negative proposition is true, the particular negative
under it is true.
Likewise, whenever the particular affirmative proposition is false,
the universal affirmative above it is false. And whenever the par­
ticular negative proposition is false, the universal negative above it is
false.
However, if the particular affirmative proposition is true, the uni­
versal affirmative may be true or may be false, and hence is unknown;
and if the particular negative proposition is true, the universal negative
is unknown. Likewise, if the universal affirmative proposition is false,
the particular affirmative under it is unknown; and if the universal
negative proposition is false, the particular negative under it is un­
known.
THE FORMAL RELATIONS OF PROPOSITIONS

Opposition and subalternation are formal relations of propositions.
They are relations that abstract, in part, from the things signified.
For example, we can express the opposition of contradiction formally

84

OPPOSITION OF PROPOSITIONS

as Every A is B and Some A is not B. From the formal relation of
contradiction alone, we know that of the two propositions, one must
be true and the other must be false. We cannot tell, from the formal
relations alone, which of the propositions is the true one, but only that
if one is true, the other must be false.
Now a proposition is said to be “unknown” when its truth or falsity
cannot be determined by formal relations alone. However, in the
case of contradiction, no proposition is ever unknown, because con­
tradiction is a complete opposition in truth and falsity; that is, one
proposition is always true and the other always false. But in relations
of opposition apart from contradiction, a relation may arise in which
one of the propositions will not be necessarily true nor necessarily
false, and therefore will be called “unknown.” For example, in con­
trary opposition, if Every A is B is false, we cannot tell, by the formal
relation alone, whether No A is B is true or false, and hence we say
that it is “unknown.”
However, when we put propositions into words, we reveal fully
the matter. We can then determine the truth or falsity of the propo­
sitions on the part of matter as well as on the part of form. For
example, we can state a contradictory opposition in words by opposing
Every man is just to Some man is not just. When the propositions
are put into words, the formal relation of contradiction still holds
so that we can state that if one is true, the other is false. But the
matter of the propositions, as revealed in the words, tells us that in
this case the proposition Some man is not just is actually the true one,
and that Every man is just is false.
Nevertheless, whether the propositions are stated with letters or with
words, we shall, when using the Square of Opposition, consider only
the form of the proposition, and only the formal relations of truth
and falsity.
QUESTIONS---- CHAPTER ELEVEN

1. What does it mean to say that opposition is a property of the whole
proposition?
2. Define opposition.
3. Explain how the terms of propositions that are opposed must have the
same signification and the same supposition.
4. What is the basis for the division of the opposition of propositions?
5. Name the kinds of opposition and give examples of each.
6. Why is contradiction the greatest kind of opposition?
7. Why is subalternation not opposition?
8. What do the symbols *A E, I, O stand for?
9. State the rules for truth and falsity in opposition.
10. What do we mean when we say that a proposition is “unknown”?
11. What do we mean by formal relations of opposition?
12. What does the matter of a proposition add to the formal relations?

i

EXERCISE I—CHAPTER ELEVEN

Put True, False, or Unknown in the following spaces.
1. If A is true, then O is-----------------------

2. If A is false, then I is_______ ._______
3. If E is true, then A is

4. If O is false, then A is

5. If I is false, then O is
6. If O is true, then E is
7. If A is false, then E is

8. If O and E are both false, then I is----------------------9. If A is false and if O is true, then I is

10. If O is unknown and if I is true, then E is -------------------- --11. If I is true and if A is false, then E is---------- -----------12. If O is false, then E is____________ -, .. and I is

and

A is-----------------------

logic: the art of defining and reasoning,

85

copyright,

1952,

by prentice-hall, inc.

EXERCISE II—CHAPTER ELEVEN
Using the rules of the Square of Opposition, put True, False, or Unknown
in the following spaces.
1. If it is true that some animals are not tame, then

(a) Some animals are tame is

(b) All animals are tame is
2. If it is false that some games are harmful, then

(a) Every game is harmful is
(b) No game is harmful is
3. If it is true that no artist is rich, then
(a) Some artist is not rich is
(b) Some artist is rich is

4. If it is false that all men are courteous, then

(a) Not all men are courteous is_______________
(b) Some men are courteous is

(c) Every man is not courteous is
(d) No men are courteous is
(e) Some men are not courteous is-----------------------

86

EXERCISE III—CHAPTER ELEVEN

Determine whether the following propositions are validly or invalidly re­
lated according to the Square of Opposition.
1. If it is true that No politicians are bookkeep­
ers, then it is false that Some politicians are
bookkeepers.
2. If it is true that Some drama is not interesting,
then it is false that Some drama is interesting.

3. If it is true that Some apples are sweet, then
it is true that Some apples are not sweet.
4. If it is false that No Americans are redblooded, then it is true that Some Americans
are not red-blooded.

_______ ____

5. If it is false that Some food is not expensive,
then it is false that No food is expensive.

----------------------- .— ____

6. Suppose it is true that All bats are blind.
Then it would have to be false that No bats
are blind and false that Some bats are not
blind.

.______ _

7. If it is true that Some teachers are scholars,
then it is false that No teachers are scholars
and true that All teachers are scholars.

----------------------------------

8. If it is true that No logicians are bachelors
and if it is false that All logicians are bach­
elors, then it is true that Some logicians are
not bachelors.

-------------------------- --------

9. Let us suppose that I do not know whether
it is true or false that All logic texts are
stimulating. But let us suppose that I do
know it is true that Some logic texts are
stimulating. From this, then, I know that it is
false that No logic texts are stimulating. But
now I do know it is true that All logic texts
are stimulating.
10. If it is true that Not every proposition is false,
then it is false that Some propositions are true.

logic: the art of defining and reasoning,

87

copyright,

1952,

by prentice-hall, inc.

11. A sophomore claims that Some freshmen are
immature. He has to hold, then, that it is
also true that Some freshmen are not im­
mature as well as holding it is false that No
freshmen are immature.
12. If it is false that Some peanuts are not salty,
then it is false that No peanuts are salty, and
true that Some peaizuts are salty, and true that
All peanuts are salty and, finally, of course,
false that Not all peanuts are salty.
13. If it is true that No question is unimportant,
then it is false that Every question is unim­
portant and false that Some questions are un­
important.

14. If I am not sure it is false that No A is B,
but am sure it is false that Some A is not B, I
should be certain it is false that No A is B.
15. It has been said, truly, that Many brave hearts
are asleep in the deep. Hence it is true that
Some brave hearts are not asleep in the deep.

88

Chapter Twelve
OBVERSION OF PROPOSITIONS

■\X7E have seen, in the preceding chapter, how proposi’ ’ tions are put into opposition with each other. We
are now going to consider how opposed propositions can be made
equivalent in meaning by altering the terms of the propositions.
This process or relation is known as “obversion” and, like op­
position, is a property of the whole proposition. Obversion of
propositions consists of making two opposed propositions equivalent
in meaning or signification. This equivalence of opposed propo­
sitions is accomplished by adding a negative particle to the predicate
of one of the propositions. For example, Some men are veterans and
Some men are not veterans are opposed propositions. We relate
these two propositions in obversion by adding a negative particle
to the predicate of the second proposition, thus altering the second
proposition to Some men are not non-veterans. The propositions
Some men are veterans and Some men are not non-veterans remain
opposed in so far as one is affirmative and the other is negative,
but they become equivalent in meaning by the addition of the
negative particle to the predicate of the second proposition.
Let us notice the difference between formal opposition of propo­
sitions, treated in the last chapter, and obversion of propositions,
which we are now considering. Opposition of propositions changes
the quality of the proposition (from affirmative to negative or
from negative to affirmative) but keeps the same subject and the
same predicate in both propositions. Obversion of propositions
also changes the quality of the propositions but, in addition, alters
the predicate of the second proposition by adding a negative particle.
Obversion of propositions, therefore, is not strict or formal opposition,
since the changing of the predicate violates one of the conditions of
opposition.
We shall consider only the obversion or equivalence of contrary
89

90

OBVERSION OF PROPOSITIONS

propositions and of sub-contrary propositions. The obversion of
contradictory propositions and of propositions in subalternation is
not readily applicable in English, nor is it of any practical use.
THE RULES OF OBVERSION

1. Change the quality of the proposition

A change of the quality of propositions is a change from an affirma­
tive to a negative proposition, or from a negative to an affirmative
proposition. Thus, if we have an affirmative copula in a propo­
sition, then its obverted form must have a negative copula. If, how­
ever, we start with a proposition having a negative copula, then its
obverted form must have an affirmative copula.
2. Negate the predicate
If a proposition has a positive term as the predicate, then its ob­
verted form must have a negative particle before the same predicate.
If, however, a proposition has a negative predicate, then its obverted
form must have a double negation before the same predicate. This
double negation has the effect of making the predicate of the ob­
verted proposition positive again.
Let us take some examples of obversion of propositions and see
how the rules apply. We shall take, first, a proposition using only
letters or symbols, for example, Every A is B. To obtain the obversion
of this proposition, we simply apply the two rules. By changing the
quality of the proposition, we go from an affirmative to a negative
proposition. To negate the predicate, we add a negation to the
predicate of the proposition. Thus we get: No A is non-B. If we
change the letters of the propositions into words, we should have
the following as an example: Every voter is a citizen obverted to No
voter is a non-citizen.
In the second rule of obversion, it is important to remember that
the negative sign is applied to the predicate and not to the copula.
It is also important, in this connection, to distinguish between the
negative sign non and the negative sign not. The negative sign non
should always be used with a predicate or a subject of a proposition.
The negative sign not should always be used with the copula.
It might seem desirable, sometimes, to use with the predicate such
negative prefixes as in and un. For example, we might write an
obversion as follows: Every student is industrious obverts to No
student is unindustrious. The danger in this procedure is that some­
times such prefixes do not merely signify negations, but have a

OBVERSION OF PROPOSITIONS

91

certain intensive effect, which changes the original meaning of the
predicate. For example, the word unpatriotic does not signify nonpatriotic but a definite state contrary to that of patriotism. It is
always safe and advisable, therefore, to use the negative particle non
in making obversions.
It is well to recall that the correct form of the universal negative
proposition is No A is B, and not Every A is not B, nor Not all A is B.
The last two expressions signify particular negative propositions.
Hence, the following obversion would not be valid (because of the
change in quantity): Every student is patriotic to Not every student is
non-patriotic.
If the original proposition is a universal negative proposition, for
example, No A is B, we apply the two rules in the following way.
We change the quality of the proposition from negative to affirmative.
We negate the predicate of the affirmative proposition. Thus No
A is B is obverted to Every A is non-B, or No child is a voter to Every
child is a non-voter.
In particular propositions, we apply the two rules in the same way.
We obvert Some A is B to Some A is not non-B. If the original
proposition is negative, we obvert it to an affirmative proposition with
a negated predicate, for instance, Some A is not B to Some A is non-B,
or Some students are not patriotic to Some students are non-patriotic.
It is possible to start with a proposition that already has a negated
predicate, for example, Some students are non-veterans. The first
rule is applied, as before, by changing the proposition to a negative
one. The second rule calls for negating the predicate. We could
simply put another negative sign before the negated predicate, but
since a negative sign destroys whatever follows it, one negative sign
destroys the other, thus making the predicate positive. Hence, Some
students are non-veterans is obverted to Some students are not vet­
erans.
RULES OF TRUTH AND FALSITY IN OBVERSION

Since the relation of obversion makes the obverted proposition equiva­
lent in meaning to the original proposition, the rules of truth and
falsity are reduced to two. If the original proposition is true, the
obverted proposition is true. If the original proposition is false,
the obverted proposition is false.
We might add a final remark on the usefulness of obversion. As
a logical relation, obversion is not very useful, since it merely re­
states the meaning of one proposition in another form. However,
people often use obverted expressions, and since the meaning of an

92

OBVERSION OF PROPOSITIONS

obverted expression is not always clear, the process of obversion can
be used to change the obverted expression back to its direct form.
Thus, the obverted proposition Some politicians are not non-partisan
can be changed by the process of obversion back to the direct form
of Some politicians are partisan.
Furthermore, some persons think they can avoid being held to
the truth of a proposition by putting it in the obverted form. For
example, they might state that no politician is non-partisan without
wanting to state that every politician is partisan. Nevertheless, as
the rule of truth in obversion shows, the second proposition will have
to be held as true if the first one is. In other words, in asserting
that no politician is non-partisan they have committed themselves to
the position that every politician is partisan.
There is an additional practical point to be made about obversion.
Negative prefixes in propositions are frequently a source of confusion
and misunderstanding as, for example, in Some students are not
non-veterans. By the process of obversion an excess of negative
signs can be lessened or even removed altogether. After we have
examined conversion in the next chapter, we shall be able to remove
all negative signs in a proposition by a combination of obversion and
conversion.
QUESTIONS---- CHAPTER TWELVE

1.
2.
3.
4.
5.

Explain the meaning of “obversion.”
How does obversion differ from opposition?
What are the rules of obversion? Illustrate with examples.
What are the rules of truth and falsity in obversion?
What practical applications has obversion?

Illiiîiîiiiîiii

EXERCISE I—CHAPTER TWELVE

Obvert the following propositions.
1. Some A is B. ______________ ._______________

2. Every A is B.______________________ ________
3. No A is non-B. _ _____________________________
4. Some A is non-B. _______________________________
5. Some A is not B. _ __________________________ _ _
6. No A is B.

-__ _________________________

7. Every non-A is non-B. ________________________ ______
8. Every A is non-B. __ ______________________ _ ___
9. No non-A is non-B. _________________________ _____

10.

Some non-A is B._____________________________

EXERCISE II—CHAPTER TWELVE

Restate in words each of the propositions in Exercise I. Then obvert each
of the propositions.

logic: the art of defining and reasoning,

93

copyright,

1952,

by prentice-hall, inc.

EXERCISE 111—CHAPTER TWELVE

Obvert the following propositions.
1. No soldiers are cowards.

Chapter Thirteen
2. Some trees are non-oaks.

CONVERSION OF PROPOSITIONS
3. Some non-freshmen are not veterans.

4. Every Christian is non-pagan.

5. Every non-voter is non-patriotic.

6. Some politicians are not non-statesmen.

7. Some man is artistic.

8. Some fruit is not sweet.

9. All books are interesting.

10. No non-logician is eligible.

94

■I
■I
■I
■1
■I
■I
n
n

CONVERSION of propositions consists of exchanging the
'^'subject and predicate while retaining the quality and truth.
Conversion, then, is a reversing of the extremes of a proposition. For
example, in the proposition No man is a dog, we exchange the subject
and the predicate of the proposition, and obtain No dog is a man.
The conversion of propositions is the third property that follows
upon the whole proposition. We have already treated the first two
properties-—opposition and obversion—in the two preceding chapters,
and have distinguished them from each other. Let us now distinguish
carefully between conversion and obversion.
In obversion, the obverted proposition is equivalent in meaning even
though it is different in quality. In conversion, the subject and the
predicate are interchanged, with the proposition always remaining the
same in quality. Hence, when we convert an affirmative proposition,
it will remain affirmative in the converted form. When we convert
a negative proposition, it will remain negative in the converted form.
THE KINDS OF CONVERSION

1. Simple conversion

Simple conversion is the exchange of subject and predicate in a
proposition without any change in quantity. Thus, we convert a
universal negative proposition simply and get the universal negative
in the converted form. For example, No stone is a rose converts simply
to No rose is a stone.

95

96

CONVERSION OF PROPOSITIONS

2. Accidental conversion
Accidental conversion is the exchange of subject and predicate in a
proposition with a change in quantity. We convert a universal affirma­
tive proposition accidentally, as in the conversion of Every rose is a
flower to Some flower is a rose. It might seem as though we could
convert a universal affirmative proposition simply, for example, Every
rose is a flower to Every flower is a rose. There are two reasons why
we cannot convert the universal affirmative proposition simply.
One reason is that the converted proposition is false, and obtain­
ing a false proposition in conversion violates the definition of con­
version. The definition states that the subject and predicate of a
proposition are exchanged while retaining truth.
The second and more important reason why we cannot convert the
universal affirmative proposition simply is that a fallacy is committed.
In Every rose is a flower, the predicate flower is undistributed, be­
cause it is the predicate of an affirmative proposition. In the simple
conversion of that proposition, the word flower becomes distributed,
because it is now the subject of the universal proposition Every flower
is a rose. We can never go from the undistributed to the distributed,
that is, from the particular to the universal. Hence, the simple
conversion of the universal affirmative proposition is always formally
invalid.
Let us now summarize these points on conversion by stating the
rules for the valid conversion of propositions.
RULES OF CONVERSION

1. Every universal negative proposition converts simply
Since the subject and the predicate of the universal negative propo­
sition have the same distribution (the terms are both distributed),
they can be exchanged simply. Hence, the universal negative propo­
sition converts simply. No dog is a horse converts to No horse is a dog.

2. Every particular affirmative proposition converts simply
Since the subject and the predicate of the particular affirmative
proposition have the same distribution (the terms are both undis­
tributed), they can be exchanged simply. Hence, the particular affirma­
tive proposition converts simply. Some diplomats are statesmen con­
verts to Some statesmen are diplomats.

CONVERSION OF PROPOSITIONS

97

3. Every universal affirmative proposition converts accidentally

In the universal affirmative proposition, the subject and the predicate
do not have the same distribution, for the subject of a universal propo­
sition is distributed, while the predicate of an affirmative proposition is
undistributed. Hence, these terms cannot be exchanged simply.
However, they can be exchanged accidentally, as we have seen, by
changing the quantity of the proposition. In changing the proposition
from universal to particular, we keep the predicate undistributed by
making it the subject of a particular proposition. Thus, the universal
affirmative proposition converts accidentally; for example, Every rose
is a flower converts to Some flower is a rose.
We should notice that if a proposition predicates a definition or a
property, as in Every man is grammatical, it could be converted simply
in virtue of its matter, but not in virtue of its form. However, we
are considering here conversion on the part of the form of the propo­
sition. Formally considered, the universal affirmative proposition
never converts simply.
4. The particular negative proposition never converts validly

The subject and the predicate of the particular negative proposition
have different distribution. The subject is undistributed and the
predicate is distributed. Consequently, if we exchanged the subject
and the predicate of a particular negative proposition simply, we
should again have an undistributed term becoming distributed. Thus,
if we converted Some animal is not man ta Some man is not animal, the
term animal, which is undistributed in the first proposition, would be
distributed in the second proposition.
Unlike the similar case of the universal affirmative proposition, we
cannot eliminate this difficulty by accidental conversion—by a change
in quantity. If we try to change the quantity, we can only change
it to the universal negative, for we must keep the same quality in
conversion. Thus, we could try to convert Some animal is not man
to No man is animal. But again, the term animal, which is undis­
tributed in the original proposition, would be distributed in the con­
verted proposition.
There is no way, consequently, to prevent the illicit transition from
undistributed to distributed in the conversion of the particular negative
proposition. For this reason, the particular negative proposition never
converts validly. Sometimes, in virtue of the matter, the conversion of
a particular negative proposition results in a true proposition, as in
the conversion of Some men are not tall to Some tall (beings) are not

98

CONVERSION OF PROPOSITIONS

men. However, the conversion is always formally invalid because of
the illicit transition from undistributed to distributed.
RULE OF TRUTH IN CONVERSION

There is only one rule concerning truth and falsity in conversion of
propositions: If the original proposition is true, the converted propo­
sition will be true. No rule can be stated for the conversion of false
propositions, because their conversion does not necessarily and immedi­
ately result in false propositions. For example, the conversion of a
false universal affirmative proposition sometimes results in a true propo­
sition, and at other times in a false one. The conversion of the false
proposition All flowers are yellow is the true proposition Some yellow
things are flowers. But the conversion of the false proposition All
flowers are trees is the false proposition Some trees are flowers.
It is worth noticing, however, that false universal negative and false
particular affirmative propositions are always false in their converted
forms. This happens, not directly by conversion, but by a combination
of opposition and conversion. For example, Some horses are dogs
is a false proposition. But we know that its contradictory, No
horses are dogs, is true. We can now convert this proposition to
No dogs are horses, which is also true. We know, further, that the
contradictory of this last true proposition is the false proposition Some
dogs are horses, which is the converted form of the original false
proposition Some horses are dogs. By this combination of opposition
and conversion, therefore, false universal negative and false particular
affirmative propositions are shown to be false in their converted form.
The principal use of conversion is found in the study of the
syllogism. As we shall see, in the chapter on the reduction of syllogisms
to the first figure, conversion is used there to change some less evident
forms of the syllogism to more evident forms.
We can also use conversion, combined with obversion, to remove
negative signs and prefixes from propositions so as to make them clearer
in meaning and in structure. For example, consider a proposition in
such complicated structure as Every non-veteran is a non-student. It is
difficult to tell just what this proposition is asserting. However, we
can obvert it to No non-veteran is a student. Then we can convert
it to No student is a non-veteran. To get rid of the last negative sign,
we can obvert the last proposition to Every student is a veteran. Every
student is a veteran is simple and clear in meaning, compared with
Every non-veteran is a non-student.
There is a final, practical use of conversion. A knowledge of valid
conversion helps us eliminate the frequent tendency we have of em­

CONVERSION OF PROPOSITIONS

99

ploying invalidly converted propositions. We easily fall into the
error of supposing that the universal affirmative proposition converts
simply. For example, if someone thinks it is true that every intelligent
person has a high forehead, he is likely to think it is also true that
every person with a high forehead is intelligent. However, we know,
through the rules of conversion, that the universal affirmative propo­
sition converts only accidentally.
QUESTIONS---- CHAPTER THIRTEEN

1.
2.
3.
4.
5.
6.
7.
8.

What does the conversion of propositions mean?
How does conversion differ from obversion?
How does conversion differ from opposition?
What are the kinds of conversion?
Why can we not convert the universal affirmative proposition simply?
Why can we never convert the particular negative proposition validly?
What are the rules of conversion? Illustrate each rule.
What are the uses of conversion?

EXERCISE I—CHAPTER THIRTEEN
Convert the following propositions.
1. Every A is B. ______________________________ .

iii■

2. Some A is B.______________________________ _

3. No A is B. ______________________________
4. Some A is non-B. ______________________________
5. Every non-A is non-B. ______________________________

6. No non-A is B. ______________________________

7. Every A is non-B. ______________________________

i ■ ■ ■ ■ iIS S S l

8. Some non-A is B. ______________________________

EXERCISE II—CHAPTER THIRTEEN

Restate in words each of the propositions in Exercise I. Then convert
each of them.

logic: the art of defining and reasoning,

copyright,

1952,

by prentice-hall, inc.

101

Mt. Angel Abbey Library
**
IlAnarli/

r»
*iOt
«
*

07^73

EXERCISE III—CHAPTER THIRTEEN

Convert the following propositions.
1. Some students are intelligent.

2.

No square is a circle.

3.

Every oak is a tree.

4.

Some non-seniors are ineligible.

5.

All pagans are non-Christians.

6.

James hit John.

7.

All voters are citizens.

8.

Some trees have leaves.

9.

No non-alien is a citizen.

10.

No supporter of democracy believes in the tyranny of totalitarian govern­
ment.

102

ffiS E E E S S E E E E E E E E l

EXERCISE IV— CHAPTER THIRTEEN

The following exercise is intended only for those who may wish to ex­
amine opposition, obversion, and conversion further. They are used sepa­
rately or combined within the same statement. This exercise may help
students to recognize these different relations and detect whether they are
validly made. It may also assist students to acquire facility in reading pro­
positions quickly and accurately.
The statements in the exercise should be worked out as follows. De­
termine first what types of relation (opposition, obversion, conversion, or
some combination) are in the statement. Then determine whether the rules
of truth and falsity are followed. The whole statement is valid only if each
proposition (except those propositions preceded by if) follows validly from
any preceding proposition.
1. If it is true that Some statesmen are not
politicians, then it is true that Some politicians
are not statesmen.

----------------------------------

2. If it is true that No dogs are cats, then it is
true that Some dogs are not cats, and false that
Some dogs are cats, and false that All dogs are
cats, and false that No dogs are non-cats.

3. If it is true that Some novels are not interest­
ing and if it is true that Some novels are in­
teresting, then it must be false that All novels
are interesting.
----------------------------------

4. If Every A is non-B is true, then Some A is
non-B is true, and Some non-B is A is true, and
No non-B is A is false, and some Some non-B is
not A is false.

----------------------------------

5. If you hold it is true that Some agreements
are contracts, then you have to hold it is false
that All agreements are contracts.

----------------------------------

6. If it is true that All lions are animals, then it
is true that Some lions are animals, and false
that No lions are animals, and false that All
lions are non-animals.

----------------------------------

7. You claim that you do not know whether it
is true that All that glitters is not gold. But
you say you know it is false that All that
glitters is gold. Then you do know that it is
true that All that glitters is not gold.

logic: the art of defining and reasoning,

103

copyright,

1952,

by prentice-hall, inc.

8. No dogs are allowed. Hence, Non-dogs are
allowed. Hence, Cats are allowed.

9. If it is false that Some students are honest,
then it must be true that Some students are
not honest.
10. If I know it is true that Some freshmen are
intelligent students, then it is false that No
intelligent students are freshmen, and false
that All freshmen are not intelligent students.
11. If Some A is non-B is false, then Some A is not
B is false, and No A is B is false, and Every
A is non-B is false, and Every A is B is true, and
Some B is A is true, and Some B is not A is
true.

12. If I know that it is true that No non-veteran
is an alien, then I know that it is true that
Every non-veteran is a non-alien, but I do not
know whether it is true that Some non-alien
is a veteran.

