Speaker 1: Chapter twenty seven, deductive reasoning. We have seen in a
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 premisses
or bases for deductive reasoning. These two forms of 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,
rise 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
is 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, analytic 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.
One a general principle of a class is stated as
a major premise. Two, a particular thing is stated as
belonging to that general class, this statement being the minor
premiss Therefore, three, 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. One
major premiss A bird is a warm blooded, feathered, winged
oviparous vertebrate. Two minor premis the sparrow is a bird.
Therefore three conclusion, the sparrow is a warm blooded, feathered,
winged oviparous vertebrate. Or again one major premiss. Rattlesnakes frequently
bite when enraged, and their bite is poisonous. Two minor premis,
this snake before me is a rattlesnake. Therefore three 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 process 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,
everyone 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. Weightly 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 premisses 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 premisses. The therefore before the conclusion resulting from the if.
Of course, the following are the general rules governing the syllogism. One,
Every syllogism must consist of three and no more than
three propositions, namely, one the major premise, two the minor premiss,
and three the conclusion. Two. The conclusion must naturally follow
from the premisses. Otherwise the syllogism is invalid and constitutes
a fallacy or sophism. Three. One premiss at least must
be affirmative. Four If one premiss is negative, the conclusion
must be negative. Five One premiss at least must be
universal or general. Six If one premiss is particular, the
conclusion also must be particular. The last two rules five
and six contain 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 five, because from two particular premisses no conclusion can
be drawn, as for instance, one, some men are mortal.
Two 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 six, because a universal
conclusion can be drawn only from two universal premises, an
example being needless here as a 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 those 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. 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
to your attention in the next chapter to the more
common fallacies and the reason of their falsity. End of
Chapter twenty seven, Chapter twenty eight. Fallacious reasoning a fallacy
is to fined as an unsound argument or mode of arguing, which,
while appearing to be decisive of a question, is in
reality not so, or a fallacious statement or proposition in
which the error is not readily apparent. When a fallacy
is used to deceive others, it is called sophistry. It
is important that the student should understand the nature of
the fallacy and understand its most common forms. As Jevons says,
in learning how to do right, it is always desirable
to be informed as to the ways in which we
are likely to go wrong. In describing to a man
the road which he should follow, we ought to tell
him not only the turnings which he is to take,
but also the turnings which he is to avoid. Similarly,
it is a useful part of logic which teaches us
the ways and turnings by which people most commonly go
astray in reasoning. In presenting the following brief statement rearding
the more common forms of fallacy, we omit so far
as possible the technical details which belong to text books
on logic fallacies. One true collective, but false particular. An
example of this fallacy is found in the argument that
because the French race collectively are excitable, therefore a particular
Frenchman must be excitable, or that because the Jewish race
collectively are good business people, therefore the particular jew must
be a good business man. This is as fallacious as
arguing that because a man may drown in the ocean,
he should avoid the bath, basin or cup of water.
There is a vast difference between the whole of a
thing and its separate parts. Nitric acid and glycerine separately
are not explosive, but combined they form nitroglycerin, a most
dangerous and powerful explosive. Reversing this form of illustration well
remind you of the old saying salt is a good thing,
but one doesn't want to be put in pickle. Two
irrelevant conclusion. This fallacy consists in introducing in the conclusion
matter not contained in the premises, or in the confusing
of the issue. For instance, one, all men are sinful,
two John Smith is a man. Therefore three John Smith
is a horse thief. This may sound absurd, but many
arguments are as fallacious as this, and for the same reason,
or another and more subtile form. One all thieves are liars.
Two John Smith is a liar. Therefore three John Smith
is a thief. The first example arises from the introduction
of new matter, and the last from the confusion of
the issue. Three. False cause. This fallacy consists in attributing
cause to a thing which is merely incident with or
precedent to the effect. For instance, one, the cock crows
just before or at the moment of sunrise. Therefore, two
the cock crowing is the cause of the sunrise. Or again, one,
bad crops follow the election of a Whig president. Therefore,
two the Whig Party is the cause of the bad crops.
Or again one where civilization is the highest, there we
find the greatest number of high hats. Therefore, two high
hats are the cause of civilization. Four. Circular reasoning. In
this form of fallacy, the person reasoning or arguing endeavors
to explain or prove a thing by itself or its
own terms. For instance, one, the Whig Party is honest
because it advocates honest principles. Two the Whig principles are
honest because they are advocated by an honest party. A
common form of this fallacy in its phase of sophistry,
is the use of synonyms in such a manner that
they seem to express more than the original conception, whereas
they are really but other terms for the same thing.
