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Title: The Art of Logical Thinking
       or the Laws of Reasoning

Author: William Walker Atkinson

Release Date: January 13, 2013 [EBook #41838]

Language: English

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  THE ART OF
  LOGICAL THINKING

  OR

  THE LAWS OF REASONING

  By WILLIAM WALKER ATKINSON


  L.N. FOWLER & COMPANY
  7, Imperial Arcade, Ludgate Circus
  London, E.C., England

  1909
  THE PROGRESS COMPANY
  CHICAGO, ILL.




  Copyright 1909
  By
  THE PROGRESS COMPANY
  Chicago, Ill., U.S.A.




CONTENTS


      I. Reasoning                            9

     II. The Process of Reasoning            17

    III. The Concept                         25

     IV. The Use of Concepts                 37

      V. Concepts and Images                 48

     VI. Terms                               56

    VII. The Meaning of Terms                73

   VIII. Judgments                           82

     IX. Propositions                        90

      X. Immediate Reasoning                 99

     XI. Inductive Reasoning                107

    XII. Reasoning by Induction             116

   XIII. Theory and Hypotheses              125

    XIV. Making and Testing Hypotheses      132

     XV. Deductive Reasoning                144

    XVI. The Syllogism                      156

   XVII. Varieties of Syllogisms            167

  XVIII. Reasoning by Analogy               179

    XIX. Fallacies                          186




CHAPTER I.

REASONING


"Reasoning" is defined as: "The act, process or art of exercising the
faculty of reason; the act or faculty of employing reason in argument;
argumentation, ratiocination; reasoning power; disputation, discussion,
argumentation." Stewart says: "The word _reason_ itself is far from
being precise in its meaning. In common and popular discourse it denotes
that power by which we distinguish truth from falsehood, and right from
wrong, and by which we are enabled to combine means for the attainment
of particular ends."

By the employment of the reasoning faculties of the mind we compare
objects presented to the mind as percepts or concepts, taking up the
"raw materials" of thought and weaving them into more complex and
elaborate mental fabrics which we call abstract and general ideas of
truth. Brooks says: "It is the thinking power of the mind; the faculty
which gives us what has been called _thought-knowledge_, in distinction
from _sense-knowledge_. It may be regarded as the mental architect among
the faculties; it transforms the material furnished by the senses ...
into new products, and thus builds up the temples of science and
philosophy." The last-mentioned authority adds: "Its products are
twofold, _ideas_ and _thoughts_. An _idea_ is a mental product which
when expressed in words does not give a proposition; a _thought_ is a
mental product which embraces the relation of two or more ideas. The
ideas of the understanding are of two general classes; abstract ideas
and general ideas. The thoughts are also of two general classes; those
pertaining to contingent truth and those pertaining to necessary truth.
In contingent truth, we have _facts_, or immediate judgments, and
_general truths_ including _laws_ and _causes_, derived from particular
facts; in necessary truth we have _axioms_, or self-evident truths, and
the truths derived from them by reasoning, called _theorems_."

In inviting you to consider the processes of reasoning, we are
irresistibly reminded of the old story of one of Moliere's plays in
which one of the characters expresses surprise on learning that he "had
been talking prose for forty years without knowing it." As Jevons says
in mentioning this: "Ninety-nine people out of a hundred might be
equally surprised on hearing that they had been converting propositions,
syllogizing, falling into paralogisms, framing hypotheses and making
classifications with genera and species. If asked whether 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."

So, in asking you to consider the processes of reasoning we are not
assuming that you never have reasoned--on the contrary we are fully
aware that you in connection with every other person, have reasoned all
your mature life. That is not the question. While everyone reasons, the
fact is equally true that the majority of persons reason incorrectly.
Many persons reason along lines far from correct and scientific, and
suffer therefor and thereby. Some writers have claimed that the majority
of persons are incapable of even fairly correct reasoning, pointing to
the absurd ideas entertained by the masses of people as a proof of the
statement. These writers are probably a little radical in their views
and statements, but one is often struck with wonder at the evidences of
incapacity for interpreting facts and impressions on the part of the
general public. The masses of people accept the most absurd ideas as
truth, providing they are gravely asserted by some one claiming
authority. The most illogical ideas are accepted without dispute or
examination, providing they are stated solemnly and authoritatively.
Particularly in the respective fields of religion and politics do we
find this blind acceptance of illogical ideas by the multitude. Mere
assertion by the leaders seems sufficient for the multitude of followers
to acquiesce.

In order to reason correctly it is not merely necessary to have a good
intellect. An athlete may have the proper proportions, good framework,
and symmetrical muscles, but he cannot expect to cope with others of his
kind unless he has learned to develop those muscles and to use them to
the best advantage. And, in the same way, the man who wishes to reason
correctly must develop his intellectual faculties and must also learn
the art of using them to the best advantage. Otherwise he will waste his
mental energy and will be placed at a disadvantage when confronted with
a trained logician in argument or debate. One who has witnessed a debate
or argument between two men equally strong intellectually, one of whom
is a trained logician and the other lacking this advantage, will never
forget the impression produced upon him by the unequal struggle. The
conflict is like that of a powerful wrestler, untrained in the little
tricks and turns of the science, in the various principles of applying
force in a certain way at a certain time, at a certain place, with a
trained and experienced wrestler. Or of a conflict between a muscular
giant untrained in the art of boxing, when confronted with a trained and
experienced exponent of "the manly art." The result of any such conflict
is assured in advance. Therefore, everyone should refuse to rest content
without a knowledge of the art of reasoning correctly, for otherwise he
places himself under a heavy handicap in the race for success, and
allows others, perhaps less well-equipped mentally, to have a decided
advantage over him.

Jevons says in this connection: "To be a good logician is, however, far
more valuable than to be a good athlete; because logic teaches us to
reason well, and reasoning gives us knowledge, and knowledge, as Lord
Bacon said, is power. As athletes, men cannot for a moment compare with
horses or tigers or monkeys. Yet, with the power of knowledge, men tame
horses and shoot tigers and despise monkeys. The weakest framework with
the most logical mind will conquer in the end, because it is easy to
foresee the future, to calculate the result of actions, to avoid
mistakes which might be fatal, and to discover the means of doing things
which seemed impossible. If such little creatures as ants had better
brains than men, they would either destroy men or make them into slaves.
It is true that we cannot use our eyes and ears without getting some
kind of knowledge, and the brute animals can do the same. But what gives
power is the deeper knowledge called Science. People may see, and hear,
and feel all their lives without really learning the nature of things
they see. But reason is the mind's eye, and enables us to see why things
are, and when and how events may be made to happen or not to happen. The
logician endeavors to learn exactly what this reason is which makes the
power of men. We all, as I have said, must reason well or ill, but logic
is the science of reasoning and enables us to distinguish between the
good reasoning which leads to truth, and the bad reasoning which every
day betrays people into error and misfortune."

In this volume we hope to be able to point out the methods and
principles of correctly using the reasoning faculties of the mind, in a
plain, simple manner, devoid of useless technicalities and academic
discussion. We shall adhere, in the main, to the principles established
by the best of the authorities of the old school of psychology, blending
the same with those advanced by the best authorities of the New
Psychology. No attempt to make of this book a school text-book shall be
made, for our sole object and aim is to bring this important subject
before the general public composed of people who have neither the time
nor inclination to indulge in technical discussion nor academic
hair-splitting, but who desire to understand the underlying _working
principles_ of the Laws of Reasoning.




CHAPTER II.

THE PROCESS OF REASONING


The processes of Reasoning may be said to comprise four general stages
or steps, as follows:

I. _Abstraction_, by which is meant the process of _drawing off_ and
_setting aside_ from an object, person or thing, _a quality or
attribute_, and making of it a distinct object of thought. For instance,
if I perceive in a _lion_ the quality of _strength_, and am able to
think of this quality abstractly and independently of the animal--if the
term _strength_ has an actual mental meaning to me, independent of the
lion--then I have _abstracted_ that quality; the thinking thereof is an
act of _abstraction_; and the thought-idea itself is an _abstract idea_.
Some writers hold that these abstract ideas are realities, and "not mere
figments of fancy." As Brooks says: "The rose dies, but my idea of its
color and fragrance remains." Other authorities regard Abstraction as
but an act of _attention_ concentrated upon but the particular quality
to the exclusion of others, and that the abstract idea has no existence
apart from the general idea of the object in which it is included. Sir
William Hamilton says: "We can rivet our attention on some particular
mode of a thing, as its smell, its color, its figure, its size, etc.,
and abstract it from the others. This may be called Modal Abstraction.
The abstraction we have now been considering is performed on individual
objects, and is consequently particular. There is nothing necessarily
connected with generalization in abstraction; generalization is indeed
dependent on abstraction, which it supposes; but abstraction does not
involve generalization."

II. _Generalization_, by which is meant the process of forming Concepts
or General Ideas. It acts in the direction of apprehending the common
qualities of objects, persons and things, and combining and uniting them
into a single notion or _conception_ which will comprehend and include
them all. A General Idea or Concept differs from a particular idea in
that it includes within itself the qualities of the particular and other
particulars, and accordingly may be applied to any one of these
particulars as well as to the general _class_. For instance, one may
have a _particular idea_ of some _particular_ horse, which applies only
to that particular horse. He may also have a General Idea of _horse_, in
the generic or _class_ sense, which idea applies not only to the general
class of _horse_ but also to each and every _horse_ which is included in
that class. _The expression of Generalization or Conception is called a
Concept._

III. _Judgment_, by which is meant the process of comparing two objects,
persons or things, one with another, and thus perceiving their agreement
or disagreement. Thus we may compare the two concepts _horse_ and
_animal_, and perceiving a certain agreement between them we form the
judgment that: "A _horse_ is an _animal_;" or comparing _horse_ and
_cow_, and perceiving their disagreement, we form the judgment: "A
_horse_ is not a _cow_." _The expression of a judgment is called a
Proposition._

IV. _Reasoning_, by which is meant the process of comparing two objects,
persons or things, through their relation to a third object, person or
thing. Thus we may reason (a) that all mammals are animals; (b) that a
horse is a mammal; (c) that, _therefore_, a horse is an animal; the
result of the reasoning being the statement that: "A horse is an
animal." The most fundamental principle of reasoning, therefore,
consists in the comparing of two objects of thought through and by means
of their relation to a third object. _The natural form of expression of
this process of Reasoning is called a Syllogism._

It will be seen that these four processes of reasoning necessitate the
employment of the processes of Analysis and Synthesis, respectively.
Analysis means a separating of an object of thought into its constituent
parts, qualities or relations. Synthesis means the combining of the
qualities, parts or relations of an object of thought into a composite
whole. These two processes are found in all processes of Reasoning.
Abstraction is principally analytic; Generalization or Conception
chiefly synthetic; Judgment is either or both analytic or synthetic;
Reasoning is either a synthesis of particulars in Induction, or an
evolution of the particular from the general in Deduction.

There are two great classes of Reasoning; _viz._, (1) Inductive
Reasoning, or the inference of general truths from particular truths;
and (2) Deductive Reasoning, or the inference of particular truths from
general truths.

_Inductive Reasoning_ proceeds by discovering a general truth from
particular truths. For instance, from the particular truths that
individual men die we discover the general truth that "All men must
die;" or from observing that in all observed instances ice melts at a
certain temperature, we may infer that "All ice melts at a certain
temperature." Inductive Reasoning proceeds from the _known to the
unknown_. It is essentially a synthetic process. It seeks to discover
general laws from particular facts.

_Deductive Reasoning_ proceeds by discovering particular truths from
general truths. Thus we reason that as all men die, John Smith, being a
man, must die; or, that as all ice melts at a certain temperature, it
follows that the particular piece of ice under consideration will melt
at that certain temperature. Deductive Reasoning is therefore seen to be
essentially an analytical process.

Mills says of Inductive Reasoning: "The inductive method of the ancients
consisted in ascribing the character of general truths to all
propositions which are true in all the instances of which we have
knowledge. Bacon exposed the insufficiency of this method, and physical
investigation has now far outgrown the Baconian conception....
Induction, then, is that operation by which we infer that what we know
to be true in a particular case or cases, will be true in all cases
which resemble the former in certain assignable respects. In other
words, induction is the process by which we conclude that what is true
of certain individuals of a class is true of the whole class, or that
what is true at certain times will be true in similar circumstances at
all times."

Regarding Deductive Reasoning, a writer says: "Deductive Reasoning is
that process of reasoning by which we arrive at the necessary
consequences, _starting from admitted or established premises_." Brooks
says: "The general truths from which we reason to particulars are
derived from several distinct sources. Some are intuitive, as the axioms
of mathematics or logic. Some of them are derived from induction....
Some of them are merely hypothetical, as in the investigation of the
physical sciences. Many of the hypotheses and theories of the physical
sciences are used as general truth for deductive reasoning; as the
theory of gravitation, the theory of light; etc. Reasoning from the
theory of universal gravitation, Leverrier discovered the position of a
new planet in the heavens before it had been discovered by human eyes."

Halleck points out the interdependence of Inductive and Deductive
Reasoning in the following words: "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
laws_.... 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 that she chewed her cud.... 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."

The several steps of Deductive Reasoning shall now be considered in turn
as we proceed.




CHAPTER III.

THE CONCEPT


In considering the process of thinking, we must classify the several
steps or stages of thought that we may examine each in detail for the
purpose of comprehending them combined as a whole. In actual thinking
these several steps or stages are not clearly separated in
consciousness, so that each stands out clear and distinct from the
preceding and succeeding steps or stages, but, on the contrary, they
blend and shade into each other so that it is often difficult to draw a
clear dividing line. The first step or stage in the process of thinking
is that which is called _a concept_.

A concept is a mental representation of anything. Prof. Wm. James says:
"The function by which we mark off, discriminate, draw a line around,
and identify a numerically distinct subject of discourse is called
_conception_." There are five stages or steps in each concept, as
follows:

I. _Presentation._ Before a concept may be formed there must first be a
presentation of the material from which the concept is to be formed. If
we wish to form the concept, _animal_, we must first have perceived an
animal, probably several kinds of animals--horses, dogs, cats, cows,
pigs, lions, tigers, etc. We must also have received impressions from
the sight of these animals which may be reproduced by the
memory--represented to the mind. In order that we may have a full
concept of _animal_ we should have perceived every kind of animal, for
otherwise there would be some elements of the full concept lacking.
Accordingly it is practically impossible to have a _full_ concept of
anything. The greater the opportunities for perception the greater will
be the opportunity for conception. In other books of this series we have
spoken of the value and importance of the attention and of clear and
full perception. Without an active employment of the attention, it is
impossible to receive a clear perception of anything; and unless the
perception has been clear, it is impossible for the mind to form a clear
concept of the thing perceived. As Sir Wm. Hamilton has said: "An act
of attention, that is an act of concentration, seems thus necessary to
every exertion of consciousness, as a certain contraction of the pupil
is requisite to every exertion of vision.... Attention, then, is to
consciousness what the contraction of the pupil is to sight, or to the
eye of the mind what the microscope or telescope is to the bodily
eye.... It constitutes the half of all intellectual power." And Sir B.
Brodie said: "It is attention, much more than in the abstract power of
reasoning, which constitutes the vast difference which exists between
minds of different individuals." And as Dr. Beattie says: "The force
with which anything strikes the mind is generally in proportion to the
degree of attention bestowed upon it."

II. _Comparison._ Following the stage of Presentation is the stage of
Comparison. We separate our general concept of _animal_ into a number of
sub-concepts, or concepts of various kinds of animals. We compare the
pig with the goat, the cow with the horse, in fact each animal with all
other animals known to us. By this process we distinguish the points of
resemblance and the points of difference. We perceive that the wolf
resembles the dog to a considerable degree; that it has some points of
resemblance to the fox; and a still less distinct resemblance to the
bear; also that it differs materially from the horse, the cow or the
elephant. We also learn that there are various kinds of wolves, all
bearing a great resemblance to each other, and yet having marked points
of difference. The closer we observe the various individuals among the
wolves, the more points of difference do we find. The faculty of
Comparison evidences itself in inductive reasoning; ability and
disposition to analyze, classify, compare, etc. Fowler says that those
in whom it is largely developed "Reason clearly and correctly from
conclusions and scientific facts up to the laws which govern them;
discern the known from the unknown; detect error by its incongruity with
facts; have an excellent talent for comparing, explaining, expounding,
criticising, exposing, etc." Prof. William James says: "Any personal or
practical interest in the results to be obtained by distinguishing,
makes one's wits amazingly sharp to detect differences. And long
training and practice in distinguishing has the same effect as personal
interest. Both of these agencies give to small amounts of objective
difference the same effectiveness upon the mind that, under other
circumstances, only large ones would make."

III. _Abstraction._ Following the stage of Comparison is that of
Abstraction. The term "Abstraction" as used in psychology means: "The
act or process of separating from the numerous qualities inherent in any
object, the particular one which we wish to make the subject of
observation and reflection. Or, the act of withdrawing the consciousness
from a number of objects with a view to concentrate it on some
particular one. The negative act of which Attention is the positive." To
_abstract_ is "to separate or set apart." In the process of Abstraction
in our consideration of _animals_, after having recognized the various
points of difference and resemblance between the various species and
individuals, we proceed to consider some special quality of animals,
and, in doing so, we _abstract_, set aside, or separate the particular
quality which we wish to consider. If we wish to consider the _size_ of
animals, we abstract the quality of size from the other qualities, and
consider animals with reference to size alone. Thus we consider the
various degrees of size of the various animals, classifying them
accordingly. In the same way we may abstract the quality of shape, color
or habits, respectively, setting aside this quality for special
observation and classification. If we wish to study, examine or consider
certain qualities in a thing we abstract that particular quality from
the other qualities of the thing; or we abstract the other qualities
until nothing is left but the particular quality under consideration. In
examining or considering a class or number of things, we first abstract
the qualities _possessed in common_ by the class or number of things;
and also abstract or set aside the qualities _not common_ to them.

For instance; in considering classes of animals, we abstract the
combined quality of milk-giving and pouch-possessing which is possessed
in common by a number of animals; then we group these several animals in
a class which we name the _Marsupialia_, of which the opossum and
kangaroo are members. In these animals the young are brought forth in an
imperfect condition, undeveloped in size and condition, and are then
kept in the pouch and nourished until they are able to care for
themselves. Likewise, we may abstract the idea of the _placenta_, the
appendage which connects the young unborn animal with the mother, and by
means of which the foetus is nourished. The animals distinguished by
this quality are grouped together as the Placental Mammals. The
Placental Mammals are divided into various groups, by an Abstraction of
qualities or class resemblance or difference, as follows: The
_Edentata_, or toothless creatures, such as the sloths, ant-eaters,
armadillos, etc.; the _Sirenia_, so-named from their fancied resemblance
to the fabled "sirens," among which class are the sea-cows, manatees,
dugongs, etc.; the _Cetacea_, or whale family, which although fish-like
in appearance, are really mammals, giving birth to living young which
they nourish with breast-milk, among which are the whales, porpoises,
dolphins, etc.; the _Ungulata_, or hoofed animals, such as the horse,
the tapir, the rhinoceros, the swine, the hippopotamus, the camel, the
deer, the sheep, the cow, etc.; the _Hyracoidea_, having teeth
resembling both the hoofed animals and the gnawing animals, of which the
coney or rock-rabbit is the principal example; the _Proboscidea_, or
trunked animals, which family is represented by the various families of
elephants; the _Carnivora_, or flesh-eaters, represented by various
sub-families and species; the _Rodentia_, or gnawers; the _Insectivora_,
or insect feeders; the _Cheiroptera_, or finger-winged; the
_Lemuroidea_, or lemurs, having the general appearance of the monkey,
but also the long bushy tail of the fox; the _Primates_, including the
monkeys, baboons, man-apes, gibbons, gorillas, chimpanzees,
orang-outangs and Man.

