GENERALIZATION
We have seen that Sensation is translated
or interpreted into Perception; and that from
the Percepts so created we may "draw off,"
or separate, various qualities, attributes and
properties by the analytical process we call
Abstraction. Abstraction, we have seen, thus
constitutes the first step in the process of what
is called Understanding. The second step is
called Generalization or Conception.
Generalization, or Conception, is that faculty
of the mind by which we are able to combine
and group together several particular
ideas into one general idea. Thus when we
find a number of particular objects possessing
the same general qualities, attributes or properties,
we proceed to classify them by the
process of Generalization. For instance, in a
number of animals possessing certain general
and common qualities we form a concept of a
class comprising those particular animals.
Thus in the concept of cow, we include all cows—we
know them to be cows because of their
possession of certain general class qualities
which we include in our concept of cow. The
particular cows may vary greatly in size,
color and general appearance, but they possess
the common general qualities which we
group together in our general concept of cow.
Likewise by reason of certain common and
general qualities we include in our concept of
"Man," all men, black, white, brown, red or
yellow, of all races and degrees of physical
and mental development. From this generic
concept we may make race concepts, dividing
men into Indians, Caucasians, Malays, Negroes,
Mongolians, etc. These concepts in turn
may be divided into sub-races. These sub-divisions
result from an analysis of the great concept.
The great concept is built up by synthesis
from the individuals, through the sub-divisions
of minor concepts. Or, again, we may
form a concept of "Napoleon Bonaparte"
from the various qualities and characteristics
which went to make up that celebrated man.
The product of Generalization or Conception
is called a Concept. A Concept is expressed
in a word, or words, called "A Term."
A Concept is more than a mere word—it is a
general idea. And a Term is more than a
mere word—it is the expression of a general
idea.
A Concept is built up from the processes of
Perception, Abstraction, Comparison and
Generalization. We must first perceive; then
analyze or abstract qualities; then compare
qualities; then synthesize or classify according
to the result of the comparison of qualities.
By perceiving and comparing the qualities
of various individual things, we notice
their points of resemblance and difference—the
points wherein they agree or disagree—wherein
they are alike or unlike. Eliminating
by abstraction the points in which they differ
and are unlike; and, again by abstraction, retaining
in consideration the points in which
they resemble and are alike; we are able to
group, arrange or classify these "alike
things" into a class-idea large enough to embrace
them all. This class-idea is what is
known as a General Idea or a Concept. This
Concept we give a general name, which is
called a Term. In grammar our particular
ideas arising from Percepts are usually denoted
by proper nouns—our general ideas
arising from Concepts are usually denoted
by common nouns. Thus "John Smith" (particular;
proper noun) and "Man" (general;
common noun). Or "horse" (general; common),
and "Dobbin" (particular; proper).
It will be seen readily that there must be
lower and higher concepts. Every class contains
within itself lower classes. And every
class is, itself, but a lower class in a higher
one. Thus the high concept of "animal" may
be analyzed into "mammal," which in turn
is found to contain "horse," which in turn
may be sub-divided into special kinds of
horses. The concept "plant" may be sub-divided
many times before the concept "rose"
is obtained, and the latter is capable of sub-division
into varieties and sub-varieties, until
at last a particular flower is reached. Jevons
says: "We classify things together whenever
we observe that they are like each other in any
respect and, therefore, think of them together....
In classifying a collection of objects,
we do not merely put together into groups
those which resemble each other, but we also
divide each class into smaller ones in which
the resemblance is more complete. Thus the
class of white substances may be divided into
those which are solid and those which are
fluid, so that we get the two minor classes of
solid-white, and fluid-white substances. 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."
