THE ART OF
LOGICAL THINKING
OR
THE LAWS OF REASONING
By WILLIAM WALKER ATKINSON
L.N. FOWLER & COMPANY
7, Imperial Arcade, Ludgate Circus
London, E.C., England
1909
THE PROGRESS COMPANY
CHICAGO, ILL.
Copyright 1909
By
THE PROGRESS COMPANY
Chicago, Ill., U.S.A.
CONTENTS
I. Reasoning 9
II. The Process of Reasoning 17
III. The Concept 25
IV. The Use of Concepts 37
V. Concepts and Images 48
VI. Terms 56
VII. The Meaning of Terms 73
VIII. Judgments 82
IX. Propositions 90
X. Immediate Reasoning 99
XI. Inductive Reasoning 107
XII. Reasoning by Induction 116
XIII. Theory and Hypotheses 125
XIV. Making and Testing Hypotheses 132
XV. Deductive Reasoning 144
XVI. The Syllogism 156
XVII. Varieties of Syllogisms 167
XVIII. Reasoning by Analogy 179
XIX. Fallacies 186
CHAPTER I.
REASONING
"Reasoning" is defined as: "The act, process or art of exercising the
faculty of reason; the act or faculty of employing reason in argument;
argumentation, ratiocination; reasoning power; disputation, discussion,
argumentation." Stewart says: "The word _reason_ itself is far from
being precise in its meaning. In common and popular discourse it denotes
that power by which we distinguish truth from falsehood, and right from
wrong, and by which we are enabled to combine means for the attainment
of particular ends."
By the employment of the reasoning faculties of the mind we compare
objects presented to the mind as percepts or concepts, taking up the
"raw materials" of thought and weaving them into more complex and
elaborate mental fabrics which we call abstract and general ideas of
truth. Brooks says: "It is the thinking power of the mind; the faculty
which gives us what has been called _thought-knowledge_, in distinction
from _sense-knowledge_. It may be regarded as the mental architect among
the faculties; it transforms the material furnished by the senses ...
into new products, and thus builds up the temples of science and
philosophy." The last-mentioned authority adds: "Its products are
twofold, _ideas_ and _thoughts_. An _idea_ is a mental product which
when expressed in words does not give a proposition; a _thought_ is a
mental product which embraces the relation of two or more ideas. The
ideas of the understanding are of two general classes; abstract ideas
and general ideas. The thoughts are also of two general classes; those
pertaining to contingent truth and those pertaining to necessary truth.
In contingent truth, we have _facts_, or immediate judgments, and
_general truths_ including _laws_ and _causes_, derived from particular
facts; in necessary truth we have _axioms_, or self-evident truths, and
the truths derived from them by reasoning, called _theorems_."
In inviting you to consider the processes of reasoning, we are
irresistibly reminded of the old story of one of Moliere's plays in
which one of the characters expresses surprise on learning that he "had
been talking prose for forty years without knowing it." As Jevons says
in mentioning this: "Ninety-nine people out of a hundred might be
equally surprised on hearing that they had been converting propositions,
syllogizing, falling into paralogisms, framing hypotheses and making
classifications with genera and species. If asked whether they were
logicians, they would probably answer, No! They would be partly right;
for I believe that a large number even of educated persons have no clear
idea of what logic is. Yet, in a certain way, every one must have been a
logician since he began to speak."
So, in asking you to consider the processes of reasoning we are not
assuming that you never have reasoned--on the contrary we are fully
aware that you in connection with every other person, have reasoned all
your mature life. That is not the question. While everyone reasons, the
fact is equally true that the majority of persons reason incorrectly.
Many persons reason along lines far from correct and scientific, and
suffer therefor and thereby. Some writers have claimed that the majority
of persons are incapable of even fairly correct reasoning, pointing to
the absurd ideas entertained by the masses of people as a proof of the
statement. These writers are probably a little radical in their views
and statements, but one is often struck with wonder at the evidences of
incapacity for interpreting facts and impressions on the part of the
general public. The masses of people accept the most absurd ideas as
truth, providing they are gravely asserted by some one claiming
authority. The most illogical ideas are accepted without dispute or
examination, providing they are stated solemnly and authoritatively.
Particularly in the respective fields of religion and politics do we
find this blind acceptance of illogical ideas by the multitude. Mere
assertion by the leaders seems sufficient for the multitude of followers
to acquiesce.
In order to reason correctly it is not merely necessary to have a good
intellect. An athlete may have the proper proportions, good framework,
and symmetrical muscles, but he cannot expect to cope with others of his
kind unless he has learned to develop those muscles and to use them to
the best advantage. And, in the same way, the man who wishes to reason
correctly must develop his intellectual faculties and must also learn
the art of using them to the best advantage. Otherwise he will waste his
mental energy and will be placed at a disadvantage when confronted with
a trained logician in argument or debate. One who has witnessed a debate
or argument between two men equally strong intellectually, one of whom
is a trained logician and the other lacking this advantage, will never
forget the impression produced upon him by the unequal struggle. The
conflict is like that of a powerful wrestler, untrained in the little
tricks and turns of the science, in the various principles of applying
force in a certain way at a certain time, at a certain place, with a
trained and experienced wrestler. Or of a conflict between a muscular
giant untrained in the art of boxing, when confronted with a trained and
experienced exponent of "the manly art." The result of any such conflict
is assured in advance. Therefore, everyone should refuse to rest content
without a knowledge of the art of reasoning correctly, for otherwise he
places himself under a heavy handicap in the race for success, and
allows others, perhaps less well-equipped mentally, to have a decided
advantage over him.
Jevons says in this connection: "To be a good logician is, however, far
more valuable than to be a good athlete; because logic teaches us to
reason well, and reasoning gives us knowledge, and knowledge, as Lord
Bacon said, is power. As athletes, men cannot for a moment compare with
horses or tigers or monkeys. Yet, with the power of knowledge, men tame
horses and shoot tigers and despise monkeys. The weakest framework with
the most logical mind will conquer in the end, because it is easy to
foresee the future, to calculate the result of actions, to avoid
mistakes which might be fatal, and to discover the means of doing things
which seemed impossible. If such little creatures as ants had better
brains than men, they would either destroy men or make them into slaves.
It is true that we cannot use our eyes and ears without getting some
kind of knowledge, and the brute animals can do the same. But what gives
power is the deeper knowledge called Science. People may see, and hear,
and feel all their lives without really learning the nature of things
they see. But reason is the mind's eye, and enables us to see why things
are, and when and how events may be made to happen or not to happen. The
logician endeavors to learn exactly what this reason is which makes the
power of men. We all, as I have said, must reason well or ill, but logic
is the science of reasoning and enables us to distinguish between the
good reasoning which leads to truth, and the bad reasoning which every
day betrays people into error and misfortune."
In this volume we hope to be able to point out the methods and
principles of correctly using the reasoning faculties of the mind, in a
plain, simple manner, devoid of useless technicalities and academic
discussion. We shall adhere, in the main, to the principles established
by the best of the authorities of the old school of psychology, blending
the same with those advanced by the best authorities of the New
Psychology. No attempt to make of this book a school text-book shall be
made, for our sole object and aim is to bring this important subject
before the general public composed of people who have neither the time
nor inclination to indulge in technical discussion nor academic
hair-splitting, but who desire to understand the underlying _working
principles_ of the Laws of Reasoning.