In all of these cases you will see that each class or general family
possesses a certain _common quality_ which gives it its classification,
and which quality is the subject of the Abstraction in considering the
particular group of animals. Further and closer Abstraction divides
these classes into sub-classes; for instance, the family or class of the
_Carnivora_, or flesh-eaters, may be divided by further Abstraction
into the classes of seals, bears, weasels, wolves, dogs, lions, tigers,
leopards, etc. In this process, we must first make the more general
Abstraction of the wolf and similar animals into the dog-family; and the
lion, tiger and similar forms into the cat-family.

Halleck says of Abstraction: "In the process of Abstraction, we draw our
attention away from a mass of confusing details, unimportant at the
time, and attend only to qualities common to the class. Abstraction is
little else than centering the power of attention on some qualities to
the exclusion of others."

IV. _Generalization._ Arising from the stage of Abstraction is the stage
of Generalization. _Generalization_ is: "The act or process of
generalizing or making general; bringing several objects agreeing in
some point under a common or general name, head or class; an extending
from particulars to generals; reducing or arranging in a genus; bringing
a particular fact or series of facts into a relation with a wider circle
of facts." As Bolingbroke says: "The mind, therefore, makes its utmost
endeavors to _generalize_ its ideas, beginning early with such as are
most familiar and coming in time to those which are less so." Under the
head of Abstraction we have seen that through Abstraction we may
Generalize the various species into the various families, and thus, in
turn, into the various sub-families. Following the same process we may
narrow down the sub-families into species composed of various
individuals; or into greater and still greater families or groups.
Generalization is really the act of Classification, or forming into
classes all things having certain qualities or properties _in common_.
The corollary is that _all things in a certain generalized class must
possess the particular quality or property common to the class_. Thus we
know that all animals in the class of the _Carnivora_ must eat flesh;
and that all _Mammals_ possess breasts from which they feed their young.
As Halleck says: "We put all objects having like qualities into a
certain _genus_, or class. When the objects are in that class, _we know
that certain qualities will have a general application to them all_."

V. _Denomination._ Following closely upon the step of Generalization or
Classification, is the step of Denomination. By _Denomination_ we mean
"the act of naming or designating by a name." A name is the symbol by
which we think of a familiar thing without the necessity for making a
distinct mental image upon each occasion of thought. Or, it may be
considered as akin to a _label_ affixed to a thing. As in the case of
the algebraic symbols, _a_, _b_, _c_, _x_, and _y_, by the use of which
we are able to make intricate calculations easily and rapidly, so may we
use these word symbols much more readily than we could the lengthy
descriptions or even the mental images of the thing symbolized. It is
much easier for us to think "_horse_" than it would be to think the full
definition of that animal, or to think of it by recalling a mental
picture of the horse each time we wished to think of it. Or, it is much
better for us to be able to glance at a label on a package or bottle
than to examine the contents in detail. As Hobbes says: "A word taken at
pleasure to serve for a mark, which may raise in our minds a thought
like to some thought we had before, and which being pronounced to
others, may be to them a sign of what thought the speaker had or had
not, before in his mind." Mill says: "A name is a word (or set of
words) serving the double purpose of a mark to recall to ourselves the
likeness of a former thought and as a sign to make it known to others."
Some philosophers regard names as symbols of _our ideas of things_,
rather than of the things themselves; others regard them as symbols of
the things themselves. It will be seen that the value of a name depends
materially upon the correct meaning and understanding regarding it
possessed by the person using it.




CHAPTER IV.

THE USE OF CONCEPTS


Having observed the several steps or stages of a concept, let us now
consider the use and misuse of the latter. At first glance it would
appear difficult to misuse a concept, but a little consideration will
show that people very commonly fall into error regarding their concepts.

For instance, a child perceives a horse, a cow or a sheep and hears its
elders apply the term "_animal_" to it. This term is perfectly correct,
although symbolizing only a very general classification or
generalization. But, the child knowing nothing of the more limited and
detailed classification begins to generalize regarding the animal. To
it, accordingly, an "animal" is identical with the dog or the cow, the
sheep or the horse, as the case may be, and when the term is used the
child thinks that _all animals_ are similar to the particular animal
seen. Later on, when it hears the term "animal" applied to a totally
different looking creature, it thinks that a mistake has been made and
a state of confusion occurs. Or, even when a term is applied within
narrower limits, the same trouble occurs. The child may hear the term
"dog" applied to a mastiff, and it accordingly forms a concept of _dog_
identical with the qualities and attributes of the mastiff. Later,
hearing the same term applied to a toy-terrier, it becomes indignant and
cries out that the latter is no "dog" but is something entirely
different. It is not until the child becomes acquainted with the fact
that there are many kinds of creatures in the general category of "dog"
that the latter term becomes fully understood and its appropriate
concept is intelligently formed. Thus we see the importance of the step
of Presentation.

In the same way the child might imagine that because some particular
"man" had red hair and long whiskers, _all men_ were red-haired and
long-whiskered. Such a child would always form the concept of "man" as a
creature possessed of the personal qualities just mentioned. As a writer
once said, readers of current French literature might imagine that all
Englishmen were short, dumpy, red-cheeked and irascible, and that all
Englishwomen had great teeth and enormous feet; also that readers of
English literature might imagine that all Frenchmen were like monkeys,
and all Frenchwomen were sad coquettes. In the same way many American
young people believe that all Englishmen say "Don't you know" and all
Englishwomen constantly ejaculate: "Fancy!" Also that every Englishman
wears a monocle. In the same way, the young English person, from reading
the cheap novels of his own country, might well form the concept of all
Americans as long-legged, chin-whiskered and big-nosed, saying "Waal, I
want to know;" "I reckon;" and "Du tell;" while they tilted themselves
back in a chair with their feet on the mantelpiece. The concept of a
Western man, entertained by the average Eastern person who has never
traveled further West than Buffalo, is equally amusing. In the same way,
we have known Western people who formed a concept of Boston people as
partaking of a steady and continuous diet of baked beans and studiously
reading Browning and Emerson between these meals.

Halleck says: "A certain Norwegian child ten years old had the quality
_white_ firmly imbedded in his concept _man_. Happening one day to see a
negro for the first time, the child refused to call him a man until the
negro's other qualities compelled the child to revise his concept and to
eliminate whiteness. If that child should ever see an Indian or a
Chinaman, the concept would undergo still further revision. A girl of
six, reared with an intemperate father and brothers, had the quality of
_drunkenness_ firmly fixed in her concept of _man_. A certain boy kept,
until the age of eleven, _trustworthiness_ in his concept of man.
Another boy, until late in his teens thought that man was a creature who
did wrong not from determination but from ignorance, that any man would
change his course to the right path if he could but understand that he
was going wrong. Happening one day to hear of a wealthy man who was
neglecting to provide comforts for his aged mother in her last sickness,
the boy concluded that the man did not know his mother's condition. When
he informed the man, the boy was told to mind his own business. The same
day he heard of some politicians who had intentionally cheated the city
in letting a contract and he immediately revised his concept. It must be
borne in mind that most of our concepts are subject to change during our
entire life; that at first they are made only in a tentative way; that
experience may show us, at any time, that they have been erroneously
formed, that we have, abstracted too little or too much, made this class
too wide or too narrow, or that here a quality must be added or there
one taken away."

Let us now consider the mental processes involved in the formation and
use of a concept. We have first, as we have seen, the presentation of
the crude material from which the concept must be formed. Our attention
being attracted to or directed toward an object, we notice its qualities
and properties. Then we begin a process of comparison of the object
perceived or of our perception of it. We compare the object with other
objects or ideas in our mind, noting similarities and differences and
thereby leading towards classification with similar objects and opposed
dissimilar ones. The greater the range of other objects previously
perceived, the greater will be the number of relations established
between the new object or idea and others. As we advance in experience
and knowledge, the web of related objects and ideas becomes more
intricate and complex. The relations attaching to the child's concept of
horse is very much simpler than the concept of the experienced adult.
Then we pass on to the step of analysis, in which we separate the
qualities of the object and consider them in detail. The act of
abstraction is an analytical process. Then we pass on to the step of
synthesis, in which we unite the materials gathered by comparison and
analysis, and thus form a general idea or concept regarding the object.
In this process we combine the various qualities discerned by comparison
and analysis, and grouping them together as in a bundle, we tie them
together with the string of synthesis and thus have a true general
conception. Thus from the first general conception of _horse_ as a
simple thing, we notice first that the animal has certain qualities
lacking in other things and certain others similar to other things; then
we analyze the various qualities of the horse, recognized through
comparison, until we have a clear and distinct idea of the various
parts, qualities and properties of the horse; then we synthesize, and
joining together these various conceptions of the said qualities, we at
last form a clear general concept of _the horse as he is_, with all his
qualities. Of course, if we later discover other qualities attached to
the horse, we add these to our general synthesized concept--our concept
of _horse_ is enlarged.

Of course these various steps in the formation and use of a concept are
not realized as distinct acts in the consciousness, for the processes
are largely instinctive and subconscious, particularly in the case of
the experienced individual. The subconscious, or habit mind, usually
attends to these details for us, except in instances in which we
deliberately apply the will to the task, as in cases of close study, in
which we take the process from the region of the involuntary and place
it in the voluntary category. So closely related and blended are these
various steps of the process, that some authorities have disputed
vigorously upon the question as to which of the two steps, comparison
or analysis, precedes the other. Some have claimed that analysis must
precede comparison, else how could one compare without having first
analyzed the things to be compared. Others hold that comparison must
precede analysis, else how could one note a quality unless he had his
attention drawn to it by its resemblance to or difference from qualities
in other objects. The truth seems to lie between the two ideas, for in
some cases there seems to be a perception of some similarity or
difference before any analysis or abstraction takes place; while in
others there seems to be an analysis or abstraction before comparison is
possible. In this book we have followed the arrangement favored by the
latest authorities, but the question is still an open one to many minds.

As we have seen, the general concept once having been formed, the mind
proceeds to classify the concept with others having general qualities in
common. And, likewise, it proceeds to generalize from the
classification, assuming certain qualities in certain classes. Then we
proceed to make still further generalizations and classifications on an
ascending and widening scale, including seeming resemblances less
marked, until finally we embrace the object with other objects in as
large a class as possible as well as in as close and limited a sub-class
as possible. As Brooks says: "Generalization is an ascending process.
The broader concept is regarded as higher than the narrower concept; a
concept is considered higher than a percept; a general idea stands above
a particular idea. We thus go up from particulars to generals; from
percepts to concepts; from lower concepts to higher concepts. Beginning
down with particular objects, we rise from them to the general idea of
their class. Having formed a number of lower classes, we compare them as
we did individuals and generalize them into higher classes. We perform
the same process with these higher classes, and thus proceed until we
are at last arrested in the highest class, _Being_. Having reached the
pinnacle of generalization, we may descend the ladder by reversing the
process through which we ascend."

From this process of generalization, or synthesis, we create from our
simple concepts our _general concepts_. Some of the older authorities
distinguished between these two classes by terming the former
"conceptions," and reserving the term "concepts" for the general
concepts. Brooks says of this: "The products of generalization are
general ideas called _concepts_. We have already discussed the method of
forming conceptions and now consider the nature of the concept
itself.... A concept is a general idea. It is a general notion which has
in it all that is common to its own class. It is a general scheme which
embraces all the individuals of the class while it resembles in all
respects none of its class. Thus my conception of a _quadruped_ has in
it all four-footed animals, but it does not correspond in all respects
to any particular animals; my conception of a _triangle_ embraces all
triangles, but does not agree in details with any particular triangle.
The general conception cannot be made to fit exactly any particular
object, but it teems with many particulars. These points may be
illustrated with the concepts _horse_, _bird_, _color_, _animal_, etc."

So we may begin to perceive the distinction and difference between a
_concept_ and a _mental image_. This distinction, and the fact that _a
concept cannot be imaged_, is generally difficult for the beginner. It
is important that one should have a clear and distinct understanding
regarding this point, and so we shall consider it further in the
following chapter.




CHAPTER V.

CONCEPTS AND IMAGES


As we have said, a concept cannot be imaged--cannot be used as the
subject of a mental image. This statement is perplexing to the student
who has been accustomed to the idea that every conception of the mind is
capable of being reproduced in the form of a mental image. But the
apparently paradoxical statement is seen as quite simple when a little
consideration is given to it.

For instance, you have a distinct general concept of _animal_. You know
what you mean when you say or think, _animal_. You recognize an animal
when you see one and you understand what is meant when another uses the
word in conversation. But you cannot form a mental image of the concept,
_animal_. Why? Because any mental image you might form would be either a
picture of _some particular animal_ or else a composite of the qualities
of several animals. Your concept is too broad and general to allow of a
composite picture of _all animals_. And, in truth, your concept is _not
a picture of anything that actually exists_ in one particular, but an
abstract idea embracing the qualities of all animals. It is like the
algebraic _x_--a symbol for something that exists, but not the thing
itself.

As Brooks says: "A concept cannot be represented by a concrete image.
This is evident from its being general rather than particular. If its
color, size or shape is fixed by an image, it is no longer general but
particular." And Halleck says: "It is impossible to image anything
without giving that image individual marks. The best mental images are
so definite that a picture could be painted from them. A being might
come under the class _man_ and have a snub nose, blonde hair, scanty
eyebrows, and no scar on his face. The presence of one of these
individual peculiarities in the concept _man_ would destroy it. If we
form an image of an apple, it must be either of a yellow, red, green, or
russet apple, either as large as a pippin or as small as a crab-apple. A
boy was asked what he thought of when '_apple_' was mentioned. He
replied that he thought of 'a big, dark-red, apple with a bad spot on
one side, near the top.' That boy could image distinctly, but his power
of forming concepts was still in its infancy."

So we see that while a mental image must picture the particular and
individual qualities, properties and appearances of some particular unit
of a class, a _concept_ can and must contain only the _class
qualities_--that is, the qualities belonging to the entire class. The
general concept is as has been said "a general idea ... a general notion
which has in it all that is common to its own class." And it follows
that a "general idea" of this kind cannot be pictured. A picture must be
of some particular thing, while a concept is something above and higher
than particular things. We may picture _a man_, but we cannot picture
Man the concept of the race. A concept is not a reproduction of the
image of a _thing_, but on the contrary is _an idea of a class of
things_. We trust that the student will consider this point until he
arrives at a clear understanding of the distinction, and the reason
thereof.

But, while a concept is incapable of being pictured mentally as an
image, it is true that _some particular representative of a class_ may
be held in the mind or imagination as _an idealized object_, as a
general representative of the class, when we speak or think of the
general term or concept, providing that its real relation to the concept
is recognized. These idealized objects, however, are not concepts--they
are _percepts_ reproduced by the memory. It is important, however, to
all who wish to convey their thought plainly, that they be able to
convert their concepts into idealized representative objects. Otherwise,
they tend to become too idealistic and abstract for common
comprehension. As Halleck well says: "We should in all cases be ready to
translate our concepts, when occasion requires, into the images of those
individuals which the concept represents. A concept means nothing except
in reference to certain individuals. Without them it could never have
had existence and they are entitled to representation. A man who cannot
translate his concepts into definite images of the proper objects, is
fitted neither to teach, preach, nor practice any profession.... There
was, not long ago, a man very fond of talking about _fruit_ in the
abstract; but he failed to recognize an individual cranberry when it
was placed before him. A humorist remarked that a certain metaphysician
had such a love for abstractions, and such an intense dislike for
concrete things, as to refuse to eat a concrete peach when placed before
him."

In the beginning many students are perplexed regarding the difference
between a _percept_ and a _concept_. The distinction is simple when
properly considered. A percept is: "the object of an act of perception;
that which is perceived." A concept is: "a mental representation."
Brooks makes the following distinction: "A _percept_ is the mental
product of a real thing; a _concept_ is a mere idea or notion of the
common attributes of things. A _percept_ represents some particular
object; a _concept_ is not particular, but general. A _percept_ can be
described by particulars; a _concept_ can be described only by generals.
The former can usually be represented by an image, the latter cannot be
imagined, _it can only be thought_." Thus one is able to image the
_percept_ of a particular horse which has been perceived; but he is
unable to image correctly the concept of _horse_ as a class or generic
term.

In connection with this distinction between _perception_ and
_conception_, we may as well consider the subject of _apperception_, a
term favored by many modern psychologists, although others steadfastly
decline to recognize its necessity or meaning and refuse to employ it.
Apperception may be defined as: "perception accompanied by
comprehension; perception accompanied by recognition." The thing
perceived is held to be comprehended or recognized--that is, _perceived
in a new sense_, by reason of certain previously acquired ideas in the
mind. Halleck explains it as: "the perception of things in relation to
the ideas which we already possess." It follows that all individuals
possessed of equally active organs of perception, and equally active
attention, will perceive the same thing in the same way and in the same
degree. But the _apperception_ of each individual will differ and vary
according to his previous experience and training, temperament and
taste, habit and custom. For instance, the familiar story of the boy who
climbed a tree and watched the passers-by, noting their comments. The
first passer-by noticing the tree, says aloud: "That would make a good
stick of timber." "Good morning, Mr. Carpenter," said the boy. The next
man said: "That tree has fine bark." "Good morning, Mr. Tanner," said
the boy. Another said, "I bet there's a squirrel's nest up in that
tree." "Good morning, Mr. Hunter," said the boy.

The woman sees in a bird something pretty and "cunning." The hunter sees
in it something to kill. The ornithologist sees it as something of a
certain genus and species, and perhaps also as something appropriate for
his collection. The farmer perceives it to be something destructive of
either insects or crops. A thief sees a jail as something to be dreaded;
an ordinary citizen, something useful for confining objectionable
people; a policeman, something in the line of his business. And so on,
the apperception differing upon the previous experience of the
individual. In the same way the scientist sees in an animal or rock many
qualities of which the ordinary person is ignorant. Our training,
experience, prejudices, etc., affect our apperception.

And so, we see that in a measure our _concepts_ are determined not only
by our simple perceptions, but also materially by our apperceptions. We
conceive things not only as they are apparent to our senses, but also as
colored and influenced by our previous impressions and ideas. For this
reason we find widely varying concepts of the same things among
different individuals. Only an absolute mind could form an absolute
concept.




CHAPTER VI.

TERMS


In logic the words _concept_ and _term_ are practically identical, but
in the popular usage of the terms there is a distinct difference. This
difference is warranted, if we depart from the theoretical phase of
logic, for the word _concept_ really denotes an _idea_ in the mind,
while the word _term_ really denotes a _word_ or name of an idea or
concept--the symbol of the latter. In a previous chapter we have seen
that Denomination, or "the act of naming or designating by a name" is
the final step or stage in forming a concept. And it is a fact that the
majority of the words in the languages of civilized people denote
general ideas or concepts. As Brooks says: "To give each individual or
particular idea a name peculiar to itself would be impracticable and
indeed impossible; the mind would soon become overwhelmed with its
burden of names. Nearly all the ordinary words of our language are
general rather than particular. The individuals distinguished by
particular names, excepting persons and places, are comparatively few.
Most objects are named only by common nouns; nearly all of our verbs
express general actions; our adjectives denote common qualities, and our
adverbs designate classes of actions and qualities. There are very few
words in the language, besides the names of persons and places, that do
not express general ideas."

In logic the word _term_ is employed to denote _any word or words which
constitute a concept_. The word _concept_ is employed strictly in the
sense of _a subject of thought_, without reference to the words
symbolizing it. The _concept_, or subject of thought, is the important
element or fact and the _term_ denoting it is merely a convenient symbol
of expression. It must be remembered that a _term_ does not necessarily
consists of but a single word, for often many words are employed to
denote the concept, sometimes even an entire clause or phrase being
found necessary for the current _term_. For the purpose of the
consideration of the subjects to be treated upon in this book, we may
agree that: _A term is the outward symbol of a concept_; and that: _The
concept is the idea expressed by the term_.

