THOUGHT-CULTURE/PART 13
CHAPTER XIII.
REASONING
In the
preceding chapters we have seen that in the group of mental processes involved
in the general process of Understanding, there are several stages or steps,
three of which we have considered in turn, namely: (1) Abstraction; (2)
Generalization or Conception; (3) Judgment. The fourth step,
or stage, and the one which we are now about to consider, is that called
Reasoning.
Reasoning is
that faculty of the mind whereby we compare two Judgments, one with the other,
and from which comparison we are enabled to form a third judgment. It is a form
of indirect or mediate comparison, whereas, the ordinary Judgment is a form of
immediate or direct comparison. As, when we form a Judgment, we compare two
concepts and decide upon their agreement or difference; so in Reasoning we
compare two Judgments and from the comparison we draw or produce a new
Judgment. Thus, we may reason that the particular dog "Carlo" is
an animal, by the following process:
(1) All dogs
are animals; (2) Carlo is a dog; therefore, (3) Carlo is an animal. Or, in the
same way, we may reason that a whale is not a fish, as follows:
(1) All fish
are cold-blooded animals; (2) A whale is not a cold-blooded
animal; therefore, (3) A whale is not a fish.
In the
above processes it will be seen that the third and final Judgment is derived
from a comparison of the first two Judgments. Brooks states the process as
follows: "Looking at the process more closely, it will be seen that in
inference in Reasoning involves a comparison of relations. We infer the
relation of two objects from their relation to a third object. We must thus
grasp in the mind two relations and from the comparison of these two relations
we infer a third relation. The two relations from which we infer a third, are
judgments; hence, Reasoning may also be defined as the process of deriving one
judgment from two other judgments. We compare the two given judgments and from
this comparison derive the third judgment. This constitutes a single step
in Reasoning, and an argument so expressed is called a Syllogism."
The Syllogism consists
of three propositions, the first two of which express the grounds or basis of
the argument and are called the premises; the third expresses the
inference derived from a comparison of the other two and is called the conclusion.
We shall not enter into a technical consideration of the Syllogism in this
book, as the subject is considered in detail in the volume of this series
devoted to the subject of "Logic." Our concern here is to point out
the natural process and course of Reasoning, rather than to consider the
technical features of the process.
Reasoning
is divided into two general classes, known respectively as (1) Inductive
Reasoning; (2) Deductive Reasoning.
Inductive
Reasoning is the process of arriving at a general truth, law or
principle from a consideration of many particular facts and truths. Thus, if we
find that a certain thing is true of a great number of particular objects, we
may infer that the same thing is true of all objects of this
particular kind. In one of the examples given above, one of the
judgments was that "all fish are cold-blooded animals," which
general truth was arrived at by Inductive Reasoning based upon the examination
of a great number of fish, and from thence assuming that all fish
are true to this general law of truth.
Deductive
Reasoning is the reverse of Inductive Reasoning, and is a process of
arriving at a particular truth from the assumption of a general truth. Thus,
from the assumption that "all fish are cold-blooded animals," we, by
Deductive Reasoning, arrive at the conclusion that the particular fish before
us must be cold-blooded.
Inductive
Reasoning proceeds upon the basic principle that "What is true of the
many is true of the whole," while Deductive Reasoning proceeds upon
the basic principle that "What is true of the whole is true of its
parts."
Regarding
the principle of Inductive Reasoning, Halleck says: "Man has
to find out through his own experience, or that of others, the major premises
from which he argues or draws his conclusions. By induction, we examine what
seems to us a sufficient number of individual cases. We then conclude that
the rest of these cases, which we have not examined, will obey the same general
law. The judgment 'All men are mortal' was reached by induction. It was
observed that all past generations of men had died, and this fact warranted the
conclusion that all men living will die. We make that assertion as boldly as if
we had seen them all die. The premise, 'All cows chew the cud,' was laid down
after a certain number of cows had been examined. If we were to see a cow twenty
years hence, we should expect to find that she chewed the cud. It was noticed
by astronomers that, after a certain number of days, the earth regularly
returned to the same position in its orbit, the sun rose in the same place, and
the day was of the same length. Hence, the length of the year and of each
succeeding day was determined, and the almanac maker now infers that the same
will be true of future years. He tells us that the sun on the first of next
December will rise at a given time, although he cannot throw himself into the
future to verify the conclusion."
Brooks
says regarding this principle: "This proposition is founded on our
faith in the uniformity of nature; take away this belief, and all reasoning by
induction fails. The basis of induction is thus often stated to be man's
faith in the uniformity of nature. Induction has been compared to a ladder
upon which we ascend from facts to laws. This ladder cannot stand unless it has
something to rest upon; and this something is our faith in the constancy of
nature's laws."
