THOUGHT-CULTURE/PART 10
CHAPTER X.
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:
Dwelling-House |
||||
| |
||||
| |
| |
| |
| |
| |
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:—
|
Dwelling-House |
||||||||||||||||||||||
|
|
|
|||||||||||||||||||||
|
|
|
|
||||||||||||||||||||
Brick |
Not-Brick |
||||||||||||||||||||||
|
|
||||||||||||||||||||||
|
|
|
|||||||||||||||||||||
Stone |
Not-Stone |
||||||||||||||||||||||
|
|
||||||||||||||||||||||
|
|
|
|||||||||||||||||||||
Wooden |
Not-Wooden |
||||||||||||||||||||||
|
|
||||||||||||||||||||||
|
|
|
|||||||||||||||||||||
Iron |
Not-Iron |
"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 he 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 text book 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.
Comments
Post a Comment