There are three general parts or phases of Deductive Logic, namely:
Terms, Propositions and Syllogisms. Therefore, in considering Terms we
are entering into a consideration of the first phase of Deductive Logic.
Unless we have a correct understanding of Terms, we cannot expect to
understand the succeeding stages of Deductive Reasoning. As Jevons says:
"When we join terms together we make a Proposition; when we join
Propositions together, we make an argument or piece of reasoning.... We
should generally get nothing but nonsense if we were to put together any
terms and any propositions and to suppose that we were reasoning. To
produce a good argument we must be careful to obey certain rules, which
it is the purpose of Logic to make known. But, in order to understand
the matter perfectly, _we ought first to learn exactly what a term is,
and how many kinds of terms there may be_; we have next to learn the
nature of a proposition and the different kinds of propositions.
Afterwards we shall learn how one proposition may by reasoning be drawn
from other propositions in the kind of argument called the syllogism."

Now, having seen that terms are the outward symbols or expression of
concepts, and are the names of things which we join together in a
proposition, let us proceed to consider the different kinds of terms,
following the classifications adopted by the authorities.

A _term_ may contain any number of nouns, substantive or adjective or it
may contain but a single noun. Thus in, "Tigers are ferocious," the
first term is the single substantive "tigers;" the second term is the
single adjective "ferocious." And in the proposition, "The King of
England is the Emperor of India," there are two terms, each composed of
two nouns, "King of England" being the first term and "Emperor of India"
being the second term. The proposition, "The library of the British
Museum is the greatest collection of books in the world," contains
fifteen words but _only two terms_; the first term being "The library of
the British Museum," in which are two substantives, one adjective, two
definite articles and one preposition; the second term being, "the
greatest collection of books in the world," which contains three
substantives, one adjective, two articles, and two prepositions. The
above illustration is supplied by Jevons, who adds: "A logical term,
then, may consist of any number of nouns, substantive or adjective, with
the articles, prepositions and conjunctions required to join them
together; still _it is only one term if it points out, or makes us think
of a single object, or collection, or class of objects_." (A
substantive, is: "the part of speech which expresses something that
exists, either material or immaterial.")

The first classification of terms divides them into two general classes,
_viz._, (1) Singular Terms; and (2) General Terms.

A _Singular Term_ is a term denoting a single object, person or thing.
Although denoting only a single object, person or thing, it may be
composed of several words; or it may be composed of but one word as in
the case of a proper name, etc. The following are Singular Terms,
because they are terms denoting but a single object, person or thing:
"Europe; Minnesota; Socrates; Shakespeare; the first man; the highest
good; the first cause; the King of England; the British Museum; the
Commissioner of Public Works; the main street of the City of New York."
It will be noted that in all of the examples given, the Singular Term
denotes a particular something, a specific thing, a something of which
there is but one, and that one possesses particularity and
individuality. As Hyslop says: "_Oneness of kind_ is not the only or
distinctive feature of Singular Terms, but _individuality_, or
singularity, as representing a concrete individual whole."

A _General Term_ is a term which applies, in the same sense, to each and
every individual object, person or thing in a number of objects, persons
or things of the same kind, or to the entire class composed of such
objects persons or things of the same kind. For instance, "horse; man;
biped; mammal; trees; figures; grain of sand; matter," etc. Hyslop says,
regarding General Terms: "In these instances the terms denote more than
one object, and apply to all of the same kind. Their meaning is
important in the interpretation of what are called universal
propositions."

Another general classification of Terms divides them into two
respective classes, as follows: (1) Collective Terms; and (2)
Distributive Terms. Hyslop says of this classification: "This division
is based upon the distinction between aggregate wholes of the same kind
and class terms. It partly coincides with the division into Singular and
General Terms, the latter always being distributive."

A _Collective Term_ is one which denotes an aggregate or collected whole
of objects, persons or things of the same or similar kind, _which
collective whole is considered as an individual_, although composed of a
totality of separate individual objects, persons or things. Thus the
following terms: "regiment; congregation; army; family; crowd; nation;
company; battalion; class; congress; parliament; convention;" etc. are
Collective Terms, because they denote collective, aggregate or composite
wholes, considered as an individual.

A _Distributive Term_ is a term which denotes _each and every individual
object, person or thing in a given class_. For example, are the terms:
"man; quadruped; biped; mammal; book; diamond; tree." As Hyslop says:
"General terms are always distributive." Also: "It is important also to
keep clear the distinction between _class_ wholes and _collective_
wholes.... They are often confused so as to call a term denoting a
_class_ a Collective Term."

Another general classification of Terms divides them into the following
two respective classes; (1) Concrete Terms; and (2) Abstract Terms.

A _Concrete Term_ is a term denoting either a definite object, person or
thing which is subject to perception and experience, and may be
considered as actually existent concretely, as for instance: horse; man;
mountain; dollar; knife; table; etc., or else an attribute thought of
and used solely as an attribute, as for instance: "beautiful, wise,
noble, virtuous, good," etc.

An _Abstract Term_ is a term denoting the attribute, quality or property
_considered as apart from the object, person or thing_ and as having an
abstract existence, as for instance: "beauty; wisdom; nobility;
goodness; virtue," etc. As we have seen elsewhere, these qualities have
no real existence _in themselves_, but are known and thought of only in
connection with concrete objects, persons and things. Thus we cannot
know "Beauty," but may know _beautiful things_; we cannot know "Virtue,"
but we may know virtuous people, etc.

An _attribute or quality_ is _concrete_ when expressed as an
_adjective_; and _abstract_ when expressed as a _noun_; as for instance,
"beautiful" and "beauty," respectively, or "virtuous" and "virtue,"
respectively. The distinction may be summed up as follows: A Concrete
Term is _the name of a thing or of a quality of a thing expressed as an
adjective and as merely a quality_; while an Abstract Term is the name
of a quality of a thing, _expressed as a noun and as a "thing" in
itself_.

Certain terms may be used as either Concrete Terms or as Abstract Terms,
and certain authorities have seen fit to classify them as _Mixed Terms_,
as for instance the terms: "government; religion; philosophy;" etc.

Another general classification of Terms divides them into two respective
classes as follows: (1) _Positive Terms_; and (2) _Negative Terms_.

A _Positive Term_ is a term which denotes its own qualities, as for
instance: "good, human, large, square, black, strong," etc. These terms
indicate the presence of the quality denoted by the term itself.

A _Negative Term_ is a term denoting the absence of a quality, as for
instance: "inhuman, inorganic, unwell, unpleasant, non-conducive," etc.
These terms _deny_ the presence of certain qualities, rather than
_asserting_ the presence of an opposite quality. They are essentially
negative in nature and in form. Jevons says: "We may usually know a
Negative Term by its beginning with one of the little syllables un-,
in-, a-, an-, non-, or by its ending with -less." Hyslop says: "The
usual symbols of Negative Terms are _in_, _un_, _less_, _dis_, _a_, or
_an_, _anti_, _mis_, and sometimes _de_, and _non_ and _not_." Jevons
adds: "If the English language were a perfect one, every term ought to
have a Negative Term exactly corresponding to it, so that all adjectives
and nouns would be in pairs. Just as _convenient_ has its negative
_inconvenient_; metallic, non-metallic; logical, illogical; and so on;
so blue should have its negative, non-blue; literary, non-literary;
paper, non-paper. But many of these Negative Terms would be seldom or
never used, and if we happen to want them, we can make them for the
occasion by putting not-, or non-, before the Positive Term.
Accordingly, we find in the dictionary only those Negative Terms which
are much employed."

The last named authority also says: "Sometimes the same word may seem to
have two or even more distinct negatives. There is much difference
between _undressed_ and _not-dressed_, that is 'not in evening dress.'
Both seem to be negatives of 'dressed,' but this is because the word has
two distinct meanings."

Some authorities insist upon closer and further classification, as for
instance, in the case of what they call a _Privative Term_, denoting the
absence of qualities once possessed by the object, person or thing, as:
"deaf, dead, blind, dark," etc. Hyslop says that these terms "are
Positive in form and Negative in matter or meaning." Also in the case of
what they call a _Nego-positive Term_, denoting "the presence of a
positive quality expressed in a negative manner," as: disagreeable,
inhuman, invaluable, etc. These last mentioned classes however are
regarded by some as the result of "carrying too far" the tendency
toward classification, and the two general classes, Positive and
Negative, are thought sufficient for the purpose of the general student.
The same objection applies to a classification occasionally made _i.e._,
that which is called an _Infinitated Term_, denoting a term the intent
of which is to place in a distinct category every object, person or
thing other than that expressed in the corresponding Positive Term. The
intent of the term is to place the positive idea in one class, and all
else into a separate one. Examples of this class of terms are found in:
"not-I, not-animal, not-tree, unmoral," etc. Hyslop says of these terms:
"They are not always, if ever, recognized as rhetorically elegant, but
are valuable often to make clear the really negative, or infinitatively
negative nature of the idea in mind."

Another general classification of Terms divides them into two respective
classes, as follows: (1) Absolute Terms; and (2) Relative Terms.

An _Absolute Term_ is a term denoting the presence of qualities
intrinsic to the object, and not depending upon any relation to any
other object, as for instance: "man; book; horse; gun;" etc. These
terms _may be_ related to many other terms, but are _not necessarily_
related to any other.

A _Relative Term_ is a term denoting certain _necessary_ relations to
other terms, as for instance: "father; son; mother; daughter; teacher;
pupil; master; servant;" etc. Thus it is impossible to think of "child"
except in relation to "parent," or _vice versa_. The one term implies
the existence of its related term.

Hyslop says of the above classification: "Relative Terms suggest the
thought of other individuals with the relation involved as a part of the
term's meaning, while Absolute Terms suggest only the qualities in the
subject without a relation to others being necessarily involved."

Some authorities also classify terms as _higher and lower_; also as
_broad and narrow_. This classification is meant to indicate the content
and extent of the term. For instance, when we classify, we begin with
the individuals which we then group into a small class. These classes we
then group into a larger class, according to their resemblances. These
larger classes then go to form a part of still larger classes, and so
on. As these classes advance they form _broader_ terms; and as we
retreat from the general class into the less general and more
particular, the term becomes _narrower_. By some, the _broader_ term
which includes the narrower is called the _higher term_, and the
narrower are called the _lower terms_. Thus _animal_ would be a higher
and broader term than dog, cat or tiger because it includes the latter.
Brooks says: "Since a concept is formed by the union of the common
attributes of individuals, it thus embraces both attributes and
individuals. The attributes of a concept constitute what is called its
_content_; the individuals it embraces constitute its _extent_."

Accordingly, the feature of including objects in a concept or term is
called its _extension_; while the feature of including attributes or
qualities is called its intension. It follows as a natural consequence
that the greater the _extension_ of a term, the less its _intension_;
the greater its _intension_, the less its _extension_. We will
understand this more clearly when we consider that the more individuals
contained in a term, the fewer _common_ properties or qualities it can
contain; and the more common properties, the fewer individuals. As
Brooks says: "The concept _man_ has more _extension_ than _poet_,
_orator_ or _statesman_, since it embraces more individuals; and less
_intension_, since we must lay aside the distinctive attributes of poet,
orator and statesman in order to unite them in a common class _man_." In
the same way the general term _animal_ is quite extended for it includes
a large number of individual varieties of very different and varied
characteristics and qualities; as for instance, the lion, camel, dog,
oyster, elephant, snail, worm, snake, etc. Accordingly its intension
must be small for it can include only the qualities common to all
animals, which are very few indeed. The definition of the term shows how
small is its _intension_, as: "_Animal._ An organic being, rising above
a vegetable in various respects, especially in possessing sensibility,
will and the power of voluntary motion." Another narrows the intension
still further when he defines _animal_ as: "a creature which possesses,
or has possessed, life." Halleck says: "_Animal_ is very narrow in
intension, very broad in extension. There are few qualities common to
all animals, but there is a vast number of animals. To give the full
meaning of the term in _extension_, we should have to name every animal,
from the microscopic infusoria to the tiger, from the angleworm to the
whale. When we decrease the extension to one species of animal, _horse_,
the individuals are fewer, the qualities more numerous."

The importance of forming clear and distinct concepts and of grouping,
classifying and generalizing these into larger and broader concepts and
terms is recognized by all authorities and is generally regarded as
forming the real basis of all constructive thought. As Brooks says:
"Generalization lies at the basis of language: only as man can form
general conceptions is it possible for him to form a language.... Nearly
all the ordinary words in our language are general rather than
particular.... This power of generalization lies also at the basis of
science. Had we no power of forming general ideas, each particular
object would be a study by itself, and we should thus never pass beyond
the very alphabet of knowledge. Judgments, except in the simplest form,
would be impossible; and it is difficult to see how even the simplest
form of the syllogism could be constructed. No general conclusion could
be drawn from particulars, nor particular conclusions from generals; and
thus neither inductive nor deductive reasoning would be possible. The
classifications of science could not be made; and knowledge would end at
the very threshold of science."




CHAPTER VII.

THE MEANING OF TERMS


Every term has its _meaning_, or _content_, as some authorities prefer
to call it. The word or words of which the term is composed are merely
vocal sounds, serving as a symbol for the real _meaning_ of the term,
which _meaning_ exists only in the mind of the person understanding it.
To one not understanding the meaning of the term, the latter is but as a
meaningless sound, but to one understanding it the sound awakens mental
associations and representation and thus serves its purpose as a symbol
of thought.

Each concrete general term has two _meanings_, (1) the actual concrete
thing, person or object to which the term is applied; and (2) the
qualities, attributes or properties of those objects, persons or things
in consequence of which the term is applied. For instance, in the case
of the concrete term _book_, the first meaning consists of the general
idea of the thing which we think of as _a book_, and the second meaning
consists of the various qualities which go to make that thing a book, as
the printed pages, the binding, the form, the cover, etc. Not only is
that particular thing _a book_, but every other thing having the same or
similar properties also must be _a book_. And so, whenever I call a
thing _a book_ it must possess the said qualities. And, whenever I
combine the ideas of these qualities in thought, I must think of _a
book_. As Jevons says: "In reality, every ordinary general term has a
double meaning: it means the things to which it is applied, ... it also
means, in a totally different way, the qualities and peculiarities
_implied_ as being in the things. Logicians say that the number of
things to which a term applies is the _extension_ of the term; while the
number of qualities or peculiarities implied is the _intension_."

The extension and intension of terms has been referred to in the
previous chapter. The general classification of the degrees of
_extension_ of a general term is expressed by the two terms, _Genus_ and
_Species_, respectively. The classification of the character of the
_intension_ of a term is expressed by the term, _Difference_,
_Property_ and _Accident_, respectively.

_Genus_ is a term indicating: "a class of objects containing several
species; a class more extensive than a species; a universal which is
predicable of several things of different species."

_Species_ is a term denoting: "a smaller class of objects than a genus,
and of two or more of which a genus is composed; a predicable that
expresses the whole essence of its subject in so far as any common term
can express it."

An authority says: "The names _species_ and _genus_ are merely relative
and the same common term may, in one case, be the species which is
predicated of an individual, and in another case the individual of which
a species is predicated. Thus the individual, George, belongs to the
logical species Man, while Man is an individual of the logical species
Animal." Jevons says: "It is desirable to have names by which to show
that one class is contained in another, and accordingly we call the
class which is divided into two or more smaller ones, the _genus_, and
the smaller ones into which it is divided, the _species_." _Animal_ is
a _genus_ of which _man_ is a _species_; while _man_, in turn, is a
_genus_ of which _Caucasian_ is a _species_; and _Caucasian_, in turn,
becomes a _genus_ of which _Socrates_ becomes a species. The student
must avoid confusing the _logical_ meaning of the terms _genus_ and
_species_ with the use of the same terms in Natural History. _Each class
is a "genus" to the class below it in extension; and each class is a
"species" to the class above it in extension._ At the lowest extreme of
the scale we reach what is called the _infima species_, which cannot be
further subdivided, as for instance "Socrates"--this lowest species must
always be an individual object, person or thing. At the highest extreme
of the scale we reach what is _summum genus_, or highest genus, which is
never a species of anything, for there is no class higher than it, as
for instance, "being, existence, reality, truth, the absolute, the
infinite, the ultimate," etc. Hyslop says: "In reality there is but one
_summum genus_, while there may be an indefinite number of _infimae
species_. All intermediate terms between these extremes are sometimes
called _subalterns_, as being either genera or species, according to
the relation in which they are viewed."

Passing on to the classification of the character of the _intension_ of
terms, we find:

_Difference_, a term denoting: "The mark or marks by which the species
is distinguished from the rest of the genus; the specific
characteristic." Thus the color of the skin is a _difference_ between
the Negro and the Caucasian; the number of feet the _difference_ between
the biped and the quadruped; the form and shape of leaves the
_difference_ between the oak and the elm trees, etc. Hyslop says:
"Whatever distinguishes one object from another can be called the
_differentia_. It is some characteristic in addition to the common
qualities and determines the species or individual under the genus."

_Property_, a term denoting: "A peculiar quality of anything; that which
is inherent in or naturally essential to anything." Thus a _property_ is
a distinguishing mark of a class. Thus black skin is a _property_ of the
Negro race; four feet a _property_ of quadrupeds; a certain form of leaf
a _property_ of the oak tree. Thus a _difference_ between two species
may be a _property_ of one of the species.

_Accident_, a term denoting: "Any quality or circumstance which may or
may not belong to a class, accidentally as it were; or, whatever does
not really constitute an essential part of an object, person or thing."
As, for instance, the redness of a rose, for a rose might part with its
redness and still be a rose--the color is the _accident_ of the rose.
Or, a brick may be white and still be a brick, although the majority of
bricks are red--the redness or whiteness of the brick are its
_accidents_ and not its essential _properties_. Whately says:
"_Accidents_ in Logic are of two kinds--separable and inseparable. If
walking be the _accident_ of a particular man, it is a separable one,
for he would not cease to be that man though he stood still; while, on
the contrary, if Spaniard is the _accident_ connected with him, it is an
inseparable one, since he never can cease to be, ethnologically
considered, what he was born."

Arising from the classification of the meaning or content of terms, we
find the process termed "Definition."

_Definition_ is a term denoting: "An explanation of a word or term." In
Logic the term is used to denote the process of analysis in which the
_properties_ and _differences_ of a term are clearly stated. There are
of course several kinds of definitions. For instance, there is what is
called a _Real Definition_, which Whately defines as: "A definition
which explains the nature of the thing by a particular name." There is
also what is called a _Physical Definition_, which is: "A definition
made by enumerating such parts as are actually separable, such as the
hull, masts, etc., of a ship." Also a _Logical Definition_, which is: "A
definition consisting of the genus and the difference. Thus if a planet
be defined as 'a wandering star,' _star_ is the genus, and _wandering_
points out the difference between a planet and an ordinary star." An
_Accidental Definition_ is: "A definition of the _accidental_ qualities
of a thing." An _Essential Definition_ is: "a definition of the
essential _properties_ and _differences_ of an object, person or thing."

Crabbe discriminates between a Definition and an Explanation, as
follows: "A _definition_ is correct or precise; an _explanation_ is
general or ample. The _definition_ of a word defines or limits the
extent of its signification; it is the rule for the scholar in the use
of any word; the _explanation_ of a word may include both definition and
illustration; the former admits of no more words than will include the
leading features in the meaning of any term; the latter admits of an
unlimited scope for diffuseness on the part of the explainer."

Hyslop gives the following excellent explanation of the _Logical
Definition_, which as he states is the proper meaning of the term in
Logic. He states:

"The rules which regulate Logical Definition are as follows:

1. A definition should state the essential attributes of the species
defined.

2. A definition must not contain the name of word defined. Otherwise the
definition is called _a circulus in definiendo_.

3. The definition must be exactly equivalent to the species defined.

4. A definition should not be expressed in obscure, figurative, or
ambiguous language.

5. A definition must not be negative when it can be affirmative."

A correct definition necessarily requires the manifestation of the two
respective processes of Analysis and Synthesis.