Every Genus is a Species of the class next
higher than itself; and every Species is a
Genus of the classes lower than itself. Thus
it would seem that the extension in either direction
would be infinite. But, for the purposes
of finite thought, the authorities teach
that there must be a Highest Genus, which
cannot be the Species of a higher class, and
which is called the Summum Genus. The
Summum Genus is expressed by terms such
as the following: "Being;" "Existence;"
"The Absolute;" "Something;" "Thing;"
"The Ultimate Reality," or some similar term
denoting the state of being ultimate. Likewise,
at the lowest end of the scale we find
what are called the Lowest Species, or Infima
Species. The Infima Species are always individuals.
Thus we have the individual at one
end of the scale; and The Absolute at the
other. Beyond these limits the mind of man
cannot travel.
There has been much confusion in making
classifications and some ingenious plans have
been evolved for simplifying the process.
That of Jevons is perhaps the simplest, when
understood. This authority says: "All these
difficulties are avoided in the perfect logical
method of dividing each Genus into two Species,
and not more than two, so that one species
possesses a particular quality, and the other
does not. Thus if I divide dwelling-houses
into those which are made of brick and those
which are not made of brick, I am perfectly
safe and nobody can find fault with me....
Suppose, for instance, that I divide dwelling-houses
as below:
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| Brick |
Stone |
Earth |
Iron |
Wood |
"The evident objection will at once be made,
that houses may be built of other materials
than those here specified. In Australia,
houses are sometimes made of the bark of
gum-trees; the Esquimaux live in snow
houses; tents may be considered as canvas
houses, and it is easy to conceive of houses
made of terra-cotta, paper, straw, etc. All
logical difficulties will, however, be avoided if
I never make more than two species at each
step, in the following way:—
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Dwelling-House |
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| Brick |
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Not-Brick |
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Stone |
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Not-Stone |
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Wooden |
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Iron |
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"It is quite certain that I must in this division
have left a place for every possible kind
of house; for if a house is not made of brick,
nor stone, nor wood, nor iron, it yet comes under
the species at the right hand, which is not-iron,
not-wooden, not-stone, and not-brick....
This manner of classifying things may
seem to be inconvenient, but it is in reality the
only logical way."
The student will see that the process of
Classification is two-fold. The first is by
Analysis, in which the Genus is divided into
Species by reason of differences. The second
is by Synthesis, in which individuals are
grouped into Species, and Species into the
Genus, by reason of resemblances. Moreover,
in building up general classes, which is known
as Generalization, we must first analyze the
individual in order to ascertain its qualities,
attributes and properties, and then synthesize
the individual with other individuals possessing
like qualities, properties or attributes.
Brooks says of Generalization: "The mind
now takes the materials that have been furnished
and fashioned by comparison and
analysis and unites them into one single mental
product, giving us the general notion or
concept. The mind, as it were, brings together
these several attributes into a bunch or
package and then ties a mental string around
it, as we would bunch a lot of roses or cigars....
Generalization is an ascending process.
The broader concept is regarded as higher
than the narrower concept; a concept is considered
as higher than 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,
that of Being. Having reached the pinnacle
of Generalization, we may descend the ladder
by reversing the process through which we
ascend."
A Concept, then, is seen to be a general idea.
It is a general thought that embraces all the
individuals of its own class and has in it all
that is common to its own class, while it resembles
no particular individual of its class
in all respects. Thus, a concept of animal contains
within itself the minor concepts of all
animals and the animal-quality of all animals—yet
it differs from the percept of any one
particular animal and the minor concepts of
minor classes of animals. Consequently a
concept or general idea cannot be imaged or
mentally pictured. We may picture a percept
of any particular thing, but we cannot picture
a general idea or concept because the latter
does not partake of the particular qualities of
any of its class, but embraces all the general
qualities of the class. Try to picture the general
idea, or concept, of Man. You will find
that any attempt to do so will result in the
production of merely a man—some particular
man. If you give the picture dark hair, it will
fail to include the light-haired men; if you
give it white skin, it will slight the darker-skinned
races. If you picture a stout man,
the thin ones are neglected. And so on in
every feature. It is impossible to form a correct
general class picture unless we include
every individual in it. The best we can do is
to form a sort of composite image, which at
the best is in the nature of a symbol representative
of the class—an ideal image to make
easier the idea of the general class or term.