There are
two general ways of obtaining our basis for the process of Inductive Reasoning.
One of these is called Perfect Induction and the other Imperfect Induction.
Perfect Induction is possible only when we have had the opportunity of
examining every particular object or thing of which the general idea is
expressed. For instance, if we could examine every fish in the universe we
would have the basis of Perfect Induction for asserting the general truth that
"all fishes are cold-blooded." But this is practically impossible in
the great majority of cases, and so we must fall back upon more or less
Imperfect Induction. We must assume the general law from the fact that it is
seen to exist in a very great number of particular cases; upon the principle
that "What is true of the many is true of the whole." As Halleck says
regarding this: "Whenever we make a statement such as, 'All men are
mortal,' without having tested each individual case or, in other words, without
having seen every man die, we are reasoning from imperfect induction.
Every time a man buys a piece of beef, a bushel of potatoes or a loaf of bread,
he is basing his action on inference from imperfect induction. He believes that
beef, potatoes and bread will prove nutritious food, although he has not
actually tested those special edibles before purchasing them. They have
hitherto been found to be nutritious on trial and he argues that the same will
prove true of those special instances. Whenever a man takes stock in a new
national bank, a manufactory or a bridge, he is arguing from past cases that
this special investment will prove profitable. We instinctively believe in the
uniformity of nature; if we did not we should not consult our almanacs. If
sufficient heat will cause phosphorus to burn today, we conclude that the same
result will follow tomorrow if the circumstances are the same."
But, it
will be seen, much care must be exercised in making observations, experiments
and comparisons, and in making generalizations. The following general
principles will give the views of the authorities regarding this:
Atwater
gives the two general rules:
Rule of
Agreement: "If, whenever a given object or agency is present, without
counteracting forces, a given effect is produced, there is a strong evidence
that the object or agency is the cause of the effect."
Rule of
Disagreement: "If when the supposed cause is present the effect is
present, and when the supposed cause is absent the effect is wanting, there
being in neither case any other agents present to effect the result, we may
reasonably infer that the supposed cause is the real one."
Rule of
Residue: "When in any phenomena we find a result remaining after the
effects of all known causes are estimated, we may attribute it to a residual
agent not yet reckoned."
Rule of
Concomitant Variations: "When a variation in a given antecedent
is accompanied by a variation of a given consequent, they are in some
manner related as cause and effect."
Atwater
says, of the above rules, that "whenever either of these criteria is
found, free from conflicting evidence, and especially when several of them
concur, the evidence is clear that the cases observed are fair representatives
of the whole class, and warrant a valid universal inductive conclusion."
We now
come to what is known as Hypothesis or Theory, which is an assumed general
principle—a conjecture or supposition founded upon observed and tested facts.
Some authorities use the term "theory" in the sense of "a
verified hypothesis," but the two terms are employed loosely and the usage
varies with different authorities. What is known as "the probability of a
hypothesis" is the proportion of the number of facts it will explain. The
greater the number of facts it will explain, the greater is its "probability."
A Hypothesis is said to be "verified" when it will account for all
the facts which are properly to be referred to it. Some very critical
authorities hold that verification should also depend upon there being no other
possible hypotheses which will account for the facts, but this is
generally considered an extreme position.
A
Hypothesis is the result of a peculiar mental process which seems to act in the
direction of making a sudden anticipatory leap toward a theory, after the mind
has been saturated with a great body of particular facts. Some have spoken of
the process as almost intuitive and, indeed, the testimony of
many discoverers of great natural laws would lead us to believe that the
Subconscious region of the mind is most active in making what La Place has
called "the great guess" of discovery of principle. As Brooks says:
"The forming of hypotheses requires a suggestive mind, a lively fancy, a
philosophic imagination, that catches a glimpse of the idea through the form,
or sees the law standing behind the fact."
Thomson
says: "The system of anatomy which has immortalized the name of Oken, is
the consequence of a flash of anticipation which glanced through his mind when
he picked up in a chance walk the skull of a deer, bleached and disintegrated
by the weather, and exclaimed, after a glance, 'It is part of a vertebral
column.' When Newton saw the apple fall, the anticipatory question flashed
through his mind, 'Why do not the heavenly bodies fall like this apple?' In
neither case had accident any important share; Newton and Oken were prepared by
the deepest previous study to seize upon the unimportant fact offered to them,
and show how important it might become; and if the apple and the deer-skull had
been wanting, some other falling body, or some other skull, would have touched
the string so ready to vibrate. But in each case there was a great step of
anticipation; Oken thought he saw the type of the whole skeleton in a single
vertebra, whilst Newton conceived at once that the whole universe was full of
bodies tending to fall."