_Analysis_ is a term denoting: "The separation of anything into its
constituent elements, qualities, properties and attributes." It is seen
at once that in order to correctly define an object, person or thing, it
is first necessary to analyze the latter in order to perceive its
essential and accidental properties or differences. Unless the
qualities, properties and attributes are clearly and fully perceived, we
cannot properly define the object itself.

_Synthesis_ is a term denoting: "The act of joining or putting two or
more things together; in Logic: the method by composition, in opposition
to the method of resolution or analysis." In stating a definition we
must necessarily join together the various essential qualities,
properties and attributes, which we have discovered by the process of
analysis; and the synthesized combination, considered as a whole, is the
definition of the object expressed by the term.




CHAPTER VIII.

JUDGMENTS


The first step in the process of reasoning is that of Conception or the
forming of Concepts. The second step is that of Judgment, or the process
of perceiving the agreement or disagreement of two conceptions.

_Judgment_ in Logic is defined as: "The comparing together in the mind
of two notions, concepts or ideas, which are the objects of
apprehension, whether complex or incomplex, and pronouncing that they
agree or disagree with each other, or that one of them belongs or does
not belong to the other. Judgment is therefore affirmative or negative."

When we have in our mind two concepts, we are likely to compare them one
with the other, and to thus arrive at a conclusion regarding their
agreement or disagreement. This process of comparison and decision is
what, in Logic, is called _Judgment_.

In every act of Judgment there must be at least two concepts to be
examined and compared. This comparison must lead to a Judgment
regarding their agreement or disagreement. For instance, we have the two
concepts, _horse_ and _animal_. We examine and compare the two concepts,
and find that there is an agreement between them. We find that the
concept _horse_ is included in the higher concept of _animal_ and
therefore, we assert that: "_The horse is an animal._" This is a
statement of _agreement_ and is, therefore, a _Positive Judgment_. We
then compare the concepts _horse_ and _cow_ and find a disagreement
between them, which we express in the statement of the Judgment that:
"_The horse is not a cow._" This Judgment, stating a disagreement is
what is called a _Negative Judgment_.

In the above illustration of the comparison between the concepts _horse_
and _animal_ we find that the second concept _animal_ is broader than
the first, _horse_, so broad in fact that it includes the latter. The
terms are not equal, for we cannot say, in truth, that "an animal is the
horse." We may, however, include a _part_ of the broader conception with
the narrower and say: "some animals are horses." Sometimes both
concepts are of equal rank, as when we state that: "Man is a rational
animal."

In the process of Judgment there is always the necessity of the choice
between the Positive and the Negative. When we compare the concepts
_horse_ and _animal_, we must of necessity decide either that the horse
_is_ an animal, or else that it is _not_ an animal.

The importance of the process of Judgment is ably stated by Halleck, as
follows: "Were isolated concepts possible, they would be of very little
use. Isolated facts are of no more service than unspun wool. We might
have a concept of a certain class of three-leaved ivy, as we might also
of poisons. Unless judgment linked these two concepts and decided that
this species of ivy is poisonous, we might take hold of it and be
poisoned. We might have a concept of bread and also one of meat, fruit
and vegetables. If we also had a concept of food, unrelated to these, we
should starve to death, for we should not think of them as foods. A
vessel, supposing itself to be far out at sea, signaled another vessel
that the crew were dying of thirst. That crew certainly had a concept of
drinkable things and also of water. To the surprise of the first, the
second vessel signaled back, 'Draw from the sea and drink. You are at
the mouth of the Amazon.' The thirsty crew had not joined the concept
_drinkable_ to the concept of water over the ship's side. A man having
taken an overdose of laudanum, his wife lost much valuable time in
sending out for antidotes, because certain of her concepts had not been
connected by judgment. She had good concepts of coffee and of mustard;
she also knew that an antidote to opium was needed; but she had never
linked these concepts and judged that coffee and mustard were antidotes
to opium. The moment she formed that judgment she was a wiser woman for
her knowledge was related and usable.... Judgment is the power
revolutionizing the world. The revolution is slow because nature's
forces are so complex, so hard to be reduced to their simplest forms and
so disguised and neutralized by the presence of other forces....
Fortunately judgment is ever silently working and comparing things that,
to past ages, have seemed dissimilar; and it is continually abstracting
and leaving out of the field of view those qualities which have simply
served to obscure the point at issue."

Judgment may be both analytic or synthetic in its processes; and it may
be neither. When we compare a narrow concept with a broader one, as a
part with a whole, the process is synthetic or an act of combination.
When we compare a part of a concept with another concept, the process is
analytic. When we compare concepts equal in rank or extent, the process
is neither synthetic nor analytic. Thus in the statement that: "A horse
is an animal," the judgment is synthetic; in the statement that: "some
animals are horses," the judgement is analytic; in the statement that:
"a man is a rational animal," the judgment is neither analytic nor
synthetic.

Brooks says: "In one sense all judgments are synthetic. A judgment
consists of the union of two ideas and this uniting is a process of
synthesis. This, however, is a superficial view of the process. Such a
synthesis is a mere mechanical synthesis; below this is a
thought-process which is sometimes analytic, sometimes synthetic and
sometimes neither analytic nor synthetic."

The same authority states: "The act of mind described is what is known
as _logical judgment_. Strictly speaking, however, every intelligent act
of the mind is accompanied with a _judgment_. To know is to discriminate
and, therefore, to judge. Every sensation or cognition involves a
knowledge and so a judgment that it exists. The mind cannot think at all
without judging; to think is to judge. _Even in forming the notions
which judgment compares, the mind judges._ Every notion or concept
implies a previous act of judgment to form it: in forming a concept, we
compare the common attributes before we unite them; and comparison is
judgment. It is thus true that 'Every concept is a contracted judgment;
every judgment an expanded concept.' This kind of judgment, by which we
affirm the existence of states of consciousness, discriminate qualities,
distinguish percepts and form concepts, is called _primitive or
psychological judgment_."

In Logical Judgment there are two aspects; _i.e._, Judgment by Extension
and Judgment by Intension. When we compare the two concepts _horse_ and
_animal_ we find that the concept _horse_ is contained in the concept
_animal_ and the judgment that "_a horse is an animal_" may be
considered as a Judgment by Extension. In the same comparison we see
that the concept _horse_ contains the _quality of animality_, and in
attributing this quality to the _horse_, we may also say "_the horse is
an animal_," which judgment may be considered as a Judgment by
Intension. Brooks says: "Both views of Judgment are correct; the mind
may reach its judgment either by extension or by intension. The method
by extension is usually the more natural."

When a Judgment is expressed in words it is called a Proposition. There
is some confusion regarding the two terms, some holding that a Judgment
and a proposition are identical, and that the term "proposition" may be
properly used to indicate the judgment itself. But the authorities who
seek for clearness of expression and thought now generally hold that:
"_A Proposition is a Judgment expressed in words._" In the next chapter,
in which we consider Propositions, we shall enter into a more extended
consideration of the subject of Judgments as expressed in Propositions,
which consideration we omit at this point in order to avoid repetition.
Just as the respective subjects of Concepts and Terms necessarily blend
into each other, so do the respective subjects of Judgments and
Propositions. In each case, too, there is the element of the mental
process on the one hand and the verbal expression of it on the other
hand. It will be well to keep this fact in mind.




CHAPTER IX.

PROPOSITIONS


We have seen that the first step of Deductive Reasoning is that which we
call Concepts. The second step is that which we call Propositions.

In Logic, a _Proposition_ is: "A sentence, or part of a sentence,
affirming or denying a connection between the terms; limited to express
assertions rather than extended to questions and commands." Hyslop
defines a Proposition as: "any affirmation or denial of an agreement
between two conceptions."

_Examples of Propositions_ are found in the following sentences: "The
rose is a flower;" "a horse is an animal;" "Chicago is a city;" all of
which are affirmations of agreement between the two terms involved; also
in: "A horse is not a zebra;" "pinks are not roses;" "the whale is not a
fish;" etc., which are denials of agreement between the terms.

The _Parts of a Proposition_ are: (1) the _Subject_, or that of which
something is affirmed or denied; (2) the _Predicate_, or _the
something_ which is affirmed or denied regarding the _Subject_; and (3)
the _Copula_, or the verb serving as a link between the Subject and the
Predicate.

       *       *       *       *       *

In the Proposition: "Man is an animal," the term _man_ is the Subject;
the term _an animal_ is the Predicate; and the word _is_, is the Copula.
The Copula is always some form of the verb _to be_, in the present tense
indicative, in an affirmative Proposition; and the same with the
negative particle affixed, in a negative Proposition. The Copula is not
always directly expressed by the word _is_ or _is not_, etc., but is
instead expressed in some phrase which implies them. For instance, we
say "he runs," which implies "he is running." In the same way, it may
appear at times as if the Predicate was missing, as in: "God is," by
which is meant "God is existing." In some cases, the Proposition is
inverted, the Predicate appearing first in order, and the Subject last,
as in: "Blessed are the peacemakers;" or "Strong is Truth." In such
cases judgment must be used in determining the matter, in accordance
with the character and meaning of the terms.

An _Affirmative Proposition_ is one in which the Predicate is _affirmed_
to agree with the Subject. A _Negative Proposition_ is one in which the
agreement of the Predicate and Subject is _denied_. Examples of both of
these classes have been given in this chapter.

Another classification of Propositions divides them in three classes, as
follows (1) Categorical; (2) Hypothetical; (3) Disjunctive.

A _Categorical Proposition_ is one in which the affirmation or denial is
made without reservation or qualification, as for instance: "Man is an
animal;" "the rose is a flower," etc. The fact asserted may not be
_true_, but the statement is made positively as a statement of reality.

A _Hypothetical Proposition_ is one in which the affirmation or denial
is made to depend upon certain conditions, circumstances or
suppositions, as for instance: "If the water is boiling-hot, it will
scald;" or "if the powder be damp, it will not explode," etc. Jevons
says: "Hypothetical Propositions may generally be recognized by
containing the little word 'if;' but it is doubtful whether they really
differ much from the ordinary propositions.... We may easily say that
'boiling water will scald,' and 'damp gunpowder will not explode,' thus
avoiding the use of the word 'if.'"

A _Disjunctive Proposition_ is one "implying or asserting an
alternative," and usually containing the conjunction "or," sometimes
together with "either," as for instance: "Lightning is sheet or forked;"
"Arches are either round or pointed;" "Angles are either obtuse, right
angled or acute."

Another classification of Propositions divides them in two classes as
follows: (1) Universal; (2) Particular.

A _Universal Proposition_ is one in which the _whole quantity_ of the
Subject is involved in the assertion or denial of the Predicate. For
instance: "All men are liars," by which is affirmed that _all_ of the
entire race of men are in the category of liars, not _some_ men but
_all_ the men that are in existence. In the same way the Proposition:
"No men are immortal" is Universal, for it is a _universal denial_.

A _Particular Proposition_ is one in which the affirmation or denial of
the Predicate involves only a _part or portion_ of the whole of the
Subject, as for instance: "_Some_ men are atheists," or "_Some_ women
are not vain," in which cases the affirmation or denial does not involve
_all_ or the _whole_ of the Subject. Other examples are: "A _few_ men,"
etc.; "_many_ people," etc.; "_certain_ books," etc.; "_most_ people,"
etc.

Hyslop says: "The signs of the Universal Proposition, when formally
expressed, are _all_, _every_, _each_, _any_, _and whole_ or words with
equivalent import." The signs of Particular Propositions are also
certain adjectives of quantity, such as _some_, _certain_, _a few_,
_many_, _most_ or such others as denote _at least a part_ of a class.

The subject of the Distribution of Terms in Propositions is considered
very important by Logicians, and as Hyslop says: "has much importance in
determining the legitimacy, or at least the intelligibility, of our
reasoning and the assurance that it will be accepted by others." Some
authorities favor the term, "Qualification of the Terms of
Propositions," but the established usage favors the term
"Distribution."

The definition of the Logical term, "Distribution," is: "The
distinguishing of a universal whole into its several kinds of species;
the employment of a term to its fullest extent; the application of a
term to its fullest extent, so as to include all significations or
applications." A Term of a Proposition is _distributed_ when it is
employed in its fullest sense; that is to say, _when it is employed so
as to apply to each and every object, person or thing included under
it_. Thus in the proposition, "All horses are animals," the term
_horses_ is distributed; and in the proposition, "Some horses are
thoroughbreds," the term _horses_ is not distributed. Both of these
examples relate to the distribution of the _subject_ of the proposition.
But the predicate of a proposition also may or may not be distributed.
For instance, in the proposition, "All horses are animals," the
predicate, _animals_, is not distributed, that is, _not used in its
fullest sense_, for all _animals_ are not _horses_--there are _some_
animals which are not horses and, therefore, the predicate, _animals_,
not being used in its fullest sense is said to be "_not distributed_."
The proposition really means: "All horses are _some_ animals."

There is however another point to be remembered in the consideration of
Distribution of Terms of Propositions, which Brooks expresses as
follows: "Distribution generally shows itself in the form of the
expression, but sometimes it may be determined by the thought. Thus if
we say, 'Men are mortal,' we mean _all men_, and the term men is
distributed. But if we say 'Books are necessary to a library,' we mean,
not 'all books' but 'some books.' The _test of distribution_ is whether
the term applies to '_each and every_.' Thus when we say 'men are
mortal,' it is true of each and every man that he is mortal."

The Rules of Distribution of the Terms of Proposition are as follows:

1. All _universals_ distribute the _subject_.

2. All _particulars_ do not distribute the _subject_.

3. All _negatives_ distribute the _predicate_.

4. All _affirmatives_ do not distribute the _predicate_.

The above rules are based upon logical reasoning. The reason for the
first two rules is quite obvious, for when the subject is _universal_,
it follows that the _whole subject_ is involved; when the subject is
_particular_ it follows that _only a part_ of the subject is involved.
In the case of the third rule, it will be seen that in every _negative_
proposition the _whole of the predicate_ must be denied the subject, as
for instance, when we say: "Some _animals_ are _not horses_," the whole
class of _horses_ is cut off from the subject, and is thus
_distributed_. In the case of the fourth rule, we may readily see that
in the affirmative proposition the whole of the predicate _is not
denied_ the subject, as for instance, when we say that: "Horses are
animals," we do not mean that horses are _all the animals_, but that
they are merely a _part or portion_ of the class animal--therefore, the
predicate, _animals_, is not distributed.

In addition to the forms of Propositions given there is another class of
Propositions known as _Definitive or Substitutive Propositions_, in
which the Subject and the Predicate are exactly alike in extent and
rank. For instance, in the proposition, "A _triangle_ is a _polygon of
three sides_" the two terms are interchangeable; that is, may be
substituted for each other. Hence the term "substitutive." The term
"definitive" arises from the fact that the respective terms of this kind
of a proposition necessarily _define_ each other. All logical
definitions are expressed in this last mentioned form of proposition,
for in such cases the subject and the predicate are precisely equal to
each other.




CHAPTER X.

IMMEDIATE REASONING


In the process of Judgment we must compare two concepts and ascertain
their agreement of disagreement. In the process of Reasoning we follow a
similar method and compare two judgments, the result of such comparison
being the deduction of a third judgment.

The simplest form of reasoning is that known as Immediate Reasoning, by
which is meant the deduction of one proposition from another which
_implies_ it. Some have defined it as: "_reasoning without a middle
term_." In this form of reasoning _only one proposition is required for
the premise_, and from that premise the conclusion is deduced directly
and without the necessity of comparison with any other term of
proposition.

The two principal methods employed in this form of Reasoning are; (1)
Opposition; (2) Conversion.

_Opposition_ exists between propositions having the same subject and
predicate, but differing in quality or quantity, or both. The Laws of
Opposition are as follows:

I. (1) If the universal is true, the particular is true. (2) If the
particular is false, the universal is false. (3) If the universal is
false, nothing follows. (4) If the particular is true, nothing follows.

II. (1) If one of two contraries is true, the other is false. (2) If one
of two contraries is false, nothing can be inferred. (3) Contraries are
never both true, but both may be false.

III. (1) If one of two sub-contraries is false, the other is true. (2)
If one of two sub-contraries is true, nothing can be inferred concerning
the other. (3) Sub-contraries can never be both false, but both may be
true.

IV. (1) If one of two contradictories is true, the other is false. (2)
If one of two contradictories is false, the other is true. (3)
Contradictories can never be both true or both false, but always one is
true and the other is false.

In order to comprehend the above laws, the student should familiarize
himself with the following arrangement, adopted by logicians as a
convenience:

                 {Universal  {Affirmative (A)
                 {           {Negative    (E)
  Propositions   {
                 {           {Affirmative (I)
                 {Particular {Negative    (O)

Examples of the above: Universal Affirmative (A): "All men are mortal;"
Universal Negative (E): "No man is mortal;" Particular Affirmative (I):
"Some men are mortal;" Particular Negative (O): "Some men are not
mortal."

The following examples of abstract propositions are often used by
logicians as tending toward a clearer conception than examples such as
given above:

(A) "All A is B."

(I) "Some A is B."

(E) "No A is B."

(O) "Some A is not B."

These four forms of propositions bear certain logical relations to each
other, as follows:

A and E are styled _contraries_. I and O are _sub-contraries_; A and I
and also E and O are called _subalterns_; A and O and also I and E are
styled _contradictories_.

A close study of these relations, and the symbols expressing them, is
necessary for a clear comprehension of the Laws of Opposition stated a
little further back, as well as the principles of Conversion which we
shall mention a little further on. The following chart, called the
Square of Opposition, is also employed by logicians to illustrate the
relations between the four classes of propositions:

   A       CONTRARIES       E
   +------------------------+
   |\                     / |
   | \                   /S |
   | C\                 /E  |
   |  O\               /I   |
   |   N\             /R    |
   |    T\           /O     |
  S|     R\         /T      |S
  U|      A\       /C       |U
  B|        \     /I        |B
  A|         \   /D         |A
  L|          \ /           |L
  T|          / \           |T
  E|         /  D\          |E
  R|        /    I\         |R
  N|       /A     C\        |N
  S|      /R       T\       |S
   |     /T         O\      |
   |    /N           R\     |
   |   /O             I\    |
   |  /C               E\   |
   | /                  S\  |
   |/                     \ |
   +------------------------+
   I    SUB-CONTRARIES      O

_Conversion_ is the process of immediate reasoning by which we infer
from a given proposition another proposition having the predicate of
the original for its subject and the subject of the original for its
predicate; or stated in a few words: _Conversion is the transposition of
the subject and predicate of a proposition_. As Brooks states it:
"Propositions or judgments are _converted_ when the subject and
predicate change places in such a manner that the resulting judgment is
an inference from the given judgment." The new proposition, resulting
from the operation or Conversion, is called the Converse; the original
proposition is called the Convertend.

_The Law of Conversion_ is that: "No term must be distributed in the
Converse that is not distributed in the Convertend." This arises from
the obvious fact that nothing should be affirmed in the derived
proposition than there is in the original proposition.

There are three kinds of Conversion; _viz_: (1) Simple Conversion; (2)
Conversion by Limitation; (3) Conversion by Contraposition.

In _Simple Conversion_ there is no change in either quality or quantity.
In _Conversion by Limitation_ the quality is changed from universal to
particular. In Conversion by Negation the quality is changed but not
the quantity. Referring to the classification tables and symbols given
in the preceding pages of this chapter, we may now proceed to consider
the application of these methods of Conversion to each of the four kinds
of propositions; as follows:

_The Universal Affirmative_ (symbol A) proposition is converted by
Limitation, or by a change of quality from universal to particular. The
predicate not being "distributed" in the convertend, we must not
distribute it in the converse by saying "_all_." Thus in this case we
must convert the proposition, "all men are mortal" (A), into "some
mortals are men" (I).

_The Universal Negative_ (symbol E) is converted by Simple Conversion,
in which there is no change in either quality or quantity. For since
both terms of "E" are distributed, they may both be distributed in the
converse without violating the law of conversion. Thus "No man is
mortal" is converted into: "No mortals are men." "E" is converted into
"E."

