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."