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.