From the above we may see the fundamental
differences between a Percept and a Concept.
The Percept is the mental image of a
real object—a particular thing. The Concept
is merely a general idea, or general notion, of
the common attributes of a class of objects or
things. A Percept arises directly from sense-impressions,
while a Concept is, in a sense, a
pure thought—an abstract thing—a mental
creation—an ideal.
A Concrete Concept is a concept embodying
the common qualities of a class of objects, as
for instance, the concrete concept of lion, in
which the general class qualities of all lions
are embodied. An Abstract Concept is a concept
embodying merely some one quality generally
diffused, as for instance, the quality of
fierceness in the general class of lions. Rose
is a concrete concept; red, or redness, is an
abstract concept. It will aid you in remembering
this distinction to memorize Jevons' rule:
"A Concrete Term is the name of a Thing; an
Abstract Term is the name of a Quality of a
Thing."
A Concrete Concept, including all the particular
individuals of a class, must also contain
all the common qualities of those individuals.
Thus, such a concept is composed of the
ideas of the particular individuals and of their
common qualities, in combination and union.
From this arises the distinctive terms known
as the content, extension and intension of concepts,
respectively.
The content of a concept is all that it includes—its
full meaning. The extension of a
concept depends upon its quantity aspect—it
is its property of including numbers of individual
objects within its content. The intension
of a concept depends upon its quality aspect—it
is its property of including class or
common qualities, properties or attributes
within its content.
Thus, the extension of the concept horse
covers all individual horses; while its intension
includes all qualities, attributes, and
properties common to all horses—class qualities
possessed by all horses in common, and
which qualities, etc., make the particular animals
horses, as distinguished from other animals.
It follows that the larger the number of particular
objects in a class, the smaller must be
the number of general class qualities—qualities
common to all in the class. And, that the
larger the number of common class qualities,
the smaller must be the number of individuals
in the class. As the logicians express it, "the
greater the extension, the less the intension;
the greater the intension, the less the extension."
Thus, animal is narrow in intension,
but very broad in extension; for while there
are many animals there are but very few qualities
common to all animals. And, horse is
narrower in extension, but broader in intension;
for while there are comparatively few
horses, the qualities common to all horses are
greater.
The cultivation of the faculty of Generalization,
or Conception, of course, depends
largely upon exercise and material, as does
the cultivation of every mental faculty, as we
have seen. But there are certain rules, methods
and ideas which may be used to advantage
in developing this faculty in the direction of
clear and capable work. This faculty is developed
by all of the general processes of
thought, for it forms an important part of all
thought. But the logical processes known as
Analysis and Synthesis give to this faculty
exercise and employment particularly adapted
to its development and cultivation. Let us
briefly consider these processes.
Logical Analysis is the process by which we
examine and unfold the meaning of Terms. A
Term, you remember, is the verbal expression
of a Concept. In such analysis we endeavor
to unfold and discover the quality-aspect and
the quantity-aspect of the content of the concept.
We seek, thereby, to discover the particular
general idea expressed; the number of
particular individuals included therein; and
the properties of the class or generalization.
Analysis depends upon division and separation.
Development in the process of Logical
Analysis tends toward clearness, distinctness,
and exactness in thought and expression.
Logical Analysis has two aspects or phases,
as follows: (1) Division, or the separation of
a concept according to its extension, as for instance
the analysis of a genus into its various
species; and (2) Partition, or the separation
of a concept into its component qualities, properties
and attributes, as for instance, the analysis
of the concept iron into its several qualities
of color, weight, hardness, malleability,
tenacity, utility, etc.