Passing
from the consideration of Inductive Reasoning to that of Deductive Reasoning we
find ourselves confronted with an entirely opposite condition. As 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."
Deductive
Reasoning is, as we have seen, dependent upon the process of deriving
a particular truth from a general law, principle or truth, upon the fundamental
axiom that: "What is true of the whole is true of its parts." It is
an analytical process, just as Inductive Reasoning is synthetical. It is a
descending process, just as Inductive Reasoning is ascending.
Halleck
says of Deductive Reasoning: "After induction has classified certain
phenomena and thus given us a major premise, we 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 major premise, e.g. 'All
scorpions are dangerous.' Deduction takes this as a fact, making no inquiry
about its truth. When a new object is presented, say a possible scorpion, the
only troublesome step is to decide whether the object is really a scorpion.
This may be a severe task on judgment. The average inhabitant of the
temperate zone would probably not care to risk a hundred dollars on his ability
to distinguish a scorpion from a centipede, or from twenty or thirty other
creatures bearing some resemblance to a scorpion. Here there must be accurately
formed concepts and sound judgment must be used in comparing them. As soon as
we decide that the object is really a scorpion, we complete the deduction in
this way:—'All scorpions are dangerous; this creature is a
scorpion; this creature is dangerous.' The reasoning of early
life must be necessarily inductive. The mind is then forming general
conclusions from the examination of individual phenomena. Only after general
laws have been laid down, after objects have been classified, after major
premises have been formed, can deduction be employed."
What is
called Reasoning by Analogy is really but a higher degree of
Generalization. It is based upon the idea that if two or more things resemble
each other in many particulars, they are apt to resemble each other in other
particulars. Some have expressed the principle as follows: "Things that
have some things in common have other things in common." Or as Jevons
states it: "The rule for reasoning by analogy is that if two or more
things resemble each other in many points, they will probably resemble each
other also in more points."
This form
of reasoning, while quite common and quite convenient, is also very dangerous.
It affords many opportunities for making false inferences. As Jevons says:
"In many cases Reasoning by Analogy is found to be a very uncertain guide.
In some cases unfortunate mistakes are committed. Children are sometimes killed
by gathering and eating poisonous berries, wrongly inferring that they can be
eaten, because other berries, of a somewhat similar appearance, have been found
agreeable and harmless. Poisonous toadstools are occasionally mistaken for
mushrooms, especially by people not accustomed to gather them.... There is no
way in which we can really assure ourselves that we are arguing safely by
analogy. The only rule that can be given is this, that the more things
resemble each other, the more likely is it that they are the same in other
respects, especially in points closely connected with those observed."
Halleck
says: "In argument or reasoning we are much aided by the habit of
searching for hidden resemblances. We may here use the term analogy in
the narrower sense as a resemblance of ratios. There is analogical relation
between autumnal frosts and vegetation on the one hand, and death and human
life on the other. Frosts stand in the same relation to vegetation that death
does to life. The detection of such a relation cultivates thought. If we are to
succeed in argument, we must develop what some call a sixth sense for the
detection of such relations.... Many false analogies are manufactured and it is
excellent thought training to expose them. The majority of people think so
little that they swallow false analogies just as newly-fledged robins swallow
small stones dropped into their open mouths.... The study of poetry may be made
very serviceable in detecting analogies and cultivating the reasoning powers.
When the poet brings clearly to mind the change due to death, using as an
illustration the caterpillar body transformed into the butterfly spirit, moving
with winged ease over flowing meadows, he is cultivating our apprehension of
relations, none the less valuable because they are beautiful."
There are
certain studies which tend to develop the power or faculty of Inductive
Reasoning. Any study which leads the mind to consider classification and
general principles, laws or truth, will tend to develop the faculty of
deduction. Physics, Chemistry, Astronomy, Biology and Natural History are
particularly adapted to develop the mind in this particular direction.
Moreover, the mind should be directed to an inquiry into the causes of things.
Facts and phenomena should be observed and an attempt should be made not only
to classify them, but also to discover general principles moving them.
Tentative or provisional hypotheses should be erected and then the facts
re-examined in order to see whether they support the hypotheses or theory.
Study of the processes whereby the great scientific theories were erected, and
the proofs then adduced in support of them, will give the mind the habit of thinking
along the lines of logical induction. The question ever in the mind in
Inductive Reasoning is "Why?" The dominant idea in Inductive
Reasoning is the Search for Causes.