_The Particular Affirmative_ (symbol I) is also converted by Simple
Conversion in which there is no change in either quality or quantity.
For since neither term is distributed in "I," neither term may be
distributed in the converse, and the latter must remain "I." For
instance; the proposition: "Some men are mortal" is converted into the
proposition, "Some mortals are men."

_The Particular Negative_ (symbol O) is converted by Conversion by
Negation, in which the quality is changed but not the quantity. Thus in
converting the proposition: "Some men are not mortal," we must _not_ say
"some mortals are not men," for in so doing we would distribute _men_ in
the predicate, where it is not distributed in the convertend. Avoiding
this, _we transfer the negative particle from the copula to the
predicate_ so that the convertend becomes "I" which is converted by
Simple Conversion. Thus we transfer "Some men are not mortal" into "Some
men are not-mortal" from which we easily convert (by simple Conversion)
the proposition: "Some not-mortals are men."

It will be well for students, at this point, to consider the three
following Fundamental Laws of Thought as laid down by the authorities,
which are as follows:

_The Law of Identity_, which states that: "The same quality or thing is
always the same quality or thing, no matter how different the conditions
in which it occurs."

_The Law of Contradiction_, which states that: "No thing can at the same
time and place both be and not be."

_The Law of Excluded Middle_, which states that: "Everything must either
be or not be; there is no other alternative or middle course."

Of these laws, Prof. Jevons, a noted authority, says: "Students are
seldom able to see at first their full meaning and importance. All
arguments may be explained when these self-evident laws are granted; and
it is not too much to say that the whole of logic will be plain to those
who will constantly use these laws as the key."




CHAPTER XI.

INDUCTIVE REASONING


Inductive Reasoning, as we have said, is the process of discovering
general truth from particular truths, or inferring general laws from
particular facts. Thus, from the experience of the individual and the
race regarding the particular truth that each and every man under
observation has been observed to die sooner or later, it is inferred
that _all_ men die, and hence, the induction of the general truth that
"All men must die." Or, as from experience we know that the various
kinds of metals expand when subjected to heat, we infer that _all_
metals are subject to this law, and that consequently we may arrive by
inductive reasoning at the conclusion that: "All metals expand when
subjected to heat." It will be noticed that the conclusion arrived at in
this way by Inductive Reasoning forms the fundamental premise in the
process of Deductive Reasoning. As we have seen elsewhere, the two
processes, Inductive and Deductive Reasoning, respectively are
interdependent--resting upon one another.

Jevons says of Inductive Reasoning: "In Deductive Reasoning we inquire
how we may gather the truth contained in some propositions called
Premises, and put into another proposition called the Conclusion. We
have not yet undertaken to find out how we can learn what propositions
really are true, but only _what propositions are true when other ones
are true_. All the acts of reasoning yet considered would be called
_deductive because we deduce, or lead down the truth from premises to
conclusion_. It is an exceedingly important thing to understand
deductive inference correctly, but it might seem to be still more
important to understand _inductive inference_, by which we gather the
truth of general propositions from facts observed as happening in the
world around us." 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.... Only after general laws have been laid down, after objects have
been classified, after major premises have been formed, can deduction be
employed."

Strange as may now appear, it is a fact that until a comparatively
recent period in the history of man, it was held by philosophers that
the only way to arrive at all knowledge was by means of Deductive
Reasoning, by the use of the Syllogism. The influence of Aristotle was
great and men preferred to pursue artificial and complicated methods of
Deductive Reasoning, rather than to reach the truth by obtaining the
facts from Nature herself, at first hand, and then inferring general
principle from the facts so gathered. The rise of modern scientific
methods of reasoning, along the lines of Inductive Inference, dates from
about 1225-1300. Roger Bacon was one of the first to teach that we must
arrive at scientific truth by a process of observation and
experimentation on the natural objects to be found on all sides. He made
many discoveries by following this process. He was ably seconded by
Galileo who lived some three hundred years later, and who also taught
that many great general truths might be gained by careful observation
and intelligent inference. Lord Francis Bacon, who lived about the same
time as Galileo, presented in his _Novum Organum_ many excellent
observations and facts regarding the process of Inductive Reasoning and
scientific thought. As Jevons says: "Inductive logic inquires by what
manner of reasoning we can gather the laws of nature from the facts and
events observed. Such reasoning is called induction, or inductive
inquiry, and, as it has actually been practiced by all the great
discoverers in science, it consists in four steps."

The _Four Steps in Inductive Reasoning_, as stated by Jevons, are as
follows:

_First Step._--Preliminary observation.

_Second Step._--The making of hypotheses.

_Third Step._--Deductive reasoning.

_Fourth Step._--Verification.

It will be seen that the process of Inductive Reasoning is essentially
_a synthetic process_, because it operates in the direction of combining
and uniting particular facts or truths into general truths or laws which
comprehend, embrace and include them all. As Brooks says: "The
particular facts are united by the mind into the general law; the
general law embraces the particular facts and binds them together into a
unity of principle and thought. Induction is thus a process of thought
from the parts to the whole--a synthetic process." It will also be seen
that the process of Inductive Reasoning is essentially _an ascending
process_, because it ascends from particular facts to general laws;
particular truths to universal truths; from the lower to the higher, the
narrower to the broader, the smaller to the greater.

Brooks says of Inductive Reasoning: "The relation of induction to
deduction will be clearly seen. Induction and Deduction are the
converse, the opposites of each other. Deduction derives a particular
truth from a general truth; Induction derives a general truth from
particular truths. This antithesis appears in every particular.
Deduction goes from generals to particulars; Induction goes from
particulars to generals. Deduction is an analytic process; Induction is
a synthetic process. Deduction is a descending process--it goes from
the higher truth to the lower truth; Induction is an ascending
process--it goes from the lower truth to the higher. They differ also in
that Deduction may be applied to necessary truths, while Induction is
mainly restricted to contingent truths." Hyslop says: "There have been
several ways of defining this process. It has been usual to contrast it
with Deduction. Now, deduction is often said to be reasoning from
general to particular truths, from the containing to the contained
truth, or from cause to effect. Induction, therefore, by contrast is
defined as reasoning from the particular to the general, from the
contained to the containing, or from effect to cause. Sometimes
induction is said to be reasoning from the known to the unknown. This
would make deduction, by contrast, reasoning from the unknown to the
known, which is absurd. The former ways of representing it are much the
better. But there is still a better way of comparing them. Deduction _is
reasoning in which the conclusion is contained in the premises_. This is
a ground for its certitude and we commit a fallacy whenever we go beyond
the premises as shown by the laws of the distribution of terms. In
contrast with this, then, we may call inductive reasoning _the process
by which we go beyond the premises in the conclusion_.... The process
here is to start from given facts and to infer some other probable facts
more general or connected with them. In this we see the process of going
beyond the premises. There are, of course, certain conditions which
regulate the legitimacy of the procedure, just as there are conditions
determining deduction. They are _that the conclusion shall represent the
same general kind as the premises_, with a possibility of accidental
differences. But it goes beyond the premises in so far as _known_ facts
are concerned."

The following example may give you a clearer idea of the processes of
Inductive Reasoning:

_First Step._ Preliminary Observation. _Example_: We notice that all the
particular _magnets_ which have come under our observation _attract
iron_. Our mental record of the phenomena may be stated as: "A, B, C, D,
E, F, G, etc., and also X, Y, and Z, all of which are _magnets_, in all
observed instances, and at all observed times, _attract iron_."

_Second Step._ The Making of Hypotheses. _Example_: Upon the basis of
the observations and experiments, as above stated, and applying the
axiom of Inductive Reasoning, that: "What is true of the many, is true
of the whole," we feel justified in forming a hypothesis or inference of
a general law or truth, applying the facts of the particulars to the
general, whole or universal, thus: "_All_ magnets attract iron."

_Third Step._ Deductive Reasoning. _Example_: Picking up a magnet
regarding which we have had no experience and upon which we have made no
experiments, we reason by the syllogism, as follows: (1) _All_ magnets
attract iron; (2) _This thing_ is a magnet; therefore (3) _This thing_
will attract iron. In this we apply the axiom of Deductive Reasoning:
"Whatever is true of the whole is true of the parts."

_Fourth Step._ Verification. _Example_: We then proceed to test the
hypothesis upon the particular magnet, so as to ascertain whether or not
it agrees with the particular facts. If the magnet does not attract
iron we know that either our hypothesis is wrong and that _some_ magnets
do _not_ attract iron; or else that our _judgment_ regarding that
particular "thing" being a magnet is at fault and that it is _not_ a
magnet. In either case, further examination, observation and experiment
is necessary. In case the particular magnet _does_ attract iron, we feel
that we have verified our hypothesis and our judgment.




CHAPTER XII.

REASONING BY INDUCTION


The term "Induction," in its logical usage, is defined as follows: "(a)
The process of investigating and collecting facts; and (b) the deducing
of an inference from these facts; also (c) sometimes loosely used in the
sense of an inference from observed facts." Mill says: "_Induction_,
then, is that operation of the mind, by which we infer that what we know
to be true in a particular case or cases, will be true in all cases
which resemble the former in certain assignable respects. In other
words, _Induction_ is the process by which we conclude that what is true
of certain individuals of a class, is true of the whole class, or that
what is true at certain times will be true in similar circumstances at
all times."

The _Basis of Induction_ is the axiom that: "_What is true of the many
is true of the whole_." Esser, a well known authority, states this axiom
in rather more complicated form, as follows: "That which belongs or does
not belong to many things of the same kind, belongs or does not belong
to all things of the same kind."

This basic axiom of Induction rests upon the conviction that Nature's
laws and manifestations are regular, orderly and _uniform_. If we assume
that Nature does not manifest these qualities, then the axiom must fall,
and all inductive reason must be fallacious. As Brooks well says:
"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." Some
authorities have held that this perception of the uniformity of Nature's
laws is in the nature of an _intuitive_ truth, or an inherent law of our
intelligence. Others hold that it is in itself an _inductive_ truth,
arrived at by experience and observation at a very early age. We are
held to have noticed the uniformity in natural phenomena, and almost
instinctively infer that this uniformity is continuous and universal.

The authorities assume the existence of two kinds of Induction, namely:
(1) Perfect Induction; and (2) Imperfect Induction. Other, but similar,
terms are employed by different authorities to designate these two
classes.

_Perfect Induction_ necessitates a knowledge of _all_ the particulars
forming a class; that is, _all_ the individual objects, persons, things
or facts comprising a class must be known and enumerated in this form of
Induction. For instance, if we _knew positively_ all of Brown's
children, and that their names were John, Peter, Mark, Luke, Charles,
William, Mary and Susan, respectively; and that each and every one of
them were freckled and had red hair; then, in that case, instead of
simply _generalizing_ and stating that: "John, Peter, Mark, Luke,
Charles, William, Mary and Susan, who are _all_ of Brown's children, are
freckled and have red hair," we would save words, and state the
inductive conclusion: "All Brown's children are freckled and have red
hair." It will be noticed that in this case _we include in the process
only what is stated in the premise itself_, and we do not extend our
inductive process beyond the actual data upon which it is based. This
form of Induction is sometimes called "Logical Induction," because the
inference is a logical necessity, without the possibility of error or
exception. By some authorities it is held not to be Induction at all, in
the strict sense, but little more than a simplified form of enumeration.
In actual practice it is seldom available, for it is almost impossible
for us to know all the particulars in inferring a general law or truth.
In view of this difficulty, we fall back upon the more practical form of
induction known as:

_Imperfect Induction_, or as it is sometimes called "Practical
Induction," by which is meant the inductive process of reasoning in
which we assume that the particulars or facts actually known to us
correctly represent those which are not actually known, and hence the
whole class to which they belong. In this process it will be seen that
_the conclusion extends_ beyond the data upon which it is based. In this
form of Induction we must actually employ the principle of the axiom:
"What is true of the many is true of the whole"--that is, must _assume_
it to be a fact, not because we _know_ it by actual experience, but
because we infer it from the axiom which also agrees with past
experience. The conclusion arrived at may not always be true in its
fullest sense, as in the case of the conclusion of Perfect Induction,
but is the result of an inference based upon a principle which gives us
a reasonable right to assume its truth in absence of better knowledge.

In considering the actual steps in the process of Inductive Reasoning we
can do no better than to follow the classification of Jevons, mentioned
in the preceding chapter, the same being simple and readily
comprehended, and therefore preferable in this case to the more
technical classification favored by some other authorities. Let us now
consider these four steps.

_First Step._ Preliminary observation. It follows that without the
experience of oneself or of others in the direction of observing and
remembering particular facts, objects, persons and things, we cannot
hope to acquire the preliminary facts for the generalization and
inductive inference necessary in Inductive Reasoning. It is necessary
for us to form a variety of clear Concepts or ideas of facts, objects,
persons and things, before we may hope to generalize from these
particulars. In the chapters of this book devoted to the consideration
of Concepts, we may see the fundamental importance of the formation and
acquirement of correct Concepts. Concepts are the fundamental material
for correct reasoning. In order to produce a perfect finished product,
we must have perfect materials, and a sufficient quantity of them. The
greater the knowledge one possesses of the facts and objects of the
outside world, the better able is he to reason therefrom. Concepts are
the raw material which must feed the machinery of reasoning, and from
which the final product of perfected thought is produced. As Halleck
says: "There must first be a presentation of materials. Suppose that we
wish to form the concept _fruit_. We must first perceive the different
kinds of fruit--cherry, pear, quince, plum, currant, apple, fig, orange,
etc. Before we can take the next step, we must be able to form distinct
and accurate images of the various kinds of fruit. If the concept is to
be absolutely accurate, not one kind of fruit must be overlooked.
Practically this is impossible; but many kinds should be examined. Where
perception is inaccurate and stinted, the products of thought cannot be
trustworthy. No building is firm if reared on insecure foundations."

In the process of Preliminary Observation, we find that there are two
ways of obtaining a knowledge of the facts and things around us. These
two ways are as follows:

I. By _Simple Observation_, or the perception of the happenings which
are manifested without our interference. In this way we perceive the
motion of the tides; the movement of the planets; the phenomena of the
weather; the passing of animals, etc.

II. By the _Observation of Experiment_, or the perception of happenings
in which we interfere with things and then observe the result. An
_experiment_ is: "A trial, proof, or test of anything; an act,
operation, or process designed to discover some unknown truth, principle
or effect, or to test some received or reputed truth or principle."
Hobbes says: "To have had many _experiments_ is what we call
_experience_." Jevons says: "Experimentation is observation with
something more; namely, regulation of the things whose behavior is to be
observed. The advantages of experiment over mere observation are of two
kinds. In the first place, we shall generally know much more certainly
and accurately with what we are dealing, when we make experiments than
when we simply observe natural events.... It is a further advantage of
artificial experiments, that they enable us to discover entirely new
substances and to learn their properties.... It would be a mistake to
suppose that the making of an experiment is inductive reasoning, and
gives us without further trouble the laws of nature. _Experiments only
give us the facts upon which we may afterward reason...._ Experiments
then merely give facts, and it is only by careful reasoning that we can
learn when the same facts will be observed again. _The general rule is
that the same causes will produce the same effects._ Whatever happens in
one case will happen in all like cases, provided that they are really
like, and not merely apparently so.... When we have by repeated
experiments tried the effect which all the surrounding things might have
on the result, we can then reason with much confidence as to similar
results in similar circumstances.... In order that we may, from our
observations and experiments, learn the law of nature and become able to
foresee the future, we must perform the process of generalization. To
generalize is to draw a general law from particular cases, and to infer
that what we see to be true of a few things is true of the whole genus
or class to which these things belong. It requires much judgment and
skill to generalize correctly, because everything depends upon the
number and character of the instances about which we reason."

Having seen that the first step in Inductive Reasoning is Preliminary
Observation, let us now consider the next steps in which we may see what
we do with the facts and ideas which we have acquired by this
Observation and Experiment.




CHAPTER XIII.

THEORY AND HYPOTHESES


Following Jevons' classification, we find that the Second Step in
Inductive Reasoning is that called "The Making of Hypotheses."

A _Hypothesis_ is: "A supposition, proposition or principle _assumed or
taken for granted_ in order to draw a conclusion or inference in proof
of the point or question; a proposition assumed or taken for granted,
though not proved, for the purpose of deducing proof of a point in
question." It will be seen that a Hypothesis is merely held to be
_possibly or probably true_, and _not certainly true_; it is in the
nature of a _working assumption_, whose truth must be tested by observed
facts. The assumption may apply either to the _cause_ of things, or to
the _laws_ which govern things. Akin to a hypothesis, and by many people
confused in meaning with the latter, is what is called a Theory.

A _Theory_ is: "A verified hypothesis; a hypothesis which has been
established as, apparently, the true one." An authority says "_Theory_
is a stronger word than _hypothesis_. A _theory_ is founded on
principles which have been established on independent evidence. A
_hypothesis_ merely assumes the operation of a cause which would account
for the phenomena, but has not evidence that such cause was actually at
work. Metaphysically, a theory is nothing but a hypothesis supported by
a large amount of probable evidence." Brooks says: "When a hypothesis is
shown to explain all the facts that are known, these facts being varied
and extensive, it is said to be verified, and becomes a theory. Thus we
have the theory of universal gravitation, the Copernican theory of the
solar system, the undulatory theory of light, etc., all of which were
originally mere hypotheses. This is the manner in which the term is
usually employed in the inductive philosophy; though it must be admitted
that it is not always used in this strict sense. Discarded hypotheses
are often referred to as theories; and that which is actually a theory
is sometimes called a hypothesis."

The steps by which we build up a hypothesis are numerous and varied. In
the first place we may erect a hypothesis by the methods of what we have
described as Perfect Induction, or Logical Induction. In this case we
proceed by simple generalization or simple enumeration. The example of
the freckled, red-haired children of Brown, mentioned in a previous
chapter, explains this method. It requires the examination and knowledge
of every object or fact of which the statement or hypothesis is made.
Hamilton states that it is the only induction which is absolutely
necessitated by the laws of thought. It does not extend further than the
plane of experience. It is akin to mathematical reasoning.

Far more important is the process by which hypotheses are erected by
means of inferences from Imperfect Induction, by which we reason from
the known to the unknown, transcending experience, and making true
inductive inferences from the axiom of Inductive Reasoning. This process
involves the subject of Causes. Jevons says: "The cause of an event is
that antecedent, or set of antecedents, from which the event always
follows. People often make much difficulty about understanding what the
cause of an event means, but it really means nothing beyond _the things
that must exist before in order that the event shall happen afterward_."

Causes are often obscure and difficult to determine. The following five
difficulties are likely to arise: I. The cause may be out of our
experience, and is therefore not to be understood; II. Causes often act
conjointly, so that it is difficult to discover the one predominant
cause by reason of its associated causes; III. Often the presence of a
counteracting, or modifying cause may confuse us; IV. Often a certain
effect may be caused by either of several possible causes; V. That which
appears as a _cause_ of a certain effect may be but a co-effect of an
original cause.

Mill formulated several tests for ascertaining the causal agency in
particular cases, in view of the above-stated difficulties. These tests
are as follows: (1) The Method of Agreement; (2) The Method of
Difference; (3) The Method of Residues; and (4) The Method of
Concomitant Variations. The following definitions of these various tests
are given by Atwater as follows:

_Method 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."

_Method of Difference_: "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."

_Method 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."

_Method 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 adds: "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 inductive conclusion."

Jevons gives us the following valuable rules:

I. "Whenever we can alter the quantity of the things experimented on, we
can apply _a rule for discovering which are causes and which are
effects_, as follows: We must vary the quantity of one thing, making it
at one time greater and at another time less, and if we observe any
other thing which varies just at the same times, it will in all
probability be an _effect_."

II. "When things vary regularly and frequently, there is _a simple rule,
by following which we can judge whether changes are connected together
as causes and effects_, as follows: Those things which change in exactly
equal times are in all likelihood connected together."