13. Paul, a promising student in logic, declares
that it is false that Some flowers are trees. He
also declares that there is no way, in which he
can determine the falsity of the proposition
No trees are flowers.
14. Henry, an unpromising student in logic, made
up the following statement: If it is true that
No gnat is a bat, then it is true that No bat
is a gnat, and true that Every bat is a non-gnat,
and true that Some bat is a non-gnat, and
true that Some bat is not a gnat, and true that
Some gnat is not a bat, and false that Some
non-bat is not a non-gnat.
15. Take the
Some eggs
contradict
tradict it.

following proposition as false:
are doughnuts. Obvert it. Then
it. Then convert it. Then con­
Then obvert it. You now have

16. Take the following proposition as false:
Some ravens are ducks. Can you, by valid
relations of opposition, obversion, or con­
version, arrive at No non-ducks are ravens
as false? _ __________ _

104

Chapter Fourteen
THE COMPOUND PROPOSITION

TN the divisions of the proposition in Chapter Nine, we first
■'■divided the proposition, according to unity
*,
into categorical
and compound. We shall now investigate the compound proposition
further and specify its kinds.
As we have already seen, a compound proposition is one by con­
junction, because it signifies a complex composition in the intellect.
The compound proposition, accordingly, has a connective as its copula,
uniting categorical propositions as parts of the compound proposition.
The proposition If horses are animals, then horses have sensation is
a compound proposition; the connectives if . . . then serve to unite
the categorical propositions “horses are animals” and “horses have
sensation.”
The compound proposition is divided, first, into explicitly and im­
plicitly compound propositions. An explicitly compound proposition
is one whose complex composition is fully revealed in the expression
of the proposition, as in the example just given. An implicitly com­
pound proposition is one that appears to be a categorical proposition
but is actually a disguised compound proposition, capable of being re­
solved into two or more propositions. Implicitly compound propo­
sitions are sometimes called “exponibles,” that is, propositions that
can be exposed. For example, the proposition God alone is eternal
appears to be a categorical proposition. In reality, the proposition is
implicitly compound, because it signifies a complex composition
in the intellect. It can be resolved into two propositions, God
is eternal, and No other is eternal. The word “alone” is the key word.
It signifies the implicitly complex composition of the proposition.
All implicitly compound propositions will have some key word signify­
ing the complex composition.

105

106

THE COMPOUND PROPOSITION

EXPLICITLY COMPOUND PROPOSITIONS

1. The conditional proposition
A conditional proposition is a compound proposition in which two
or more categorical propositions are joined by the connectives if . . .
then. Sometimes only the if is stated, with then presupposed. For
example, If a stone is a body, it has weight is a conditional propo­
sition. The first part of the conditional proposition (the if part) is
called the “antecedent.” The last part of the conditional proposition
(the then part) is called the “consequent.” The relation of the two
parts of the conditional proposition is called the “sequence.”
The truth of a conditional proposition requires that the sequence
be good, that is, valid. If the sequence is bad or invalid, the con­
ditional proposition is false. Hence, in a true conditional propositions
the second proposition must necessarily follow from the first. If the
second proposition does not have a necessary relation with the first,
then the conditional proposition is not true.
We might recall that we have been using the conditional proposition
in the Square of Opposition. We said, for example, If A is true, then 1
is true. Now this is a true conditional proposition. If we had said
If I is true, then O is true, this would have been a false conditional
proposition, because the second proposition does not follow necessarily
from the first.
Consequently, in the conditional proposition, it does not matter
whether the categorical propositions composing it are true or false.
All that matters is that the consequent, the second part of the propo­
sition, follow necessarily from the antecedent, the first part of the
proposition. Hence, the following conditional proposition, If man is
a dog, then man barks is a true conditional proposition even though
the two categorical propositions composing it are false.

2. Copulative proposition
A copulative proposition is a compound proposition in which two or
more categorical propositions are joined by a connective such as and.
Thus, Peter is a doctor and Paul is a lawyer is a copulative proposi­
tion, as is also the shortened form, Peter and Paul are students. How­
ever, the proposition Peter and Paul are cousins is not a copulative
proposition, but a categorical proposition, for the supposition of the
predicate in this proposition requires that Peter and Paul together
form the subject.
For a copulative proposition to be true, all the categorical propo­
sitions composing it must be true. If any one of the composing cate-

107

THE COMPOUND PROPOSITION

gorical propositions is false, then the whole copulative proposition is
false. Thus, The wise conserve and the foolish dissipate is a true
copulative proposition because each categorical proposition is true.
If one or both of the categorical propositions are false, the copulative
proposition is false, as in Man is an animal and man has wings.
The copulative proposition is only a material connection of cate­
gorical propositions. It presents no formal relation of propositions,
such as the conditional proposition. Its value depends solely upon
the truth of its joined parts. The usual true-false test employs the
copulative type of proposition, and hence the rule of truth for the
copulative proposition (A statement is not true unless all its parts are
true.) is followed in such a test.
3. The disjunctive proposition

A disjunctive proposition is a compound proposition in which cate­
gorical propositions are joined by the connectives either ... or.
Sometimes or alone is used, with either presupposed. Thus, Either a
student passes a course or he does not pass a course is a disjunctive
proposition. The window is open or shut is also a disjunctive propo­
sition.
A strict or proper disjunctive proposition asserts that one and only
one part of the proposition can be true, as in the examples given. A
loose or improper disjunctive proposition asserts that one part of the
proposition must be true whether the other parts are true or not, as
in James or John or Henry is coming.
IMPLICITLY COMPOUND PROPOSITIONS

(exPONIBLES)

1. The exclusive proposition

The exclusive proposition is one that contains such particles as
alone and only. These exclusive particles qualify either the subject
or the predicate of the proposition. We have already mentioned God
alone is eternal as an example. We can resolve this into God is
eternal and Nothing other than God is eternal, or simply, No other is
eternal. In resolving the exclusive proposition, there will always be
two explicit propositions: one will affirm that the predicate belongs to
the subject; the other will deny that the predicate belongs to any
other subject. This is all contained implicitly in the signification
of the particle only or alone.
Let us take another example: Only students are freshmen. This
will be resolved into Students are freshmen and None other than stu­
dents are freshmen. We can, however, state this resolution more

108

THE COMPOUND PROPOSITION

simply as follows: Students are freshmen and All freshmen are stu­
dents. We can do this because None other than students are freshmen
is equivalent to All freshmen are students by a combination of obversion and conversion. First of all, None other than students are
freshmen is the same as No non-students are freshmen. No non­
students are freshmen can be converted to No freshmen are non­
students, which is then obverted to All freshmen are students. Con­
sequently, while the exclusive proposition is resolved directly into an
affirmative and a negative proposition, it can also be resolved more
evidently into two affirmative propositions. It is more evident to re­
solve Only A is B into A is B and Every B is A than into A is B and
None other than A is B.

2. The exceptive proposition

The exceptive proposition is one that contains such particles as except
and unless. In the exceptive proposition, something contained under
the subject is excluded from the predicate. Thus, Every student
except John passed the examination is an exceptive proposition. We
can resolve this into: Every student other than John passed the test,
John is a student and John did not pass the test. If, however, the
proposition were Every student except one passed the test, it would be
resolved to: One student did not pass the test, and Every other student
passed the test. In this case, the word “one” could only refer to
“student,” and hence there is no third proposition.
3. The reduplicative proposition

The reduplicative proposition is one that contains such particles as
as, inasmuch as, as such, and so forth. These particles or connectives
qualify the subject; they modify or restrict the subject. Thus, Man
as an animal is mortal is reduplicative. It resolves into the following
propositions: Man is an animal, and As animal, he is mortal.
THE TRUTH OF EXPONIBLES

The rule for the truth of implicitly compound propositions is the
same as the rule for the truth of copulative propositions, since they
are resolved into copulative propositions. Hence, the implicitly com­
pound proposition is true only if every exponible is true. It is im­
portant to be sure that all the propositions are resolved and true before
judging that the implicitly compound proposition itself is true.

THE COMPOUND PROPOSITION

109

QUESTIONS---- CHAPTER FOURTEEN

1. What kind of unity does a compound proposition have? Why?
2. What kind of copula does the compound proposition have?
3. What is the major division of compound propositions? Explain each
member of the division.
4. What is a conditional proposition?
5. When is a conditional proposition true or valid?
6. What do we mean by the “antecedent,” “consequent,” and “sequence” in
the conditional proposition?
7. What is a copulative proposition?
8. When is a copulative proposition true?
9. What is a disjunctive proposition?
10. Distinguish between a strict disjunctive proposition and a loose dis­
junctive proposition.
11. What is an exclusive proposition?
12. Justify the following process. Only A is B is resolved into (Some) A is B
and Every B is A.
13. What is an exceptive proposition? Illustrate with an example.
14. What is a reduplicative proposition? Illustrate with an example.
15. What is the rule of truth for exponible propositions?

Part Three
THE THIRD ACT OF THE INTELLECT;

REASONING

■I
■I
«I
■I
M
M

n
H

I

I

Chapter Fifteen

ARGUMENTATION

■I
■I
■I
■I
■I
■I
■I
■I

■I
Ml
■I

A S we start Part Three, it may be well to refer again to the
-¿^-order of logic and indicate what we are to consider in this
last part. As we saw in the Introduction, logic is the art that guides
us in coming to know the unknown from what is previously known.
An unknown object is either simple, as tree, man, or redness, or com­
plex, as Man is artistic. A simple object is known by the first act of
the intellect, the act of simple apprehension. The simple object is
most perfectly manifested in a definition. We have covered this in
Part One.
A complex object is made known by means of argumentation. Argu­
mentation requires two additional acts of the intellect: the act of
composition or division, and the act of reasoning. The act of com­
position or division is the second act of the intellect, and we have
treated this in Part Two of logic. Having considered the proposition,
its various kinds and properties, we can now proceed to the third act
of the intellect—reasoning. Reasoning is needed to manifest fully an
unknown complex object. We shall now treat reasoning and especially
the syllogism, which is the perfect type of argumentation.
An argumentation is a process of reasoning. In the act of reason­
ing, as distinct from the other acts of the intellect, we acquire knowl­
edge of a new truth by means of truths already known. Some truths
are obtained independently, some in subordination to others. We
obtain truths independently of each other by composition or division,
that is, by composing a predicate with a subject or by dividing a
predicate from a subject, as in the second act of the intellect.
Other truths are obtained from truths subordinated to each other.
In the reasoning process, the third act of the intellect, we arrive at
a new truth by relating and subordinating several truths. For example,
we can say Every animal is mortal and Every human being is an animal.
By relating these two truths or propositions to each other and by
113

114

ARGUMENTATION

subordinating the second proposition to the first, we arrive at a new
truth, Every human being is mortal. This subordination is according
to the universality of the propositions, not according to their greater
or lesser importance. Reasoning consists essentially in this move­
ment from one truth to another, that is, in discursive operation. We
call the third truth a “new” truth because we know it as true by means
of the two previously known truths.
An argumentation is defined as a composite expression in which, one
thing being given, another follows. In the example in the preceding
paragraph, the first two truths constitute something as given, and the
third truth follows from them. That which is given is called the
antecedent; that which follows is called the consequent.
In the example used, the first two truths constitute the antecedent
in such a way that one of the truths is subordinated to the other. The
subordinated truth is the second proposition, Every human being is an
animal. It is the subordinated proposition because it is lesser in
universality than the first proposition. Every animal is mortal is the
first proposition, to which the second is subordinated, because the first
is greater in universality. The third proposition, which follows from
the other two as a conclusion from them, is the consequent. The
consequent concludes the act of reasoning. The full argumentation,
in terms of antecedent and consequent, is the following:
Every
„ '
Every
Every

animal
is...
mortal.
,
. , II
human being is an animal.)
human being is mortal.

, ,
,
(antecedent)
'
'
(consequent)

We also speak of the act of reasoning as an act of inference. In­
ference is the act of passing from the antecedent to the consequent.
Hence we speak of inferring the consequent from the antecedent,
or the conclusion from premises.
An inference (or sequence) may be valid or invalid. A valid
inference occurs when the antecedent really infers the consequent,
that is, when there is a real connection and dependence of the con­
sequent upon the antecedent. An invalid inference occurs when
the antecedent only appears to infer the consequent, that is, when
there is no real connection and no dependence of the consequent upon
the antecedent. We shall examine later when an inference is valid
or invalid.
We can, however, state certain general principles of argumentation.
First, a false consequent cannot follow from a true antecedent. The
reason for this is that the consequent is contained implicitly within
the antecedent, and hence, if the antecedent is true, the consequent
inferred from it will have to be true. However, a true consequent

ARGUMENTATION

115

may follow from a false antecedent. This does not mean that a
false antecedent causes a true consequent precisely as the consequent
is true but, rather, that a true consequent can be accidentally con­
nected with a false antecedent. In other words, a false antecedent
can cause a consequent to follow, but cannot cause the consequent
to follow as true. For example, the antecedent Every flower is an
animal and Every dog is a flower—a false antecedent—causes the
consequent Every dog is an animal to follow, but does not cause
that consequent to follow as true, that is, the antecedent is not the
cause of the truth of the consequent.
There are two kinds of argumentation: deductive and inductive.
Deductive argumentation is the same as the syllogism. We have been
using a syllogism as an example of argumentation. It should be
emphasized that deductive argumentation, or the syllogism, proceeds
properly from the more universal to the less universal; the syllogism,
therefore, properly remains on the plane of universality. The ex­
ample we have been using makes this clear.
Every animal is mortal.
(more universal)
Every human being is an animal.
(less universal)
Therefore, every human being is mortal, (conclusion)

Inductive argumentation, which is the same as induction, proceeds
from singulars to the universal. Induction proves that a charac­
teristic belongs to a common subject by producing corresponding
singulars. For example, we argue from the fact that this man is
capable of speech, and another man is capable of speech, and so of
all individual men, to the universal Every man is capable of speech.
Let us now consider argumentation in detail. We shall treat
the syllogism at some length, because it is the perfect type of argu­
mentation. Induction, the second and less perfect type of argu­
mentation, will be considered after the syllogism.
QUESTIONS---- CHAPTER FIFTEEN

1. State the order of the three parts of logic and the relation of the third
part to the other two.
2. How does the act of reasoning differ from the other acts of the intellect?
3. What do we mean by arriving at a “new” truth in the act of reasoning?
4. What is an argumentation?
5. Explain the antecedent and the consequent of an argumentation. Illus­
trate with an example.
6. What is meant by “inference”?
7. When is an inference valid? When is it invalid?
8. Why cannot a false consequent follow from a true antecedent?
9. How can a true consequent follow from a false antecedent?

116

ARGUMENTATION

10. What are the two kinds of argumentation? Define each kind.
11. Deduction has sometimes been defined as that which proceeds from the
universal to the singular. Criticize this definition.
12. Illustrate an inductive argumentation with an original example, and
show how it exemplifies the meaning of induction.

Chapter Sixteen
THE SYLLOGISM

qpHE syllogism, most simply defined, is a composite expression
in which, certain things being given, something else neces­
sarily follows. The syllogism is here defined as argumentation, for,
as we have mentioned, the syllogism is the perfect type of argu­
mentation. We can expand this definition in the following way:
The syllogism is an argumentation in which two propositions, as the
antecedent, unite two terms with a third or middle term, from which
a third proposition, as the consequent, is inferred necessarily.
Let us take the following as an example of a syllogism.
Every animal is a substance.
Every dog is an animal.
Therefore, every dog is a substance.

In the antecedent, the terms dog and substance are the two terms
that are united with the third, or middle, term animal. In the
consequent, the two terms dog and substance are united with each
other because of their union with the middle term.
THE MATTER OF THE SYLLOGISM

We distinguish between the proximate matter and the remote matter
of the syllogism.
The three propositions of the syllogism constitute the proximate
matter. The first two propositions of the syllogism are called the
“premises,” that is, propositions leading to a conclusion. The third
proposition of the syllogism is called the “conclusion.” The word
“therefore” introduces the conclusion, as a sign of the inference.
The premises are divided into major and minor. The major
premise has the predicate of the conclusion appearing in it. The
minor premise has the subject of the conclusion appearing in it.
117

118

THE SYLLOGISM

The reason why the premise which contains the predicate of the con­
clusion is called the major premise is that the predicate of the con­
clusion is taken as greater in universality than the subject. For this
reason the predicate of the conclusion, as it appears in the major
premise, is called the ‘“major extreme.” The other premise is called
the minor premise because it contains the subject of the conclusion,
which is taken as less universal than the predicate of the conclusion.
Hence the subject of the conclusion, as it appears in the minor
premise, is called the “minor extreme.” Now with this terminology
added, let us look again at the syllogism we have given.
(major extreme)

Every animal is a substance.
(minor extreme)

(minor premise)

Every dog is an animal.
(minor)

(major premise')

(major)

Therefore, every dog is a substance

(conclusion)

The syllogistic terms constitute the remote matter of the syllogism.
A syllogistic term is the subject or predicate into which the propo­
sition is resolved. The copula is not one of the syllogistic terms;
it serves, rather, to connect them.
The syllogistic terms, accordingly, are the major, the minor, and
the middle term. Each of these terms appears twice, and no more
than twice, in a syllogism. As we have seen, the term standing as
the predicate of the conclusion and appearing in the major premise
is the major term or extreme. The term standing as the subject of
the conclusion and appearing in the minor premise is the minor term.
The term found in each of the premises, uniting the major and minor
terms, is the middle term. The middle term has two functions.
(1) It is the link between the major and minor terms. (2) It is the
term that is middle in universality and in position in the premises.
Using the letters M to symbolize the middle term, S to symbolize
the subject of the conclusion, the minor term, and P to symbolize the
predicate of the conclusion, the major term, let us repeat the syllogism.
Every animal is a substance.
(M A P)
Every dog is an animal.
(S A M)
Therefore, every dog is a substance. (S A P)

The letter A stands for a universal affirmative proposition. Recall
that the major premise is defined as the one having the predicate
of the conclusion in it, and that the minor premise is defined as the
one having the subject of the conclusion in it. These definitions in­
dicate the order to look for in examining a syllogism. The logical
order of reasoning demands that the major premise should appear

119

THE SYLLOGISM

first in the syllogism, even though occasionally we find syllogisms in
which the minor premise is first. Hence, when analyzing the struc­
ture of a syllogism, the conclusion should be examined first in order
to determine the major term (the predicate of the conclusion) and
the minor term (the subject of the conclusion). From this, we can
determine which premise is the major premise and which the minor.
THE FORM OF THE SYLLOGISM

The form of the syllogism is constituted by mood and figure.
The mood of a syllogism is the disposition of the propositions of the
syllogism (1) according to quality—affirmative and negative—and
(2) according to quantity—universal and particular. For example,
if we have a syllogism composed of three universal affirmative proposi­
tions, the mood of the syllogism will be wholly universal affirmative,
or, as expressed by symbols, A-A-A.
It is evident that we can have a variety of moods in a syllogism,
depending upon the quality and the quantity of the propositions
making up the syllogism. Thus, we can have A-A-A as a mood, or
E-A-E, or I-A-I, or E-I-O, and so forth. As we shall see later, only
certain moods are valid in a syllogism. When giving the mood alone,
without adding the syllogistic terms, we shall always presuppose the
logical order of reasoning: major premise, minor premise, and con­
clusion. Hence, the mood E-I-O means that the major premise is a
universal negative proposition, the minor premise is a particular
affirmative, and the conclusion is a particular negative.
The figure of a syllogism is the disposition of terms in the syllogism.
Since the middle term appears twice in the premises, the figures of
the syllogism are derived from the various possible locations of the
middle term in relation to the major and minor terms.
For example, we can relate the three terms of a syllogism in such
a way that the major is affirmed or denied of the middle, and the
middle is affirmed or denied of the minor. In this way, we obtain
the first figure of the syllogism. Thus, let the major term be organism,
the middle term animal, and the minor term man. By affirming the
major term of the middle, we get:
Every animal is an organism.

By affirming the middle term of the minor, we get:
Every man is an animal.

From these two premises, we get as a conclusion:
Every man is an organism.

120

THE SYLLOGISM

In symbols, we get the following disposition of terms, which con­
stitutes the first figure:
M—P
S — M
S — P

Consequently, when the middle term stands as the subject of the
major premise and the predicate of the minor premise, we have the
first figure of the syllogism. The first figure of the syllogism is called
the perfect figure, because in this disposition of terms, the middle term is
middle in universality and has the middle position in the premises. As
subject of the major premise and predicate of the minor premise, the
middle term clearly stands between the major and minor extremes.
In this figure, the position of the major extreme is the position of
greatest universality and that of the minor the position of least
universality. The first figure is thus the figure most evident to us.
However, we can have other dispositions of terms in a syllogism.
The middle term can be affirmed or denied of both the major term
and the minor term. The middle term thus stands as the predicate
of both premises. Thus, let animal be the middle term, stone the
major term, and horse the minor term. By denying animal of stone
we get:
No stone is an animal.

By affirming animal of horse we get:
Every horse is an animal.

From these two premises, we get as a conclusion:
No horse is a stone.

In symbols, we get the following disposition of terms, which con­
stitutes the second, figure of the syllogism:
P—M
S — M
S — P

Notice, in this disposition of terms, that the predicate of the con­
clusion stands as the subject of the major premise. The appearance
of the symbol P in the subject position of the major premise (P — M) is
necessitated by the middle term’s being in the predicate position of
both premises. Hence, the predicate of the conclusion will have to

121

THE SYLLOGISM

appear in the subject position of the major premise. For this reason,
and particularly because the middle term does not occupy the middle
position, the second figure is less evident and less perfect than the
first figure.
We can have still another disposition of terms in a syllogism.
Both the major and minor terms can be affirmed or denied of the
middle term. The middle term thus stands as the subject of both
premises, and the major and the minor as the predicates. Thus, let
tree be the middle term, green the major term, and plant the minor
term. By affirming green of tree, we get:
Some tree is green.

By affirming plant of tree we get:
Every tree is a plant.

From these two premises, we get as a conclusion:
Some plant is green.

In symbols, we get the following disposition of terms, which con­
stitutes the third figure of the syllogism:
M—P
M — S
S — P

Notice, in this disposition of terms, that the subject of the con­
clusion stands as the predicate of the minor premise. The appearance
of the symbol S in the predicate position of the minor premise is
necessitated by the middle term’s being the subject of both premises.
Hence, the subject of the conclusion will have to appear in the
predicate position of the minor premise. Here, again, the middle term
does not occupy the middle position, and hence the third figure,
like the second figure, is less evident and less perfect than the first
figure.
It might seem as though there could be a fourth figure of the
syllogism, as though we could arrange the terms in such a way that
the middle term could be put in the predicate position of the major
premise and in the subject position of the minor premise, as follows:
P—M
M — S
S — P

122

THE SYLLOGISM

With words, we should have something like the following:
Every man is an animal.
Every animal is a substance.
Therefore, some substance is a man.

Galen, a logician of the second century a.d., is reputed to have
introduced such a disposition of terms into the syllogism and to have
called it the fourth figure. It is frequently given as a fourth figure
at the present time.
However, the so-called fourth figure is not a legitimate figure of
the syllogism. To appreciate this point, let us recall that a syllogism
should represent an order of judgment that proceeds from the more
universal to the less universal. The so-called fourth figure inverts
this order of judgment by having its major term less universal than
its minor term. Furthermore, the so-called fourth figure has its
middle term put in the position of the most universal extreme in the
major premise and in the position of the least universal extreme in
the minor premise. Putting the middle term in these positions is
contrary to the very notion of a middle term.
We can conclude, therefore, that the so-called fourth figure has no
meaning as a syllogistic figure. Let us also mention here that the
so-called fourth figure should not be confused with the first figure
when it concludes indirectly, which we shall consider at the end
of the next chapter.
QUESTIONS---- CHAPTER SIXTEEN

What is the definition of a syllogism?
Expand the definition of the syllogism, giving an original example.
What are the antecedent and the consequent of a syllogism?
What is the proximate matter of the syllogism?
Is every proposition a premise? Explain.
Distinguish between the major and the minor premise.
What is a major extreme? What is a minor extreme?
What is the remote matter of a syllogism?
What are the syllogistic terms?
How do we tell which is the major premise of a syllogism?
What is meant by the “mood” of the syllogism?
What is meant by the “figure” of the syllogism?
How are the terms of a syllogism arranged in the first figure of a
syllogism?
14. Construct a syllogism in the first figure, using the mood E-A-E, with X
as the middle term, Y as the minor term, and Z as the major term.
15. Why is the first figure called the “perfect” figure?
16. How are the terms of a syllogism arranged in the second figure of the
syllogism?

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.

the syllogism

123

17. Construct a syllogism in the second figure, using the mood E-I-O, with
X as the middle term, Y as the minor term, and Z as the major term.
18. How are the. terms of a syllogism arranged in the third figure?
19. Construct a syllogism in the third figure, using the mood I-A-I, with X
as the middle term, Y as the minor term, and Z as the major term.
20. Why is the so-called fourth figure not a legitimate syllogistic figure?

Chapter Seventeen
PRINCIPLES ARD RULES OF

THE SYLLOGISM

T N the preceding chapter, we considered the definition of the
■‘■syllogism, and its matter and form. We shall now examine
the syllogism from the standpoint of validity, that is, determine when
the various moods of the syllogism are valid in the different figures.
We want to know, in other words, when the form of syllogistic
reasoning is valid apart from any specific matter, not by excluding
all matter from the syllogism—for any syllogism must have its proxi­
mate and remote matter—but by analyzing the form of reasoning
in the syllogism. For example, we shall determine whether the
mood A-A-A is valid in all figures, or in none of the figures, or in
some of them, and so with the other moods, regardless, for the time
being, whether we are reasoning about God, man, or the elements.
First, however, we must note that the syllogism, as a kind of argu­
mentation, rests on the possibility of truly predicating one thing of
many; for unless we can use a universal in this way, we cannot have
a middle term, and without the middle term we cannot have a syl­
logism. How can we conclude that C is A unless there is some middle
term B, in which both C and A participate, that is to say, in which
one of these terms is predicated of B, and B, in turn, is predicated of the
other? In other words, why is A predicated of C (C is A)? Only
because A is predicated of B and B is predicated of C.
Let us try to see why this is so by stating the fundamental prin­
ciples upon which every syllogism rests.
THE FUNDAMENTAL PRINCIPLES OF THE SYLLOGISM

The first principle of the syllogism is: Two things that are the same
with a third thing are the same with each other. This principle is
125

* «av«i

126

PRINCIPLES AND RULES OF THE SYLLOGISM

The conclusion Every dog is mortal follows precisely because dog
and mortal are both united in the universal animal. The middle
term animal is the reason why the conclusion follows. In other
words, the identity or sameness of mortal with dog follows from the
identity or sameness the middle term has in relation to each of the
other two terms.
If a syllogism is proving a negative conclusion, the first principle
of the syllogism is stated negatively in the following way: Two things,
one of which is the same, the other not the same, with a third thing,
are different from each other. The following syllogism illustrates the
negative statement of the principle:

w

Every animal is mortal.
Every dog is an animal.
Therefore, every dog is mortal.

«

evident as soon as its terms are understood, and is immediately re­
ducible to the principle of contradiction: “A thing cannot both be
and not be at the same time and in the same respect.” We have al­
ready made use of this first principle in analyzing the syllogism,
but we shall now consider it explicitly to see its full application.
This principle applies to the syllogism in the following way. The
respect in which the subject and the predicate are united in the con­
clusion must be the same respect in which each is related to the third
(middle) term in the premises. By “respect” we mean that the
terms, especially the middle term, must be the same in reality and
in reason, that is, one and the same nature in reality must be represented
by the terms, and the terms must keep the same signification and
supposition. The following syllogism will exemplify this point.

