In the graded divisions of Natural History genus and species are fixed names for certain grades. Thus: Vertebrates form a "division"; the next subdivision, e.g., Mammals, Birds, Reptiles, etc., is called a "class"; the next, e.g., Rodents, Carnivora, Ruminants, an "order"; the next, e.g., Rats, Squirrels, Beavers, a "genus"; the next, e.g., Brown rats, Mice, a "species".
Vertebrates (division).
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Mammals, Birds, Reptiles, etc. (class).
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Rodents, Ruminants, Carnivors, etc. (order).
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Rats, Squirrels, Beavers, etc. (genus).
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Brown rats, Mice, etc. (species).
If we subdivide a large class into smaller classes, and, again, subdivide these subdivisions, we come at last to single objects.
Men
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Europeans, Asiatics, etc.
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Englishmen, Frenchmen, etc.
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John Doe, Richard Roe, etc.
A table of higher and lower classes arranged in order has been known from of old as a tree of division or classification. The following is Porphyry's "tree":—
The single objects are called Individuals, because the division cannot be carried farther. The highest class is technically the Summum Genus, or Genus generalissimum; the next highest class to any species is the Proximum Genus; the lowest group before you descend to individuals is the Infima Species, or Species specialissima.
The attribute or attributes whereby a species is distinguished from other species of the same genus, is called its differentia or differentiæ. The various species of houses are differentiated by their several uses, dwelling-house, town-house, ware-house, public-house. Poetry is a species of Fine Art, its differentia being the use of metrical language as its instrument.
A lower class, indicated by the name of its higher class qualified by adjectives or adjective phrases expressing its differential property or properties, is said to be described per genus et differentiam. Examples: "Black-bird," "note-book," "clever man," "man of Kent," "eminent British painter of marine subjects". By giving a combination of attributes common to him with nobody else, we may narrow down the application of a name to an individual: "The Commander-in-Chief of the British forces at the battle of Waterloo".
Other attributes of classes as divided and defined, have received technical names.
An attribute common to all the individuals of a class, found in that class only, and following from the essential or defining attributes, though not included among them, is called a Proprium.
An attribute that belongs to some, but not to all, or that belongs to all, but is not a necessary consequence of the essential attributes, is called an Accident.
The clearest examples of Propria are found in mathematical figures. Thus, the defining property of an equilateral triangle is the equality of the sides: the equality of the angles is a proprium. That the three angles of a triangle are together equal to two right angles is a proprium, true of all triangles, and deducible from the essential properties of a triangle.
Outside Mathematics, it is not easy to find propria that satisfy the three conditions of the definition. It is a useful exercise of the wits to try for such. Educability—an example of the proprium in mediæval text-books—is common to men, and results from man's essential constitution; but it is not peculiar; other animals are educable. That man cooks his food is probably a genuine proprium.
That horses run wild in Thibet: that gold is found in California: that clergymen wear white ties, are examples of Accidents. Learning is an accident in man, though educability is a proprium.
What is known technically as an Inseparable Accident, such as the black colour of the crow or the Ethiopian, is not easy to distinguish from the Proprium. It is distinguished only by the third character, deducibility from the essence.2
Accidents that are both common and peculiar are often useful for distinguishing members of a class. Distinctive dresses or badges, such as the gown of a student, the hood of a D.D., are accidents, but mark the class of the individual wearer. So with the colours of flowers.
Genus, Species, Differentia, Proprium, and Accidens have been known since the time of Porphyry as the Five Predicables. They are really only terms used in dividing and defining. We shall return to them and endeavour to show that they have no significance except with reference to fixed schemes, scientific or popular, of Division or Classification.
Given such a fixed scheme, very nice questions may be raised as to whether a particular attribute is a defining attribute, or a proprium, or an accident, or an inseparable accident. Such questions afford great scope for the exercise of the analytic intellect.
We shall deal more particularly with degrees of generality when we come to Definition. This much has been necessary to explain an unimportant but much discussed point in Logic, what is known as the inverse variation of Connotation and Denotation.
Connotation and Denotation are often said to vary inversely in quantity. The larger the connotation the smaller the denotation, and vice versâ. With certain qualifications the statement is correct enough, but it is a rough compendious way of expressing the facts and it needs qualification.
The main fact to be expressed is that the more general a name is, the thinner is its meaning. The wider the scope, the shallower the ground. As you rise in the scale of generality, your classes are wider but the number of common attributes is less. Inversely, the name of a species has a smaller denotation than the name of its genus, but a richer connotation. Fruit-tree applies to fewer objects than tree, but the objects denoted have more in common: so with apple and fruit-tree, Ribston Pippin and apple.
Again, as a rule, if you increase the connotation you contract the area within which the name is applicable. Take any group of things having certain attributes in common, say, men of ability: add courage, beauty, height of six feet, chest measurement of 40 inches, and with each addition fewer individuals are to be found possessing all the common attributes.
This is obvious enough, and yet the expression inverse variation is open to objection. For the denotation may be increased in a sense without affecting the connotation. The birth of an animal may be said to increase the denotation: every year thousands of new houses are built: there are swarms of flies in a hot summer and few in a cold. But all the time the connotation of animal, house, or fly remains the same: the word does not change its meaning.
It is obviously wrong to say that they vary in inverse proportion. Double or treble the number of attributes, and you do not necessarily reduce the denotation by one-half or one-third.
It is, in short, the meaning or connotation that is the main thing. This determines the application of a word. As a rule if you increase meaning, you restrict scope. Let your idea, notion, or concept of culture be a knowledge of Mathematics, Latin and Greek: your men of