III. "It is very difficult to explain how it is that we can ever reason
from one thing to a class of things by generalization, _when we cannot
be sure that the things resemble each other in the important points_....
Upon what grounds do we argue? We have to get a general law from
particular facts. This can only be done by going through all the steps
of inductive reasoning. Having made certain observations, we must frame
hypotheses as to the circumstances, or laws from which they proceed.
Then we must reason deductively; and after verifying the deductions in
as many cases as possible, we shall know how far we can trust similar
deductions concerning future events.... It is difficult to judge when we
may, and when we may not, safely infer from some things to others in
this simple way, without making a complete theory of the matter. _The
only rule_ that can be given to assist us is that _if things resemble
each other in a few properties only, we must observe many instances
before inferring that these properties will always be joined together in
other cases_."




CHAPTER XIV.

MAKING AND TESTING HYPOTHESES


The older philosophers and logicians were often at a loss how to
reasonably account for the origin of hypotheses. It will be seen, after
giving the matter a little thought, that the actual formation of the
hypothesis is more than a mere grouping together or synthesis of facts
or ideas--there is another mental process which actually evolves the
hypothesis or theory--which gives _a possible reason_. What is this
mental process? Let us consider the matter. Brooks well says: "The
hypotheses of science originate in what is called anticipation. They are
not the result of a mere synthesis of facts, for no combination of facts
can give the law or cause. We do not see the law; we see the facts and
_the mind thinks the law_. By the power of anticipation, the mind often
leaps from a few facts to the cause which produces them or the law which
governs them. Many hypotheses were but _a happy intuition of the mind_.
They were the result of what La Place calls 'a great guess,' or what
Plato so beautifully designates as 'a sacred suspicion of truth.' 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."

The student of The New Psychology sees in the mental operation of the
forming of the hypothesis--"the mind thinking the law"--but an instance
of the operation of the activities of the Subconscious Mind, or even the
Superconscious Mind. (See the volume on the Subconscious Mind in this
series.) Not only does this hypothesis give the explanation which the
old psychology has failed to do, but it agrees with the ideas of others
on the subject as stated in the above quotation from Brooks; and
moreover agrees with many recorded instances of the formation of great
hypotheses. Sir Wm. Hamilton discovered the very important mathematical
law of quaternions while walking one day in the Dublin Observatory. He
had pondered long on the subject, but without result. But, finally, on
that eventful day he suddenly "felt the galvanic circle of thought"
close, and the result was the realization of the fundamental
mathematical relations of the problem. Berthelot, the founder of
Synthetic Chemistry, has testified that the celebrated experiments which
led to his remarkable discoveries were seldom the result of carefully
followed lines of conscious thought or pure reasoning processes; but,
instead, came to him "of their own accord," so to speak, "as from a
clear sky." In these and many other similar instances, the mental
operation was undoubtedly purely subjective and subconscious. Dr. Hudson
has claimed that the "Subjective Mind" cannot reason inductively, and
that its operations are purely and distinctly deductive, but the
testimony of many eminent scientists, inventors and philosophers is
directly to the contrary.

In this connection the following quotation from Thomson is interesting:
"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 to 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 a type of the whole skeleton in a
single vertebra, while Newton conceived at once that the whole universe
was full of bodies tending to fall.... The discovery of Goethe, which
did for the vegetable kingdom what Oken did for the animal, that the
parts of a plant are to be regarded as metamorphosed leaves, is an
apparent exception to the necessity of discipline for invention, since it
was the discovery of a poet in a region to which he seemed to have paid
no especial or laborious attention. But Goethe was himself most anxious
to rest the basis of this discovery upon his observation rather than his
imagination, and doubtless with good reason.... As with other great
discoveries, hints had been given already, though not pursued, both of
Goethe's and Oken's principles. Goethe left his to be followed up by
others, and but for his great fame, perhaps his name would never have
been connected with it. Oken had amassed all the materials necessary for
the establishment of his theory; he was able at once to discover and
conquer the new territory."

It must not be supposed, however, that all hypotheses flashing into the
field of consciousness from the Subconsciousness, are necessarily true
or correct. On the contrary many of them are incorrect, or at least only
partially correct. The Subconsciousness is not infallible or
omniscient--it merely produces results according to the material
furnished it. But even these faulty hypotheses are often of value in the
later formation of a correct one. As Whewell says: "To try wrong guesses
is with most persons the only way to hit upon right ones." Kepler is
said to have erected at least twenty hypotheses regarding the shape of
the earth's orbit before he finally evolved the correct one. As Brooks
says: "Even incorrect hypotheses may be of use in scientific research,
since they may lead to more correct suppositions." The supposition of
the circular motions of the heavenly bodies around the _earth_ as a
center, which lead to the conception of epicycles, etc., and at last to
the true theory is an illustration of this. So the 'theory of
phlogiston' in chemistry, made many facts intelligible, before the true
one of 'oxidation' superseded it. And so, as Thomson says, "with the
theory that 'Nature abhors a vacuum,' which served to bring together so
many cognate facts not previously considered as related. Even an
incorrect conception of this kind has its place in science, so long as
it is applicable to the facts; when facts occur which it cannot explain,
we either correct it or replace it with a new one. The pathway of
science, some one remarks, is strewn with the remains of discarded
hypotheses."

Halleck says regarding the danger of hasty inference: "Men must
constantly employ imperfect induction in order to advance; but great
dangers attend inductive inferences made from too narrow experience. A
child has experience with one or two dogs at his home. Because of their
gentleness, he argues that all dogs are gentle. He does not, perhaps,
find out the contrary until he has been severely bitten. His induction
was too hasty. He had not tested a sufficiently large number of dogs to
form such a conclusion. From one or two experiences with a large crop in
a certain latitude, a farmer may argue that the crop will generally be
profitable, whereas it may not again prove so for years. A man may have
trusted a number of people and found them honest. He concludes that
people as a rule are honest, trusts a certain dishonest man, and is
ruined. The older people grow, the more cautious they generally become
in forming inductive conclusions. Many instances are noted and compared;
but even the wisest sometimes make mistakes. It once was a generally
accepted fact that all swans were white. Nobody had ever seen a dark
swan, and the inference that all swans were white was regarded as
certainly true. Black swans were, however, found in Australia."

Brooks says regarding the probability of hypotheses: "The probability of
a hypothesis is in proportion to the number of facts and phenomena it
will explain. The larger the number of facts and phenomena that it will
satisfactorily account for, the greater our faith in the correctness of
our supposition.... If there is more than one hypothesis in respect to
the facts under consideration, that one which accounts for the greatest
number of facts is the most probable.... In order to verify a hypothesis
it must be shown that it will account for all the facts and phenomena.
If these facts are numerous and varied, and the subject is so thoroughly
investigated that it is quite certain that no important class of facts
has been overlooked, the supposition is regarded as true, and the
hypothesis is said to be verified. Thus the hypothesis of the 'daily
rotation' of the earth on its axis to account for the succession of day
and night is accepted as absolutely true. This is the view taken by Dr.
Whewell and many other thinkers in respect to the verification of a
hypothesis. Some writers, however, as Mill and his school, maintain that
in order to verify a hypothesis, we must show not only that it explains
all the facts and phenomena, but that there is no other possible
hypothesis which will account for them.... The former view of
verification is regarded as the correct one. By the latter view, it is
evident that a hypothesis could never be verified."

Jevons says: "In the fourth step (verification), we proceed to compare
these deductions with the facts already collected, or when necessary and
practicable, we make new observations and plan new experiments, so as to
find out whether the hypothesis agrees with nature. If we meet with
several distinct disagreements between our deductions and our
observations, it will become likely that the hypothesis is wrong, and we
must then invent a new one. In order to produce agreement it will
sometimes be enough to change the hypothesis in a small degree. When we
get hold of a hypothesis which seems to give results agreeing with a few
facts, we must not at once assume that it is certainly correct. We must
go on making other deductions from it under various circumstances, and,
whenever it is possible, we ought to verify these results, that is,
compare them with facts observed through the senses. When a hypothesis
is shown in this way to be true in a great many of its results,
especially when it enables us to predict what we should never otherwise
have believed or discovered, it becomes certain that the hypothesis
itself is a true one.... Sometimes it will happen that two or even three
quite different hypotheses all seem to agree with certain facts, so that
we are puzzled which to select.... When there are thus two hypotheses,
one as good as the other, we need to discover some fact or thing which
will agree with one hypothesis and not with the other, because this
immediately enables us to decide that the former hypothesis is true and
the latter false."

In the above statements regarding the _verification_ of hypotheses we
see references made to the testing of the latter upon the "facts" of the
case. These _facts_ may be either the observed phenomena or facts
apparent to the perception, or else _facts_ obtained by deductive
reasoning. The latter may be said to be facts which are held to be true
if the hypothesis be true. Thus if we erect the hypothesis that "All men
are mortal," we may reason deductively that it will follow that each and
every thing that is a _man_ must die sooner or later. Then we test our
hypotheses upon _each and every man_ whom we may subject to observation
and experiment. If we find a single man who does not die, then the test
disproves our hypotheses; if on the contrary all men (the "facts" in the
case) prove to be mortal, then is our hypotheses proven or established.
The deductive reasoning in this case is as follows: "_If_ so-and-so is
true regarding such-and-such a class; and if this particular thing
belongs to that class; then it will follow that so-and-so is true
regarding this particular thing." This argument is expressed in what is
called a Hypothetical Proposition (see Chapter IX), the consideration of
which forms a part of the general subject of Deductive Reasoning.
Therefore as Jevons has said, "Deductive Reasoning is the Third Step in
Inductive Reasoning, and precedes Verification", which we have already
considered. Halleck says: "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 major premise.... Deduction takes that as a fact, making no
inquiry about 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."

In view of the above facts, we shall now proceed to a consideration of
that great class of Reasoning known under the term--Deductive
Reasoning.




CHAPTER XV.

DEDUCTIVE REASONING


We have seen that there are two great classes of reasoning, known
respectively, as (1) Inductive Reasoning, or the discovery of general
truth from particular truths; and (2) Deductive Reasoning, or the
discovery of particular truths from general truths.

As we have said, Deductive Reasoning is the process of discovering
particular truths from a general truth. Thus from the general truth
embodied in the proposition "All horses are animals," when it is
considered in connection with the secondary proposition that "Dobbin is
a horse," we are able to deduce the particular truth that: "Dobbin is an
animal." Or, in the following case we deduce a particular truth from a
general truth, as follows: "All mushrooms are good to eat; this fungus
is a mushroom; therefore, this fungus is good to eat." A deductive
argument is expressed in a deductive syllogism.

Jevons says regarding the last stated illustration: "Here are three
sentences which state three different facts; but when we know the two
first facts, we learn or gather the third fact from the other two. When
we thus learn one fact from other facts, we _infer or reason_, and we do
this in the mind. Reasoning thus enables us to ascertain the nature of a
thing without actual trial. If we always needed to taste a thing before
we could know whether it was good to eat or not, cases of poisoning
would be alarmingly frequent. But the appearance and peculiarities of a
mushroom may be safely learned by the eye or the nose, and reasoning
upon this information and the fact already well known, that mushrooms
are good to eat, we arrive without any danger or trouble at the
conclusion that the particular fungus before us is good to eat. _To
reason, then, is to get some knowledge from other knowledge._"

The student will recognize that Deductive Reasoning is essentially _an
analytic process_, because it operates in the direction of analyzing a
universal or general truth into its particulars--into the particular
parts which are included within it--and asserting of them that "what is
true of the general is true of the particular." Thus in the general
truth that "All men are mortal," we see included the particular truth
that "John Smith is mortal"--John Smith having been discovered to be a
man. We deduce the particular truth about John Smith from the general
truth about "all men." We analyze "all men" and find John Smith to be
one of its particular parts. Therefore, "Deduction is an inference from
the whole to its parts; that is, an analytic process."

The student will also recognize that Deductive Reasoning is essentially
_a descending process_, because it operates in the direction of a
descent from the universal to the particular; from the higher to the
lower; from the broader to the narrower. As Brooks says: "Deduction
descends from higher truths to lower truths, from laws to facts, from
causes to phenomena, etc. Given the law, we can by deduction descend to
the facts that fall under the law, even if we have never before seen the
facts; and so from the cause we may pass down to observed and even
unknown phenomena."

The general truths which are used as the basis of Deductive Reasoning
are discovered in several ways. The majority arise from Inductive
Reasoning, based upon experience, observation and experiment. For
instance in the examples given above, we could not truthfully assert our
belief that: "All horses are animals" unless we had previously studied
both the horse and animals in general. Nor without this study could we
state that "Dobbin is a horse." Nor could we, without previous study,
experience and experiment truthfully assert that: "All mushrooms are
good to eat;" or that "this fungus is a mushroom;" and that "therefore,
this fungus is good to eat." Even as it is, we must be sure that the
fungus really is a mushroom, else we run a risk of poisoning ourselves.
General truths of this kind are _not intuitive_, by any means, but are
based upon our own experience or the experience of others.

There is a class of general truths which are called _intuitive_ by some
authorities. Halleck says of these: "Some psychologists claim that we
have knowledge obtained neither through induction nor deduction; that
we recognize certain truths the moment we perceive certain objects,
without any process of inference. Under the head of intuitive knowledge
are classified such cases as the following: We perceive an object and
immediately know that it is a time relation, as existing now and then.
We are said to have an intuitive concept of time. When we are told that
the whole is greater than a part; that things equal to the same thing
are equal to each other; that a straight line cannot enclose space, we
_immediately_, or intuitively, recognize the truth of these statements.
Attempts at proof do not make us feel surer of their truth.... We say
that it is self-evident, or that we know the fact intuitively. The
axioms of mathematics and logic are said to be intuitive."

Another class of authorities, however, deny the nature of intuitive
knowledge of truth, or intuitive truths. They claim that all our ideas
arise from sensation and reflection, and that what we call "intuition"
is merely the result of sensation and reflection _reproduced by memory
or heredity_. They hold that the _intuitions_ of animals and men are
simply the representation of experiences of the race, or individual,
arising from the impressions stored away in the subconsciousness of the
individual. Halleck states regarding this: "This school likens intuition
to instinct. It grants that the young duck knows water instinctively,
plunges into it, and swims without learning. These psychologists believe
that there was a time when this was not the case with the progenitors of
the duck. They had to gain this knowledge slowly through experience.
Those that learned the proper aquatic lesson survived and transmitted
this knowledge through a modified structure, to their progeny. Those
that failed in the lesson perished in the struggle for existence....
This school claims that the intuition of cause and effect arose in the
same way. Generations of human beings have seen the cause invariably
joined to the effect; hence, through inseparable association came the
recognition of their necessary sequence. The tendency to regard all
phenomena in these relations was with steadily increasing force
transmitted by the laws of heredity to posterity, until the recognition
of the relationship has become an intuition."

Another class of general truths is merely hypothetical. Hypothetical
means "Founded on or including a hypothesis or supposition; assumed or
taken for granted, though not proved, for the purpose of deducing proofs
of a point in question." The hypotheses and theories of physical science
are used as general truths for deductive reasoning. Hypothetical general
truths are in the nature of premises assumed in order to proceed with
the process of Deductive Reasoning, and without which such reasoning
would be impossible. They are, however, as a rule not mere assumptions,
but are rather in the nature of assumptions rendered plausible by
experience, experiment and Inductive Reasoning. The Law of Gravitation
may be considered hypothetical, and yet it is the result of Inductive
Reasoning based upon a vast multitude of facts and phenomena.

The _Primary Basis of Deductive Reasoning_ may be said to rest upon the
logical axiom, which has come down to us from the ancients, and which is
stated as follows: "_Whatever is true of the whole is true of its
parts_." Or, as later authorities have expressed it: "Whatever is true
of the general is true of the particular." This axiom is the basis upon
which we build our Deductive Reasoning. It furnishes us with the
validity of the deductive inference or argument. If we are challenged
for proof of the statement that "This fungus is good to eat," we are
able to answer that we are justified in making the statement by the
self-evident proposition, or axiom, that "Whatever is true of the
general is true of the particular." If the general "mushroom" is good to
eat, then the particular, "this fungus" being a mushroom, must also be
good to eat. All horses (general) being animals, then according to the
axiom, Dobbin (particular horse) must also be an animal.

This axiom has been stated in various terms other than those stated
above. For instance: "Whatever may be affirmed or denied of the whole,
may be denied or affirmed of the parts;" which form is evidently derived
from that used by Hamilton who said: "What belongs, or does not belong,
to the containing whole, belongs or does not belong, to each of the
contained parts." Aristotle formulated his celebrated Dictum as follows:
"Whatever can be predicated affirmatively or negatively of any class or
term distributed, can be predicated in like manner of all and singular
the classes or individuals contained under it."

There is another form of Deductive Reasoning, that is a form based upon
another axiom than that of: "Whatever is true of the whole is true of
the parts." This form of reasoning is sometimes called Mathematical
Reasoning, because it is the form of reasoning employed in mathematics.
Its axiom is stated as follows: "Things which are equal to the same
thing, are equal to one another." It will be seen that this is the
principle employed in mathematics. Thus: "x equals y; and y equals 5;
therefore, x equals 5." Or stated in logical terms: "A equals B; B
equals C; therefore, A equals C." Thus it is seen that this form of
reasoning, as well as the ordinary form of Deductive Reasoning, is
strictly _mediate_, that is, made through the medium of a third thing,
or "two things being compared through their relation to a third."

Brooks states: "The real reason for the certainty of mathematical
reasoning may be stated as follows: First, its ideas are definite,
necessary, and exact conceptions of quantity. Second, its definitions,
as the description of these ideas are necessary, exact, and indisputable
truths. Third, the axioms from which we derive conclusions by comparison
are all self-evident and necessary truths. Comparing these exact ideas
by the necessary laws of inference, the result must be absolutely true.
Or, stated in another way, using these definitions and axioms as the
premises of a syllogism, the conclusion follows inevitably. There is no
place or opportunity for error to creep in to mar or vitiate our derived
truths."

In conclusion, we wish to call your attention to a passage from Jevons
which is worthy of consideration and recollection. Jevons says: "There
is a simple rule which will enable us to test the truth of a great many
arguments, even of many which do not come under any of the rules
commonly given in books on logic. This rule is that _whatever is true of
one term is true of any term which is stated to be the same in meaning
as that term_. In other words, we may always _substitute one term for
another if we know that they refer to exactly the same thing_. There is
no doubt that a horse is some animal, and therefore the head of a horse
is the head of some animal. This argument cannot be brought under the
rules of the syllogism, because it contains four distinct logical terms
in two propositions; namely, horse, some animal; head of horse, head of
some animal. But it easily comes under the rule which I have given,
because we have simply to put 'some animal' instead of 'a horse'. A
great many arguments may be explained in this way. Gold is a metal;
therefore a piece of gold is a piece of metal. A negro is a fellow
creature; therefore, he who strikes a negro, strikes a fellow creature."

The same eminent authority says: "When we examine carefully enough the
way in which we reason, it will be found _in every case to consist in
putting one thing or term in place of another, to which we know it to
have an exact resemblance in some respect_. We use the likeness as a
kind of bridge, which leads us from a knowledge of one thing to a
knowledge of another; thus _the true principle of reasoning may be
called the substitution of similars, or the passing from like to like_.
We infer the character of one thing from the character of something
which acts as a go-between, or third term. When we are certain there is
an exact likeness, our inference is certain; when we only believe that
there probably is, or guess that there is, then our inferences are only
probable, not certain."




CHAPTER XVI.

THE SYLLOGISM


The third and highest phase or step in reasoning--the step which follows
after those styled Conception and Judgment--is generally known by the
general term "Reasoning," which term, however, is used to include the
two precedent steps as well as the final step itself. This step or
process consists of the comparing of two objects, persons or things,
through their relation to a third object, person or thing. As, for
instance, we reason (a) that all mammals are animals; (b) that a horse
is a mammal; and (c) that, _therefore_, a horse is an animal. The most
fundamental principle of this step or reasoning consists in the
comparing of two objects of thought through and by means of their
relation to a third object. The natural form of expression of this
process of reasoning is called a "Syllogism."