The conclusion No oak is a mineral follows precisely because tree,
the middle term, is predicated of every oak, but is not united in any
way to mineral. Here, again, the middle term is the reason why the
conclusion follows, for no oak can be a mineral if no tree, which
includes oak, is a mineral.
This first principle is a common principle. The next two prin­
ciples are particular applications of it. They state the relation of a
universal to its inferiors, a relation every syllogism must presuppose
in order to be valid.
The second principle of the syllogism is stated in the following
way: Whatever is affirmed universally of a subject or a whole is

*

No tree is a mineral.
Every oak is a tree.
Therefore, no oak is a mineral.

PRINCIPLES AND RULES OF THE SYLLOGISM

127

affirmed of everything contained under that subject or whole. This
principle is traditionally known as the dictum de omni (that is,
“said of all”. Thus, whatever is affirmed universally of animal (for
example, substance) must be affirmed universally of everything con­
tained under animal. Hence, since Every animal is a substance, then
Every dog is a substance, for dog is contained under animal, of which
substance has been affirmed universally.
The third principle of the syllogism is stated in the following way:
Whatever is denied universally of a subject or a whole is denied of
everything contained under that subject or whole. This principle
is traditionally known as the dictum de nullo (that is, “said of none”).
Thus, whatever is denied universally of animal (for example, stone)
must be denied universally of everything contained under animal.
Hence, since No animal is a stone, then No dog is a stone, for dog
is contained under animal, of which stone has been denied universally.
The principles dictum de omni and dictum de nullo are verifiable
directly only in the first figure; this direct verification is another sigh
that the first figure of the syllogism is the perfect figure.
THE RULES OF THE SYLLOGISM

The rules of the syllogism are based upon the fundamental principles
of the syllogism. The rules help us to apply the fundamental prin­
ciples more easily; they help us to determine what moods are valid
in the three figures of the syllogism. Actually, if we were acute enough
logically, we could determine the valid moods of the syllogism from
the principles alone, for every deductive argument is valid in virtue
of the fundamental principles. The task, however, is simplified by
these rules of the syllogism, which we shall now consider.
1. A syllogism must have only three terms

As we have seen, the terms of a syllogism are the major, minor, and
middle. Since two terms are united with a middle term, and then
are united with each other, each term appears twice in a syllogism.
Each term, used twice, must have the same signification and the same
kind of supposition; otherwise there will be the fallacy of four terms.
No one would suppose that the following example is a valid
syllogism:
Every sophomore is a student.
Every freshman is immature.
Therefore, every freshman is a student.

128

PRINCIPLES AND RULES OF THE SYLLOGISM

In such an example, we obviously have the fallacy of four terms; in
fact, we do not have a middle term at all. But the following example
might seem to be a valid syllogism:
Animal is a genus.
Man is an animal.
Therefore, man is a genus.

But this example also has the fallacy of four terms, although it
appears to have only three terms. The supposition of the middle
term animal changes, for in the major premise, animal is used in
simple supposition, while in the minor premise it is used in personal
supposition. Hence this example really has four terms, and is there­
fore an invalid syllogism.
It is evident, also, from this first rule that the middle term can
never appear in the conclusion. Since each term can appear only
twice in a syllogism, and since the middle term must appear in both
premises (otherwise it would not be a middle term), the middle
term can never appear in the conclusion. This point is stated some­
times as a separate rule of the syllogism, but its connection with the
first rule is close enough to warrant its being included in it. The
following syllogism is invalid because of the presence of the middle
term in the conclusion:
Every plant is an organism.
No plant is a human being.
Therefore, no human being is a plant.

2. Any term distributed, in the conclusion must also be distributed in
the premises
As we have seen, the premises are the cause of the conclusion. As
an effect, the conclusion cannot have more than is contained in the
premises, which are its cause. If a term is distributed or universal
in the conclusion, but is undistributed or particular in the premise
then the effect is greater than its cause. This would be the fallacy of
having more in the conclusion than there is in the premise. The
following example violates the second rule of the syllogism:
Every senator is a citizen.
No governor is a senator.
Therefore, no governor is a citizen.

In this example, the term citizen in the conclusion is distributed,
since the predicate of every negative proposition is distributed. But
the term citizen is undistributed in the major premise, for the predicate

PRINCIPLES AND RULES OF THE SYLLOGISM

129

of every affirmative proposition is undistributed. Hence, the con­
clusion does not follow. (In other words, what is true of some citizens
is not necessarily true of every citizen.)
It is important, at this point, to review the rules for distribution of
terms in Chapter Ten. It is practically impossible to test the validity
of a syllogism without knowing the rules for distributed and undis­
tributed terms in a proposition.

3. The middle term must be distributed at least once
No relation can be established between the major and minor terms
in the conclusion unless the middle term is distributed at least once in
the premises. If the middle term were undistributed in both premises,
some of the inferiors under the middle term might refer to the major
term while others might refer to the minor term. In other words,
no sameness would be established between the middle term and the
other two terms in the premises, and hence no conclusion could follow.
The following is an example of a syllogism in which the middle term
is undistributed in both premises:
Every dog is an animal.
Every cat is an animal.
Therefore, every cat is a dog.

4. From two negative premises, no conclusion follows

This rule states such a direct application of the first principle of the
syllogism that it hardly needs to be formulated. If a syllogism has two
negative premises, then the premises explicitly deny any relation of
sameness between the middle term and the other two terms. Since,
then, the premises tell us nothing about the relation of the middle
term with the major and minor, we cannot tell whether or not the
major and minor are related to each other. Hence nothing can be
proved from two negative premises, as the following example shows:
No plant is an animal.
No man is a plant.
Therefore, no man is an animal.

It might seem, to some, as though two negative premises should yield
a negative conclusion. Suppose that someone were to argue: No tree
is a stone; no man is a tree; therefore, no man is a stone. Does not
this conclusion seem to follow as true? The conclusion, of course, is
true, but its truth is not caused by the premises. Although it is true
that no tree is a stone and true that no man is a tree, we have no

130

PRINCIPLES AND RULES OF THE SYLLOGISM

sameness esablished through the middle term by which we can prove
that no man is a stone. However, we could prove the truth of No
man is a stone by showing that something universally affirmed of man
is universally denied of stone, as in the following:
No stone is an animal, (animal is not predicated of stone,)
Every man is an animal, (but animal is predicated of man,)
Therefore, no man is a stone, (therefore, stone is not predicated of man)

5. The conclusion always follows the weaker part

A particular proposition is called weaker in relation to a universal
proposition. A negative proposition is called weaker in relation to an
affirmative proposition.
Hence, if one premise is universal, and the other particular, the
conclusion will always be particular. If one premise is affirmative,
and the other negative, the conclusion will always be negative. If one
premise is both particular and negative, the conclusion will always be
both particular and negative. The following example violates this
rule of the syllogism:
Some actor is handsome.
Every actor is a human being.
Therefore, every human being is handsome.

In practically all cases, a violation of this rule is also a violation of
another rule of the syllogism. Thus, in addition to violating the rule
on following the weaker part, the syllogism above has an undistributed
minor term in the premise and a distributed minor term in the con­
clusion (that is, human being is the predicate of an affirmative propo­
sition in the minor premise, and hence undistributed, and is the sub­
ject of a universal proposition in the conclusion, and hence dis­
tributed).
In addition to these five rules, sometimes the following rule is given:
From two particular premises, no conclusion follows. While this is
a handy rule to know for quick examination of a syllogism, it adds
nothing to the rules already given. Every time a syllogism has two
particular premises, either the middle term will be undistributed or
else a term will be distributed in the conclusion and undistributed in
the premises. Hence, this statement about two particular premises
should not be formulated into a separate rule.
In the light of the principles and rules of the syllogism, we can now
determine which moods are valid in the different figures of the syl­
logism It is evident that in any one figure there are sixteen possible
moods, or combinations of premises of different quality and quantity,
from which a conclusion might be drawn:

I

■
■
■

131

PRINCIPLES AND RULES OF THE SYLLOGISM

AAAA
AEIO

EEEE
AEIO

I I I I
AEIO

OOOO
AEIO

Let us recall that A is to stand for the universal affirmative proposi­
tion; E for the universal negative; I for the particular affirmative; and
O for the particular negative.
The letters given in the columns
above are to be read downwards, with the top letter standing for the
major premise, and the bottom letter for the minor. Thus, the second
column has A at the top and E at the bottom, and stands for a uni­
versal affirmative major premise and a universal negative minor premise.
A conclusion can be drawn validly from each of these combinations
of premises only if no rule, and consequently no fundamental prin­
ciple of the syllogism, is violated. Since there are three figures, with
sixteen possible moods in each figure, there is a total of forty-eight
possible moods. However, not all of these moods are valid. To de­
termine which of these are valid, we shall examine the sixteen moods
of the first figure, then the moods of the second figure, and, finally, the
moods of the third figure, testing them with the principles and rules of
the syllogism.
We shall determine which moods are valid in an exercise at the
end of this chapter. As an introduction to this exercise, let us try
working out a few of the moods now. Suppose that we want to de­
termine whether the mood E —- A is valid in the first figure. We know
that the first letter stands for the major premise, the second for the
minor premise, and that E stands for a universal negative proposition,
A for a universal affirmative proposition. We shall use S, P, and M
for the syllogistic terms. As we have seen, S stands for the subject
of the conclusion, the minor term; P stands for the predicate of the
conclusion, the major term; M stands for the middle term. Hence,
we have the following:
No M is P.
Every S is M.

(E)
(A)

The question now is: Can we validly get a conclusion from these two
premises?
No M is P.
(E)
Every S is M. (A)
Therefore ?
(?)

First, let us refer to the fundamental principles of the syllogism to see
whether a valid conclusion can be drawn from these premises. In the
major premise, we are saying No M is P. P is being separated from M
and from whatever is included under M. In the minor premise, we are

132

PRINCIPLES AND RULES OF THE SYLLOGISM

saying Every S is M. S is included under M. But P is separated from
M and from everything under M. Therefore, P is separated also from
S:
No M is P.
Every S is M.
Therefore, no S is P.

(P is separated from M.)
(S is included under M.)
(Therefore, P is separated from S.)

We conclude, then, that No S is P can be drawn as a valid con­
clusion from a universal negative major premise, and a universal
affirmative minor premise, in the first figure.
Showing the validity of a syllogism this way, through its funda­
mental principles, is the most intelligible way to make the reasoning
process evident. We can also test the validity of a syllogism through
the rules, which are applications of the principles. Let us now test
the same syllogism with the rules:
No M is P.
Every S is M.
Therefore ?

Notice first that the major premise is negative. The fifth rule
tells us that the conclusion always follows the weaker part. We
recall that the negative proposition is weaker than the affirmative.
We can, then, eliminate A and I propositions as possible conclusions,
since they are affirmative. This leaves E and O propositions as
possible conclusions. Since both premises are universal, and since
we always want to prove as much as^ possible, we should try an E
conclusion:
No M is P.
Every S is M.
Therefore, no S is P.

As long as we are using symbols instead of words (emphasizing the
form of the syllogism more than the matter), the first rule will never be
violated, for we can always presuppose the same signification and
supposition with the three symbols. We can eliminate, therefore,
any consideration of the first rule.
The second rule states that any term distributed in the conclusion
must also be distributed in the premises. The conclusion has two
distributed terms (the subject of a universal proposition is always
distributed, and the predicate of a negative proposition is always
distributed). Hence, we shall have to check both the major and minor
terms in the premises. The major term P is the predicate of a negative
major premise and is, therefore, distributed. The minor term S

PRINCIPLES AND RULES OF THE SYLLOGISM

133

is the subject of a universal minor premise and is therefore also
distributed. Hence, the second rule is observed.
The third rule states that the middle term must be distributed at
least once. In the major premise, the middle term is the subject of
a universal proposition, and hence is distributed. The third rule is
thus satisfied. We might go on to observe that the middle term
is undistributed in the minor premise, since the middle term stands
as the predicate of an affirmative proposition. But this does not
matter, since the rule only calls for the middle term to be dis­
tributed once, and the middle term is distributed in the major premise.
If the middle term were also distributed in the minor premise, the
rule would still be observed, since it only calls for the middle term
to be distributed at least once; the rule does not exclude the dis­
tribution of the middle term in both premises.
The fourth rule states that no conclusion follows from two nega­
tive premises. The syllogism we are considering has only one negative
premise, and hence the fourth rule is not violated.
The fifth rule states that the conclusion must follow the weaker
part. As we noted in the beginning, this syllogism has a negative
major premise, which is weaker than an affirmative premise. The
conclusion of this syllogism is negative and is therefore following the
weaker part. Hence, the fifth rule is satisfied.
Since all the rules of the syllogism are observed, we may conclude
that the following mood is valid in the first figure of the syllogism:
No M is P.
Every S is M.
Therefore, no S is P.

We might add that it is not necessary to consider an O conclusion
in this mood, for an E proposition, being universal, includes the O
proposition, which is particular. We should always draw the stronger
conclusion when we can.
Let us consider another mood, this time A-A in the second figure:
Every P is M.
Every S is M.
Therefore ?.

It is worth noticing at once that both the premises are affirmative.
When a syllogism has two affirmative premises, a negative conclusion
can never be validly obtained. Although no rule of the syllogism states
this point explicitly, we know it indirectly from the rule that the
conclusion always follows the weaker part. Since both premises are
affirmative, there is no negative, that is, weaker, part for the con-

134

PRINCIPLES AND RULES OF THE SYLLOGISM

elusion to follow. Therefore, the conclusion will retain the strength
of the premises—it will be affirmative. If we tried to draw a negative
conclusion from two affirmative premises, we should always violate
either the second or third rule of the syllogism. Hence, we can
eliminate an E and an O proposition as possible valid conclusions.
We have A and I propositions left as possibilities. Since both premises
are universal, let us try an A conclusion:
Every P is M.
Every S is M.
Therefore, every S is P.

Here, again, we need not concern ourselves with the first rule of
the syllogism, since we are using symbols, which retain the same
signification and supposition. The second rule states that any term
distributed in the conclusion must be distributed in the premises.
In this syllogism, we see that only the subject of the conclusion is
distributed (for it is the subject of a universal proposition; the
predicate, being the predicate of an affirmative proposition, is un­
distributed). Hence, we need to check only the minor term S in its
premise. This is also the subject of a universal proposition, and is
therefore distributed. The second rule is thus satisfied.
The third rule states that the middle term must be distributed at
least once. In the major premise, the middle terms stands as the
predicate of an affirmative proposition and is, therefore, undistributed.
Consequently, we must check the middle term in the minor premise.
But the middle term in the minor premise is also the predicate of an
affirmative proposition and is, therefore, undistributed. Hence, the
middle term in this syllogism is undistributed in both premises. The
third rule of the syllogism is thus violated.
There is no point in continuing with the other rules of the syllogism,
for the violation of one rule is enough to make the syllogism invalid.
And it will be of no help to try an I proposition as the conclusion,
for the middle term will still be undistributed in both premises. We
have already eliminated E and O propositions as conclusions. We
conclude, then, that A — A cannot yield a valid conclusion in the
second figure.
Before proceeding to the questions and exercises at the end of the
chapter, let us notice that some syllogisms can conclude indirectly.
An indirect conclusion occurs when the major term appears as the
subject of the conclusion and the minor term appears as the predicate,
as in the following example:

principles and rules of the syllogism

Some texts are books.
No novels are texts.
Therefore, some books are not novels.

135

(Some M is P.)
(No S is M.)
(Therefore, some P is not S.)

In the first figure, the valid moods leading to an indirect con­
clusion are: A-A-I; E-A-E; A-I-I; A-E-O; and I-E-O. Of these five
valid moods, the first three can be obtained by a direct conclusion in
the first figure (A-A-I is included under A-A-A). In the first figure,
then, there are really only two combinations of premises yielding an
indirect conclusion:
Every M is P.
No S is M.
Therefore, some P is not S.

and

Some M is P.
No S is M.
Therefore, some P is not S.

These two moods are properly called the “indirect moods” of the
first figure. No indirect mood of concluding constitutes a distinct
figure, but is simply the consequence of a particular mood in a given
figure. There are, therefore, indirect moods but not indirect figures.
Their only value consists in obtaining a conclusion that could not
be reached directly.
QUESTIONS---- CHAPTER SEVENTEEN

1.
2.
3.
4.

5.
6.
7.
8.
9.
10.

11.
12.
13.
14.

Upon what does the syllogism, as a type of argumentation, primarily rest?
Explain and illustrate the first principle of the syllogism.
Explain and illustrate the second and third principles of the syllogism.
What is the relation of the rules of the syllogism to the principles of the
syllogism?
How do we commit the fallacy of four terms?
Why can we not have a term distributed in the conclusion when it is
undistributed in the premise?
Why must the middle term be distributed at least once?
If I have as premises No B is A and No C is B, why does it not follow
that No C is At
When is one proposition “weaker” than another proposition?
Why is it not necessary to give as a rule that from two particular premises
no conclusion follows? Illustrate.
Is the mood A-O-O valid in any figure?
Why is the mood A-A-A not valid in the second figure? Why not in
the third figure?
Which mood is valid in all three figures?
State the special rules of the syllogism for each figure.

EXERCISE I—CHAPTER SEVENTEEN

)

This is an exercise for determining the valid moods of the syllogism.
In this exercise, first work out the conclusions to the combinations of
premises for Figure I. These combinations are given with the major
premise at the top and the minor premise at the bottom. The lines drawn
at the bottom of the rows of letters separate the premises from the possible
conclusions that can be obtained. Work out the combinations in the order
given, that is, do A-A first, then A-E, then A-I, and so forth. If a conclusion
can be validly drawn, put the letter standing for the kind of proposition
(A, E, 1, or O) underneath the combination of premises. If no conclusion
can be validly drawn, leave the space blank. Do Figure II and Figure III
in the same manner, observing the different disposition of terms for each
figure.
After the valid moods have been determined for each figure, answer the two
questions asked under each figure. The answers to these questions give the
special rules of the syllogism, that is, rules that apply specifically to each
figure.
Figure 1
Recall where the middle term must be for Figure I.
AAAA
EEEE
lili
AEIO
AEIO
AEIO

OOOO
AEIO

After the valid moods have been determined, state what kind of proposition
(universal, particular, affirmative or negative) must always appear:
(a) as the major premise in Figure I
(&) as the minor premise in Figure I
Figure II
Recall where the middle term must be for Figure II.
AAAA
EEEE
I I I I
AEIO
AEIO
AEIO

OOOO
AEIO

After the valid moods have been determined, state what kind of proposition
must always appear:
(a) as the major premise in Figure II
(&) as one of the two premises in Figure II
Figure III
Recall where the middle term must be for Figure III.
AAAA
EEEE
I I I I
AEIO
AEIO
AEIO

OOOO
AEIO

After the valid moods have been determined, state what kind of proposition
must always appear:
(a) as the minor premise in Figure III
(&) as a conclusion in Figure III
logic: the art of defining and reasoning,

137

copyright,

1952,

by prentice-hall, inc.

EXERCISE II—CHAPTER SEVENTEEN
Write in the conclusions to the following syllogisms when the conclusions
can be obtained validly and directly. If no conclusion follows, draw a line,
and state which rule is violated.
I.

Every X is Y.
Some Z is X.

2.

No X is Y.

Some Z is X.

3. Every X is Y.

Every X is Z.

4. No X is Y.

Some Z is Y.

5. Some Y is X.
No Z is Y.

6. No X is Z.

Some Y is not Z.

logic: the art of defining and reasoning,

139

copyright,

1952, BY

prentice-hall, inc.

7. Every Y is X.

Some Z is X.

8. Some Z is not X.
Every Z is Y.

9. No Y is X.

Every Z is Y.

10.

Some Y is not X.
Some Z is Y.

140

EXERCISE III—CHAPTER SEVENTEEN

Mark the following syllogisms valid or invalid. If the syllogism is invalid
explain why or state the rule violated.
1.

Every man is rational.
Every man is vegetative.
Therefore, every vegetative being is rational.

2.

No tyrants are statesmen.
Some men are tyrants.
Therefore, some men are not statesmen.

3.

No athletic person is an invalid.
Some syllogisms are invalid.
Therefore, some syllogisms are not athletic.

4.

Every cow is an animal.
No tree is a cow.
Therefore, no tree is an animal.

5.

Everything actual is knowable.
God is actual.
Therefore, God is knowable.

6.

Everything infinite is imperfect.
God is most perfect.
Therefore, God is not infinite.

7.

No plants think.
All men think.
Therefore, no men are plants.

8.

Some students are not artistic.
Some students are freshmen.
Therefore, some freshmen are not artistic.

logic: the art of defining and reasoning,

141

copyright,

1952,

by prentice-hall, inc.

9.

All tenors are talented.
Not all singers are tenors.
Therefore, not all singers are talented.

10.

Some novels are entertaining.
All novels are books.
Therefore, some books are entertaining.

11.

Whatever has a soul is alive.
Some bodies are alive.
Therefore, some bodies have souls.

12.

Every biped is an animal.
Every animal is mortal.
Therefore, every biped is mortal.

13.

Every tree is a substance.
No tree is a stone.
Therefore, no stone is a tree.

14.

No substance is an accident.
Every quantity is an accident.
Therefore, no quantity is a substance.

15.

Every premise is a composite expression.
Every premise is a proposition.
Therefore, every proposition is a composite expression.

16.

Some trees are not oaks.
All elms are trees.
Therefore, no elms are oaks.

142

EXERCISE IV—CHAPTER SEVENTEEN

Consider the following propositions as conclusions.
prove them validly in any figure.
1.

Every tree is a substance.

2.

Some men are not composers.

3.

No man is an ape.

4.

Some food.is fattening.

5.

Not every man is honest.

logic: the art of defining and reasoning,

143

copyright,

1952,

Construct premises to

by prentice-hall, inc.

EXERCISE V—CHAPTER SEVENTEEN

Consider the following propositions as either a major premise or a minor
premise. Supply the other premise and draw valid conclusions from them.
1.

Some student is not polite.

2.

No saint is a sinner.

3.

Some men are just.

4.

Every poet is an artist.

5.

Some wars are not justified.

144

Chapter Eighteen
REDUCTIOR OF SYLLOGISMS TO
THE FIRST FIGURE

TN the preceding chapter we emphasized that the first figure
-*is the perfect figure and that the second and third figures
are imperfect, departing from the true and evident order of reasoning
that the syllogism should have. Consequently, the four moods of the
first figure are perfect moods, the four moods of the second figure and
the six moods of the third figure are imperfect. Compare the following
three moods, one in each figure of the syllogism:
Fig- I
No M is P.
Some S is M.
Some S is not P.

ng. ii
No P is M.
Some S is M.
Some S is not P.

Fig. Ill
No M is P.
Some M is S.
Some S is not P.

It is clear that an argument is more evident in the first figure than in
the second or third, primarily because the middle term occupies the
middle position in the first figure. It is clear also that the mood in
Figure II could be changed easily to the mood in Figure I by con­
verting the major premise.
Fig. II
Fig. I
No P is M.---------- » No M is P.
Some S is M.
Some S is M.
Some S is not P.
Some S is not P.

Likewise, the mood in Figure III could be changed easily to the mood
in Figure I by converting the minor premise.
Fig- I
No M is P.
■> Some S is M.
Some S is not P.

Fig. Ill
No M is P.
Some M is S.
Some S is not P.
145

146

REDUCTION OF SYLLOGISMS TO THE FIRST FIGURE

We call such an operation the reduction of a syllogism to the first
figure, that is, the reduction of the imperfect moods of the second and
third figures to the perfect moods of the first figure. We can reduce
all the moods of the second and third figures to those of the first figure.
However, not all the imperfect moods reduce so easily to the perfect
moods as the examples we used. In both cases we only had to convert a
premise simply to make the reduction. If we were to go through all
the imperfect moods and reduce them to the perfect moods, we should
find that in some cases we convert both conclusions and premises
simply, and in other cases convert premises accidentally. We should
discover also that in two cases the premises would have to be changed
around, that is, transposed. And in two other cases it would become
apparent that the only reduction possible is by contradiction.
It would be a stimulating exercise to go through all the imperfect
moods (except A-0-0 in Figure II and O-A-O in Figure III, which
present special difficulties) and figure out how each imperfect mood is
reduced to a perfect mood in the first figure. The following model
could be used as an example:
Every dog is an animal.
No stone is an animal.
Therefore, no stone is a dog.

How can this mood in Figure II be reduced to a perfect mood in
Figure I?
Let us notice first that the middle term in Figure I has to be in the
subject position in the major premise. The middle term is “animal.”
The simplest solution would be to convert the major premise, Every
dog is an animal. But this proposition is a universal affirmative, and
must be converted accidentally to: Some animal is a dog. The syl­
logism would then appear as follows:
Some animal is a dog.
No stone is an animal.
Therefore, no stone is a dog.

This syllogism, though now in Figure I, is invalid. The term “dog”
in the conclusion is distributed, but is undistributed in the major
premise. Furthermore, the conclusion is universal, whereas the major
premise is particular; the conclusion is not following the weaker part.
This solution, therefore, will not work.
However, the universal negative proposition in the minor premise
will convert simply: No stone is an animal to No animal is a stone.
The syllogism would then appear this way:

reduction of syllogisms to the first figure

147

Every dog is an animal.
No animal is a stone.
Therefore, no stone is a dog.

But this syllogism is not in Figure I. In fact, the middle term is in
the predicate position in the major premise and in the subject position
in the minor premise, which is an unsyllogistic order, that is, the middle
term is in the most universal position in the major premise and in the
least universal position in the minor premise. It cannot properly func­
tion as a middle term in such a position.
However, if we change the premises around, we shall get the middle
term in its right position in Figure I:
No animal is a stone.
Every dog is an animal.

In changing the premises around, we are making the major premise
of Figure II the minor premise of Figure I, and the minor premise of
Figure II the major premise of Figure I. Consequently, we are also
changing the major term in Figure II to the minor term in Figure I,
and the minor term in Figure II to the major term in Figure I. For
this reason, we shall also have to convert the conclusion in Figure II,
No stone is a dog, to No dog is a stone, to make it the conclusion in
Figure I.
The reduction is now complete and can be diagrammed in the
following way:
Figure I

Figure II

Every dog is an animal.-—_____
No stone is an animal.------

!e¿ to

No animal is a stone.
Every dog is an animal.