There are certain rules of Division which
should be observed, the following being a simple
statement of the same:
I. The division should be governed by a uniform
principle. For instance it would be illogical
to first divide men into Caucasians,
Mongolians, etc., and then further sub-divide
them into Christians, Pagans, etc., for the first
division would be according to the principle of
race, and the second according to the principle
of religion. Observing the rule of the "uniform
principle" we may divide men into races,
and sub-races, and so on, without regard to
religion; and we may likewise divide men according
to their respective religions, and then
into minor denominations and sects, without
regard to race or nationality. The above rule
is frequently violated by careless thinkers and
speakers.
II. The division should be complete and
exhaustive. For instance, the analysis of a
genus should extend to every known species
of it, upon the principle that the genus is
merely the sum of its several species. A textbook
illustration of a violation of this rule is
given in the case of the concept actions, when
divided into good-actions and bad-actions, but
omitting the very important species of indifferent-actions.
Carelessness in observance
of this rule leads to fallacious reasoning and
cloudy thinking.
III. The division should be in logical sequence.
It is illogical to skip or pass over intermediate
divisions, as for instance, when we
divide animals into horses, trout and swallows,
omitting the intermediate division into
mammals, fish and birds. The more perfect
the sequence, the clearer the analysis and the
thought resulting therefrom.
IV. The division should be exclusive.
That is, the various species divided from a
genus, should be reciprocally exclusive—should
exclude one another. Thus to divide
mankind into male, men and women, would be
illogical, because the class male includes men.
The division should be either: "male and female;"
or else: "men, women, boys, girls."
The exercise of Division along these lines,
and according to these rules, will tend to improve
one's powers of conception and analysis.
Any class of objects—any general concept—may
be used for practice. A trial will
show you the great powers of unfoldment contained
within this simple process. It tends to
broaden and widen one's conception of almost
any class of objects.
There are also several rules for Partition
which should be observed, as follows:
I. The partition should be complete and
exhaustive. That is, it should unfold the full
meaning of the term or concept, so far as is
concerned its several general qualities, properties
and attributes. But this applies only
to the qualities, properties and attributes
which are common to the class or concept, and
not to the minor qualities which belong solely
to the various sub-divisions composing the
class; nor to the accidental or individual qualities
belonging to the separate individuals in
any sub-class. The qualities should be essential
and not accidental—general, not particular.
A famous violation of this rule was had
in the case of the ancient Platonic definition
of "Man" as: "A two-legged animal without
feathers," which Diogenes rendered absurd
by offering a plucked chicken as a "man" according
to the definition. Clearness in
thought requires the recognition of the distinction
between the general qualities and the
individual, particular or accidental qualities.
Red-hair is an accidental quality of a particular
man and not a general quality of the class
man.
II. The partition should consider the qualities,
properties and attributes, according to
the classification of logical division. That is,
the various qualities, properties and attributes
should be considered in the form of
genus and species, as in Division. In this
classification, the rules of Division apply.
It will be seen that there is a close relationship
existing between Partition and Definition.
Definition is really a statement of the
various qualities, attributes, and properties of
a concept, either stated in particular or else
in concepts of other and larger classes. There
is perhaps no better exercise for the cultivation
of clear thought and conception than Definition.
In order to define, one must exercise
his power of analysis to a considerable extent.
Brooks says: "Exercises in logical definition
are valuable in unfolding our conception.
Logical definition, including both the genus
and the specific difference, gives clearness,
definiteness and adequacy to our conceptions.
It separates a conception from all other conceptions
by fixing upon and presenting the essential
and distinctive property or properties
of the conception defined. The value of exercises
in logical definition is thus readily
apparent."
If the student will select some familiar term
and endeavor to define it correctly, writing
down the result, and will then compare the
latter with the definition given in some standard
dictionary, he will see a new light regarding
logical definition. Practice in definition,
conducted along these lines, will cultivate the
powers of analysis and conception and will,
at the same time, tend toward the acquiring of
correct and scientific methods of thought and
clear expression.
Hyslop gives the following excellent Rules
of Logical Definition, which should be followed
by the student in his exercises:
"I. A definition should state the essential
attributes of the species defined.
