YOUR MIND AND HOW TO USE IT /PART 27
CHAPTER XXVII.
Deductive Reasoning.
WE have
seen in the preceding chapter that from particular facts we reason inductively
to general principles or truths. We have also seen that one of the steps of
inductive reasoning is the testing of the hypothesis by deductive reasoning. We
shall now also see that the results of inductive reasoning are used as premises
or bases for deductive reasoning. These two forms of reasoning are opposites
and yet complementary to each other; they are in a sense independent and yet
are interdependent. Brooks says: "The two methods of reasoning are the
reverse of each other. One goes from particulars to generals; the other from
generals to particulars. One is a process of analysis; the other is a process
of synthesis. One rises from facts to laws; the other descends from laws to
facts. Each is independent of the other, and each is a valid and essential
method of inference."
Halleck
well expresses the spirit of deductive reasoning as follows: "After
induction has classified certain phenomena and thus given us a major premise,
we may proceed deductively to apply the inference to any new specimen that
can be shown to belong to that class. Induction hands over to deduction a
ready-made premise. Deduction takes that as a fact, making no inquiry regarding
its truth. Only after general laws have been laid down, after objects have been
classified, after major premises have been formed, can deduction be
employed."
Deductive
reasoning proceeds from general principles to particular facts. It is a
descending process, analytical in its nature. It rests upon the fundamental
axiomatic basis that "whatever is true of the whole is true of its
parts," or "whatever is true of the universal is true of the
particulars."
The
process of deductive reasoning may be stated briefly as follows: (1) A general
principle of a class is stated as a major premise; (2) a particular
thing is stated as belonging to that general class, this statement being
the minor premise; therefore (3) the general class principle is
held to apply to the particular thing, this last statement being the conclusion.
(A "premise" is "a proposition assumed to be true.")
The
following gives us an illustration of the above process:—
I. (Major premise)—A bird is a warm-blooded, feathered,
winged, oviparous vertebrate.
II. (Minor premise)—The sparrow is a bird; therefore
III. (Conclusion)—The sparrow is a warm-blooded, feathered,
winged, oviparous vertebrate.
Or,
again:—
I. (Major premise)—Rattlesnakes frequently bite when
enraged, and their bite is poisonous.
II. (Minor premise)—This snake before me is a rattlesnake;
therefore
III. (Conclusion)—This snake before me may bite when
enraged, and its bite will be poisonous.
The
average person may be inclined to object that he is not conscious of going
through this complicated process when he reasons about sparrows or
rattlesnakes. But he does, nevertheless. He is not conscious of the
steps, because mental habit has accustomed him to the process, and it is
performed more or less automatically. But these three steps manifest in all
processes of deductive reasoning, even the simplest. The average person is like
the character in the French play who was surprised to learn that he had
"been talking prose for forty years without knowing it." Jevons says
that the majority of persons are equally surprised when they find out that they
have been using logical forms, more or less correctly, without having realized
it. He says: "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."
There
are many technical rules and principles of logic which we cannot attempt to
consider here. There are, however, a few elementary principles of correct
reasoning which should have a place here. What is known as a "syllogism"
is the expression in words of the various parts of the complete process of
reasoning or argument. Whately defines it as follows: "A syllogism is an
argument expressed in strict logical form so that its conclusiveness is
manifest from the structure of the expression alone, without any regard to the
meaning of the term." In short, if the two premises are
accepted as correct, it follows that there can be only one true logical
conclusion resulting therefrom. In abstract or theoretical reasoning the word
"if" is assumed to precede each of the two premises, the
"therefore" before the conclusion resulting from the "if,"
of course. The following are the general rules governing the syllogism:—
I.
Every syllogism must consist of three, and no more than three, propositions,
namely (1) the major premise, (2) the minor premise, and (3) the conclusion.
II.
The conclusion must naturally follow from the premises, otherwise the syllogism
is invalid and constitutes a fallacy or sophism.
III.
One premise, at least, must be affirmative.
IV.
If one premise is negative, the conclusion must be negative.
V.
One premise, at least, must be universal or general.
VI.
If one premise is particular, the conclusion also must be particular.
The
last two rules (V. and VI.) contain the essential principles of all the rules
regarding syllogisms, and any syllogism which breaks them will be found also to
break other rules, some of which are not stated here for the reason that they
are too technical. These two rules may be tested by constructing syllogisms in
violation of their principles. The reason for them is as follows: (Rule V.)
Because "from two particular premises no conclusion can be drawn,"
as, for instance: (1) Some men are mortal; (2) John is a man. We cannot reason
from this either that John is or is not mortal.
The major premise should read "all men." (Rule VI.)
Because "a universal conclusion can be drawn only from two universal
premises," an example being needless here, as the conclusion is so
obvious.
Cultivation
of Reasoning Faculties.
There
is no royal road to the cultivation of the reasoning faculties. There is but
the old familiar rule: Practice, exercise, use. Nevertheless there are
certain studies which tend to develop the faculties in question. The study
of arithmetic, especially mental arithmetic, tends to develop correct habits of
reasoning from one truth to another—from cause to effect. Better still is the
study of geometry; and best of all, of course, is the study of logic and the
practice of working out its problems and examples. The study of philosophy and
psychology also is useful in this way. Many lawyers and teachers have drilled
themselves in geometry solely for the purpose of developing their logical
reasoning powers.
Brooks
says: "So valuable is geometry as a discipline that many lawyers and
others review their geometry every year in order to keep the mind drilled to
logical habits of thinking. * * * The study of logic will aid in the
development of the power of deductive reasoning. It does this, first, by
showing the method by which we reason. To know how we reason, to see the laws
which govern the reasoning process, to analyze the syllogism and see its
conformity to the laws of thought, is not only an exercise of reasoning but
gives that knowledge of the process that will be both a stimulus and a guide to
thought. No one can trace the principles and processes of thought without
receiving thereby an impetus to thought. In the second place, the study of
logic is probably even more valuable because it gives practice in deductive
thinking. This, perhaps, is its principal value, since the mind reasons
instinctively without knowing how it reasons. One can think without the
knowledge of the science of thinking just as one can use language correctly
without a knowledge of grammar; yet as the study of grammar improves one's
speech, so the study of logic can but improve one's thought."
In
the opinion of the writer hereof, one of the best though simple methods of
cultivating the faculties of reasoning is to acquaint one's self thoroughly
with the more common fallacies or forms of false reasoning—so
thoroughly that not only is the false reasoning detected at once but also
the reason of its falsity is readily understood. To understand
the wrong ways of reasoning is to be on guard against them. By guarding against
them we tend to eliminate them from our thought processes. If we eliminate the
false we have the true left in its place. Therefore we recommend the weeding of
the logical garden of the common fallacies, to the end that the flowers of pure
reason may flourish in their stead. Accordingly, we think it well to call your
attention in the next chapter to the more common fallacies, and the reason of
their falsity.
Comments
Post a Comment