Therefore, no stone is a dog. converted to> Therefore, no dog is a stone.

We can also use a formula designed to make the reduction of syl­
logisms relatively quick and easy. An ingenious list of Latin names
has been devised to facilitate the reduction of imperfect moods to per­
fect moods. These names signify, by means of their vowels, the valid
moods of each figure of the syllogism:

A —A —A
E —A —E
A —I— I
E —I — O

Figure I
Barbara
(major, minor, conclusion}
Celarent
Darii
Ferio

148

REDUCTION OF SYLLOGISMS TO THE FIRST FIGURE

E —A —E
A— E —E
E—I— O
A —0 — 0

Figure II
Cesare
Cames tres
Festino
Baroco

A—A— I
E —A —O
I—A—I
A— I — I
O—A—O
E— I —O

Figure III
Daraptz
Felapton
Dz’samz's
Datzsz
Bocardo
Fen son

The names also signify, by means of certain consonants, how to
reduce the moods of the second and third figures to those of the first
figure. The first letter of each name in the second and third figures
tells which moods of the first figure these imperfect moods reduce to.
Thus, Cesare in the second figure is to be reduced to Celarent in
the first; Disarms in the third figure is to be reduced to Darii in the
first.
In addition, certain consonants within the names tell what process
to use in reducing the imperfect moods to the perfect moods. These
consonants are: 5 for simple conversion; p (per accidens in Latin)
for accidental conversion; m (mutatio in Latin) for changing the
premises around, that is, transposing them; and c for reduction by
contradiction. These consonants always refer to the vowels preceding
them.
Let us now use an example. The name Disamis signifies the follow­
ing: (1) This mood of the third figure is to be reduced to Darii in
Figure I. (2) The major premise I is to be converted simply (Dz’S).
(3) The minor premise A is to be changed in position with the major
premise (aM). (4) The conclusion is to be converted simply (iS).
Thus, we see that every letter in the word Disamis signifies something.
Now let us work it out with an example.
Some voters are soldiers.

D
I
S

All voters are citizens.

A
M

Therefore, some citizens are soldiers.

I
S

reduction of syllogisms to the FIRST FIGURE

We want to reduce this syllogism to Darii in Figure I.
the first premise to:
Some soldiers are voters.

149

We convert

(DIS)

We exchange the position of the second premise with that of the
first:
All voters are citizens. (AM)
Some soldiers are voters.

We convert the conclusion simply, and thus get the full syllogism
in the perfect mood Darii in Figure I:
All voters are citizens.
Some soldiers are voters.
Therefore, some soldiers are citizens.

(IS)

It should be noticed that the argument is in better logical order in
Figure I than in Figure III. The middle term is in the middle
position in Figure I. Furthermore, the major premise of the argument
is really All voters are citizens, as in Figure I, because it is more
universal.
Let us take another example, this time of reduction by contradiction,
which is more difficult because it is not a direct reduction. It is an
indirect reduction showing, through a perfect mood of Figure I, that
the imperfect mood is valid. There are only two cases of reduction by
contradiction: Baroco in Figure II and Bocardo in Figure III. Let us
take Baroco in Figure II, where B signifies reduction by means of
Barbara in Figure I, and c signifies reduction by contradiction. Let
us use the following syllogism:
All voters are citizens.
Some Americans are not citizens.

B
A
R
O
C

Therefore, some Americans are not voters. O

This reduction, because it is by contradiction, assumes that an op­
ponent admits the premises of the argument but denies the conclusion.
If he denies the conclusion, then he holds the contradictory of the
conclusion to be true, namely, All Americans are voters.
We now take the opponent’s position and construct a syllogism in
Barbara out of it. Remember that the opponent has admitted the

150

REDUCTION OF SYLLOGISMS TO THE FIRST FIGURE

premises but denied the conclusion.
major premise as it is:

Hence, we can take the original

All voters are citizens.

To this we add the contradictory o£ the conclusion, which the
opponent claims is true:
All Americans are voters.

Drawing the conclusion from these premises, we now have this
syllogism:
All voters are citizens.

B
A
R

All Americans are voters.

B
A
R

Therefore, all Americans are citizens.

A

But notice that the conclusion All Americans are citizens contra­
dicts the original minor premise in Baroco, Some Americans are not
citizens. The opponent, however, has admitted the truth of that
premise. He cannot contradict his own position. Hence, he cannot
deny the original conclusion in Baroco while admitting the premises.
Therefore, the original syllogism in Baroco is valid, and is shown to
be so indirectly, by the process of contradiction, through the perfect
mood of Barbara.
The other imperfect moods of the syllogism can be reduced to the
perfect moods in similar ways. The process of reduction is useful
chiefly for showing the superiority of Figure I, wherein reasoning is
manifested according to perfect logical order and in the most evident
manner.
QUESTIONS---- CHAPTER EIGHTEEN

1. Why is the first figure the perfect and most evident one.
2. Why were the Latin names Barbara, Celarent, and so forth, devised?
3. Explain the signification of the vowels and the consonants in the Latin
names.
4. What does the reduction by contradiction show?
5. What is the usefulness of reducing syllogisms to the first figure?

EXERCISE—CHAPTER EIGHTEEN

Reduce the following syllogisms to the first figure.

1.

Every A is B.
Some C is not B.
Therefore, some C is not A.

2.

Every B is A.
Every B is C.
Therefore, some C is A.

3.

Every A is B.
No C is B.
Therefore, No C is A.

4.

No sinner is virtuous.
Every saint is virtuous.
Therefore, no saint is a sinner.

5.

Some concessions are not justified.
All concessions are compromises.
Therefore, some compromises are not justified.

logic: the art of defining and reasoning,

151

copyright,

1952,

by prentice-hall, inc.

Chapter jineteen
THE ABBREVIATED SYLLOGISM

'“THE abbreviated syllogism is a categorical syllogism—with
one proposition missing. The missing proposition may be
a premise or the conclusion. Every man has sensation, because every
man is an animal is an abbreviated syllogism.
According to present usage, the name “enthymeme” is given to any
abbreviated statement of an argument. In traditional logic, however,
the name “enthymeme” is applied only to a specific type of argument
proceeding from probabilities or signs. This type of argument is used
principally by the rhetorician. For example, the rhetorician might
argue that a man is guilty from the sign that he is trembling. The
rhetorician states his argument in this abbreviated form, expecting the
hearer to supply the complete statement of the argument. Thus, in the
example, a hearer would supply, at least implicitly, the complete argu­
ment: Whoever is trembling is guilty; this man is trembling; therefore,
this man is guilty. Enthymemes used by the rhetorician usually do not
have the universality necessary for a true syllogism, and for this reason
most enthymemes cannot be expanded into a true syllogism.
From this particular characteristic of stating arguments in shortened
form, the name “enthymeme” has been extended to any abbreviated
argumentation. Usage has somewhat sanctioned this extended mean­
ing of the term, but we shall keep the distinction between abbreviated
syllogism and the specific type of abbreviated syllogism known as
the enthymeme, which is primarily found in rhetorical argumentation.
It is important to consider the abbreviated syllogism because we con­
stantly use this informal way of stating syllogistic reasoning. We
are not likely to say: Every human being is capable of speech; no ape
is capable of speech; therefore, no ape is a human being. We are
more likely to say: No ape is a human being, because no ape is capable
of speech, without stating the full argument.
153

154

THE ABBREVIATED SYLLOGISM

Now, while it is all right to speak informally in this way, it is im­
portant to recognize the full process of reasoning implied in this
shortened form of argument. The precise logical significance of the
informal expression is contained in the expansion of the abbreviated
syllogism, as we gave it in the preceding paragraph. It is important,
then, to know how to analyze abbreviated syllogisms and to expand
them quickly. We shall then be able to see what the full argument is
and to avoid fallaces in thinking, for, while the abbreviated syllogism
is a convenient mode of expression, it is also a frequent source of
fallacies. The missing proposition of the abbreviated syllogism often
hides fallacies.
Let us take the first example we gave of an abbreviated syllogism and
examine the procedure for expanding it into a full syllogism, after
which we can test its validity. This abbreviated syllogism was: Every
man has sensation, because every man is an animal. We are stating
as true, Every man has sensation. We are also stating why it is true,
because man is an animal. The first statement is the proposition we
are trying to prove, and consequently is a conclusion. The second
statement is a reason for the conclusion, and consequently is a premise.
This example, then, is an abbreviated syllogism with a missing
premise.
THE PROCEDURE FOR EXPANDING AN ABBREVIATED
SYLLOGISM

1. Look for the conclusion first

There are two ways of discovering which of the two propositions in
an abbreviated syllogism is the conclusion.
The first way is to examine the structure of the thought expressed.
The conclusion is always the proposition to be proved. A premise,
on the contrary, is always a reason proving a conclusion. In the ex­
ample, we wish to prove that every man has sensation by means of the
proposition that every man is an animal. Once we know that the
statement to be proved is the conclusion, then we not only know that
the other proposition is a premise, but we also know which premise
it is. In the example—Every man has sensation, because every man
is an animal—we know that the given premise is the minor premise
because the subject of the conclusion, the minor term, is repeated in
the given premise. We then know that the missing premise is the
major premise. We can now construct the missing major premise by
combining the predicate of the conclusion with the middle term,
Every animal has sensation. Finally, we can arrange the three propo­
sitions in their correct syllogistic order, and check for validity.

THE ABBREVIATED SYLLOGISM

155

Every animal has sensation, (the missing major premise)
Every man is an animal.
(the given minor premise)
Therefore, every man has sensation.

The second way of discovering which of two propositions is the
conclusion is to look for key words in the abbreviated syllogism. These
key words will introduce a conclusion or a premise. Such words as
therefore, hence, and consequently, introduce a conclusion. For ex­
ample:
Logic is a liberal art, and therefore logic is useful.

Such words as because, since, and the conjunction for, introduce a
premise. They signify a causal connection because the premises are
the cause of the conclusion. For example:
No dog is a stone, because every dog is alive.
or
Because every dog is alive, no dog is a stone.

2. If there is no conclusion, the abbreviated syllogism contains two
premises
An abbreviated syllogism with two premises is not nearly so frequent
as one with a premise and a conclusion. We can detect an abbreviated
syllogism with two premises either negatively or positively: negatively,
by the absence of key words introducing a premise or a conclusion;
positively, by such key words as and or but, which serve to join premises.
The following is an example of an abbreviated syllogism with two
premises:
Every gentleman is courteous and every student is a gentleman.
CHOICE OF FIGURES IN EXPANDING AN ABBREVIATED

SYLLOGISM

In some of the abbreviated syllogisms containing a premise and a con­
clusion, there is a choice of figures in expanding them into full syl­
logisms. Consider the following abbreviated syllogism, in which letters
stand for terms: Every X is Y because every X is Z. It is clear that this
abbreviated syllogism contains the conclusion and the minor premise:
_________________ (missing major)
Every X is Z.
Therefore, every X is Y.

THE ABBREVIATED SYLLOGISM

156

It is possible to expand this abbreviated syllogism in either of the
following ways:
Figure I
Every Z is Y.
Every X is Z.
Therefore, every X is Y.

Figure II
Every Y is Z.
Every X is Z.
Therefore, every X is Y.

Now the question is, which figure should we use to expand the ab­
breviated syllogism? If we expand it in Figure I, the argument will
be in a valid mood. If we expand it in Figure II, the argument will
be in an invalid mood.
One way to solve this question is to look at the conclusion of the
abbreviated syllogism. If the conclusion is true, or at least probably
true, then expand the abbreviated syllogism in the figure having
the valid mood. Suppose that the abbreviated syllogism is Paul has
sensation because he is rational. This would appear as follows:
(missing major premise)
Paul is rational.
Therefore, Paul has sensation.

Notice that we have a syllogism containing singular propositions.
We can, of course, have syllogisms with singular propositions, but we
should be aware that such syllogisms depart from the proper notion
of the syllogism, which is on the level of universality. Syllogisms con­
taining singular propositions, therefore, participate imperfectly in the
proper notion of the syllogism. When singular propositions are used
in a syllogism, they function like the universal affirmative or the uni­
versal negative proposition.
The conclusion of the abbreviated syllogism Paul has sensation is
true. Since this is the case, the abbreviated syllogism should be ex­
panded in the figure having the valid mood, Figure I in this case:
Everyone who is rational has sensation.
Paul is rational.
Therefore, Paul has sensation.

Suppose, however, the abbreviated syllogism is Every capitalist is
reactionary because every capitalist is anti-Communist. This ab­
breviated syllogism would appear as follows:
(missing major premise)
Every capitalist is anti-Communist.
Therefore, every capitalist is reactionary.

THE ABBREVIATED SYLLOGISM

157

The conclusion of this argument is not true. Now this abbreviated
syllogism could be expanded in the following way:
Every anti-Communist is reactionary.
Every capitalist is anti-Communist.
Therefore, every capitalist is reactionary.

In this expansion, the syllogism is valid in Figure I. If one is only
concerned with stating the correct formal expansion of the abbreviated
syllogism, the argument can be treated in this way. We should then
point out that one or more of the propositions in the argument is false
even though the form of the syllogism is valid.
It is usually more effective in actual discussion, however, to show
that the argument is bad in form, since a defect in an argument can
be recognized more readily by seeing that the conclusion does not follow
from the premises. For this reason, it would be better to expand this
abbreviated syllogism in Figure II, where the formal fallacy of the
undistributed middle term is made evident:
Every reactionary is anti-Communist.
Every capitalist is anti-Communist.
Therefore, every capitalist is reactionary.

We conclude, therefore, that when there is a choice of figures in
expanding the abbreviated syllogism, and when the conclusion is false
—or when the reason adduced in the premise does not appear cogent
—it is better to expand the abbreviated syllogism in the figure having
the invalid mood, thus showing the weakness of the argument.
QUESTIONS—CHAPTER NINETEEN

1. What is an abbreviated syllogism?
2. What is the proper meaning of an enthymeme? What is the distinction
between an enthymeme and an abbreviated syllogism?
3. Why is it important to consider the abbreviated syllogism?
4. How do we discover the conclusion of an abbreviated syllogism?
5. What key words introduce premises? Why do they introduce premises?
6. How can we tell when the conclusion is missing from an abbreviated
syllogism?
7. When there is a choice of figures, how is an abbreviated syllogism expanded?
8. Make up three original abbreviated syllogisms and expand them.

EXERCISE—CHAPTER NINETEEN

Expand the following abbreviated syllogisms. If, after expansion, the
argument is invalid, explain why the argument is bad or state the rule violated.

1.

Every A is B, because every C is B.

2.

No C is A; therefore no C is B.

3.

Since every Z is X. everv X is Y.

4.

Every animal is a body, for every animal is an organism.

5.

Some sports are strenuous, because all football games are sports.

logic: the art of defining and reasoning,

159

copyright,

1952,

by prentice-hall, inc.

6.

All mice are rodents but no squirrels are mice.

7.

Every Christian is a Fascist, because every Fascist is anti-Communist.

8.

No students are ignorant, because some students are freshmen.

9.

No women are good drivers, since no women are men.

10.

John Jones is an enemy of education, because he criticizes educators.

160

Chapter Twenty
THE COMPOUND SYLLOGISM

'T'HE syllogism is divided essentially into the categorical and
compound (or hypothetical). Let us recall that in Chapter
Nine we divided the proposition into the categorical and compound.
The division of the syllogism is based upon this division of the propo­
sition. We shall now consider the compound syllogism and its main
kinds.
A compound syllogism is one in which the major premise is a com­
pound proposition and the minor premise is a categorical proposition.
The minor premise must either posit (affirm) or destroy (deny) one of
the parts of the compound proposition in the major premise.
It might seem as though we could define the compound syllogism
more simply as a syllogism that contains compound propositions.
We should then be led, however, to regard the following as a com­
pound syllogism:
If X is, then Y is.
If Z is, then X is.
Therefore, if Z is, then Y is.

This argument, however, is not a compound syllogism; it is still a
categorical syllogism. The compound syllogism does not depend upon
a connection of the terms, but on the connection between the propo­
sitions of the syllogism. Therefore, it is necessary to state in the
definition of the compound syllogism not only that the major premise
is a compound proposition, but that the minor premise must either
posit or destroy one part of the compound proposition, as in the
following:
If X is, then Y is.
X is.
Therefore, Y is.
161

162

THE COMPOUND SYLLOGISM

The compound syllogism itself is divided into the conditional and
the disjunctive syllogism. The basis for the division is whether the
major premise is a conditional or a disjunctive proposition. (Some­
times a conjunctive syllogism is also listed, in which the major premise
is a conjunctive proposition, for example, X cannot at the same time
be Y and Z. The conjunctive syllogism, however, is reducible to the
conditional syllogism, just as the conjunctive proposition is reducible to
the conditional proposition.)
THE CONDITIONAL SYLLOGISM

The conditional syllogism is the more important compound syllogism.
A conditional syllogism is a compound syllogism having a conditional
proposition as the major premise and a categorical proposition as the
minor premise. The conditional proposition, as we saw in Chapter
Fourteen, has an antecedent and a consequent. Now the minor
premise of a conditional syllogism must either posit or destroy the
antecedent or the consequent of the major premise. We shall consider
first whether the minor premise should posit the antecedent or the
consequent. Let us try both cases.
I£ Paul walks, Paul moves.
Paul walks.
Therefore, Paul moves.

In this conditional syllogism, the minor premise posits the antecedent
and the conclusion posits the consequent. The syllogism is valid be­
cause Paul’s moving necessarily follows upon Paul’s walking. Let us
try the other possibility.
If Paul walks, Paul moves.
Paul moves.
Therefore, Paul walks.

In this conditional syllogism, the minor premise posits the conse­
quent and the conclusion posits the antecedent. But this syllogism is
not valid because Paul’s walking is not a necessary consequence of
Paul’s moving; his movement might be only the movement of pointing.
There must be a necessary dependence of the consequent upon the
antecedent if the conditional syllogism is to be valid. Hence, we
infer the following rule for the conditional syllogism: When the
minor premise posits the antecedent, the conclusion must posit the
consequent.
We must also consider whether the minor premise should destroy

163

THE COMPOUND SYLLOGISM

the antecedent or the consequent in the major premise.
the following syllogism:

Let us examine

If Paul walks, Paul moves.
Paul is not walking.
Therefore, Paul is not moving.

This is a conditional syllogism in which the minor premise destroys
the antecedent and the conclusion destroys the consequent. However,
it is not valid because Paul’s not moving does not necessarily follow
upon Paul’s not walking, since, again, he could be pointing. The
conclusion, therefore, does not follow from the premises. Let us try
the other possibility.
If Paul walks, Paul moves.
Paul is not moving.
Therefore, Paul is not walking.

In this syllogism, the minor premise destroys the consequent and
the conclusion destroys the antecedent. This syllogism is valid because
Paul’s not walking necessarily follows upon Paul’s not moving, that is,
Paul cannot walk without moving. Hence, we infer a second rule
for the conditional syllogism: When the minor premise destroys the
consequent, the conclusion must destroy the antecedent.
The conditional syllogism has two figures. The first figure is based
upon the first rule of the conditional syllogism, namely, when we
posit the antecedent in the minor premise we must posit the consequent
in the conclusion. The second figure is based upon the second rule of
the syllogism, namely, when we destroy the consequent in the minor
premise we must destroy the antecedent in the conclusion. There are
four moods for each figure—four possible ways of validly working out
the rule for each figure. The figures and moods are given below.
First Figure
(positing antecedent to
positing consequent)
I. If A is B, A is C.
A is B.
Therefore, A is C.

Second Figure
(destroying consequent to
destroying antecedent)
I. If A is B, A is C.
A is not C.
Therefore, A is not B.

II. If A is B, A is not C.
A is B.
Therefore, A is not C.

II. If A is B, A is not C.
A is C.
Therefore, A is not B.

III. If A is not B, A is C.
A is not B.
Therefore, A is G.

III. If A is not B, A is C.
A is not C.
Therefore, A is B.

164

THE COMPOUND SYLLOGISM

IV. If A is not B, A is not C.
A is not B.
Therefore, A is not C.

IV. If A is not B, A is not C.
A is C.
Therefore, A is B.

Some confusion may arise in certain moods because of the words
“positing” and “destroying.” For example, in the first figure, the
minor premise posits the antecedent. When the antecedent of the
conditional proposition in the major premise is negative, as in the
third mood of the first figure, then to “posit” the antecedent in the
minor premise means to repeat the antecedent in its negative form.
If one were to make this antecedent in the minor premise affirmative,
it would “destroy” the antecedent of the major premise. Consequently,
to “posit” the antecedent in the minor premise means to repeat the
antecedent just as it was in the major premise. The following example
illustrates this point.
If a man is not breathing, he is dead.
This man is not breathing, (positing the antecedent)
Therefore, he is dead.

In the second figure, the minor premise destroys the consequent. If
the consequent in the major premise is negative, then to “destroy” it
in the minor premise means that it must be affirmed in the minor
premise, since to “destroy” a negation is to make an affirmation. Thus,
the second mood of the second figure would appear as follows:
If a man is breathing, he is not dead.
This man is dead, (destroying the consequent)
Therefore, he is not breathing.
THE DISJUNCTIVE SYLLOGISM

A disjunctive syllogism is a compound syllogism having a disjunctive
proposition as its major premise and a categorical proposition as its
minor premise. The minor premise either posits or destroys one
member of the disjunction. As we saw in Chapter Fourteen, a dis­
junctive proposition has categorical propositions joined by the con­
nectives either . . . or. Since a disjunctive proposition is the major
premise of the disjunctive syllogism, the minor premise must either
posit one member of the disjunction and the conclusion destroy the
other, or the minor premise must destroy one member of the dis­
junction and the conclusion posit the other. Thus we have two
figures for the disjunctive syllogism and two moods for each figure.

THE COMPOUND SYLLOGISM

165

Figure I
(the minor posits')
I. X is either A or B.
X is A.
Therefore, X is not B.

Figure II
(the minor destroys)
I. X is either A or B.
X is not A.
Therefore, X is B.

II. X is either A or B.
XisB.
Therefore, X is not A.

II. X is either A or B.
X is not B.
Therefore, X is A.

We must presume, in these figures, that we have a strict disjunctive
proposition as the major premise. The strict disjunctive proposition
asserts that one and only one of two alternatives can be true, that is,
both alternatives cannot be true. Therefore we can posit one member
in the minor premise and destroy the other in the conclusion or destroy
one member in the premise and posit the other in the conclusion.
Thus, we can argue as follows:
Ten is either odd or even.
Ten is not odd.
Therefore, ten is even.

It is evident that in the disjunctive syllogism everything depends
upon the disjunction in the major premise. The question one should
always ask, in examining a disjunctive syllogism, is, “Does the major
premise contain a strict disjunction?” or “Is there a third possibility?”
If the disjunction is a strict one, then when the minor premise is true,
the conclusion necessarily follows. Consider, however, the following
argument:
A man is either a Communist or a Fascist.
This man is not a Communist.
Therefore, he is a Fascist.

E E E

This syllogism is not valid, because the disjunction in the major
premise is not a strict one. A man may be neither a Communist nor
a Fascist. Nevertheless, arguments like this are frequently used and
often accepted uncritically.
Sometimes a disjunctive syllogism has a loose or improper disjunction
in the major premise. Such a syllogism, although it departs from the
proper disjunctive syllogism, has a certain limited use. The improper
disjunctive syllogism has a major premise in which there are more
than two members. In this kind of syllogism, the following rules
must be observed. (1) When one member is posited in the minor
premise, the other members must be destroyed in the conclusion.
For example:

1

166

THE COMPOUND SYLLOGISM

Paul is a freshman, sophomore, junior, or senior.
Paul is a freshman.
Therefore, Paul is not a sophomore or a junior or a senior.

And (2) When one member is destroyed in the minor premise, the other
members must be posited disjunctively in the conclusion. For ex­
ample:
Paul is a freshman, sophomore, junior, or senior.
Paul is not a senior.
Therefore, Paul is a freshman or a sophomore or a junior.

QUESTIONS---- CHAPTER TWENTY

1. Define the compound syllogism.
2. What is the difference between the compound syllogism and the cate­
gorical syllogism?
3. Explain the antecedent and the consequent of a conditional proposition.
What does the conditional syllogism do with the antecedent and the
consequent of the conditional proposition?
4. What necessary condition must be realized for the conditional syllogism
to be valid?
5. Criticize the following conditional syllogism:
If it was raining, I wore a brown hat.
I wore a brown hat.
Therefore, it was raining.
6. Give original, valid examples of conditional syllogisms in any two moods
of the first figure and any two moods of the second figure.
7. What is the relation between the rules for the conditional syllogism and
the general principles of argumentation given in Chapter Fifteen?
8. Define a disjunctive syllogism.
9. Criticize the following disjunctive syllogism:
A student is either intelligent or lazy.
This student is lazy.
Therefore, he is not intelligent.
10. What is an improper disjunctive syllogism?

GENERAL EXERCISE ON SYLLOGISTIC REASONING
(Chapters Seventeen to Twenty)
In the following excerpt, paraphrased and condensed from the Summa
Theologica of St. Thomas Aquinas, examine the reasoning employed. State
all categorical syllogisms, abbreviated syllogisms or compound syllogisms in
full and logical form, and check for validity. The third part of I answer that
can be omitted, as well as the replies to objections.

Whether God Is a Body?
(Summa Theologica, I, Q. Ill, Art. 1)
Objection 1. It seems that God is a body. Now a body is that which has
three dimensions. But God has three dimensions, according to Sacred
Scripture, which says: “He is higher than Heaven, and what wilt thou do?
He is deeper than Hell, and how wilt thou know? The measure of Him is
longer than the earth and broader than the sea” (Job, xi, 8, 9). Therefore,
God is a body.
Objection 2. Everything that has a figure is a body, since figure is a
quality of quantity. But God seems to have figure, for it is written: “Let
us make a man to our image and likeness,” (Gen. i, 26), and a figure is called
an image, as is also said in Scripture (cf. Heb. i, 3). Therefore, God is a body.
Objection 3. Everything that has corporeal parts is a body. But Scripture
attributes corporeal parts to God, when it says: “Hast thou an arm like God?”
(Job, xl, 4). And again: “The eyes of the Lord are upon the just” (Psalms,
xxxiii, 16). And also: “The right hand of the Lord hath wrought strength”
(Psalms, cxvii, 16). Therefore, God is a body.
Objection 4. If God has posture, then God has a body. But things per­
taining to posture are said of God in Scripture: “I saw the Lord sitting”
(Isa. vi, 1). And also: “He standeth up to judge” (Isa. iii, 13). Therefore,
God is a body.
On the contrary: It is said in Scripture: “God is a spirit” (John iv, 24).