In regard
to the pitfalls of Inductive Reasoning—the fallacies, so-called, Hyslop says:
"It is not easy to indicate the inductive fallacies, if it be even
possible, in the formal process of induction.... It is certain, however, that
in respect to the subject-matter of the conclusion in inductive reasoning there
are some very definite limitations upon the right to transcend the premises. We
cannot infer anything we please from any premises we please. We must conform to
certain definite rules or principles. Any violation of them will be a fallacy.
These rules are the same as those for material fallacies in deduction, so that
the fallacies of induction, whether they are ever formal or not, are at least
material; that is they occur whenever equivocation and presumption are
committed. There are, then, two simple rules which should not be violated. (1)
The subject-matter in the conclusion should be of the same general kind as in
the premises. (2) The facts constituting the premises must be accepted and
must not be fictitious."
One may
develop his faculty or power of Deductive Reasoning by pursuing
certain lines of study. The study of Mathematics, particularly in its branch of
Mental Arithmetic is especially valuable in this direction. Algebra and
Geometry have long been known to exercise an influence over the mind which
gives to it a logical trend and cast. The processes involved in Geometry are
akin to those employed in Logical reasoning, and must necessarily train the
mind in this special direction. As 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 Grammar, Rhetoric and the Languages, are also valuable in the culture
and development of the faculty of Deductive Reasoning. The study of Psychology
and Philosophy have value in this connection. The study of Law is very valuable
in creating logical habits of thinking deductively.
But in the
study of Logic we have possibly the best exercise in the development and
culture of this particular faculty. As Brooks well says: "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 cannot but improve one's thought."
The study
of the common fallacies, such as "Begging the Question,"
"Reasoning in a Circle," etc., is particularly important to the
student, for when one realizes that such fallacies exist, and is able to detect
and recognize them, he will avoid their use in framing his own arguments, and
will be able to expose them when they appear in the arguments of others.
The
fallacy of "Begging the Question" consists in assuming as a proven
fact something that has not been proven, or is not accepted as proven by the
other party to the argument. It is a common trick in debate. The fact assumed
may be either the particular point to be proved, or the premise necessary to
prove it. Hyslop gives the following illustration of this fallacy: "Good
institutions should be united; Church and State are good institutions;
therefore, Church and State should be united." The above syllogism seems
reasonable at first thought, but analysis will show that the major premise
"Good institutions should be united" is a mere assumption without
proof. Destroy this premise and the whole reasoning fails.
Another
form of fallacy, quite common, is that called "Reasoning in a
Circle," which consists in assuming as proof of a proposition the
proposition itself, as for instance, "This man is a rascal, because
he is a rogue; he is a rogue, because he is a rascal."
"We see through glass, because it is transparent."
"The child is dumb, because it has lost the power of speech."
"He is untruthful, because he is a liar." "The
weather is warm, because it is summer; it is summer, because
the weather is warm."
These and
other fallacies may be detected by a knowledge of Logic, and the perception and
detection of them strengthens one in his faculty of Deductive Reasoning. The
study of the Laws of the Syllogism, in Logic, will give to one a certain
habitual sense of stating the terms of his argument according to these laws,
which when acquired will be a long step in the direction of logical thinking,
and the culture of the faculties of deductive reasoning.
In
concluding this chapter, we wish to call your attention to a fact often
overlooked by the majority of people. Halleck well expresses it as follows:
"Belief is a mental state which might as well be classed under emotion as
under thinking, for it combines both elements. Belief is a part inference from
the known to the unknown, and part feeling and emotion." Others have
gone so far as to say that the majority of people employ their intellects
merely to prove to themselves and others that which they feel
to be true, or wish to be true, rather than to ascertain what
is actually true by logical methods. Others have said that
"men do not require arguments to convince them; they want
only excuses to justify them in their feelings, desires or
actions." Cynical though this may seem, there is sufficient truth in it to
warn one to guard against the tendency.
Jevons
says, regarding the question of the culture of logical processes of thought:
"Monsieur Jourdain, an amusing person in one of Moliere's plays, expressed
much surprise on learning that he had been talking prose for more than forty
years without knowing it. Ninety-nine people out of a hundred might be equally
surprised on hearing that they had long been converting propositions,
syllogizing, falling into paralogisms, framing hypotheses and making
classifications with genera and species. If asked if 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.
It may be asked:—If we cannot help being logicians, why do we need logic books
at all? The answer is that there are logicians, and logicians. All
persons are logicians in some manner or degree; but unfortunately many people
are bad ones and suffer harm in consequence. It is just the same in other
matters. Even if we do not know the meaning of the name, we are all athletes in
some manner or degree. No one can climb a tree or get over a gate without being
more or less an athlete. Nevertheless, he who wishes to do these actions really
well, to have a strong muscular frame and thereby to secure good health and
personal safety, as far as possible, should learn athletic exercises."
Comments
Post a Comment