The process of reasoning which gives rise to the expression of the
argument in the form of a Syllogism must be understood if one wishes to
form a clear conception of the Syllogism. The process itself is very
simple when plainly stated, although the beginner is sometimes puzzled
by the complicated definitions and statements of the authorities. Let us
suppose that we have three objects, A, B and C, respectively. We wish to
compare C and B, but fail to establish a relation between them at first.
We however are able to establish a relation between A and B; and between
C and A. We thus have the two propositions (1) "A equals B; and (2) C
equals A". The next step is that of inferring that "if A equals B, and C
equals A, then it must follow, logically, _that C equals B_." This
process is that of indirect or mediate comparison, rather than
_immediate_. C and B are not compared directly or immediately, but
indirectly and through the medium of A. A is thus said to _mediate_
between B and C.

This process of reasoning embraces three ideas or objects of thought, in
their expression of propositions. It comprises the fundamental or
elemental form of reasoning. As Brooks says: "The simplest movement of
the reasoning process is the comparing of two objects through their
relation to a third." The result of this process is an argument
expressed in what is called a Syllogism. Whately says that: "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 terms." Brooks says: "All
reasoning can be and naturally is expressed in the form of the
syllogism. It applies to both inductive and deductive reasoning, and is
the form in which these processes are presented. Its importance as an
instrument of thought requires that it receive special notice."

In order that the nature and use of the Syllogism may be clearly
understood, we can do no better than to at once present for your
consideration the well-known "Rules of the Syllogism," an understanding
of which carries with it a perfect comprehension of the Syllogism
itself.

The Rules of the Syllogism state that in order for a Syllogism to be a
_perfect_ Syllogism, it is necessary:

I. _That there should be three, and no more than three, Propositions._
These three propositions are: (1) the _Conclusion_, or thing to be
proved; and (2 and 3) the Premises, or the means of proving the
Conclusion, and which are called the Major Premise and Minor Premise,
respectively. We may understand this more clearly if we will examine the
following example:

_Major Premise_: "Man is mortal;" (or "A is B").

_Minor Premise_: "Socrates is a man;" (or "C is A"). Therefore:

_Conclusion_: "Socrates is mortal" (or "C is B").

It will be seen that the above Syllogism, whether expressed in words or
symbols, is logically valid, because the conclusion must logically
follow the premises. And, in this case, the premises being true, it must
follow that the conclusion is true. Whately says: "A Syllogism is said
to be valid when the conclusion logically follows from the premises; if
the conclusion does not so follow, the Syllogism is invalid and
constitutes a Fallacy, if the error deceives the reasoner himself; but
if it is advanced with the idea of deceiving others it constitutes a
Sophism."

The reason for Rule I is that only three propositions--a Major Premise,
a Minor Premise, and a Conclusion--are needed to form a Syllogism. If we
have more than _three_ propositions, then we must have more than two
premises from which to draw one conclusion. The presence of more than
two premises would result in the formation of two or more Syllogisms, or
else in the failure to form a Syllogism.

II. _That there should be three and no more than three Terms._ These
Terms are (1) The Predicate of the Conclusion; (2) the Subject of the
Conclusion; and (3) the Middle Term which must occur in both premises,
being the connecting link in bringing the two other Terms together in
the Conclusion.

The _Predicate of the Conclusion_ is called the _Major_ Term, because it
is the greatest in extension compared with its fellow terms. The
_Subject of the Conclusion_ is called the _Minor_ Term because it is the
smallest in extension compared with its fellow terms. The Major and
Minor Terms are called the _Extremes_. The Middle Term operates between
the two Extremes.

The _Major Term_ and the _Middle Term_ must appear in the _Major
Premise_.

The _Minor Term_ and the _Middle Term_ must appear in the _Minor
Premise_.

The _Minor Term_ and the _Major Term_ must appear in the _Conclusion_.

Thus we see that _The Major Term_ must be the Predicate of the
Conclusion; the _Minor Term_ the Subject of the Conclusion; the _Middle
Term_ may be the Subject or Predicate _of either of the premises_, but
_must always be found once in both premises_.

The following example will show this arrangement more clearly:

In the Syllogism: "Man is mortal; Socrates is a man; therefore Socrates
is mortal," we have the following arrangement: "Mortal," the Major Term;
"Socrates," the Minor Term; and "Man," the Middle Term; as follows:

_Major Premise_: "Man" (_middle term_) is mortal (_major term_).

_Minor Premise_: "Socrates" (_minor term_) is a man (_major term_).

_Conclusion_: "Socrates" (_minor term_) is mortal (_major term_).

The reason for the rule that there shall be "_only three_" terms is that
reasoning consists in comparing _two terms_ with each other through the
medium of a _third term_. There _must be_ three terms; if there are
_more_ than three terms, we form two syllogisms instead of one.

III. _That one premise, at least, must be affirmative._ This, because
"from two negative propositions nothing can be inferred." A negative
proposition asserts that two things differ, and if we have two
propositions so asserting difference, we can infer nothing from them. If
our Syllogism stated that: (1) "Man is _not_ mortal;" and (2) that
"Socrates is _not_ a man;" we could form no Conclusion, either that
Socrates _was_ or _was not_ mortal. There would be no logical connection
between the two premises, and therefore no Conclusion could be deduced
therefrom. Therefore, at least one premise must be affirmative.

IV. _If one premise is negative, the conclusion must be negative._ This
because "if one term agrees and another disagrees with a third term,
they must disagree with each other." Thus if our Syllogism stated that:
(1) "Man is _not_ mortal;" and (2) that: "Socrates is a man;" we must
announce the Negative Conclusion that: (3) "Socrates is _not_ mortal."

V. _That the Middle Term must be distributed; (that is, taken
universally) in at least one premise._ This "because, otherwise, the
Major Term may be compared with one part of the Middle Term, and the
Minor Term with another part of the latter; and there will be actually
no common Middle Term, and consequently no common ground for an
inference." The violation of this rule causes what is commonly known as
"The Undistributed Middle," a celebrated Fallacy condemned by the
logicians. In the Syllogism mentioned as an example in this chapter, the
proposition "_Man_ is mortal," really means "_All_ men," that is, Man in
his universal sense. Literally the proposition is "All men are mortal,"
from which it is seen that Socrates being "_a_ man" (or _some_ of _all_
men) must partake of the quality of the universal Man. If the Syllogism,
instead, read: "_Some_ men are mortal," it would not follow that
Socrates _must_ be mortal--he might or might not be so. Another form of
this fallacy is shown in the statement that (1) White is a color; (2)
Black is a color; hence (3) Black must be White. The two premises
_really_ mean "White is _some_ color; Black is _some_ color;" and not
that either is "_all_ colors." Another example is: "Men are bipeds;
birds are bipeds; hence, men are birds." In this example "bipeds" is not
distributed as "_all_ bipeds" but is simply not-distributed as "_some_
bipeds." These syllogisms, therefore, not being according to rule, must
fail. They are not true syllogisms, and constitute fallacies.

To be "_distributed_," the Middle Term must be the Subject of a
Universal Proposition, or the Predicate of a Negative Proposition; to be
"_undistributed_" it must be the Subject of a Particular Proposition, or
the Predicate of an Affirmative Proposition. (See chapter on
Propositions.)

VI. _That an extreme, if undistributed in a Premise, may not be
distributed in the Conclusion._ This because it would be illogical and
unreasonable to assert more in the conclusion than we find in the
premises. It would be most illogical to argue that: (1) "All horses are
animals; (2) no man is a horse; therefore (3) no man is an animal." The
conclusion would be invalid, because the term _animal_ is distributed in
the conclusion, (being the predicate of a negative proposition) while it
is not distributed in the premise (being the predicate of an affirmative
proposition).

As we have said before, any Syllogism which violates any of the above
six syllogisms is invalid and a fallacy.

There are two additional rules which may be called derivative. Any
syllogism which violates either of these two derivative rules, also
violates one or more of the first six rules as given above in detail.

The _Two Derivative Rules of the Syllogism_ are as follows:

VII. _That one Premise at least must be Universal._ This because "from
two particular premises no conclusion can be drawn."

VIII. _That if one premise is Particular, the Conclusion must be
particular also._ This because only a universal conclusion can be drawn
from two universal premises.

The principles involved in these two Derivative Rules may be tested by
stating Syllogisms violating them. They contain the essence of the other
rules, and every syllogism which breaks them will be found to also break
one or more of the other rules given.




CHAPTER XVII.

VARIETIES OF SYLLOGISMS


The authorities in Logic hold that with the four kinds of propositions
grouped in every possible order of arrangement, it is possible to form
nineteen different kinds of valid arguments, which are called the
_nineteen moods of the syllogism_. These are classified by division into
what are called _the four figures_, each of which figures may be known
by the position of the middle term in the premises. Logicians have
arranged elaborate and curious tables constructed to show what kinds of
propositions when joined in a particular order of arrangement will make
sound and valid syllogisms. We shall not set forth these tables here, as
they are too technical for a popular presentation of the subject before
us, and because they are not necessary to the student who will
thoroughly familiarize himself with the above stated Laws of the
Syllogism and who will therefore be able to determine in every case
whether any given argument is a correct syllogism, or otherwise.

In many instances of ordinary thought and expression the _complete_
syllogistic form is omitted, or not stated at full length. It is common
usage to omit one premise of a syllogism, in ordinary expression, the
missing premise being inferred by the speaker and hearer. A syllogism
with one premise unexpressed is sometimes called an _Enthymene_, the
term meaning "in the mind." For instance, the following: "We are a free
people, therefore we are happy," the major premise "All free people are
happy" being omitted or unexpressed. Also in "Poets are imaginative,
therefore Byron was imaginative," the minor premise "Byron was a poet"
is omitted or unexpressed. Jevons says regarding this phase of the
subject: "Thus in the Sermon on the Mount, the verses known as the
Beatitudes consist each of one premise and a conclusion, and the
conclusion is put first. 'Blessed are the merciful: for they shall
obtain mercy.' The subject and the predicate of the conclusion are here
inverted, so that the proposition is really 'The merciful are blessed.'
It is evidently _understood_ that 'All who shall obtain mercy are
blessed,' so that the syllogism, when stated at full length, becomes:
'All who shall obtain mercy are blessed; All who are merciful shall
obtain mercy; Therefore, all who are merciful are blessed.' This is a
perfectly good syllogism."

Whenever we find any of the words: "_because_, _for_, _therefore_,
_since_," or similar terms, we may know that there is an argument, and
usually a syllogism.

We have seen that there are three special kinds of Propositions, namely,
(1) Categorical Propositions, or propositions in which the affirmation
or denial is made without reservation or qualification; (2) Hypothetical
Propositions, in which the affirmation or denial is made to depend upon
certain conditions, circumstances, or suppositions; and (3) Disjunctive
Propositions, in which is implied or asserted an _alternative_.

The forms of reasoning based upon these three several classes of
propositions bear the same names as the latter. And, accordingly the
respective syllogisms expressing these forms of reasoning also bear the
class name or term. Thus, a Categorical Syllogism is one containing
only categorical propositions; a Hypothetical Syllogism is one
containing one or more hypothetical propositions; a Disjunctive
Syllogism is one containing a disjunctive proposition in the major
premise.

_Categorical Syllogisms_, which are far more common than the other two
kinds, have been considered in the previous chapter, and the majority of
the examples of syllogisms given in this book are of this kind. In a
Categorical Syllogism the statement or denial is made positively, and
without reservation or qualification, and the reasoning thereupon
partakes of the same positive character. In propositions or syllogisms
of this kind it is asserted or assumed that the premise is true and
correct, and, if the reasoning be logically correct it must follow that
the conclusion is correct, and the new proposition springing therefrom
must likewise be Categorical in its nature.

_Hypothetical Syllogisms_, on the contrary, have as one or more of their
premises a hypothetical proposition which affirms or asserts something
provided, or "if," something else be true. Hyslop says of this: "Often
we wish first to bring out, if only conditionally, the truth upon which
a proposition rests, so as to see if the connection between this
conclusion and the major premise be admitted. The whole question will
then depend upon the matter of treating the minor premise. This has the
advantage of getting the major premise admitted without the formal
procedure of proof, and the minor premise is usually more easily proved
than the major. Consequently, one is made to see more clearly the force
of the argument or reasoning by removing the question of the material
truth of the major premise and concentrating attention upon the relation
between the conclusion and its conditions, so that we know clearly what
we have first to deny if we do not wish to accept it."

By joining a hypothetical proposition with an ordinary proposition we
create a Hypothetical Proposition. For instance: "_If_ York contains a
cathedral it is a city; York _does_ contain a cathedral; therefore, York
is a city." Or: "If _dogs_ have four feet, they are quadrupeds; dogs
_do_ have four feet; therefore dogs _are_ quadrupeds." The Hypothetical
Syllogism may be either affirmative or negative; that is, its
hypothetical proposition may either hypothetically _affirm_ or
hypothetically _deny_. The part of the premise of a Hypothetical
Syllogism which conditions or questions (and which usually contains the
little word "if") is called the Antecedent. The major premise is the one
usually thus conditioned. The other part of the conditioned proposition,
and which part states what will happen or is true under the conditional
circumstances, is called the Consequent. Thus, in one of the above
examples: "If dogs have four feet" is the Antecedent; and the remainder
of the proposition: "they are quadrupeds" is the Consequent. The
Antecedent is indicated by the presence of some conditional term as:
_if_, _supposing_, _granted that_, _provided that_, _although_, _had_,
_were_, etc., the general sense and meaning of such terms being that of
the little word "_if_." The Consequent has no special indicating term.

Jevons gives the following clear and simple _Rules regarding the
Hypothetical Syllogism_:

I. "If the Antecedent be affirmed, the consequent may be affirmed. If
the Consequent be denied, the Antecedent may be denied."

II. "Avoid the fallacy of affirming the consequent, or denying the
antecedent. This is a fallacy because of the fact that the conditional
statement made in the major premise _may not be the only one_
determining the consequent." The following is an example of "Affirming
the Consequent:" "_If_ it is raining, the sky is overclouded; the sky
_is_ overclouded; therefore, it _is raining_." In truth, the sky may be
overclouded, and still it may _not_ be raining. The fallacy is still
more apparent when expressed in symbols, as follows: "_If_ A is B, C is
D; C _is_ D; therefore, A is B." The fallacy of denying the Antecedent
is shown by the following example: "_If_ Radium were cheap it would be
useful; Radium is _not_ cheap; therefore Radium _is not_ useful." Or,
expressed in symbols: "_If_ A is B, C is D; A is _not_ B; therefore C
_is not_ D." In truth Radium may be useful although not cheap. Jevons
gives the following examples of these fallacies: "If a man is a good
teacher, he thoroughly understands his subject; but John Jones
thoroughly understands his subject; therefore, he is a good teacher."
Also, "If snow is mixed with salt it melts; the snow on the ground is
_not_ mixed with salt; therefore it does _not_ melt."

Jevons says: "To affirm the consequent and then to infer that we can
affirm the antecedent, is as bad as breaking the third rule of the
syllogism, and allowing an undistributed middle term.... To deny the
antecedent is really to break the fourth rule of the syllogism, and to
take a term as distributed in the conclusion which was not so in the
premises."

Hypothetical Syllogisms may usually be easily reduced to or converted
into Categorical Syllogisms. As Jevons says: "In reality, hypothetical
propositions and syllogisms are not different from those which we have
more fully considered. _It is all a matter of the convenience of stating
the propositions._" For instance, instead of saying: "If Radium were
cheap, it would be useful," we may say "Cheap Radium would be useful;"
or instead of saying: "If glass is thin, it breaks easily," we may say
"Thin glass breaks easily." Hyslop gives the following _Rule for
Conversion_ in such cases: "Regard the antecedent of the hypothetical
proposition as the subject of the categorical, and the consequent of
the hypothetical proposition as the predicate of the categorical. In
some cases this change is a very simple one; in others it can be
effected only by a circumlocution."

The third class of syllogisms, known as _The Disjunctive Syllogism_, is
the exception to the law which holds that all good syllogisms must fit
in and come under the Rules of the Syllogism, as stated in the preceding
chapter. Not only does it refuse to obey these Rules, but it fails to
resemble the ordinary syllogism in many ways. As Jevons says: "It would
be a great mistake to suppose that all good logical arguments must obey
the rules of the syllogism, which we have been considering. Only those
arguments which connect two terms together by means of a middle term,
and are therefore syllogisms, need obey these rules. A great many of the
arguments which we daily use are of this nature; but there are a great
many other kinds of arguments, some of which have never been understood
by logicians until recent years. One important kind of argument is known
as the Disjunctive Syllogism, though it does not obey the rules of the
syllogism, or in any way resemble syllogisms."

The Disjunctive Syllogism is one having a disjunctive proposition in its
major premise. The disjunctive proposition also appears in the
conclusion when the disjunction in the major premise happens to contain
more than two terms. A disjunctive proposition, we have seen, is one
which possesses alternative predicates for the subject in which the
conjunction "_or_" (sometimes accompanied by "_either_") appears. As for
instance: "Lightning is sheet _or_ forked;" or, "Arches are _either_
round or pointed;" or, "Angles are either obtuse, or right angled, or
acute." The different things joined together by "or" are called
Alternatives, the term indicating that we may choose between the things,
and that if one will not answer our purpose we may take the other, or
one of the others if there be more than one _other_.

The _Rule regarding the Use of Disjunctive Syllogisms_ is that: "If one
or more alternatives be denied, the rest may still be affirmed." Thus if
we say that "A is B or C," or that "A is either B or C," we may _deny_
the B but still affirm the C. Some authorities also hold that "If we
affirm one alternative, we must deny the remainder," but this view is
vigorously disputed by other authorities. It would seem to be a valid
rule in cases where the term "either" appears as: "A is _either_ B _or_
C," because there seems to be an implication that one or the other alone
can be true. But in cases like: "A is B _or_ C," there may be a
possibility of _both being true_. Jevons takes this latter view, giving
as an example the proposition: "A Magistrate is a Justice-of-the-Peace,
a Mayor, or a Stipendiary Magistrate," but it does not follow that one
who is a Justice-of-the-Peace may not be at the same time a Mayor. He
states: "After affirming one alternative we can only deny the others _if
there be such a difference between them that they could not be true at
the same time_." It would seem that both contentions are at the same
time true, the example given by Jevons illustrating his contention, and
the proposition "The prisoner is either guilty or innocent" illustrating
the contentions of the other side.

A _Dilemma_ is a conditional syllogism whose Major Premise presents
some sort of alternative. Whately defines it as: "A conditional
syllogism with two or more antecedents in the major, and a disjunctive
minor." There being two mutually exclusive propositions in the Major
Premise, the reasoner is compelled to admit one or the other, and is
then caught between "the two horns of the dilemma."




CHAPTER XVIII.

REASONING BY ANALOGY


What is called Reasoning by Analogy is one of the most elementary forms
of reasoning, and the one which the majority of us most frequently
employ. It is a primitive form of hasty generalization evidencing in the
natural expectation that "things will happen as they have happened
before in like circumstances." The term as used in logic has been
defined as "Resemblance of relations; Resemblances of any kind on which
an argument falling short of induction may be founded." Brooks says:
"Analogy is that process of thought by which we infer that if two things
resemble each other in one or more particulars, they will resemble each
other in some other particular."

Jevons states the _Rule for Reasoning by Analogy_, as follows: "If two
or more things resemble each other in many points, they will probably
resemble each other also in more points." Others have stated the same
principle as follows: "When one thing resembles another in known
particulars, it will resemble it also in the unknown;" and "If two
things agree in several particulars, they will also agree in other
particulars."