I answer that: God is in no way a body, and this can be shown in three
ways. First, because all bodies are moved, as is evident by induction. Now,
it has been shown previously (Q. II, Art. 3) that since God is the First Mover,
He is not moved. Therefore, it is clear that God is not a body.
Second, because the first being cannot be in potency, for potency is posterior
to act. Now it was shown above (Q. II, Art. 3) that God is the first being.
Therefore, it is impossible that potency be in God. Every body is in potency,
because every body is continuous. Now the continuous is divisible to in­
finity. But God is not divisible to infinity. Therefore, it is impossible that
God is a body.
Third, because God is the most noble of beings, as was shown previously
(Q. II, Art. 3). Now, it is impossible for a body to be the most noble of
beings. For a body is either living or non-living, and it is evident that a
living body is more noble than a non-living body. But a living body is not
living in so far as it is a body, otherwise all bodies would be living. There­
fore, its living must be by something else, just as our body lives through the
soul. Now, that by which a body lives is more noble than a body. There­
fore, it is impossible that God is a body.
167

Reply to Objection 1. As was said previously (Q. I, Art. 9), Sacred
Scripture presents spiritual and divine things under the likeness of corporeal
things. Hence, when it attributes three dimensions to God under the likeness
of corporeal quantity, it designates His virtual quantity. Thus, by depth it
signifies His power of knowing hidden things; by height, the excellence of
His power above all others; by length, the duration of His existence; by
breadth, His act of love for all. . . .
Reply to Objection 2. Man is said to be in the image of God, not ac­
cording to his body, but with respect to that whereby man excels the other
animals. Hence, when it is said in Scripture “Let us make man to our image
and likeness,” there is added, “And let him have dominion over the fishes
of the sea” (Gen. i, 26). Now, man excels all animals by his reason and
intellect. Hence, it is according to his reason and intellect, which are in­
corporeal, that man is said to be in the image of God.
Reply to Objection 3. Corporeal parts are attributed to God in Scripture
because of His acts, according to a certain likeness. For example, the act of
the eye is to see, and hence the eye attributed to God signifies His power
of seeing intellectually, not sensibly. And it is the same with other corporeal
parts.
Reply to Objection 4. Whatever pertains to posture is likewise at­
tributed to God only by a certain likeness. God is said to be “sitting” be­
cause of His immutability and authority. He is said to be “standing” be­
cause of His power of overcoming whatever is opposed to Him.

168

Chapter Twenty-one
INDUCTION

T N Chapter Fifteen we treated argumentation in general and
-L-made the division of argumentation into its two main kinds:
deductive and inductive. Deductive argumentation is the same as
the syllogism, which we have discussed.
We shall now consider induction, but before treating induction
directly, two points should be stressed. The first is the reason for
treating induction after deduction. Since the syllogism is the funda­
mental kind of argumentation, induction must be studied and under­
stood in relation to the syllogism. We cannot, in fact, understand the
validity of the formal consequence that belongs to induction except in
relation to the syllogism, where the formal consequence is perfectly
realized. From the standpoint of argumentation as such, induction
is less perfect.
The second point is that a logical analysis of induction is con­
cerned with only a few fundamental notions. To appreciate this, it
is necessary to distinguish between the consideration of induction as
a mode of argumentation, which belongs to logic, and the application
of induction in various branches of philosophy and experimental
science. The latter consideration is more complex and deservedly
needs extensive elaboration. But such a treatment of induction does
not belong in a logic text, particularly an elementary logic text. It is
the business of the logician simply to analyze induction as a mode of
reasoning; this common mode of inductive reasoning is then applied
variously in the different sciences.
We defined induction in Chapter Fifteen as an argumentation pro­
ceeding from singulars to universals. By “singulars” we understand
primarily the singulars perceived by sense. More broadly, “singulars”
also means “less universal,” in which case induction is understood to
proceed from the less universal to the more universal; for example, we
can reason from the different kinds of motion to the nature of motion
169

170

INDUCTION

itself. In the primary meaning of induction, however, we proceed
from the singulars known by sense to a universal judgment. The
“universals” in the definition refer to universal judgments drawn from
singular instances.
All argumentation, whether syllogistic or inductive, rests upon a con­
nection of terms. Let us recall that the middle term has two func­
tions: (1) it connects the extremes, and (2) in the perfect figure of the
syllogism, it is also middle in universality. Hence, a syllogism in the
first figure proves that two extremes (a subject and a predicate) are
joined with each other by means of a middle term that connects them
by being middle in universality. Thus, if we are proving that Z is X
in the perfect figure of the syllogism, we do so by reason of a middle
term Y, which connects them and is middle in universality.
Induction establishes a relation between one extreme and a middle
by means of the other extreme. In induction, the two functions of
the middle are distinct. Let us take the terms X, Y, and Z again.
Induction proves that X belongs to Y by reason of Z. Here Y functions
as a middle in universality (that is, X is said of Y and Y is said of Z),
and Z, as an extreme, has the function of connecting X and Y in the
conclusion. Let us notice, then, the essential opposition between the
syllogism and induction. In the perfect figure of the syllogism, the
term used to connect the terms of the conclusion is also a true universal
that is middle in universality. In induction, however, the term used
to connect the terms of the conclusion is not a true universal, but an
enumeration of singulars. It is the absence of a truly universal middle
term to connect the terms of the conclusion that essentially distinguishes
induction from the syllogism. An inductive argument would thus ap­
pear as follows, first in symbols, and then in words:
Every Z is X.
Every Z is Y.
Therefore, every Y is X.

Peter, Paul, James, John, and all other individuals are mortal.
Peter, Paul, James, John, and all other individuals are all men.
Therefore, every man is mortal.

In the first proposition, the subject is an enumeration of the indi­
viduals. We make this enumeration the subject of the characteristic
mortal that we want to conclude of it. In the second proposition, we
again use the enumeration of individuals as the subject, but we now
identify it with the universal all men. In the conclusion, we can then
predicate mortal of the universal that embraces the enumeration of the
singulars, every man.
The complete enumeration of the singulars is necessary for the

INDUCTION

171

validity of the formal consequence of induction. By this we do not
mean that we have to count all the singular instances or have experience
of each of them. We mean, rather, that the form of induction requires
that the note of universality be present in the enumeration. It is suf­
ficient, for universality, to say “and all others” after the actual particular
instances we cite, for this is all that is required for universality on the
part of the form of logic. For universality on the part of matter, how­
ever, we must go to the things signified to justify the universality as­
sumed for the form of inductive argumentation. The considerations
on the part of matter will determine whether our induction is certain
or only probable. The following induction, because of the matter,
will be only probable.
In September of this year, last year, the year before that, etc., the first frost has
occurred.
What we say of September of this year, last year, the year before that, etc., can
be said of every September.
Therefore, every September brings the first frost.

Our concern with induction, however, is only with the universality
required by the form of logic. The universality required on the part
of matter is considered in more advanced courses in logic and in the
different sciences as they employ induction. For example, in the ex­
perimental sciences induction gives only probability of varying degrees
because the experimental method has no way of establishing the
necessary connection of the predicate with the subject. In some
branches of philosophy, particularly in moral philosophy, inductive
argumentation is often probable rather than certain.
We have spoken of induction as a form of reasoning less perfect
than the syllogism. The syllogism is the perfect form of reasoning
because a necessary consequence is established through the middle
term, which functions as a truly universal middle connecting the
extremes. The necessity of the consequence in inductive reasoning,
however, is evident to us only as we see that it participates virtually in
the more perfect form of the syllogism. By reducing induction ma­
terially to the syllogism, we shall see how it participates virtually in
the syllogism.
We speak of this as a material reduction because we could never
reduce the inductive form of argumentation to the syllogistic form.
The reason for this is that the syllogism uses a truly universal middle
to prove a mediate proposition, a proposition whose terms admit of a
mean; but induction uses an extreme, the enumeration of the singulars,
to prove an immediate proposition, a proposition whose terms admit of
no true mean.

172

INDUCTION

Reducing induction materially to the syllogism, then, means arrang­
ing the terms of induction in common syllogistic form, that is, so that
the fundamental principles of the syllogism will apply. We do this
by the simple conversion of the second premise of the inductive argu­
ment.
Thus, the inductive argument:
Every Z is X.
Every Z is Y.
Therefore, every Y is X.

is materially reduced to:
Every Z is X.
Every Y is Z.
Therefore, every Y is X.

We are permitted to convert simply the second premise of the in­
ductive argument to the second premise of the syllogism because of
the identity established between the enumeration of singulars (Z)
and the universal nature found in the singulars (F). However, this
is not a reduction to the syllogism in its proper sense, for in the
restatement of the inductive argument in syllogistic form, there is
not a true middle term for the syllogism, but only the enumeration
of singulars (Z) substituting for the middle term. The reduction does
indicate, nevertheless, how the verification of the formal consequence in
induction must depend upon the fundamental principles of the syl­
logism, and that complete enumeration of the singulars is necessary for
the consequence of the inductive form.
The primary purpose of induction is to make first principles and
immediate propositions evident. We grasp the terms of first prin­
ciples by seeing then inductively in several instances, as, for example,
we know the immediate truth of Every whole is greater than its part
by seeing several instances of it. Thus, induction enables us to grasp
first principles with ease and certainty. This is necessary because we
use first principles as premises of the primary syllogisms, upon which
all other syllogisms depend.
QUESTIONS---- CHAPTER TWENTY-ONE

1.
2.
3.
4.
5.

Why is induction treated after deduction?
To what extent does logic treat inductive argumentation?
Define induction. Explain the word “singulars.”
How does induction prove a conclusion?
In induction, what term is used to show the connection of the terms of
the conclusion?

INDUCTION

173

6. What is the essential distinction between induction and the syllogism?
7. In what way is the complete enumeration of singulars necessary in in­
duction?
8. What do we mean by the "complete enumeration of singulars”?
9. Distinguish between universality on the part of form and universality on
the part of matter.
10. How is universality on the part of matter established in induction?
11. Why is there only a material reduction of induction to the syllogism?
12. Why can the second premise of an inductive argument be converted
simply?
13. How does induction depend on the syllogism?
14. What is the primary purpose of induction?

Chapter Twenty-two

argumentation materially
CONSIDERED

'T'HUS far we have considered argumentation primarily on
the part of form; our treatment has been of the syllogistic
form and the inductive form of reasoning. Since an elementary text
in logic should include certain things pertaining to the matter of
logic, we must now take up, at least in a summary manner, argumenta­
tion on the part of matter. The consideration of the matter of
argumentation is more difficult and extensive than the consideration
of the form, and therefore constitutes the main part of an advanced
course in logic. Nevertheless, a text in logic would be incomplete
without a consideration of scientific demonstration, and other major
distinctions made on the part of the matter of argumentation.
This order of considering argumentation with the emphasis first on
the form, and then on the matter, is given by Aristotle in his Prior.
Analytics and Posterior Analytics. The word “analytics” signifies the
resolution of the conclusion of a scientific proof back to its principles.
Hence, to know scientifically is to see a thing in its causes and prin­
ciples. For example, we know scientifically that every human being
is mortal when we grasp the cause of human death, namely the in­
evitable separation of the principles of human nature, body and soul.
Resolution of the conclusion on the part of form is called “prior
analytics.” This resolution is prior because we can abstract the com­
mon formality of reasoning, which is more known to us than its
realization in a given matter. Resolution of the conclusion on the part
of matter is called “posterior analytics.” This resolution is posterior
because it is less known to us. In the Posterior Analytics Aristotle
considers the most perfect kind of matter in which the form of reason­
ing can be realized, namely, necessary matter.
We shall divide this chapter according to the several kinds of matter
175

176

ARGUMENTATION MATERIALLY CONSIDERED

in which argumentation is found. First we shall treat demonstration,
that is, reasoning in necessary matter; then dialectics, which is reason­
ing in probable matter. We shall also consider rhetorical argumenta­
tion and poetic argumentation. Since logic must also treat defective
reasoning, we shall consider, in a separate chapter, sophistics, that is,
fallacious reasoning.
I. DEMONSTRATION

Demonstration is reasoning to a necessary conclusion. The syllogism
used in this kind of reasoning is demonstrative. The demonstrative
syllogism produces science in the strict sense. Science, according to
the subject possessing it, is called either “doctrine” or “discipline.”
“Doctrine” means science as possessed by a teacher, that is, by one who,
knowingly scientifically, assists in producing science in another. “Dis­
cipline” means the receiving of science by one who learns from another,
that is, by a student from a teacher.
The prequisites for demonstration

The human intellect obtains science in a discursive manner, by
proceeding from the knowledge of one thing to that of another. Dis­
cursive knowledge proceeds from pre-existing knowledge to the knowl­
edge of a conclusion, for the human intellect advances by going from
something already known to something not yet known. We must
presuppose, then, the knowledge of whether something is and also
what it is; otherwise, we could not advance to the knowledge of some­
thing else. But we must determine more precisely what these pre­
requisites are for demonstration.
In a perfect demonstration we seek a conclusion in which a property
is affirmed of its subject, as in the following example:
Every rational animal is grammatical.
Every man is a rational animal.
Therefore, every man is grammatical.

In the conclusion, the property grammatical belong necessarily, only,
and always to the subject man. We see that this is true because of the
premises in which the definition of man serves as the middle term, and
is the cause of the connection of the property with the subject in the
conclusion. Consequently, we must have foreknowledge of the follow­
ing three things for demonstration:
(1) Principles (premises)
(2) Subject
(3) Property

ARGUMENTATION MATERIALLY CONSIDERED

177

We must have foreknowledge of the premises in the sense that we
must know whether the premises are true. We must have foreknowl­
edge of the subject in the sense that we must know the real definition
of the subject—-what it is. The foreknowledge of the property need
only be a nominal definition, that is, what it is by name, since we can
see the necessary connection between the property and the subject with­
out having to know the real definition of the property. The real
definition of the property becomes evident in the conclusion of the
demonstration where it is predicated of its proper subject.

Definition of demonstration
Let us state first what we mean by “science” in its strict sense. It is
that kind of knowledge by which we know the cause on which a
thing depends, that it is the cause of that thing, and that the thing
cannot be other than it is. This is to know the proper cause of a
thing. More briefly defined, science is certain knowledge through
causes.
We can now define demonstration; and first according to its final
cause. Demonstration is a syllogism that produces science. It causes
science in us, not only as an act, but as a habit, a permanent disposition.
We shall define demonstration, secondly, on the part of matter.
Demonstration is a syllogism containing premises that are true, primary,
immediate, and that are prior to, better known than, and causes of the
conclusion.
Notice that the definition of demonstration on the part of matter
follows from the definition according to its purpose. Thus, from the
kind of conclusion sought, that is, a scientific conclusion, we deduce the
kind of premises required. Hence we define demonstration on the
part of matter in terms of premises that are true, primary, immediate,
and so forth.
The premises must be true because, although a true conclusion can
follow from false premises, a true conclusion can be proved only from
true premises. The truth of a premise is proved by making it stand
as a conclusion following from other true premises. It is evident that
not every premise can be proved to be true, for such a process would
be infinite. If one thought that every premise had to have its truth
demonstrated, he would logically have to hold that nothing could be
proved, for the demonstrated truth of any premise depends upon prov­
ing the truth of something prior to it, and this on something else
prior, and so on infinitely. Consequently, nothing could be un­
qualifiedly proved, which is to say, really demonstrated. But since we
know that some propositions can be demonstrated to be true, it follows

178

ARGUMENTATION MATERIALLY CONSIDERED

that there is not an infinite regress in demonstration, and that there
are some premises true without proof, that is, self-evident.
Self-evident propositions are the ultimate premises from which all
demonstration is derived. A self-evident proposition is one in which
the predicate is included in the essence of the subject. For example,
in Man is an animal, animal forms part of the essence of man.
Now, if the essence of both the predicate and the subject is known to us,
then the proposition is self-evident to us. Propositions of this kind are
the ultimate premises, the first principles of all demonstration. Some
of these propositions are self-evident to all, for example, that every
whole is greater than its part. Others are self-evident only to some,
namely, to those who examine and study the nature of the subject
and the predicate. For example, the proposition Ideas are not in
space is self-evident to those who understand what ideas are and what
space is.
But if the essence of the predicate and the subject of a proposition
are not known to us, and if the predicate is contained in the essence
of the subject, then such a proposition is self-evident in itself, but not
to us; for example, the proposition God exists. This proposition, not
being self-evident to us, has to be proved.
Now in the very first demonstration concerning a subject, we first
predicate the definition of the subject in a self-evident proposition.
We use this definition of the subject to demonstrate that a property in­
heres in the subject. We then use this property to show the connection
between a second property and the subject.
We have said, in the definition of demonstration, that the premises
must be true. They are true either as proved or as self-evident.
Further, the premises must be primary, in the sense that any syllogism
can be ultimately reduced to the first premises, the self-evident propo­
sitions that prove all other propositions. The premises must be im­
mediate in the sense that they have no middle term by which they are
proved, since they are indemonstrable. This refers again to self-evident
propositions.
The premises are also prior to the conclusion in the sense that they
must be prior in their truth, for it is by knowing the truth of the
premises that we know the truth of the conclusion. The premises are
better known than the conclusion because, according to our mode of
knowing, we must proceed to a new truth from truths we already
know. The premises, finally, are causes of the conclusion because of
the middle term, which unites the premises and therefore produces
the conclusion as an effect.

ARGUMENTATION MATERIALLY CONSIDERED

179

Kinds of demonstration

Demonstration is an analogous notion. The principal kind is
demonstration by proper cause {propter quid demonstration). It is
this kind that we have discussed so far because, in an analogous
notion, we must start with the primary analogate, the other analogates
having meaning only in relation to the primary one. The secondary
kind of demonstration is demonstration of the fact {quia demonstra­
tion).
Demonstration by proper cause gives the proximate cause for the
identification of the predicate with the subject in the conclusion.
We have this kind of demonstration when the middle term is the
definition of the subject. Through such a middle term, we prove
that a property belongs to the subject of the conclusion. The follow­
ing is an example of a demonstration by proper cause:
Every rational animal is capable of humor.
Every man is a rational animal.
Therefore, every man is capable of humor.

Demonstration of the fact is one that proves the truth of the con­
clusion without manifesting the proximate cause of this truth. This
kind of demonstration proceeds from an effect in the premises, to the
cause in the conclusion. Thus, we argue from the existence of a watch,
as an effect, to the existence of the art of watchmaking, as a cause, in
the conclusion. Demonstration of the fact can also proceed from a
remote cause in the premises to an effect in the conclusion. Thus,
animal is a remote cause of grammatical in man, for animal is the
genus of man; it is a remote cause in predication; that is, man, who is
animal, is grammatical.
However, we cannot argue that because something is an animal,
therefore it is grammatical—the cause is too far removed. We may,
however, argue that because something is not an animal, therefore it
is not grammatical. Hence, demonstration of the fact from remote
cause consists chiefly in showing the truth about some fact negatively.
We also divide demonstration accidentally into a priori and a
posteriori. An a priori demonstration proves the effect from the
cause. Thus we prove from the nature of man that he is capable of
making works of art. An a posteriori demonstration proves the cause
from the effect. Thus we prove from an examination taken by a
student the extent of his knowledge when taking the examination.
Let us compare the two divisions of demonstration we have given.
Demonstration by proper cause and demonstration of the fact is the

180

ARGUMENTATION MATERIALLY CONSIDERED

primary division because it is based upon the kind of truth obtained.
The division into a priori and a posteriori demonstration is a secondary
and accidental division, based upon whether our reasoning starts from
the cause or the effect. Demonstration by proper cause, since it
proceeds from cause to effect, will always be a priori demonstration.
Demonstration of the fact will be a priori demonstration if it proceeds
from remote cause to effect; if it proceeds from effect to cause, it will
be a posteriori demonstration.
Demonstration is the final cause of logic. Everything considered in
logic is taken up ultimately to achieve demonstrative argument. In
fact, it is only through demonstration that we get science, strictly
speaking.
It is not easy to achieve demonstration nor are we able to use it
very frequently, since it presupposes knowledge and certitude not often
possible to man. We should, nevertheless, understand what demon­
stration is. We should be able to distinguish the different kinds of
demonstration as they are used in various parts of philosophy; in
mathematics, where demonstration is most manifest for us; and in other
sciences. But since most of our knowledge is probable rather than
certain, opinion rather than science, we must next examine dialectical
argumentation.
II. DIALECTICS

Dialectical reasoning is like demonstrative reasoning in that it em­
ploys the syllogistic form, directly deducing conclusions from premises.
A dialectical syllogism differs from a demonstrative syllogism in at
least two ways: (1) A dialectical syllogism deduces conclusions from
probable premises, the conclusion sharing in the probability of the
premises; a demonstrative syllogism deduces certain conclusions from
certain principles. (2) A dialectical syllogism produces opinion in the
mind of the knower, whereas a demonstrative syllogism produces science
in the mind of the knower. Opinion is the assent to something be­
cause of a probable motive or reason, but with fear that the opposite
may be true. Hence, a dialectical syllogism, most simply defined, is
probable argumentation.
We are defining dialectics here in relation to the primary form of
argumentation, syllogistic argumentation. Now just as demonstrative
argumentation is either syllogistic or inductive, so dialectical argu­
mentation is syllogistic or inductive. In demonstrative argumenta­
tion, we use induction to arrive at certain principles. In dialectical
argumentation, we use induction to arrive at probable principles.

ARGUMENTATION MATERIALLY CONSIDERED

181

However, we shall treat dialectical argumentation primarily in terms of
the syllogistic form of reasoning.
We argue dialectically when we reason from probable principles
which are generally held. By “generally held,” we mean that they are
held by men commonly, or by a majority of men, or by experts in
various fields. Hence, we adhere to the principles, not on the strength
or evidence of their truth, since this is not certain, but upon their
likelihood or upon their general acceptance by others. In demonstrative
argument, on the contrary, we adhere to the principles because of their
own truth and evidence, and it makes no difference who or how many
hold such principles. It follows, then, that where we can have truth
and certainty in the principles, we should employ demonstrative argu­
mentation, and not confuse it with dialectical argumehtation. On
the other hand, if we cannot have truth and certainty in our principles,
then we should not pretend to use demonstrative argumentation, but
should make use of dialectical argumentation.
Let us now outline the doctrine of dialectical argumentation—the
general nature and method by which conclusions are deduced from
probable principles. The consideration of how dialectical argu­
mentation is applied in the different sciences is not our concern in logic.
A dialectical syllogism, like any other syllogism, infers a conclusion
from the connection of terms in the premises. Although the con­
clusion of the dialectical syllogism is only probable, nevertheless the
probable conclusion follows necessarily, by reason of the form, from
the premises. Consider, for example, the following syllogism:
Every citizen honors his country.
John Jones is a citizen.
Therefore, John Jones honors his country.

