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:

"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:—

"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.