There is a difference between generalization by induction, and by
analogy. In inductive generalization the rule is: "What is true of the
many is true of all;" while the rule of analogy is: "things that have
some things in common have other things in common." As Jevons aptly
remarks: "Reasoning by Analogy differs only in degree from that kind of
reasoning called 'Generalization.' When _many things_ resemble each
other in a _few properties_, we argue about them by Generalization. When
a _few things_ resemble each other in _many properties_, it is a case of
analogy." Illustrating Analogy, we may say that if in A we find the
qualities, attributes or properties called _a_, _b_, _c_, _d_, _e_, _f_,
_g_, respectively, and if we find that in B the qualities, etc., called
_a_, _b_, _c_, _d_, _e_, respectively, are present, then we may reason
by analogy that the qualities _f_ and _g_ must also belong to B.

Brooks says of this form of reasoning: "This principle is in constant
application in ordinary life and in science. A physician, in visiting a
patient, says this disease corresponds in several particulars with
typhoid fever, hence it will correspond in _all_ particulars, and _is_
typhoid fever. So, when the geologist discovers a fossil animal with
large, strong, blunt claws, he infers that it procured its food by
scratching or burrowing in the earth. It was by analogy that Dr.
Buckland constructed an animal from a few fossil bones, and when
subsequently the bones of the entire animal were discovered, his
construction was found to be correct." Halleck says: "In argument or
reasoning we are much aided by the habit of searching for hidden
resemblances.... The detection of such a relation cultivates thought. If
we are to succeed in argument, we must develop what some call a sixth
sense of such relations.... 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 flowering meadows, he is
cultivating our apprehension of relations, none the less valuable
because they are beautiful."

But the student must be on guard against the deceptive conclusions
sometimes arising from Reasoning by Analogy. As Jevons says: "In many
cases Reasoning by Analogy is found to be a very uncertain guide. In
some cases unfortunate mistakes are made. 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 gathering them. In Norway mushrooms are seldom seen, and are not
eaten; but when I once found a few there and had them cooked at an inn,
I was amused by the people of the inn, who went and collected toadstools
and wanted me to eat them also. This was clearly a case of mistaken
reasoning by analogy. Even brute animals reason in the same way in some
degree. The beaten dog fears every stick, and there are few dogs which
will not run away when you pretend to pick up a stone, even if there be
no stone to pick up." Halleck says: "Many false analogies are
manufactured, and it is excellent thought training to expose them. The
majority of people think so little that they swallow these false
analogies just as newly fledged robins swallow small stones dropped into
their open mouths.... This tendency to think as others do must be
resisted somewhere along the line, or there can be no progress." Brooks
says: "The argument from Analogy is plausible, but often deceptive. Thus
to infer that since American swans are white, the Australian swan is
white, gives a false conclusion, for it is really black. So to infer
that because John Smith has a red nose and is a drunkard, then Henry
Jones who also has a red nose is also a drunkard, would be a dangerous
inference.... Conclusions of this kind drawn from analogy are frequently
fallacious."

Regarding the _Rule for Reasoning from Analogy_, Jevons says: "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 closely two things resemble each other, the more likely it is that
they are the same in other respects, especially in points closely
connected with those observed.... In order to be clear about our
conclusions, we ought in fact never to rest satisfied with mere analogy,
but ought to try to discover the general laws governing the case. In
analogy we seem to reason from one fact to another fact without
troubling ourselves either with deduction or induction. But it is only
by a kind of guess that we do so; it is not really conclusive reasoning.
We ought properly to ascertain what general laws of nature are shown to
exist by the facts observed, and then infer what will happen according
to these laws.... We find that reasoning by analogy is not to be
depended upon, unless we make such an inquiry into the causes and laws
of the things in question, that we really employ inductive and deductive
reasoning."

Along the same lines, Brooks says: "The inference from analogy, like
that from induction, should be used with caution. Its conclusion must
not be regarded as certain, but merely as reaching a high degree of
probability. The inference from a part to a part, no more than from a
part to the whole, is attended with any rational necessity. To attain
certainty, we must show that the principles which lie at the root of the
process are either necessary laws of thought or necessary laws of
nature; both of which are impossible. Hence analogy can pretend to only
a high degree of probability. It may even reach a large degree of
certainty, but it never reaches necessity. We must, therefore, be
careful not to accept any inference from analogy as true until it is
proved to be true by actual observation and experiment, or by such an
application of induction as to remove all reasonable doubt."




CHAPTER XIX.

FALLACIES


A _Fallacy_ is: "An unsound argument or mode of arguing, which, while
appearing to be decisive of a question, is in reality not so; an
argument or proposition apparently sound, but really fallacious; a
fallacious statement or proposition, in which the error is not apparent,
and which is therefore likely to mislead or deceive; sophistry."

In Deductive Reasoning, we meet with two classes of Fallacies; namely,
(1) Fallacious Premise; and (2) Fallacious Conclusion. We shall now
consider each of these in turn.

_Fallacious Premise_ is in effect _an unwarranted assumption of
premises_. One of the most common forms of this kind of Fallacy is known
as "_Begging the Question_," the principle of which is the assumption of
a fundamental premise which is not conceded; the unwarrantable
assumption of that which is to be proved; or the assumption of that by
which it is to be proved, without proving it. Its most common form is
that of boldly stating some unproven fact, authoritatively and
positively, and then proceeding to use the statement as the major
premise of the argument, proceeding logically from that point. The
hearer perceiving the argument proceeding logically often fails to
remember that _the premise has been merely assumed_, without warrant and
without proof and omitting the hypothetical "_if_." One may proceed to
argue logically from the premise that "The moon is made of green
cheese," but the whole argument is invalid and fallacious because of the
fact that the person making it has "begged the question" upon an
unwarranted premise. Hyslop gives a good example of this form of fallacy
in the case of the proposition "Church and State should be united."
Proof being demanded the advocate proceeds to "beg the question" as
follows: "Good institutions should be united; Church and State are good
institutions; therefore, Church and State should be united." The
proposition that "Good institutions should be united" is fallacious,
being merely assumed and not proven. The proposition sounds reasonable,
and few will feel disposed to dispute it at first, but a little
consideration will show that while _some_ good institutions may well be
united, it is _not_ a general truth that _all_ should be so.

"Begging the Question" also often arises from _giving a name to a
thing_, and then assuming that we have _explained_ the thing. This is a
very frequent practice with many people--they try to _explain_ by merely
applying names. An example of this kind is had in the case of the person
who tried to explain why one could see through a pane of glass by saying
"because it is transparent." Or when one explains that the reason a
certain substance breaks easily is "because it is brittle." Moliere
makes the father of a dumb girl ask why his daughter is dumb. The
physician answers: "Nothing is more easy than to explain it; it comes
from her having lost the power of speech." "Yes, yes," objects the
father, "but the cause, if you please, why she has lost the power of
speech." The physician gravely replies: "All our best authors will tell
you that it is the impeding of the action of the tongue."

Jevons says: "The most frequent way, perhaps, in which we commit this
kind of fallacy is to employ names which imply that we disapprove of
something, and then argue that because it is such and such, it must be
condemned. When two sportsmen fall out in some manner relating to the
subject of game, one will, in all probability, argue that the act of the
other was 'unsportsmanlike,' and therefore should not have been done.
Here is to all appearance a correct syllogism:

"No unsportsmanlike act should be done; John Robinson's act was
unsportsmanlike: Therefore, John Robinson's act should not have been
done.

"This is quite correct in form; but it is evidently the mere semblance
of an argument. 'Unsportsmanlike' means _what a sportsman should not
do_. The point to be argued was whether the act fell within the
customary definition of _what was unsportsmanlike_."

Arising from "Begging the Question," and in fact a class of the latter,
is what is called "Reasoning in a Circle." In this form of fallacy one
assumes as proof of a proposition the proposition itself; or, uses the
conclusion to prove the premise. For instance: "This man is a rascal
because he is a rogue; and he is a rogue because he is a rascal." Or,
"It is warm because it is summer; and it is summer because it is warm."
Or "He never drinks to excess, because he is never intemperate in
drinking."

Brooks says: "Thus to argue that a party is good because it advocates
good measures, and that certain measures are good because they are
advocated by so excellent a party, is to reason in a circle. So when
persons argue that their church is the true one, because it was
established by God, and then argue that since it is the true church it
must have been founded by God, they fall into this fallacy. To argue
that 'the will is determined by the strongest motive' and to define the
strongest motive as 'that which influences the will,' is to revolve in a
circle of thought and prove nothing. Plato commits this error when he
argues the immortality of the soul from its simplicity, and afterwards
attempts to prove its simplicity from its immortality." It needs care to
avoid this error, for it is surprising how easily one falls into it.
Hyslop says: "The fallacy of Reasoning in a Circle occurs mostly in
long arguments where it can be committed without ready detection....
When it occurs in a long discourse it may be committed without easy
discovery. It is likely to be occasioned by the use of synonyms which
are taken to express more than the conception involved when they do
not." What is called a Vicious Circle is caused when the conclusion of
one syllogism is used for a proposition in another syllogism, which in
its turn comes to be used as a basis for the first or _original
syllogism_.

_Fallacious Conclusion_ is in effect _an unwarranted or irrelevant
assumption of a logical conclusion_. There are many forms of this
fallacy among which are the following:

_Shifting ground_, which consists in the pretence of proving one thing
while in reality merely a similar or related thing is being proved. In
this class is the argument that because a man is profane he must
necessarily be dishonest; or that because a man denies the inspiration
of the Scriptures he must be an atheist.

_Fallacious Questioning_, in which two or more related questions are
asked, and the answer of one is then applied to the other. For
instance: "You assert that the more civilized a community, the more
silk-hats are to be found in it?" "Yes." "Then, you state that silk-hats
are the promoters and cause of civilization in a community?" A question
of this kind is often so arranged that an answer either in the
affirmative or the negative will lead to a false or fallacious
inference. For instance, the question once asked a respectable citizen
on the witness stand: "Have you stopped beating your mother?" An answer
of either "Yes" or "No," was out of the question, for it would have
placed the witness in a false position, for he had never beaten his
mother, nor been accused of the same.

_Partial Proof_, in which the proof of a partial or related fact is used
to infer a proof of the whole fact or a related one. For instance, it is
fallacious to argue that a man has been guilty of drunkenness by merely
proving that he was seen entering a saloon.

_Appeal to Public Opinion_, in which the prejudices of the public are
appealed to rather than its judgment or reason. In politics and
theological argument this fallacy is frequent. It is no argument, and is
reprehensible.

_Appeal to Authority, or Reverence_, in which the reverence and respect
of the public for certain persons is used to influence their feelings in
place of their judgment or reason. For instance: "Washington thought
so-and-so, and therefore it must be right;" or "It is foolish to affirm
that Aristotle erred;" or "It has been believed by men for two thousand
years, that, etc;" or "What our fathers believed must be true." Appeals
of this kind may have their proper place, but they are fallacies
nevertheless, and not real argument.

_Appeal to Profession_, in which an appeal is made to practices,
principles or professions of the opponent, rather than to reason or
judgment. Thus we may argue that a certain philosophy or religion cannot
be sound or good, because certain people who hold it are not consistent,
or not worthy, moral or sober. This argument is often used effectively
against an opponent, and is valid against him personally. But it is no
valid argument against his philosophy or belief, because he may act in
violation of them, or he may change his practices and still adhere to
his beliefs--the two are not joined.

_Appeal to General Belief_, in which an appeal is made to general or
universal belief, although the same may be unsupported by proof. This is
quite common, but is no real argument. The common opinion may be
erroneous, as history proves. A few centuries ago this argument could
have been used in favor of the earth being flat, etc. A half-century ago
it was used against Darwin. Today it is being used against other new
ideas. It is a fallacy by its very nature.

_Appeal to Ignorance_, in which an appeal is made to the ignorance of
the opponent that his conviction may follow from his inability to prove
the contrary. It is virtually no argument that: "So-and-so must be true,
_because you cannot prove that it is not_." As Brooks says: "To argue
that there is no material world, because we cannot explain how the mind
knows it to exist, is the celebrated fallacy of Hume in philosophy. The
fact that we cannot find a needle in a haystack is no proof that it is
not there."

_Introduction of New Matter_, also called _Non Sequitur_, in which
matter is introduced into the conclusion that is not in the premises.
Hyslop gives the following example of it: "All men are _rational_;
Socrates is a man; therefore, Socrates is _noble_." De Morgan gives the
following more complex example: "Episcopacy is of Scripture origin; The
Church of England is the only Episcopal church in England; therefore,
the church established is the church that ought to be supported."

Other fallacies, resembling in some respects those above mentioned, are
as follows:

_Fallacy of Ambiguous Terms_, in which different meanings of the same
word are used to produce the fallacious argument. As Jevons says: "A
word with two distinct meanings _is really two words_."

_Confusion between Collective and General Meanings of a Term_, of which
Jevons says: "It would be obviously absurd to argue that because _all_
the books in the British Museum Library are sure to give information
about King Alfred, therefore any particular book will be sure to give
it. By '_all_ the books in the British Museum Library,' we mean all
_taken together_. There are many other cases where the confusion is not
so evident, and where great numbers of people are unable to see the
exact difference."

_Arguing from the Collective to the General_, in which the fallacy
consists of arguing that because something is true of the whole of a
group of things, therefore it is true of any of those things. Jevons
says: "_All_ the soldiers in a regiment may be able to capture a town,
but it is absurd to suppose that therefore _every_ soldier in the
regiment could capture the town single handed. White sheep eat a great
deal more than black sheep; but that is because there are so many more
of them."

_Uncertain Meaning of a Sentence_, from which confusion arises and
fallacious argument may spring. Jevons says: "There is a humorous way of
proving that a cat must have three tails: Because a cat has one tail
more than _no_ cat; and _no cat_ has two tails; therefore, _any_ cat has
three tails." Here the fallacy rests upon a _punning_ interpretation of
"no."

_Proving the Wrong Conclusion_, in which the attempt to confuse
conclusions is made, with the result that some people will imagine that
the case is established. Jevons says: "This was the device of the
Irishman, who was charged with theft on the evidence of three witnesses,
who had seen him do it; he proposed to call _thirty_ witnesses who had
_not_ seen him do it. Equally logical was the defense of the man who was
called a materialist, and who replied, 'I am not a materialist; I am a
barber.'"

_Fallacy of Unsuccessful Argument_, in which is attempted the illogical
conclusion that _because a certain argument has failed the opposite
conclusion is proven_. This fallacy is quite common, especially in cases
of juries. One side fails to prove certain contentions, and the jury
leaps to the conclusion that the opposite contention must be correct.
This is clearly fallacious, for there is always the possibility of a
_third_ explanation. In the case of a claim of _alibi_ juries are apt to
fall into this fallacy. The failure of the attempt to establish an
_alibi_ is often held to be in the nature of proof of the guilt of the
accused. Old trial lawyers assert that a failure to establish a claimed
_alibi_ tends to injure the chance of the accused more than direct
evidence against him. Yet, as all logical reasoners will see, there is
no logical validity in any such inference. As Jevons has well said: "_No
number of failures in attempting to prove a proposition really disprove
it_." At the end of each failure the case simply stands in the same
position as before the attempt; _i.e._, "not proven."

_All Violations of the Rules of the Syllogism_ constitute fallacies, as
may be seen by forming a syllogism in violation of one or more of the
rules.

The logicians, particularly those of ancient times, took great pains to
discover and _name_ new variations of fallacies, many of which were
hair-splitting in nature, and not worthy of being considered seriously.
Some of those which we have enumerated may possibly be open to the same
criticism, but we have omitted many of the worst offenders against
practical common sense. An understanding of the fundamental Laws of
Reasoning is sufficient to expose and unmask all fallacies, and such
understanding is far more valuable than the memorizing of the _names_ of
hair-splitting fallacies which would not deceive a child.

In addition to the above stated fallacies of Deductive Reasoning, there
are other fallacies which are met with in _Inductive Reasoning_. Let us
briefly consider them.

_Hasty and False Generalization_ is a common fallacy of this class.
Persons sometimes see certain qualities in a few individuals of a class,
and mistakenly infer that _all_ the individuals in that class must
possess these same qualities. Travelers frequently commit this fallacy.
Englishmen visiting the United States for a few weeks have been known to
publish books upon their return home making the most ridiculous
generalizations regarding the American people, their assertions being
based upon the observation of a few scattered individuals, often not at
all representative. Americans traveling abroad commit similar errors. A
flying trip through a country does not afford the proper opportunity for
correct generalization. As Brooks says: "No hypothesis should be
accepted as true until the facts are so numerous that there can be no
doubt of its being proved."

_Fallacies of Observation_ result from incorrect methods of observation
among which may be mentioned the following: (1) _Careless Observation_,
or inexact perception and conception; (2) _Partial Observation_, in
which one observes only a part of the thing or fact, omitting the
remainder, and thus forming an incomplete and imperfect concept of the
thing or fact; (3) _Neglect of Exceptions and Contradictory Facts_, in
which the exceptions and contradictory facts are ignored, thereby giving
undue importance to the observed facts; (4) _Assumption of Facts_ which
are not real facts, or the assumption of the truth of things which are
untrue; (5) _Confusing of Inferences with Facts_, which is most
unwarrantable.

_Fallacies of Mistaken Cause_ result from the assumption of a thing as a
cause, when it is not so, of which the following are familiar examples:
_Substituting the Antecedent for the Cause_, which consists in assuming
a mere antecedent thing for a _cause_ of another thing. Thus one might
assume that the crowing of the cock was the _cause_ of daybreak, because
it _preceded_ it; or that a comet was the cause of the plague which
followed its appearance; or in the actual case in which a child reasoned
that doctors _caused_ deaths, because observation had shown that they
always visited persons before they died; or that crops failed because a
President of a certain political party had been inaugurated a few months
before. Some fallacies of everyday reasoning are quite as illogical as
those just mentioned. _Substituting the Symptom for the Cause_, which
consists in assuming as a _cause_ some mere symptom, sign or incident of
the real cause. To assume that the pimples of measles were the _cause_
of the disease, would be to commit a fallacy of this kind. We have
mentioned elsewhere the fallacy which would assume silk-hats to be the
cause of Civilization, instead of being a mere incident of the latter.
Politicians are fond of assuming certain incidents or signs of a period,
as being the _causes_ of the prosperity, culture and advancement of the
period, or the reverse. One might argue, with equal force, that
automobiles were the causes of national prosperity, pointing to the fact
that the more automobiles to be seen the better the times. Or, that
straw hats produced hot weather, for similar reasons.

_The Fallacy of Analogy_ consists in assuming a resemblance or identity,
where none exists. We have spoken of this in another chapter. Brooks
says, also: "It is a fallacy to carry an analogy too far; as to infer
from the parable of the praying of the importunate woman that God
resembles the unjust judge."

In conclusion, we would call your attention to the following words from
Jevons, in which he expresses the gist of the matter: "It is impossible
too often to remind people that, on the one hand, _all correct reasoning
consists in substituting like things for like things_, and inferring
that what is true of one will be true of all which are similar to it in
the points of resemblance concerned in the matter. On the other hand,
_all incorrect reasoning consists in putting one thing for another where
there is not the requisite likeness_. It is the purpose of the rules of
deductive and inductive logic to enable us to judge as far as possible
when we are thus rightly or wrongly reasoning from some things to
others."


FINIS.




TRANSCRIBER'S NOTE:


Obvious typos and printer errors have been corrected without comment. In
addition to obvious errors, the following changes have been made:

  Page 18: "Idea" changed to "Ideas" in the phrase, "... forming
    Concepts or General Ideas."

  Page 71: "infuoria" changed to "infusoria" in the phrase, "... the
    microscopic infusoria...."

  Page 135: "disciple" changed to "discipline" in the phrase, "...
    necessity of discipline for invention...."

Other than the above changes, no attempt has been made to correct common
spelling, punctuation, grammar, etc. The author's usage is preserved as
printed in the original publication.





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