This syllogism is dialectical because it is only a probable truth that
every citizen honors his country. In virtue of the probable truth of
the major premise, it is only probably true, as an inference, that John
Jones honors his country. Nevertheless, because of the connection
of the terms in the syllogism, the conclusion necessarily follows.
Notice, then, that in a dialectical syllogism, we are inclined to accept
the conclusion as true, although not without a kind of fear that the
opposite may be true.
A dialectical syllogism is made up of dialectical propositions just
as a demonstrative syllogism is made up of scientific propositions. A
scientific proposition is a proposition that is certain, excluding com­
pletely the opposite possibility, as, Every human being is mortal. A
dialectical proposition is a proposition that is probable, not excluding,

182

ARGUMENTATION MATERIALLY CONSIDERED

therefore, the opposite possibility, as, Every mother loves her child.
Let us note, however, that a scientific proposition may be treated as
dialectical by a person who does not recognize the proposition as
scientific. Thus, God is an immaterial being is a scientific propo­
sition, but may be treated as dialectical by a person who does not have
sufficient knowledge of God.
A syllogism is made up not only of propositions, which compose or
divide simple objects, but also of simple objects themselves, known
by definitions. A demonstrative syllogism uses definitions of simple
objects, which explain natures adequately as they are known in differ­
ent sciences. Such a definition explains the principles of a nature as
it is studied in a given science. For example, in moral science the
definition would have to explain the voluntary nature of human acts,
whereas in psychology the definition would have to explain the vital
nature of human acts. However, in a dialectical syllogism we can
use definitions of simple objects that are inadequate in a given science.
If, in psychology, we define man as a featherless, biped animal, this
definition would be dialectical because it does not define man ade­
quately in terms of his proper principles, but inadequately in terms
of common accidents.
It should be added that a definition can be dialectical in one science
and scientific in another. If, in psychology, anger is defined as a
desire for revenge, this definition would be dialectical. It defines
anger in terms of principles of moral science rather than those of
psychology. It would be a scientific definition in moral science.
Dialectical argumentation will concern a dialectical problem. A
dialectical problem is an inquiry about the composition of the objects
signified in the proposition. It asks whether the objects are to be
united or not. For example, Is two-footed animal a definition of
man? is a dialectical problem. There are as many dialectical prob­
lems as there are dialectical propositions. The dialectical problem
adds the note of inquiry to the dialectical proposition. It inquires
about something on which men either hold no opinion for or against,
or where common opinion clashes with that of authorities, or where
authorities differ among themselves. Dialectical problems also include
questions difficult to answer because they are vast and complicated, for
example, whether complete natural happiness is attainable or not.
Furthermore, every dialectical proposition or problem concerns a
predicate which is either a property, a definition, a genus, or an ac­
cident. These are not to be taken merely as the predicables in the
first act of the intellect; they are, rather, the actual predicates from
which the dialectical propositions and problems are formed. Although,
according to its universality, animal is an instance of the predicable

ARGUMENTATION MATERIALLY CONSIDERED

183

“genus” (in so far as animal can be said of inferiors), nevertheless it is
not an actual predicate until we state a proposition or a problem, for
example, is it true that man is an animal?
Having discussed the kinds of dialectical problems, we shall now list
the various means to be used in reasoning dialectically. There are
four common means that will supply us with reasonings for problems.
The first and most important is the ability to choose and determine
the probable propositions from which we are to argue. As we have
seen, we may take opinions generally held, as being likely sources of
argument, or we may construct an argument based upon the authority
of one qualified in the field. We may also take from a science some
proposition that admits of common application to other sciences. For
example, from the logical principle that contraries pertain to the same
genus, we can argue that a doctor should know both health and disease.
The second means of dialectical argumentation is the ability to
distinguish the various senses in which a particular expression is used.
Thus, we should know how to test the meaning of a word to see
whether it retains the same meaning or is ambiguous. For example,
we can show that the word “sharp” has more than one meaning by ex­
amining the meaning of its contraries. If its contraries have diverse
meanings, then we can argue that “sharp” also has diverse meanings.
Thus, in the case of a musical note, the contrary of sharp is flat, while
in the case of a blade, the contrary of sharp is dull. Since its contraries
have various meanings, the word “sharp” will also have several mean­
ings, corresponding to the meanings of its contraries.
The third means of dialectical argumentation is the ability to dis­
cover differences between things. For example, we might start with
the common principle that wherever there are contraries, opposite
effects are to be expected. We notice such a diversity of effects in
observing the operation of the good man and the bad man, and from
this we can conclude that the good man is contrary to the bad man.
The fourth means of dialectical argumentation is the ability to
penetrate the likenesses of things. Thus, we can propose an argument
resting upon a similarity between things that are in some way differ­
ent. For example, we can argue that as A is to B, so C is to D, or,
as an image is to the power of sensation, so a concept is to the power of
thinking. An argument based upon similarities is very useful for
induction, in which we argue from the enumeration of similar cases to
a universal statement. This kind of argument is frequently used by
the experimental scientist.
A treatise on dialectics should now discuss the particular means of
argumentation that are proper to each of the four predicates mentioned
above, namely, property, definition, genus, and accident. We shall not

184

ARGUMENTATION MATERIALLY CONSIDERED

go into detail on these in an elementary treatment of dialectics. Such
a treatment, however, would discuss the ways of testing whether a given
predicate is a property, a definition, a genus, or an accident, of its sub­
ject. Thus, in the case of a property, we should discuss whether the
predicate is stated so as to be coextensive with the subject, and so on.
Dialectical argumentation is useful in at least three ways. It has
the immediate and obvious use of developing skill in argument. By
employing the means of dialectical argumentation, we shall see how
to lay down a plan or outline of inquiry and pursue it to a tentative
resolution of the problem. Secondly, dialectical argument is useful for
meeting opinions held by various persons. We learn to detect views
that are matters of opinion, and to deal with them dialectically in
order to see what truth or error is in them. Thirdly, dialectical
argument is of special use in philosophy, for by it we can raise diffi­
culties on both sides of a question and thus dispose the ground for a
demonstrative resolution of the question, if one can be made. Dia­
lectical argument is especially needed to explain and defend the first
principles of a science, since the first principles of a science cannot be
demonstrated. It indicates the self-evidence of such principles and
meets any attacks or objections that may be raised against the primacy
and evidence of these principles. For example, we can manifest and
defend the principle of contradiction dialectically.
Dialectical argumentation has a particularly important application
today in the experimental physical sciences, where the inductive argu­
ment is dialectical. The universal necessity of most statements in
these sciences is neither evident nor certain, but only probable. For
example, we do not see why atoms have to move at the speed they
do, but from several observations we construct the universal law stating
that they do. We then grant its universal application.
From the knowledge of dialectical argumentation, we derive the more
common notion of a dialectical process, whether in reasoning or in
reality. In reasoning, the process means arguing both sides of a
question, thus arriving at a resolution as to the more probable position
or the one that more closely approaches the truth. As long as the
process is only an approach to the truth, it remains dialectical.
The gradual approach to the knowledge of physical natures is also
a dialectical process. We cannot know the proper nature, principles,
and causes of many concrete things in the physical order, but we can
approach closer and closer to a real knowledge of them dialectically
by proposing theories or probable explanations, and then verifying
them through experimentation, making better theories that ex­
plain more than the former theories, again verifying them, and so
on. As with all dialectical procedure, we can approach closer to a

ARGUMENTATION MATERIALLY CONSIDERED

185

real explanation in terms of proper causes, but we shall never be
able to achieve this unless we are able to use demonstrative argu­
mentation.
This notion of process toward a term has also been applied to the
real order in the thesis, antithesis, and synthesis of the Hegelians.
They employed this process to explain the unfolding of universal being
into the many particular kinds of being that now exist. The Com­
munistic notion of the necessity of violent revolution between classes
in order to arrive at a new social and economic order is another example
of a dialectical process. Since this process is one that will continue
to be repeated in an ever new form, it is dialectical in nature. Hence
arises the significance of the phrase “dialectical materialism” as applied
to the doctrine of Communism.
III. RHETORICAL ARGUMENTATION

Rhetorical and dialectical argumentation have much in common.
Both deal, more or less, with all things, not being limited to one kind
of subject matter. Both discuss and defend either side of a question,
and hence both proceed from probabilities, not from certainties. They
proceed from common principles, not from proper principles. On all
these points, dialectic and rhetoric differ from demonstrative argu­
mentation.
Dialectic and rhetoric differ from each other in the following ways.
Dialectic is an instrument for discussion and dispute in philosophy and
in science, whereas rhetoric is an instrument for convincing people
generally. Dialectic, for the most part, is concerned with universal
questions and problems, abstracting from singular circumstances of
person, place and time. Rhetoric is especially concerned with moral
and political questions, which are often restricted to singular circum­
stances of person, place, and time. Dialectic tends to use a strict
and contracted form of argumentation; rhetoric, a looser and more
expansive form. Dialectic uses reasons for proving points; rhetoric
uses the movement of the emotions and hence persuades rather than
proves.
Rhetoric, consequently, is defined as the ability to employ, in any
given situation, the available means of persuasion. By rhetorical argu­
ment, we seek to persuade someone on almost any subject. The
rhetorician argues by using the enthymeme and the example. The
enthymeme is the rhetorical syllogism and is the more effective kind
of persuasion. It is an argumentation proceeding from probabilities or
signs. The enthymeme has the form of an abbreviated syllogism, that
is, a syllogism without one of its premises. When used by the

186

ARGUMENTATION MATERIALLY CONSIDERED

rhetorician, the enthymeme usually lacks the universality necessary for
a proper syllogism.
For example, we might argue that John Jones should not be elected
mayor because he has lived too short a time in the city. This is an
enthymeme arguing from the probability, omitted in the enthymeme,
that those who have lived too short a time in a city should not be
elected mayor. As we have mentioned, the enthymeme does not
usually have the universality necessary for the true syllogism, but it is
intended to satisfy only for persuasive purposes. An example of an
enthymeme arguing from a sign is, John Jones is guilty because he
trembles. The condition of trembling is taken as a sign of guilt. It is
evident, from this instance, that the rhetorical syllogism persuades
rather than proves.
The argument from an example is like an inductive argument.
When two statements are of the same order, but one is more familiar
than the other, the more familiar one can be used as an example to
manifest the other one. The following would be an argument of this
kind. If the United States spends 70 per cent of its peacetime budget
on arms, it will go to war, because Germany under Hitler did this
and went to war. The instance of Germany under Hitler (or France
under Napoleon) serves as a familiar example to manifest a presumed
parallel situation. The argument from an example differs from a
strict inductive argument in that induction derives its proof from all
the particular cases, whereas the argument from an example argues
from one or more particular cases to another case.
There are three modes of persuasion. The first depends upon
the personal character of the speaker who, in speaking, makes us
regard him as an upright person, for we are more readily inclined to
believe honorable persons than others. The character of a person is
usually his most effective means of persuasion. The second mode of
persuasion depends upon the listeners, upon the way their emotions
move in relation to the speech, for as we are emotionally inclined
so are we likely to judge. The third mode of persuasion is the speech
itself, the proof or apparent proof contained in the persuasive argu­
ment. ■
Accordingly, the prerequisites for a good rhetorician are the follow­
ing. He must be able to reason logically, for although rhetoric aims
to stir the emotion of the listener so as to persuade him to accept a
position, still the rhetorician must employ reasoning to accomplish
such persuasion. The rhetorician must understand human character
and what makes human character good, for the rhetorician has the ob­
ligation to persuade men to accept what is just or honorable or good.
Finally, the rhetorician must know the emotions, their different kinds,

ARGUMENTATION MATERIALLY CONSIDERED

187

and how they are aroused, for persuasive argument relies upon an
arousing of the emotions in order to move a person to accept a position,
and to act.
There are three kinds of rhetoric, determined in relation to the
listener. If the listener is one who must judge future events, then the
rhetoric is political. For example, the listener may be a member of a
legislative body, who must decide political issues, or he may be an
ordinary citizen, who must decide for whom to vote. The purpose of
political rhetoric is to show the expediency or harmfulness of a certain
course of action.
If the listener is one who must judge past events, then the rhetoric
is forensic or juridical. The listener may be a juror in the courtroom
who, in hearing a case, must judge the goodness or badness of an action
done previously. The purpose of forensic rhetoric is to establish the
justice or injustice of a certain action.
If the listener is one who is judging what is taking place at the
moment, and is concerned only with the present, the rhetoric is
ceremonial. The listener may be hearing a speech at some banquet
or other public occasion, where a testimonial is being given to an
outstanding citizen. The purpose of ceremonial rhetoric is to praise
or censure a human being.
Rhetorical argument is useful, for it is often the only way in which
a point can be established, either because the point itself is too obscure
or inevident to be manifested in any other way, or because some persons
cannot be convinced at all except by persuasive argument. Further,
through rhetoric we know how to use persuasion on both sides of a
question, not for the purpose of actually trying to make someone believe
that what is wrong is right, but in order to recognize an unfair argu­
ment when it appears, and so be able to refute it. Finally, rhetoric is a
means of defending oneself by argument, and there are times when one
should defend himself. Frequently, rhetoric is the only kind of argu­
ment possible, and one should use it at such a time, for one has a right
to use rhetoric for any good purpose.
One should not, therefore, look down on rhetorical argument, or
think that all such argument is bad or unfair because it has been em­
ployed perversely. For although great injury has been done by those
who have abused rhetoric, great good has also been accomplished by
those who have used it rightly.
IV. POETIC ARGUMENTATION

Although it may seem strange to include it in logic, poetics is never­
theless a part of rational philosophy and, in fact, is a distinct kind of
argumentation. The purpose of all argumentation is to lead one to a

188

ARGUMENTATION MATERIALLY CONSIDERED

new truth from previous knowledge. Poetry, although the weakest
form of argumentation, does lead us to new truths. In doing so poetry
has its own means of inducing assent to truth. As a part of rational
philosophy, poetics should consider at least the means the poet uses,
the objects the poet represents, and the end of poetry. We shall be
using the terms “poetics” and “poetry” in a generic sense, as referring
to all works of fine art employing words and sounds as means of
representation.
The poet seeks to induce assent to truth by a pleasing representation
of truth. Just as forms and colors are used by the painter in his
representations, so words and sounds are used by the poet. He uses
words chiefly to compose metaphors and similes, whereby, because of
the lack of intelligibility in contingent things, a poetically imaginative
meaning is read into things. He uses sounds in a pleasing manner by
the employment of rhyme, alliteration, rhythm, and so on.
Now the poet presents his truth in terms of an image, for men
naturally delight in images. Indeed, in the very making of the image,
the poet makes his meaning. Hence, one will attain this truth, not
directly in itself, but in the image that the poet presents. By repre­
senting the image in a pleasing manner, the poet leads one to agree with
his judgment. For example, Shakespeare induces us to accept the
universal judgment that uncontrolled ambition can lead to a man’s
downfall by giving us a particular representation of this in the person
and action of Macbeth. From the acceptance of this particular repre­
sentation we are led to accept the universal judgment. We realize
that what has happened to Macbeth could happen to ourselves or to
anyone.
The image attained by the poet is in the rational order; his image
is presented in words, which can be known only by the intellect. In
an intimate union of sense and intellectual knowing lie the strength
and appeal of the poet, for while he does attain something universal,
he attains it strikingly, vividly, and familiarly, as it is realized in the
singular. We see, as it were, the universal concretized. Through the
image in words, a truth is conveyed, a truth contained in a judgment.
Herein, then, lies the significance of the phrase “argument of the play”
that we find stated as an introductory summary in a program. This
rationality of the poetic image is not attained by the images of the other
fine arts. For this reason, poetry is the most intellectual of the fine
arts and is the only one that has argumentation, properly speaking.
The objects the poet represents are human actions of agents who are
necessarily either good or bad, since it is the first property of human
action to be good or bad. Consequently, in his work of representing
human actions, the poet must present a judgment bearing on the

ARGUMENTATION MATERIALLY CONSIDERED

189

morality of these acts; the poet cannot abstract from the first property
of human action. This does not mean, however, that he “moralizes”
art in the sense of imposing morality upon art, but that in treating the
proper matter of his art he must, as artist, observe faithfully the nature
of that matter, namely, that some human actions are good and others
are bad. He has the obligation as artist to represent good human
action as good and bad human action as bad.
The intrinsic end of poetry is to represent truth and to cause delight
in the knowledge of this representation. In realizing this end, the
poet also introduces an order into the movement of the passions. For
example, in a tragedy the poet arouses and resolves the appropriate
emotions of pity and fear. We experience a certain satisfaction in this
exercise of the emotions and a relief from the turbulent disorder often
found in them.
The extrinsic end of poetry is to make men disposed to acquire
virtue and to avoid vice. This is accomplished both by the acceptance
of the judgment made by the poet and by the ordering of the passions
(the poetic catharsis of the emotions). More men are led to the acquir­
ing of virtue through representations than they are through reasoning
bearing directly on morality. Accompanying this extrinsic end, there
is the recreational effect of release from the cares and frustrations of
everyday life. By introducing something of a rational order into a
course of events, the poet relieves the irrationality that we often face
in our daily lives.
QUESTIONS---- CHAPTER TWENTY-TWO

1. What does “analytics” mean? Explain prior analytics and posterior
analytics.
2. Why is argumentation considered first on the part of form?
3. What does it mean to know in a “discursive” manner?
4. Is the following a perfect demonstration? Explain.
Every animal is living.
Every dog is an animal.
Therefore, every dog is living.
5. Of what things must we have foreknowledge in order to demonstrate?
In what does the foreknowledge consist in each case?
6. Define science in the strict sense.
7. Define demonstration on the part of matter. What is the relation of this
definition to the definition of demonstration according to final cause?
8. Can a true conclusion follow from false premises? Explain.
9. Can every premise be proved true? Explain.
10. When is a proposition self-evident? Give examples.
11. Explain how premises are “prior” to the conclusion, “better known” than
the conclusion, and “causes” of the conclusion.
12. What is the principal kind of demonstration? Illustrate with an example.
13. What is the meaning of “demonstration of the fact”?

190

ARGUMENTATION MATERIALLY CONSIDERED

14. What is the difference between a priori demonstration and a posteriori
demonstration? What kind of division of demonstration is this?
15. How does the division of demonstration into proper cause and of the
fact compare with the division of demonstration into a priori and a
posteriori?
16. How does a dialectical syllogism differ from a demonstrative syllogism?
17. Explain the following statement: “We argue dialectically when we reason
from probable principles which are generally held.”
18. Does a probable conclusion follow probably from the premises? Explain.
19. What is a dialectical proposition?
20. When is a definition dialectical?
21. What is a dialectical problem? How does it differ from a dialectical
proposition?
22. From what predicates are dialectical problems formed?
23. What are the four common means of dialectical argumentation? Give
examples of each kind.
24. In what ways is dialectical argument useful?
25. What is a “dialectical process”? How is it applied to the real order?
26. What do dialectical and rhetorical argumentation have in common?
27. How does rhetorical argumentation differ from dialectical argumentation?
28. Define rhetoric.
29. What is an enthymeme?
30. From what does an enthymeme argue?
31. Explain the argument from example.
32. What are the modes of persuasion? Which do you think would be most
effective? Why?
33. What are the prerequisites for a good rhetorician?
34. Explain the three kinds of rhetoric.
35. How is rhetorical argument useful?
36. Why is poetry considered in logic?
37. How does the poet use words and sounds?
38. Explain the role of the image in poetry. How does the poetic image
lead to an assent to truth?
39. In what sense must poetry as art be moral?
40. What are the intrinsic and extrinsic ends of poetry?

Chapter Twenty-three
SOPHISTICAL REASONING

OPHISTICAL reasoning is reasoning used for sophistical
refutation. It appears to be genuine reasoning but actually
is fallacious. Sophistics, therefore, is that part of logic concerned
with the defective syllogism. A sophistic argument is a syllogism that
seems to infer a conclusion from probable premises but, because of
one fallacy or another, does not really do so. The defect in the argu­
ment occurs either on the part of matter alone or on the part of both
matter and form.
A person who deliberately uses such fallacious reasoning is called
a “sophist.” A sophist is one who would rather appear to be wise
than be wise without appearing so; he wishes to appear wise for his
own personal gain. A sophist argues for the sake of refuting his
opponent, rather than for the sake of truth. He will pursue a point
fallaciously rather than admit that he is in error. The art of the
sophist, as Aristotle explains, is the semblance of wisdom without the
reality. By intention, therefore, the sophist deceives.
Now it is clearly not the aim of a student of logic to become a
sophist. But it is the business of the student of logic to recognize a
sophist, and to avoid fallacies in his own reasoning as far as possible.
Let us therefore examine the kinds of fallacious reasoning in order to
uncover the sources of fallacy in argumentation.
Fallacies are divided into fallacies of language (arising from the
abuse of words) and fallacies apart from language (arising from the
abuse of reasoning about things). We shall consider fallacies of
language first, because they are the most frequent source of sophistic
argumentation.

S

191

192

SOPHISTICAL REASONING

FALLACIES OF LANGUAGE

1. Fallacy of equivocation

Equivocation is the use of a word with two diverse meanings. If
an argument is constructed in which one of the terms, most frequently
the middle term, is used with two different meanings, the argument
contains the fallacy of equivocation, as in the following example:
Whatever is immaterial is unimportant.
Whatever is spiritual is immaterial.
Therefore, whatever is spiritual is unimportant.

The equivocation in this example consists of using immaterial with
one meaning in the major premise and with quite another meaning
in the minor premise. This is also called the “fallacy of four terms,”
which was referred to in the rules of the syllogism in Chapter Seventeen.
In his Sophistical Refutations, Aristotle uses the following example,
with an equivocation in the minor term:
A man who has recovered is well.
The sick man has recovered.
Therefore, the sick man is well.

2. Fallacy of amphiboly
Amphiboly (literally, “ambiguous speech”) is an ambiguity in a
phrase or in the grammatical structure of a sentence. Dangling modi­
fiers, pronouns with ambiguous antecedents, and misplaced modifiers
are occasions of misunderstanding that lead to fallacies in logic. For
example, in the sentence He told his father that he was afraid it is
not clear who is afraid; it could be the father or the one who told his
father. A less obvious, though more serious, ambiguity in gram­
matical structure occurs in the following argument:
Every judgment of man is liable to error.
God’s judgment of the people of Sodom was a judgment of man.
Therefore, God’s judgment is liable to error.

In this example, judgment of man in the major premise is used to
signify the judgment man himself makes, which is fallible. In the
minor premise, judgment of man is used to signify a judgment God
makes of man.

SOPHISTICAL REASONING

193

3. Fallacy of composition and division

This fallacy consists in combining objects in the conclusion that were
not combined or taken together in the premises, or vice versa. Such
a shift may occur also from one premise to the other. Consider the
following argument:
Three and two are odd and even.
Five is three and two.
Therefore, five is odd and even.

In the major premise, three and two must be taken separately so as
to mean that three is odd and two is even. In the minor premise,
five is three and two only if three and two are taken together. Because
of this shift from the separation of three and two in the major premise
to the composition of three and two in the minor premise, the con­
clusion does not properly follow.

4. Fallacy of accent

The fallacy of accent arises through a difference in accentuation of
the same word and results in an ambiguity of meaning. The word
“invalid” carries two quite different meanings according to whether
the accent is placed on the first or second syllable. Likewise with the
word “incense,” for it is one thing to incense a person, at a religious
service for example, and quite another to incense a person.
Emphasis upon different words within a sentence often gives rise to
various meanings that easily cause misunderstanding. In the ques­
tion What is your friend doing? a different meaning is implied each
time the emphasis is put on a different wo\ d.
5. Fallacy of form of expression

The fallacy of form of expression arises when things different in
meaning are expressed in the same form. For example, the word
“inattention” is like the word “intention” in form, but “inattention”
has a negative meaning whereas “intention” has a positive meaning.
Hence, one would be misled by the form of expression if he were to
argue that “intention” must be a negative word because it begins with
the same prefix that “inattention” does.
Fallacious arguments of this kind are sometimes quite serious. A
well known instance occurs in John Stuart Mill’s Utilitarianism. In
Chapter Four of the book, he gives the following argument:

194

SOPHISTICAL REASONING

The only proof capable of being given that an object is visible, is that
people actually see it. The only proof that a sound is audible, is that people
hear it: and so of the other sources of our experience. In like manner, I
apprehend, the sole evidence it is possible to produce that anything is
desirable, is that people do actually desire it.

Mills’s argument is that what is seen is visible, what is heard is
audible, and therefore what is desired is desirable. But “visible”
means what is actually seen and “audible” means what is actually heard,
whereas “desirable” means what should be desired. The argument
presumes that because “desirable” has the same form of expression
as “visible” and “audible,” it is the same in meaning.
FALLACIES APART FROM LANGUAGE

1. Fallacy of accident

The fallacy of accident arises from confusing an accidental attribute
of a thing with what is essential to the thing, or the confusion of an
accidental predicate with an essential predicate. For example, the
predicate white is said accidentally of man, since it does not belong
to the essence of man to be of this or that color. However, arguments
are frequently given in which the color of man is confused with what
is essential to man. Racism, as argued and practiced in various
countries, is based on the fallacy that the accident of color, or of
race, constitutes an essential difference between human beings.
Aristotle uses the following as an example of the fallacy of the
accident: The product of a small number with a small number
would have to be a small number: ten is a small number; one
hundred is ten times ten; therefore, one hundred is a small number.
It is accidental to the number one hundred that it be regarded in
groups of tens, and although the groups are small in number, the
number itself is not small.
Another example sometimes given is the confusion of the abuse
of a thing with the use of a thing. One might thus argue, fallaciously,
that no one should be allowed to drink wine because people get
intoxicated by it. Likewise, one might argue, fallaciously, that private
property is evil because it leads to selfishness or to the excessive ac­
cumulation of wealth.
2. Fallacy of the relative to the absolute

This fallacy argues from what is true only relatively, or qualifiedly,
to what is true absolutely, or without qualification. We can also
understand that fallacy as arguing from the truth of the particular to

SOPHISTICAL REASONING

195

the truth of the universal. We are all familiar with arguments pur­
porting to show that all members of a nation or religion are evil, or
superstitious, or ignorant, because a few of the members are.
In general, this fallacy consists of using a proposition, which has a
qualified meaning, as though it applied in all circumstances and with­
out restriction. One thus argues fallaciously that the commandment
“Thou shalt not kill’ forbids fighting for one’s country. But the
meaning and context of the commandment forbids killing unjustly,
that is, murdering. Again, one may argue that freedom is an absolute
good, without recognizing that necessary and justifiable limitations may
be placed upon freedom in different times and circumstances. The
fallacy in this argument is the assumption that freedom is an absolute
good rather than a good relative to an end.

3. Fallacy of ignoring the issue
This fallacy consists of refuting a point that is not the point in
question, or of proving something that is not the point of issue. An
example of this fallacy is the argument that a liberal education is
not practical because it does not result immediately in a cash dividend.
There are various forms of the fallacy of ignoring the issue. One
may confuse the person with the issue (argument ad hominem) by
arguing that one’s opponent cannot know the meaning of justice,
since he never practices it. One may use emotional or physical force
(argument ad baculum) by threatening an opponent, thus seeking to
make him concede the point through fear. One may use an appeal
to the audience (argument ad populum) by arousing their passion and
prejudice, thus seeking to settle the matter emotionally rather than
upon its own merits. One may use an argument from misplaced
authority (argument ad verecundiam) by arguing from the authority
a man has in one field as though it held equally well in another. For
example, one might seek to prove or disprove freedom of the will from
the authority of an experimental scientist.

4. Fallacy of begging the question

This fallacy arises from presupposing in the premises the conclusion
that has to be demonstrated from the premises. Thus, one might
argue that to return borrowed money is right because justice is a
virtue. But justice as a virtue means that one should give to others
what is due to them. Therefore, one cannot assume in the premises
that justice is a virtue, since he is trying to prove that a certain action
is right, that is, virtuous, in the conclusion.
Arguing in a circle is an extended form of begging the question.

196

SOPHISTICAL REASONING

A circular argument occurs when a premise is used to prove a con­
clusion, and then the conclusion is used to prove the premise. For
example, one might try to arrive at the existence of God from the
idea of God as existing in the human mind. If he then tried to
argue the reliability of the human powers of knowing from the
existence of God, he would be arguing in a circle.
•
5. Fallacy of the consequent
This fallacy consists of supposing that because the consequent
necessarily follows from the antecedent, then the antecedent necessarily
follows from the consequent. Thus, because it is true that if X is
then Y is (from antecedent to consequent), one might also suppose
the reverse, that if Y is then X is (consequent to antecedent). Hence,
one might argue, if whenever it rains the ground is wet, then if the
ground is wet it has rained.
We considered the relation of the consequent to the antecedent when
we discussed the conditional syllogism in Chapter Twenty. Just as
there are two valid ways of concluding the conditional syllogism, so
there are two invalid ways, which we shall recall here. In affirmative
arguments, the fallacy of the consequent arises by affirming the conse­
quent in the minor premise and then affirming the antecedent in the
conclusion, as in the following:
If something is generated, it has a beginning.
The human soul has a beginning.
Therefore, the human soul is generated.

In negative arguments, the fallacy of the consequent arises by denying
the antecedent in the minor premise and the consequent in the con­
clusion:
If something is generated, it has a beginning.
The human soul is not generated.
Therefore, the human soul does not have a beginning.

