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 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.