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 a.n.a.lytical process we call Abstraction. Abstraction, we have seen, thus const.i.tutes 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 _cla.s.sify_ 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 cla.s.s 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 cla.s.s 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 a.n.a.lysis 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 a.n.a.lyze or abstract qualities; then compare qualities; then synthesize or cla.s.sify 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 cla.s.sify these "_alike things_" into _a cla.s.s-idea_ large enough to embrace them all.

This cla.s.s-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 cla.s.s contains within itself lower cla.s.ses. And every cla.s.s is, itself, but a lower cla.s.s in a higher one. Thus the high concept of "animal" may be a.n.a.lyzed 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 cla.s.sify things together whenever we observe that they are like each other in any respect and, therefore, think of them together.... In cla.s.sifying a collection of objects, we do not merely put together into groups those which resemble each other, but we also divide each cla.s.s into smaller ones in which the resemblance is more complete. Thus the cla.s.s of _white substances_ may be divided into those which are solid and those which are fluid, so that we get the two minor cla.s.ses of solid-white, and fluid-white substances. It is desirable to have names by which to show that one cla.s.s is contained in another and, accordingly, we call the cla.s.s 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 cla.s.s next higher than itself; and every Species is a Genus of the cla.s.ses 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 cla.s.s, 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 cla.s.sifications 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 n.o.body 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 cla.s.sifying things may seem to be inconvenient, but it is in reality the only logical way."

The student will see that the process of Cla.s.sification is two-fold. The first is by a.n.a.lysis, 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 cla.s.ses, which is known as Generalization, we must first _a.n.a.lyze_ 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 a.n.a.lysis 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 cla.s.s. Having formed a number of lower cla.s.ses, we compare them as we did individuals and generalize them into higher cla.s.ses. We perform the same process with these higher cla.s.ses and thus proceed until we are at last arrested in the highest cla.s.s, 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 cla.s.s and has in it all that is common to its own cla.s.s, while it resembles _no_ particular individual of its cla.s.s 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 cla.s.ses 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 cla.s.s, but embraces all the general qualities of the cla.s.s. 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 cla.s.s 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 cla.s.s--an ideal image to make easier the _idea_ of the general cla.s.s 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 cla.s.s 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 cla.s.s of objects, as for instance, the concrete concept of _lion_, in which the general cla.s.s 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 cla.s.s 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 cla.s.s, 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 _quant.i.ty_ 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 cla.s.s 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--cla.s.s 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 cla.s.s, the smaller must be the number of general cla.s.s qualities--qualities common to all in the cla.s.s. And, that the larger the number of common cla.s.s qualities, the smaller must be the number of individuals in the cla.s.s. 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 a.n.a.lysis and Synthesis give to this faculty exercise and employment particularly adapted to its development and cultivation. Let us briefly consider these processes.

_Logical a.n.a.lysis_ 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 a.n.a.lysis we endeavor to unfold and discover the _quality-aspect_ and the _quant.i.ty-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 cla.s.s or generalization. a.n.a.lysis depends upon division and separation. Development in the process of Logical a.n.a.lysis tends toward clearness, distinctness, and exactness in thought and expression. Logical a.n.a.lysis has two aspects or phases, as follows: (1) _Division_, or the separation of a concept according to its _extension_, as for instance the a.n.a.lysis of a genus into its various species; and (2) _Part.i.tion_, or the separation of a concept into its component qualities, properties and attributes, as for instance, the a.n.a.lysis 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 a.n.a.lysis 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 ill.u.s.tration 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 pa.s.s 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 a.n.a.lysis 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 cla.s.s _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 a.n.a.lysis.

Any cla.s.s 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 cla.s.s of objects.

There are also several rules for Part.i.tion which should be observed, as follows:

I. _The part.i.tion 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 cla.s.s or concept, and not to the minor qualities which belong solely to the various sub-divisions composing the cla.s.s; nor to the accidental or individual qualities belonging to the separate individuals in any sub-cla.s.s. 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 cla.s.s _man_.

II. _The part.i.tion should consider the qualities, properties and attributes_, according to the cla.s.sification 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 cla.s.sification, the rules of Division apply.

It will be seen that there is a close relationship existing between Part.i.tion 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 cla.s.ses.

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 a.n.a.lysis 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 a.n.a.lysis 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 a.n.a.lysis. 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 cla.s.ses. These cla.s.ses, or species, we then combine with similar ones, into a larger cla.s.s or genus; and then, according to the same process, into broader cla.s.ses as we have shown in the first part of this chapter.