6. Fallacy of the false cause

The fallacy of the false cause supposes that something is the cause
of an effect when in reality it is not. Thus, something might be as­
sumed to be a cause merely because it is prior in time. This par­
ticular form of the fallacy is often referred to as post hoc, ergo propter
hoc (after this, therefore because of this); for example, morning comes
after night, therefore morning is caused by night. Again, one might
suppose that, what accompanies an action is the cause of that action;

SOPHISTICAL REASONING

197

for example, because one’s arms swing when walking, therefore the
swinging of the arms is the cause of the walking. Or, finally, one
might suppose that a condition is a cause, for example, that light is the
cause of seeing.
7. Fallacy of the complex question
This fallacy puts questions in such a way that any answer given
implies more than a simple admission. The question asked is usually
a complex one to which a simple “Yes” or “No” cannot be given.
Thus, someone might ask: “Was the impeachment of President Andrew
Johnson justifiable and constitutional?” The answer seems to be that
it was constitutional but not justifiable, and in such a case a simple
answer of “Yes” or “No” would not suffice.
Under this fallacy is included a question so worded as to place the
answerer in an unfair, if not impossible, position. The famous
question “Have you stopped beating your wife?” is an instance of this
type of fallacy. If one answers “Yes” to the question, he implies that
he has been beating his wife. If he answers “No,” he implies that
he is still beating her. This type of question is called a “leading
question” and is ruled out of court in legal debates.

EXERCISE ON FALLACIES— CHAPTER TWENTY-THREE
There is no complete enumeration of the kinds of fallacies. They cannot
be exhaustively classified because the errors the human intellect can make
are infinite. Hence, it is not so important to name the kind of fallacy as
it is to see that a process of reasoning is fallacious and to see how it can be
refuted. In each of the following exercises, examine the reasoning to see
where the fallacy lies and how it can be refuted. If possible, name the kind
of fallacy.

1. Whoever has a virtue has the mean.
Whoever is mean is nasty.
Therefore, whoever has a virtue is nasty.

2. Many college students have great ability and are conscientious workers.
John Jones, for instance, is a conscientious worker.
Therefore, John Jones must have great ability.

3. He who studies least learns least.
He who studies most has least to learn.
Therefore, he who studies most learns least.

4. It is either raining or it is not raining.
It is not raining.
Therefore, it is raining.

5. When thoroughly stewed, you remove the bones torn the chicken.

6. The management reserves the right to exclude any man or woman they
think proper.

logic: the art of defining and reasoning,

199

copyright,

1952,

by prentice-hall, inc.

7. The college newspaper quoted the senior class president as saying that half
of the freshman were dumb. In the next issue of the paper, the senior
class president had a letter printed, saying: “I was misquoted. What I
said was that half of the freshmen were not dumb.”

8. It is certainly true that if a person has been running rapidly, then he is
short of breath. It must be just as true that if a person is short of breath,
then he has been running rapidly.

9. Some girls are attractive.
Betty is some girl.
Therefore, Betty is attractive.

10. No prophet is honored in his home town. I observe that I am not honored
in my home town. So I can only conclude that I am a prophet.

11. The following account appeared in a newspaper:
Is there a God? This question was answered in the negative by a retired
professor of philosophy. “There are so many concepts of God that to answer
the question about His existence flatly is to get nowhere,” he stated. No
good God, he continued, would permit the suffering that is rampant through­
out the world. He cited the example of the agony thousands of small children
went through during World War II. To say this is due to the sins of their
parents or that boys and girls will receive their reward in heaven is begging
the question.
After all, he went on, man is only one of many creatures that have been
on top of the heap in the world’s struggle. And man came along late in the
process of evolution. “I’m sure if the dogs ever had a convention, they would
as certainly proclaim themselves leaders of the world as we human beings do,”
he observed.
The retired professor of philosophy prefers to be known as a “reverent
agnostic.” He looks like the pastor of a fashionable church. He believes
people should lead an intelligent, decent, honest, humanitarian life. “Such
a life depends on getting at the truth about the world in which we live and
ourselves and in having faith in mankind,” he said.
“I want everyone to live the most livable life possible,” he concluded.

12. He killed his daughter Ruth and is therefore ruthless.

200

13. Alcohol is commonly recognized as a germicide. It is a known fact that
most germs are carried in the blood stream. Therefore, in order to stay
healthy, we should keep a sufficient quantity of alcohol in the blood at
all times.

14. Nothing is better than heaven.
Half a loaf is better than nothing.
Therefore, half a loaf is better than heaven.

15. The distinguished visiting lecturer concluded with the following words:
“Now if all nature were adaptive and every part of an organism were to
fit as the parts of a watch, the argument from design might hold. But think
of man’s vermiform appendix that is not only useless but often a source of
grave danger and death; think of his useless ear muscles that are present but
can accomplish no useful function; think of the functionless breasts of males;
think of the vestigial tail, the ill-adapted wisdom teeth, etc. Does it seem
reasonable to suppose that these useless structures were designed in their
present form? If some parts of an organism are obviously not designed, is it
likely that others were designed and that the useless parts merely slipped
in by mistake? Such considerations as these, and others equally conclusive,
make it impossible for us, as seekers after truth, to accept the view that
adaptation in nature is the result of intelligent design.”

16. All men are human.
No women are men.
Therefore, no women are human.

17. The newspaper reported the arrival by plane of Professor X, whose latest
book on Comparative Intelligence of Insects and Men has caused a stir in
intellectual circles. Professor X gave the following quotation to the press:
“The majority of species have degenerated and become extinct, or, what
is perhaps worse, gradually lost many of their functions. The ancestors of
oysters and barnacles had heads. Snakes have lost their limbs, and penguins
their power of flight. Man may just as easily lose his intelligence.”

18. Radio commercial: “Our automobiles are out of this world.
and see them.”

logic: the art of defining and reasoning,

201

copyright,

1952,

Come down

by prentice-hall, inc.

19. Sign on a construction job: Slow Men Working.

20. The invention of machinery increased productivity. Increased produc­
tivity brought about the abolition of slavery. The abolition of slavery
increased the dignity of man. Therefore, the invention of machinery
increased the dignity of man.

21. A man held a trained flea in his right hand and said, “Jump!” The flea
jumped to his left hand. He repeated the command and the flea returned
to the man’s right hand. Then the man removed the flea’s hind legs
and once again commanded, “Jump!” The flea remained where it was.
This proves that the flea hears through its legs.

22. The professor of logic concluded by saying, “The only thing that is certain
is that there is no certainty.”

23. The existence of God is self-evident. For by the name “God” is signified
that thing than which nothing greater can be conceived. But that which
exists both actually and mentally is greater than that which exists men­
tally. Therefore, since as soon as the name “God” is understood it exists
mentally, it also follows that it exists actually. Therefore, the proposition
“God exists” is self-evident.

24. Communism will flourish wherever living conditions are bad and especially
where there is a wide gulf between the standards of the rich and those
of the poor. Eliminate bad living conditions and you eliminate Com­
munism.

25. I asked my instructor what he thought about one of the editorials in the
college paper. He said that he had not read it. He then asked everyone
in the English office, but not one of them had read it. This shows how
little interest the faculty takes in student affairs.

202

26. If you believe that voting in public office should be kept secret, then you
should believe that voting in the senate should be kept secret.

27. “I shall put it to you on cold, logical grounds,” concluded the Director of
Statistical Research. “If there is no God then there is no absolute
morality. Now it is self-evident that there is no absolute morality since
everything changes and progress is ever upward. Therefore, there is no
God. Besides, the notion of a God is a hang-over from medievalism and
all morality is a reactionary device designed to subjugate the working
people. Furthermore, freedom of speech is the only moral value that is
good and all moralists attack freedom of speech, for they attack me and
then hide behind the camouflage that I am illogical.”

28. “If you think that our ushers are rude,” said the chief usher, “you should
see the manager.”

29. There is no democracy in a military system. Therefore, there is tyranny
in a military system and all military men are tyrants. Therefore, there
would be no democracy if a military man were elected president of a
country.

30. Newspaper headline: Revived Dead Woman Succumbs.

31. One is either good or bad.
John is neither good nor bad.
Therefore, John is not one.

32. “Madam,” said the jeweler, “this ring I am offering you is really priceless.”
“In that case,” said the young lady, who had just finished a course in
elementary logic, “I shall give you only a dollar for it, because if it is
priceless, then it is certainly worthless.”

logic: the art of defining and reasoning,

.203

copyright,

1952,

by prentice-hall, inc.

33. Catholics and Protestants are Christians.
No men are Catholics and Protestants.
Therefore, no men are Christians.

34. A draft official has said, "45 per cent of the eligibles are rejected because
they do not meet physical standards.” That winds up to drafting the
best of us to protect the worst of us and leaves the least of us to run the
country for the most of us.

35. All knowledge is caused by means of a likeness. But there can be no
likeness of a body to an incorporeal thing. If, therefore, the soul were
not a body, it could not have knowledge of corporeal things. Therefore
the soul must be a body.

204

APPENDIX

Excerpt from

Commentary of St. Thomas Aquinas

on
ARISTOTLE’S POSTERIOR ANALYTICS
*

LESSON I

1. As Aristotle says in the beginning of the Metaphysics, the human
race lives by art and reason. The Philosopher here touches upon a
certain property of man by which he differs from other animals, for
other animals are moved to their acts by natural instinct while man
is directed in his actions by the judgment of reason. The various
arts, then, serve to bring human acts to their completion in an easy
and orderly manner. In fact, art is nothing else than the certain
ordination of reason by which human acts arrive at their proper end
through determinate means.
Now reason can direct not only the acts of the inferior powers of
man, but is even directive of its own acts. It is a property of the
intellective part of man to reflect upon itself, for the intellect under­
stands itself and, similarly, reason is able to reason about its own act.
Hence, just as reason reasons about the manual acts man performs
such that it has devised, for example, the art of building, by which
man can exercise an act of this kind easily and in an orderly way,
so it is necessary to have an art that directs the very act of reason,
by which man, in the very act of reasoning, may proceed in an orderly
way, with ease, and without error.
2. This art is logic, i.e., rational science. It is rational not only
because it is according to reason, for this is common to all the arts,
but because it is concerned with the very act of reason itself as its
proper matter.
3. Consequently, it is the art of arts, because it directs us in the

* This translation is based on the. text of the Leonine Edition of the Opera Omnia
of St. Thomas Aquinas, Vol. I, pp. 138-140; Commentary on Aristotle’s Posterior
Analytics, Lesson I, nn. 1-6.
207

208

APPENDIX

act of reason from which all the arts proceed. Therefore, the parts of
logic must be taken according to the different acts of reason.
4. There are three acts of reason, the first two of which are of reason
as it is a kind of understanding.
The first action of the intellect is the understanding of things that
are simple or incomplex, according to which the intellect conceives
what a thing is. . . . The doctrine that Aristotle treats in his book
on the Categories is ordered to this operation of reason.
The second operation of the intellect is composition or division, in
which the true or the false appears. Aristotle treats the doctrine
ordered to this operation of reason in his book On Interpretation.
The third act of reason is properly the act of reasoning, which is
to proceed discursively from one thing to another so as to arrive at a
knowlédge of the unknown from that which is known. The remaining
books of Aristotle’s logical works are ordered to this act of the intellect.
5. Now it must be noted that the acts of reasoning are similar, in a
certain respect, to the acts of nature, for in this also art imitates nature
so far as possible. Now three different ways of acting are found in
the acts of nature. In some things, nature acts from necessity in such
a way that it cannot fail. In other things, nature operates with its
usual regularity, although sometimes it can fail in its proper act.
Hence in these things, there must be a twofold act. One act is that
which happens for the most part, as when a perfect animal is gen­
erated from a seed. The second act is that which happens when
nature fails in what it is proper to it, as when, because of the corrup­
tion of some principle, a monster is generated from a seed.
These three different ways of acting are likewise found in the acts
of reasoning. There is one process of reasoning inducing necessity, in
which there cannot be a defect of truth. By this kind of process of
reasoning the certitude of science is acquired. There is another process
of reasoning in which the truth is arrived at for the most part, not,
however, having necessity. There is a third process of reasoning in
which reason falls away from what is true because of a defect in some
principle that should have been observed in reasoning.
6. The part of logic devoted to the first process is called judicative
because there is judgment with the certitude of science. And since
we cannot have certain judgment concerning effects without resolution
to first principles, this part is called Analytics, i.e., proceeding in the
manner of resolution. Now this certitude of judgment, which is ob­
tained by resolution, is either from the form alone of the syllogism,
and the book of the Prior Analytics, which treats of the syllogism
simply, is ordered to this; or it is also from the matter, because proposi­
tions that are essential and necessary are used, and the book of the

APPENDIX

209

Posterior Analytics, which treats of the demonstrative syllogism is
ordered to this.
The part of logic which is called the inventive part, is devoted to
the second process of reasoning. But there is not always certitude
with invention. Hence, when something is found by invention, judg­
ment is required in order that there be certitude. Now just as in
natural things which occur for the most part, a certain gradation is
attained (for according as the power of nature is stronger so much
the more rarely does it fail in its effect), so also in the process of
reasoning which is not altogether certain, a gradation is found accord­
ing to which the reasoning process approaches more or less to perfect
certitude. Sometimes by this process, even though science is not ob­
tained, nevertheless faith or opinion is obtained, because of the prob­
ability of the propositions from which the reasoning proceeds. In
such a case, reason totally inclines to one part of a contradiction,
although with fear of the other part. The Topics or Dialectics is
ordered to this kind of reasoning, for the dialectical syllogism pro­
ceeds from probable propositions, which Aristotle treats in the book
of the Topics.
Sometimes, however, faith or opinion is not completely obtained,
but a kind of suspicion because reason does not totally incline to one
part of a contradiction, although it inclines to one part more than to
another. The Rhetoric is ordered to this kind of reasoning.
But sometimes there is only a judgment inclining to some part of
a contradiction because of a certain representation, as when a man
is brought to detest certain food because it is represented to him in
the likeness of something detestable. The Poetics is ordered to this
kind of reasoning, for poets lead us to something virtuous through
a becoming representation.
Now all of these pertain to rational philosophy, for to induce one
thing from another belongs to reason.
The part of logic called sophistic is devoted to the third way of
reasoning, (in which reason falls away from what is true because of
a defect in some principle that should have been observed in reasoning).
Aristotle treats this in the book Sophistical Refutations.

Excerpt from
ARISTOTLE’S ON INTERPRETATION
(translated from the greek)

with
Commentary of St. Thomas Aquinas
(translated from the latin)*

Chapter One
(16® 1) First we must establish what a noun is and what a verb is;
then, what are negation and affirmation, and enunciation and speech.
LESSON I

(Commentary of St. Thomas)
1. As the Philosopher says in the third book of On the Soul, there
is a twofold operation of the intellect. One is called the understand­
ing of indivisible things, by which the intellect apprehends the essence
of each thing in itself; the other is the operation of composing and
dividing. There is, in addition, a third operation, that of reasoning,
according to which reason proceeds from known things to the inquiry
of unknown things. Now, the first of these operations is ordered to
the second, because there cannot be composition and division except
of things simply apprehended. The second, in turn, is ordered to
the third, for clearly we must proceed from some known truth, to
which the intellect assents, to reach certitude about something
unknown.
2. Now since logic is called the rational science, it is necessary that
its consideration be directed toward those things belonging to the
three operations of reason previously mentioned. Hence, Aristotle

* This translation, both from the Greek of Aristotle and from the Latin of St.
Thomas, is taken from the Leonine Edition of the Opera Omnia of St. Thomas,
Vol. I, pp. 7-18; Commentary on Aristotle’s On Interpretation, Chapter One,
Lessons I-III. References in footnotes appear as they are in the Leonine Edition.
210

APPENDIX

211

determines those things belonging to the first operation of the intellect,
i. e., those conceived in the simple understanding, in the book On
the Categories. Concerning those things belonging to the second
operation, namely affirmative and negative enunciation, the Philoso­
pher determines in the book On Interpretation. He determines those
things belonging to the third operation in the book of the Prior Ana­
lytics and the books following it, in which he treats of the syllogism
absolutely, the diverse kinds of syllogism, and the species of argumenta­
tion, in which reason proceeds from one thing to another. And thus
according to the order of the three operations mentioned above, the
book On the Categories is ordered to On Interpretation, which is
ordered to the book of the Prior Analytics, and those following it.
3. Accordingly, the book which we are now examining is called
Peri Heremeneias, that is to say, On Interpretation. Now an inter­
pretation, according to Boethius, is a significant sound, which of itself
signifies something, whether it is complex or incomplex. Hence, con­
junctions and prepositions and other things of this kind are not called
interpretations because they do not of themselves signify something.
Similarly, even sounds signifying naturally but not from purpose, or
with the imagination of signifying something, such as the sounds of
brute animals, cannot be called interpretations, for the one who inter­
prets intends to explain something. Hence only nouns and verbs
and speech are called interpretations, and these he determines in
this book.
However, the noun and the verb seem to be more principles of
interpretation than interpretations. In fact, he seems to interpret who
shows something to be true or false. Therefore, only enunciative
speech, in which the true or the false is found, is called interpretation.
Other kinds of speech, such as optatives and imperatives, are ordered
more to expressing volition than to interpreting what is in the intellect.
Therefore, this book is entitled On Interpretation as though it were
called On Enunciative Speech, in which the true or false is found.
Hence the noun and the verb are treated here only in so far as they
are parts of the enunciation, for it is proper to each science to treat
the parts of a subject as well as its passions. Therefore, it is clear
to which part of philosophy this book belongs, what its necessity is,
and what its place is among the books of logic.
4. The Philosopher, as an introduction to this work, explains one
by one the things that are to be treated in this book. Since every
science begins with the things which concern the principles, and the
parts of composites are the principles of composites, therefore, who­
ever intends to treat of the enunciation must begin with its parts.
Hence he says: First we must establish, i. e., define, what a noun is

212

APPENDIX

and what a verb is. In the Greek it is, First we must posit, which
signifies the same thing, for, because demonstrations presuppose defini­
tions from which they conclude, definitions are rightly called positions.
Hence he sets before us only definitions of the things we must treat,
because from definitions other things are known.
5. If someone should ask why it was necessary here to determine more
about simple dictions, namely the noun and the verb, when simple
dictions were treated in the book On the Categories, the answer is
that simple dictions can be considered in three ways. The first way
is as they signify, absolutely, simple apprehensions, and this considera­
tion belongs to the book On the Categories. In another way, simple
dictions can be considered according to the formality of parts of the
enunciation, and it is in this way that they are determined in this
book. Hence, they are treated here under the formality of noun
and verb, and under this formality they signify something with time
or without time, and other things of this kind, which belong to the
notion of dictions as they constitute an enunciation. In a third way,
simple dictions are considered according as the syllogistic order is con­
stituted from them, and he thus determines about them under the
formality of terms in the book of the Prior Analytics.
6. It might also be asked why, having made no mention of the other
parts of speech, he determines about the noun and the verb alone.
To this it must be said that, because he intends to determine about
simple enunciation, it suffices to treat only those parts of the enuncia­
tion from which of necessity simple speech is made up.1 Now a simple
enunciation can be made up of only a noun and a verb, but it cannot
be made up from other parts of speech without these. Hence it was
sufficient for Aristotle to determine about these two. Or it can be
said that only nouns and verbs are the principal parts of speech. Pro­
nouns, which do not name a nature but determine a person and hence
are put in place of nouns, are comprehended under nouns. The par­
ticiple, which signifies with time, although it may also have similarities
with the noun, is comprehended under the verb. The others are more
connectives of the parts of speech, signifying a relation of one to an­
other, than parts of speech themselves, as nails and other things of
this kind are not parts of a ship, but things joining together the parts
of a ship.
7. He now adds, as though having set forth these things as principles,
the things that belong to the principal intention, saying, then what
are negation and affirmation, which are parts of the enunciation. They
1 The editor of the Leonine Edition of the Opera Omnia of St. Thomas Aquinas
suggests this alternate reading: “. . . it is sufficient to treat only those parts of
speech from which the simple enunciation is of necessity made up.”

appendix

213

are not, however, integral parts as the noun and the verb are (other­
wise every enunciation would have to be composed from affirmation
and negation), but subjective parts, i. e., species. This point is sup­
posed here but will be made clear later.
8. The following question might arise. Since enunciation is di­
vided into categorical and hypothetical, why does he not mention these
along with affirmation and negation? This can be answered by saying
that the hypothetical enunciation is composed from many categorical
propositions; hence, they do not differ except according to the differ­
ence of one and many. It can also be answered, and better, that the
hypothetical enunciation does not contain absolute truth, the knowl­
edge of which is required in demonstration, and to which this book
is principally ordered. The hypothetical enunciation signifies some­
thing as true by supposition, which is not sufficient for a demonstrative
science unless it is confirmed by the absolute truth of simple enuncia­
tion. For this reason Aristotle omitted the treatment of hypothetical
enunciations and syllogisms. But he adds and enunciation, which is
the genus of negation and affirmation; he also adds and speech, which
is the genus of enunciation.
9. If someone should ask further why he does not mention something
about vocal sound, it must be answered that vocal sound is something
natural. Hence it pertains to the consideration of natural philosophy,
as is clear in the second book of On the Soul and at the end of On the
Generation of Animals. Hence, also, vocal sound is not properly the
genus of speech but is assumed for the formation of speech, just as
natural things are assumed for the formation of artificial things.
10. It seems, also, that the order of the enunciation 2 is inverted, for
affirmation is naturally prior to negation, and enunciation, as a genus,
is prior to these, and consequently, speech to enunciation. But it
must be said that, because he had begun to enumerate from the parts,
he proceeds from the parts to the whole. Now, for the same reason
he places negation, which contains division, before affirmation, which
consists in composition, because division approaches more to the parts,
composition more to the whole. Or it can also be said, according to
some, that he places negation first because, in those things which can
be and not be, non-being, which signifies negation, is prior to being,
which signifies affirmation. But, although he places negation before
affirmation, they are simultaneous in nature because they are species
equally dividing a genus. Hence he does not refer to the fact that
one of them is placed before the other.

2 Suggested reading by the editor of the Leonine Edition: “. . . order of enumera­
tion. . . .”

ARISTOTLE’S ON INTERPRETATION

Chapter One (continued)
(16® 3) Those things, therefore, that are in vocal sound are signs of the
passions that are in the soul, and those things that are written are signs
of those that are in vocal sound.
And just as letters are not the same for all men so neither are vocal
sounds the same:
But the passions of the soul, of which these (i.e., vocal sounds), are
the first signs, are the same for all; and also the things of which these
(i.e., passions of the soul) are similitudes are the same.
We have spoken of these in the things that are said about the soul,
for it belongs to another treatise.
LESSON II

(Commentary of St. Thomas)
1. Having set forth an introduction, the Philosopher begins to follow
out what was proposed. And because those things of which he promised
to speak are significant vocal sounds, whether complex or incomplex,
he begins with a treatment of the signification of vocal sounds; he then
determines about significant vocal sounds, of which he had promised
to speak in the beginning. He does this where he says: The noun
then is a vocal sound significant, etc.1
With respect to the signification of vocal sounds, he makes two di­
visions. First, he determines what kind of signification vocal sound
has; secondly, he shows the difference between the signification of
complex vocal sounds and incomplex vocal sounds, where he says:
Now as sometimes there is, etc.12 Concerning the kind of signification
vocal sound has, he makes two divisions. First, he sets forth the order

1 Cf. Lesson IV of Commentary of St. Thomas; in Aristotle’s On Interpretation,
at the beginning of Chapter 2, 16“ 19.
2 Cf. Lesson III of Commentary of St. Thomas; in Aristotle’s On Interpretation,
at line 16“ 9.
214

APPENDIX

215

of the signification of vocal sound; secondly, he shows what kind of
signification vocal sound has, whether it is by nature or by imposition,
where he says: And just as letters are not, etc.
2. It must be considered, therefore, that he proposes three things
concerning the first point, from one of which a fourth is understood.
He proposes writing, vocal sounds, and passions of the soul from which
things are understood, for a passion exists from the impression of some
agent, and thus passions of the soul have their origin from things
themselves.
Now if man were by nature a solitary animal, the passions of the
soul, by which he would be conformed to things themselves so that
the knowledge of them would be in him, would be sufficient for him.
Man, however, is naturally a political and social animal, and hence it
has been necessary that the conceptions of one man be made known to
others, which comes about through vocal sound. Therefore, it was
necessary that there be significant vocal sounds so that men might live
together. Consequently, those who have diverse languages cannot live
well together.
Again, if man used only sensitive cognition, which regards only the
here and now, such significant vocal sound would be sufficient for him
to live with others, as is the case in the other animals, who manifest
their conceptions to each other through certain sounds. Man, how­
ever, also uses intellectual cognition, which abstracts from the here and
now. He is concerned not only with things present according to time
and place, but also with things distant in place and future in time.
Hence, in order that man might manifest his conceptions to those
distant according to place and to those who will come in future time,
the use of writing was necessary.
3. Now because logic is ordered to knowledge that must be taken
from things, the signification of vocal sound, which is immediate to
the very conceptions of the intellect, belongs to its principal consider­
ation. The signification of letters, however, being more remote, does
not belong to the consideration of logic, but rather to the consider­
ation of the grammarian. Therefore he does not begin explaining
the order of signification from letters but from vocal sounds, of which,
explaining the signification, he says, first: Those things, therefore,
that are in vocal sound are signs of the passions that are in the soul.
Now he says therefore as if concluding from premises, because he had
said above that we must determine about the noun and the verb and
the other things mentioned before. These, however, are significant
vocal sounds. Therefore, the signification of vocal sounds must be ex­
plained.
4. Now he uses this mode of speaking, saying, those things that

216

APPENDIX

are in vocal sound, and not, vocal sounds, as if he were continuing
with what he had said before. He had said we must speak of the
noun and the verb and other things of this kind. Now these things
have being in three ways: in one way, in the conception of the in­
tellect; in another way, in the utterance of the voice; in the third
way, in the writing of letters. Therefore he says, those things that
are in vocal sound, etc., as if he were saying, nouns and verbs and
the other things he had said must be defined, in so far as they are
in vocal sound, are signs. . . .
5. When he says, of the passions that are in the soul, it must be
considered that passions of the soul are commonly called the affec­
tions of the sensible appetite, as anger, joy, and other things of this
kind, as is said in the second book of the Ethics.34 And it is true that
certain sounds of men naturally signify passions of this kind, as the
groans of the sick, and of other animals, as is said in the first book
of the *Politics.
But now the discourse is about vocal sounds sig­
nificant by human institution and hence passions of the soul must be
understood here as conceptions of the intellect, which nouns and
verbs signify immediately, according to the teaching of Aristotle.
They cannot immediately signify things themselves, as appears from
the mode of signifying, for this noun man signifies human nature in
abstraction from singulars. Hence it cannot immediately signify
the singular man. And for this reason the Platonists held that it
signified the separated idea itself of man. However, man according
to its abstraction does not subsist really, according to the teaching
of Aristotle, but is only in the intellect, hence it was necessary for
Aristotle to say that vocal sounds signify the conceptions of the in­
tellect immediately and things by means of them.
6. But because it is not customary for Aristotle to call the con­
ceptions of the intellect passions, Andronicus took the position that
this book was not Aristotle’s. But we clearly find in the first book
of On the Soul 5 that he calls all the operations of the soul, passions
of the soul. Hence the very conception of the intellect can be
called a passion. It can be called so, either because we do not
understand without a phantasm, which we cannot have without a
corporeal passion, and hence the Philosopher in the third book of
On the Soul6 calls the imaginative power the passive intellect; or,
3 Aristotle’s
4 Aristotle’s
5 Aristotle’s
II.
e Aristotle’s

Ethics, Book II, Chap. 5; Commentary of St. Thomas, Lesson V.
Politics, Book I, Chap. 2; Commentary of St. Thomas, Lesson I.
On the Soul, Book I, Chap. 1; Commentary of St. Thomas, Lesson
On the Soul, Book III, Chap. 5; Commentary of St. Thomas, Lesson

APPENDIX

217

because by extension of the name passion to every reception, even
the understanding itself of the possible intellect is a certain under­
going, as is said in the third book of On the Soul.1
He uses the name passions rather than understandings, not only
because man wishes to signify to another an interior concept through
vocal sound on account of some passion of the soul, for instance
from love or hate, but also because the signification of vocal sound is
referred to the conception of the intellect, according as the con­
ception arises from things by way of a certain impression or passion.
7. Secondly, where he says, and those things that are written, etc.,
he treats the signification of writing. And according to Alexander,
he introduces this to make the preceding opinion evident, by way
of a similitude, so that the sense would be: Those things that are in
vocal sound are signs of passions of the soul, just as letters are signs
of vocal sound. He also makes this evident in what follows, where
he says, And just as letters are not, etc., introducing this as if as a
sign of the preceding, for that letters signify vocal sounds is indi­
cated by the fact that just as there are diverse vocal sounds among
different people, so there are diverse letters. According to this
exposition, he therefore did not say, of those letters that are in vocal
sound, but those things that are written, because they are called
letters in both speech and writing, although they are called letters
more properly as they are in writing. As they are in speech they
are called elements of vocal sound. However Aristotle does not say,
just as those things that are written, but makes a continuous nar­
ration; hence it is better to say, as Porphyry explains it, that Aristotle
is proceeding to complete the order of signification further. After
he has said that nouns and verbs, which are in vocal sound, are
signs of those things that are in the soul, he then adds that nouns
and verbs that are written are signs of those nouns and verbs that
are in vocal sound.
8. Then where he says: And just as letters are not, etc., he shows
the difference, with respect to the foregoing, between the things
signifying and the things signified. Concerning this, he shows what
it is to be according to nature, or not according to nature. He does
three things about this. First, he posits a certain sign by which
it is made evident that neither vocal sounds nor letters signify
naturally. Those things that signify naturally are the same for all
men. However, the signification of letters and vocal sounds, which
we are now treating, is not the same for all men. This has never
i Aristotle’s On the Soul, Book III, Chap. 4; Commentary of St. Thomas, Lesson
IX.