An historical example of circular reasoning is the following. One
the Church of England is the true church because it
was established by God. Two it must have been established
by God because it is the true Church. This form
of sophistry is most effective when employed in long arguments
in which it is difficult to detect it. Five begging
the question. This fallacy arises from the use of a
false premiss, or at least of a premise the truth
of which is not admitted by the opponent. It may
be stated simply as the unwarranted assumption of a premiss,
generally the major premiss. Many persons in public life are
you in this way. They boldly assert an unwarranted premise
and then proceed to argue logically from it. The result
is confusing to the average person, for the steps of
reasoning being logical, it seems as if the argument is sound,
the fact of the unwarranted premise being overlooked. The person
using this form of sophistry proceeds on Aaron Burr's theory
of truth being that which is boldly asserted and plausibly maintained.
Bulwin makes one of his characters mention a particularly atrocious
form of this fallacy, although an amusing one, in the
following words, whenever you are about to utter something astonishingly false,
always begin with it is an acknowledged fact, et cetera.
Sir Robert Filmer was a master of this manner of writing. Thus,
with what a solemn face that great man attempted to
cheat he would say, it is a truth undeniable that
they cannot be any multitude of men whatsoever, either great
or small, et cetera. But in that same multitude there
is one man among them, that, in nature hath a
right to be king of all the rest, as being
the next heir of Adam. Look carefully for the major
premise of propositions advanced in argument, spoken, or written. Be
sure that the person making the proposition is not begging
the question by the unwarranted assumption of the premise. General
rule of inference, Hislop says, concerning valid inferences and fallacious ones,
we cannot infer anything we please from any premisses we please.
We must conform to certain definite rules or principles. Any
violation of them will be a fallacy. There are two
simple rules which should not be violated. One, the subject
matter in the conclusion should be of the same generals
as in the premises. Two, the facts constituting the premisses
must be accepted and must not be fictitious. A close
observance of these rules will result in the detection and
avoidance of the principal forms of fallacious reasoning and sophistry.
Sophistical arguments. There are a number of tricky practices resorted
to by persons in argument that are fallacious in intent
and result, which we do not consider here in detail,
as they scarcely belong to the particular subject of this book.
A brief mention, however, may be permitted in the interest
of general information. Here are the principal ones. One arguing
that a proposition is correct because the opponent cannot prove
the contrary. The fallacy is seen when we realize that
the statement the moon is made of green cheese is
not proved because we cannot prove the contrary. No amount
of failure to disprove a proposition really proves it, and
no amount of failure to prove a proposition really disproves it.
As a general rule, the burden of proof rests upon
the person stating the proposition, and his opponent is not
called upon to disprove it or else have it considered proved.
The old cry if you cannot prove that it is
not so is based upon a fallacious conception. Two abuse
of the opponent, his party, or his cause. This is
no real argument or reasoning. It is akin to proving
a point by beating the opponent over the head. Three.
Arguing that an opponent does not live up to his
principles is now argument against the principles he advocates. A
man may advocate the principle of temperance and yet drink
to excess. This simply proves that he preaches better than
he practices, But the truth of the principle of temperance
is not affected in any way. Thereby, the proof of
this is that he may change his practices, and it
cannot be held that the change of his personal habits
improves or changes the nature of the principle. Four. Argument
of authority is not based on logic. Authority is valuable
when really worthy and merely as corroboration or adding weight,
but it is not logical argument. The reasons of the
authority alone constitute a real argument. The abuse of this
form of argument is shown in the above reference to
begging the question in a quotation from Bulwa. Five. Appeal
to prejudice or public opinion is not a valid argument,
for public opinion is frequently wrong, and prejudice is often unwarranted,
and at the best, they have nothing to do with
the case from the standpoint of logic. The abuse of
testimony and claimed evidence is also worthy of examination, but
we cannot go into the subject here. Fallacies of prejudice.
But perhaps the most dangerous of all fallacies in the
search for truth on the part of the most of
us are those which arise from the following one. The
tendency to reason from what we feel and wish to
be true, rather than from the actual facts of the case,
which causes us unconsciously to assume the mental attitude of
if the facts agree with our likes and pet theories,
all is well. If they do not, so much the
worse for the facts. Two, the tendency in all of
us to perceive only the facts that agree with our
theories and to ignore the others. We find that for
which we seek and overlook that which does not interest us.
Our discoveries follow our interest, and our interest follows our
desires and beliefs. The intelligent man or woman realizes these
tendencies of human nature and endeavors to avoid them in
his or her own reasoning, but is keenly conscious of
them in the arguments and reasoning of others. A failure
to observe and guard one's self against these tendencies results
in bigotry, intolerance, narrowness, and intellectual astigmatism.