"II. A definition must not contain the name
or word defined. Otherwise the definition is
called a circulus in definiendo (defining in a
circle).
"III. The definition must be exactly equivalent
to the species defined.
"IV. A definition should not be expressed
in obscure, figurative or ambiguous language.
"V. A definition must not be negative
when it can be affirmative."
Logical Synthesis is the exact opposite of
Logical Analysis. In the latter we strive to
separate and take apart; in the former we
strive to bind together and combine the particulars
into the general. Beginning with individual
things and comparing them with each
other according to observed points of resemblance,
we proceed to group them into species
or narrow classes. These classes, or species,
we then combine with similar ones, into a
larger class or genus; and then, according to
the same process, into broader classes as we
have shown in the first part of this chapter.
The process of Synthesis is calculated to
develop and cultivate the mind in several directions
and exercises along these lines will
give a new habit and sense of orderly arrangement,
which will be most useful to the student
in his every-day life. Halleck says: "Whenever
a person is comparing a specimen to see
whether it may be put in the same class with
other specimens, he is thinking. Comparison
is an absolutely essential factor of thought,
and classification demands comparison. The
man who has not properly classified the myriad
individual objects with which he has to
deal, must advance like a cripple. He, only,
can travel with seven-league boots, who has
thought out the relations existing between
these stray individuals and put them into their
proper classes. In a minute a business man
may put his hand on any one of ten thousand
letters if they are properly classified. In the
same way, the student of history, sociology or
any other branch, can, if he studies the subjects
aright, have all his knowledge classified
and speedily available for use.... In this
way, we may make our knowledge of the world
more minutely exact. We cannot classify
without seeing things under a new aspect."
The study of Natural History, in any or all
of its branches, will do much to cultivate the
power of Classification. But one may practice
classification with the objects around him
in his every-day life. Arranging things mentally,
into small classes, and these into larger,
one will soon be able to form a logical connection
between particular ideas and general
ideas; particular objects and general classes.
The practice of classification gives to the mind
a constructive turn—a "building-up" tendency,
which is most desirable in these days of
construction and development. Regarding
some of the pitfalls of classification, Jevons
says:
"In classifying things, we must take great
care not to be misled by outward resemblances.
Things may seem to be very much like each
other which are not so. Whales, porpoises,
seals and several other animals live in the sea
exactly like fish; they have a similar shape
and are usually classed among fish. People
are said to go whale-fishing. Yet these animals
are not really fish at all, but are much
more like dogs and horses and other quadrupeds
than they are like fish. They cannot live
entirely under water and breathe the air contained
in the water like fish, but they have to
come up to the surface at intervals to take
breath. Similarly, we must not class bats
with birds because they fly about, although
they have what would be called wings; these
wings are not like those of birds and in truth
bats are much more like rats and mice than
they are like birds. Botanists used at one
time to classify plants according to their size,
as trees, shrubs or herbs, but we now know
that a great tree is often more similar in its
character to a tiny herb than it is to other
great trees. A daisy has little resemblance
to a great Scotch thistle; yet the botanist regards
them as very similar. The lofty growing
bamboo is a kind of grass, and the sugarcane
also belongs to the same class with wheat
and oats."
Remember that analysis of a genus into its
component species is accomplished by a separation
according to differences; and species
are built up by synthesis into a genus because
of resemblances. The same is true regarding
individual and species, building up in accordance
to points of resemblance, while analysis
or separation is according to points of difference.
The use of a good dictionary will be advantageous
to the student in developing the power
of Generalization or Conception. Starting
with a species, he may build up to higher and
still higher classes by consulting the dictionary;
likewise, starting with a large class, he
may work down to the several species composing
it. An encyclopedia, of course, is still
better for the purpose in many cases. Remember
that Generalization is a prime requisite
for clear, logical thinking. Moreover, it
is a great developer of Thought.