218

APPENDIX

been doubted by anyone with respect to letters, of which not only
the nature of signifying is by imposition, but even their formation
comes about through art. Vocal sounds, however, are formed naturally.
Hence it has been questioned by some whether they signify naturally.
Aristotle determines this here by a similitude with letters, which are
not the same among all men, and so neither are vocal sounds the
same. Hence it is clear that, like letters, vocal sounds do not signify
naturally, but by human institution. However, those vocal sounds
that signify naturally, as the groans of the sick and others of this
kind, are the same for all men.
9. Secondly, where he says, but the passions of the soul, etc., he
shows that the passions of the soul exist naturally, just as things
exist naturally, by the fact that they are the same among all men.
For this reason he says, but the passions of the soul, i. e., just as the
passions of the soul are the same for all men ... so also the things
are the same ... of which the passions of the soul are similitudes.
It must be considered here that he has said that letters are signs of
yocal sounds, and similarly vocal sounds are signs of passions of the
soul; and he says passions of the soul are similitudes of things. Now
he says this because a thing is only known by the soul through some
similitude of the thing existing either in the sense or in the intellect.
But letters are signs of vocal sounds, and vocal sounds of passions, in
such a way that one’s attention is not directed to the notion of
similitude, but only the notion of institution, just as in many other
signs, as in a trumpet as a sign of war. In the passions of the soul,
however, the notion of similitude, to express things, must be con­
sidered because passions of the soul designate things naturally, and
not by institution.
10. However, some object to this position that passions of the soul,
which vocal sounds signify, are the same for all. First, because
diverse men have diverse opinions about things, and so the passions
of the soul do not seem to be the same for all men. To this Boethius
replies that Aristotle here designates by passions of the soul the con­
ceptions of the intellect, which is never deceived. Thus the con­
ceptions of the intellect must be the same among all, for if anyone
differs from the true it is because he does not understand. But
because what is false can also be in the intellect, according as the
intellect composes and divides, but not according as it knows that
which is, i. e., the essence of a thing, as is said in the third book of
On the Soul,8 this position must refer to the simple conceptions of the
intellect (which incomplex vocal sounds signify). These are the same

8 Aristotle’s' On the Soul, Book III, Chap. 6; Commentary of St. Thomas,
Lesson XI.
■

APPENDIX

219

among all men, because if anyone truly understands what man is,
whatever other thing than man he apprehends, he does not understand
man. Simple conceptions of the intellect, which vocal sounds first
signify, are of this kind. For this reason it is said in the fourth book
of the Metaphysics9 that the notion that the name signifies is the
definition. Hence he says, significantly, of the first of which these
are signs, namely as referring to the first conceptions signified first
by vocal sounds.
11. Some also raise the objection based on equivocal names, in
which the same vocal sound does not signify the same passion among
all men. Porphyry answers this by saying that a man who produces
vocal sound refers it to signify one conception of the intellect. If
another man to whom he speaks understands something else by it,
he who speaks, by explaining himself, will make the other refer the
thing understood to the same thing.
But it is better to say that the intention of Aristotle is not to
assert the identity of the conception of the soul through comparison
to vocal sound, such that of one vocal sound there is one conception,
for vocal sounds are diverse among different people; but that he in­
tends to assert the identity of the conceptions of the soul by com­
parison to things, which he likewise says are the same for all.
12. Thirdly, where he says: We have spoken of these in the things,
etc., he excuses himself from a more diligent consideration of these
things because he has determined in the book, On the Soul, the nature
of the passions of the soul and in what way they are similitudes of
things. This does not pertain to logic but to philosophy of nature.

9 Aristotle’s Metaphysics, Book IV, Chap. 4; Commentary of St. Thomas, Lesson
VII.

ARISTOTLE’S ON INTERPRETATION

Chapter One (continued)
(16a 9) Now just as there is sometimes in the soul understanding
without the true or the false, but sometimes one or the other of these
is necessarily present to it, so it is in vocal sound; for in composition
and division there is truth and falsity.
Nouns and verbs themselves, then, are similar to conception with­
out composition or division, such as “man” or “white”, when nothing
is added; for neither is yet true or false.
And a sign of this is that “goatstag” signifies something but it is not
yet true or false if “to be” or “not to be” is not added, either ab­
solutely or according to time.
lesson

in

(Commentary of St. Thomas)
1. After the Philosopher has treated the order of the signification
of vocal sounds, he continues here with the diverse signification of
vocal sounds, of which some signify the true or the false, some do
not. And concerning this he does two things: first, he sets forth
the difference; secondly, he makes it evident where he says, for in
composition, etc. Now, because conceptions of the intellect are
prior in the order of nature to vocal sounds, which are uttered to
express them, he assigns the difference that is in the significations of
vocal sounds from the similitude of the difference which is in the
intellect. Thus, this manifestation is not only from a similitude but
also from the cause which the effects imitate.
2. It must be considered, therefore, as it was said in the beginning,
that the operation of the intellect is twofold, as it is explained in
the third book of On the Soul.1 In one of these the true and false
is not found, but in the other it is found. This is why he says that
1 Aristotle’s On the Soul, Book III, Chap. 6; Commentary of St. Thomas, Lesson
XI.
220

F
APPENDIX

il
il
H
il
m
H
«
n
■

221

there is in the soul sometimes understanding without the true and
false, but sometimes of necessity it has one or the other of these.
And because significant vocal sounds are formed to express conceptions
of the intellect, hence in order that the sign be conformed to the
thing signified, it is necessary likewise that some significant sounds
signify without the true and the false, but others with the true and
false.
3. Then where he says, for in composition, etc., he makes what he
has said evident. First he makes it evident with respect to what he
has said about the intellect; secondly, with respect to what he has
said abut the similarity of vocal sounds to the intellect, where he says:
Nouns and verbs themselves, then, etc. To show, then, that the
intellect sometimes is without the true and the false, and sometimes
is with one of these, he says, first, that truth and falsity is in com­
position and division. Here it must be understood that one of the
two operations of the intellect is the knowing of indivisible things,
in so far as the intellect understands absolutely the quiddity or essence
of anything, for instance, what man is or what white is or what some­
thing else of this kind is. The other operation of the intellect is
the composing and dividing of simple concepts of this kind. He
says, therefore, that in this second operation of the intellect, i. e.,
of composing and dividing, truth or falsity is found, and so neither
is found in the first operation, as is also said in the third book of
On the Soul.2
4. There seems to be a doubt about this first point; since division
comes about through resolution to indivisible or simple things, it
seems that just as there is not truth or falsity in simple things, so
neither is there in division.
It must be said, however, that since the conceptions of the in­
tellect are similitudes of things, the things in the intellect can be
considered and named in two ways: in one way, according to them­
selves; in another way, according to the natures of things of which
they are similitudes. For instance the image of Hercules according
to itself is called bronze and is bronze; but in so far as it is a likeness
of Hercules it is named man. Thus also, if we consider the things
in the intellect according to themselves, there is always composition
and then there is truth and falsity, which is. found in the intellect
only when the intellect compares one simple concept to another.
But if what is in the intellect is referred to the thing, sometimes it is
called composition, sometimes division: composition, when the in­
tellect compares one concept to another as if apprehending the
2 Ibid.

222

APPENDIX

conjunction or identity of the things of which they are conceptions;
division, when it so compares one concept to another that it apprehends
the things to be diverse. Considered in this second way, affirmation
in vocal sounds is called composition in so far as it signifies con­
junction on the part of the thing; negation is called division in so far
as it signifies the separation of things.
5. Again, it seems that truth does not consist only in composition
and division. First, because a thing is also said to be true or false;
for example, gold is said to be true or false. It is said also that
being and true are convertible. Hence, it seems that even the simple
conception of the intellect, which is a likeness of the thing, does not
lack truth and falsity.
Furthermore, the Philosopher says in the book On the Soul3 that
the sensation of proper sensibles is always true. But sensation does
not compose or divide. Therefore, truth is not only in composition
or division.
Again, in the divine intellect there is no composition, as is proved
in the twelfth book of the Metaphysics45 and nevertheless the first
and highest truth is found there. Therefore, truth is not only in
composition and division.
6. To answer these objections, it must be considered that truth is
found in something in two ways: in one way, as it is in that which is
true; in another way, as it is in speaking or knowing what is true.
Now truth is found in that which is true in both simple things and
composite things, but truth is found in speaking and knowing what
is true, only according to composition and division. This is made
clear in what follows.
7. The true, as the Philosopher says in the sixth book of the Ethics,6
is the good of the intellect. Hence whatever is said to be true must
be said in relation to an intellect. Now vocal sounds are compared
to the intellect as signs, but things are compared to the intellect as
things of which the conceptions of the intellect are similitudes. But
it must be considered that a thing is compared to the intellect in
two ways. In one way, as the measure to the measured, and thus
natural things are compared to the human speculative intellect.
For this reason, the intellect is called true as it is conformed to the
thing, but false as it disagrees with the thing.
A natural thing, however, is not said to be true by comparison to
3 Aristotle’s On the Soul, Book II, Chap. 6; Commentary o£ St. Thomas, Lesson
XIII.
4 Aristotle’s Metaphysics, Book XII, Chap. 7; Commentary of St. Thomas,
Lesson VII.
5 Aristotle’s Ethics, Book VI, Chap. 2; Commentary of St. Thomas, Lesson II.

APPENDIX

223

our intellect, as certain ancient natural philosophers held, thinking
the truth of things consisted only in being seen. According to this
it would follow that contradictories would be at the same time true,
since contradictories fall under opinions of different men. However,
some things are called true or false by comparison to our intellect,
not essentially or formally, but effectively, in so far as they are naturally
apt of themselves to bring about a true or false estimation. It is
thus that gold is called true or false.
In another way things are compared to the intellect as the measured
to the measure. This is evident in the practical intellect, which is a
cause of things. Hence the work of an artisan is said to be true
in so far as it approaches practical reason as the measure (ratio') of
art; false, in so far as it is deficient in relation to practical reason
as the measure of art.
8. Since all natural things are compared to the divine intellect as
artifacts to art, it follows that anything is said to be true according
as it has the proper form by which it imitates divine art. Thus,
false gold is true copper. In this way being and true are convertible,
because any natural thing is conformed to divine art through its
form. Hence the Philosopher, in the first book of the Physics,
calls form something divine.6
9. Furthermore, just as a thing is called true by comparison to its
measure, so also the sense or the intellect is called true, whose measure
is the thing outside the soul. Hence, the sense is called true when
through its form (species) it is conformed to the thing existing out­
side the soul. Thus it is understood that the sensation of the proper
sensible is true. In this way also the intellect, apprehending the
essence of a thing apart from composition and division, is always
true, as is said in the third book of On the Soul.*1
It must be considered, however, that although the sensation of the
proper object is true, nevertheless, the sense does not know this to
be true, for it cannot know the relationship of its conformity to the
thing but only apprehends the thing. The intellect, however, can
know the relationship of this kind of conformity, and hence only
the intellect can know truth. For this reason the Philosopher says
in the sixth book of the Metaphysics 8 that truth is only in the mind,
as in one knowing truth. But to know this relationship of con­
formity is simply to judge it to be or not to be so in reality, which
6 Aristotle’s Physics, Book I, Chap. 9; Commentary of St. Thomas, Lesson XV.
1 Aristotle’s On the Soul, Book III, Chap. 9; Commentary of St. Thomas, Lesson
VI.
s Aristotle’s Metaphysics, Book VI, Chap. 4; Commentary of St. Thomas, Lesson
IV.

224

APPENDIX

is to compose and divide, and hence the intellect does not know
truth except by composing or dividing through judgment. This
judgment, if it is in accordance with things, will be true, for instance,
when the intellect judges a thing to be what it is, or not to be what
it is not. The judgment will be false when it is not in accordance
with the thing, namely, when it judges that what is, is not, or that
what is not, is. Consequently, it is clear that truth and falsity as
it is in the one knowing and the one speaking is only concerned with
composition and division.
This is the way in which the Philosopher speaks here. Now be­
cause vocal sounds are signs of understanding, vocal sound will be true
when signifying true understanding, but false when signifying false
understanding. However, vocal sound in so far as it is a certain
thing, is called true just like other things. Hence this vocal sound,
man is an ass, is truly vocal sound and truly a sign, but because it is
a sign of something false it is called false.
10. It must be known, however, that the Philosopher speaks of
truth here according as it pertains to the human intellect, which
judges of the conformity of things with the intellect by composing
and dividing. The judgment of the divine intellect is without com­
position and division, for just as our intellect understands material
things immaterially, so the divine intellect knows composition and
division simply.
11. Then where he says: Nouns and verbs themselves, then, etc.,
he makes evident what he has said concerning the similitude of vocal
sounds to the intellect. First, he manifests what was proposed;
secondly, he proves it by a sign where he says: And a sign of this is,
etc. He concludes therefore from what has been said before that,
since there is truth and falsity in the intellect only with composition
and division, it follows that nouns and verbs, taken separately, are
like the intellect without composition and division, as when man
or white is said, if nothing else is added. For it is not true or false
at this point; but when to be or not to be is added it becomes true
or false.
12. A true response to a question by a single noun is not an in­
stance against this position, as when someone asks: What swims in the
sea? and someone answers, fish. The verb which was posited in the
question is understood here. And just as a noun by itself does not
signify the true or false, so neither does the verb said by itself.
Nor is' the verb of the first and second person, nor the passive verb
an instance against this position, because in these a specified and
determined nominative is understood. Hence there is implicit com­
position, although not explicit.

APPENDIX

225

13. Then where he says: And a sign of this is, etc., he introduces a
sign from the composite noun, namely goatstag, which is composed
from “goat” and “stag” and which in Greek is called tragelaphos;
for tragos is “goat,” and elaphos “stag.” Nouns of this kind signify
something, namely, certain simple concepts, although of composite
things, and so it is not true or false except when io be or not to be
is added, by which a judgment of the intellect is expressed. Now
to be or not to be can be added either according to present time,
which is to be or not to be in act, and hence is said “to be” absolutely;
or according to past or future time, which is not to be absolutely,
but relatively, as when it is said that something has been or will be.
He expressly uses an example here of a noun signifying something
that does not exist in reality, in which falsity appears immediately,
and which cannot be true or false without composition and division.8
9 Suggested reading by the editor of the Leonine: “. . . in which immediately
the falsity would appear if it could be true or false without composition and
division.”

INDEX

INDEX

B
A
Abbreviated syllogism, 153-157
Barbara, Celarent, etc., 148-150
Abstraction, 3, 12, 216
Basis of division, 33-34
Accent, fallacy of, 193
Begging the question, 195-196
Accident:
fallacy of, 194
in dialectical proposition, 182
C
predicable, 13, 26
predicamental, 18, 19, 24-26
Categorical proposition, 63, 213
singular, 19
Categorical syllogism (see Syllogism)
universal, 19
Categories, 17, 23-28
Accidental conversion, 96
Circular argument, 196
Act of composition and division, xvi, 51, Co-division, 35
210-211, 220-222, 224, 225
Collective supposition, 74
Act of reasoning, xvi, 113, 210-211
Communism, 185
Act of simple apprehension, xvi, 113, Complex expression, 18
210-211, 221
Complex object, 51, 113
Action, 25, 26
Complex question, 197
Acts of reason, 208
Composite expression, 55-56
Affirmation, 212, 213, 222
Composition and division, fallacy of, 193
“All,” 74
Compound proposition:
Amphiboly, 192
distinguished from categorical, 63, 105,
Analogous name, 17, 18
213
“Analytics,” 175, 208
division of, 105
Antecedent:
explicitly, 106-107
of argumentation, 114-115
implicitly, 107-108
of conditional proposition, 106, 162- Compound syllogism, 161-166
164
Concept:
Antepredicaments, 17-19
as formal sign, 6, 7
A posteriori demonstration, 179-180
as natural sign, 8
A priori demonstration, 179-180
means of knowing, 3
Argument:
relation with word, 3
ad baculum, 195
Conceptions of the intellect, 215-222
ad hominem, 195
Conditional proposition, 106
ad populum, 195
Conditional syllogism, 162-164
ad verecundiam, 195
Conjunctive syllogism, 162
Argumentation:
Consequent:
demonstrative, 176-180, 181
fallacy of, 196
dialectical, 180-185
of argumentation, 114-115
in general, 113-115, 117
of conditional proposition, 106, 162poetic, 187-189
164
rhetorical, 153, 185-187
Contradictory opposition of propositions,
Art, 207-208
80
Art and morality, 188-189
Contrary opposition of propositions, 80
229

230

INDEX

Conventional sign, 7, 8
Conversion:
definition of, 95
kinds of, 95-96
rule of truth in, 98
rules of, 96-97
Copula, 57, 63, 64
Copulative proposition, 106-107
Customary sign, 8
D
Deduction (see Syllogism)
Definition:
dialectical, 182
kinds of, 42-43
ordering of first part of logic to, 11
rules of, 41-42
Definitum, 41-42
“De inesse” proposition, 66
Demonstration:
definition of, 177
kinds of, 179
prerequisites for, 176
Dialectical:
argumentation, 180-184
problem, 182-183
process, 184-185
proposition, 181-182
syllogism, 180-182, 209
Dialectical Materialism, 185
Dialectics, 209
Diction, simple, 212
Dictum de nullo, 127
Dictum de omni, 127
Difference, 13, 41
Disjunctive proposition, 107
Disjunctive syllogism, 164-166
Distinctions preliminary to the Cate­
gories, 17-19
Distribution, 73-75, 128-129
Division:
by opposition, 34
kinds of, 35-36
rules of, 33-35

E

Existence in a subject, 18, 19
Exponibles, 105, 107-108
Expression:
complex, 18
composite, 55-56
imperfect, 55
incomplex, 18
F

Fallacy:
of accent, 193
of accident, 194
of amphiboly, 192
of begging the question, 195
of complex question, 197
of composition and division, 193
of consequent, 196
of equivocation, 192
of false cause, 196
of form of expression, 193-194
of four terms, 127-128, 192
of ignoring the issue, 195
of relative to absolute, 194-195
False cause, 196-197
Falsity, 51-53, 55, 56, 220, 221
Figure of syllogism, 119-122
Form of expression, fallacy of, 193-194
Formal logic, xvii-xviii
Formal relation of propositions, 83-84
Formal sign, 6, 7
Formal truth, 52
G

Genus:
in dialectical proposition, 182-183
predicable, 13, 41
supreme (category), 23-24, 26

H
Habit:
category of, 26, 27
species of quality, 25
Hypothetical proposition (see Compound
proposition)
Hypothetical syllogism (see Compound
syllogism)

Enthymeme, 153, 185-186 (see also Ab­
breviated syllogism)
I
Enunciation, 211-212, 213 (see also
Proposition)
Ignoring the issue, 195
Equivocal name, 17, 18, 219
Image:
Equivocation, 192
as formal sign, 6
“Every," 74
in poetry, 188
Example, 185-186
Exceptive proposition, 108
means of knowing, 3
Exclusive proposition, 107-108
Incomplex expression, 18

231

INDEX

Indirect moods of syllogism, 134-135
Induction:
as treated in logic, 169
compared to argument from example,
186
materially reduced to syllogism, 172
notion of, 115, 169
opposed to syllogism, 170
purpose of, 172
Inference, 114
Instrumental sign, 6, 7
Interpretation, 211
Inventive part of logic, 209

J
Judgment, 51, 209, 224
Judicative part of logic, 208
L
Logic, xvii, 11, 113, 207-209
Logical universal, 12, 23, 26
M

■1
■I
■I
w

Major extreme, 118
Major premise, 117-122
Major term, 118-122
Material logic, xvii-xviii
Material supposition, 73
Metaphor, 188
Middle term, 118-122, 126-130, 170-172,
178-179
Minor extreme, 118
Minor premise, 117-122
Minor term, 118-122
Modal proposition, 66-67
Modes following upon the Categories,
27-28
Mood of syllogism, 119, 130-135
Morality and art, 189
N
Name:
analogous, 17, 18
equivocal, 17, 18
univocal, 17, 18, 23
Natural sign, 7, 8
Negation, 212, 213, 222
Non-supposing subject, 72
Noun, 12, 56-57, 211-213, 216, 217, 224,
225
O
Object:
complex, 51, 113
simple, 11, 51, 113, 182

Obversion:
distinction from opposition, 89
rules of, 90
rules of truth and falsity in, 91
Opinion, 180
Opposition (postpredicament), 27-28
Opposition of propositions:
definition of, 79
division of, 80-81
rules for truth and falsity in, 82-83
Outlining, 33
P

Passion (category), 25, 27
Passions of the soul, 215, 216, 218
Personal supposition, 73
Persuasion, modes of, 186 (see Rhetorical
argumentation)
Place, 25, 27
Poetic argumentation, 187-189
Poetics, 209
Position, 25, 27
Post hoc, ergo propter hoc, 196
Posterior Analytics, 175
Postpredicaments, 27, 28
Predicable of a subject, 18, 19
Predicables, 11-13
Predicaments, 17 (see Categories)
Premises, 117-122, 176-178
Prior Analytics, 175
Priority:
of nature, 28
of time, 28
Property, 13, 176-177, 182
Proposition:
definition of, 55
divisions of, 63-67
elements of, 56
logical form of, 57
Propter quid demonstration, 179-180
Q

Quality, 24-26
Quantity, 24-26
Quia demonstration, 179-180

R
Rational philosophy, 209
Rational science, 207, 210
Reduction of syllogisms, 145-150
Reduplicative proposition, 108
Relation, 25, 26
Relative to absolute, fallacy of, 194
Rhetoric, 209

232

INDEX

Rhetorical argumentation, 153, 185-187
Rhetorician, prerequisites for, 186-187
S

Science, 177-180
Scientific proposition, 181
Self-evident premises, 178
Semantics, 5
Sign:
conventional, 7, 8
customary, 8
definition of, 5
division of, 6
formal, 6, 7
instrumental, 6, 7
natural, 7, 8
Signification, 71, 79, 214-219
Simile, 188
Simple conversion, 95
Simple diction, 212
Simple object, 11, 51, 113, 182
Simple supposition, 73
Singular:
as opposed to universal, 11
logical, as opposed to grammatical, 64
Sophistical reasoning, 191-197, 209
Species (predicable), 13
Speech, 55, 210-211, 212, 213 (see also
Composite expression)
Square of opposition, 82
Subalternation of propositions, 81
Sub-contrary opposition of propositions,
80-81
Subdivision, 34
Substance:
category of, 24, 26
singular (first substance), 19, 24
universal (second substance), 19, 24, 26
Supposition:
definition of, 72
distinction from signification, 71
kinds of, 73
sameness of, in opposing propositions,
79
sameness of, in syllogism, 128

Syllogism:
abbreviated, 153-157
as concluding indirectly, 134-135
compound, 161-166
conditional, 162-164
conjunctive, 162
definition of, 117
demonstrative, 176-178
dialectical, 180-182, 209
disjunctive, 164-166
form of, 119-122
general rules of, 127-130
matter of, 117
principles of, 125-127
reduction of, to first figure, 145-150
special rules of, 137
T

Term (syllogistic), 118-119
Time, 25, 27
Truth:
as found in senses, 52, 223
in second act of intellect, 51, 55, 56,
220-225
moral, 52-53
practical, 52, 223
speculative, 52, 53, 222
transcendental, 52, 223
U
Universal, II, 12, 23, 26
Univocal name, 17, 18, 23

V
Verb, 56-57, 211-213, 216, 217,224
Vocal sound, 56, 213, 214, 215, 218, 220,
221, 224

W
When (category), 25, 27
Where (category), 25, 27
Whole, 35
Word, 4-5, 7. 11-12 188