2. THE PREDICABLES.
A predicable is a term which can be affirmed or predicated of any subject. In the proposition, “A man is a rational animal,” the term “rational animal” is a predicable,because it can be affirmed of the subject man.
To gain a clear knowledge of the definition it is quite necessary to understand the five predicables which we shall consider in the following order:
1. Genus.
2. Species.
3. Differentia (difference).
4. Property.
5. Accident.
(1) Genus and (2) Species.
Genus and species are relative terms and can best be defined together.
A genus is a term which stands for two or more subordinate classes.
A species is a term which represents one of the subordinate classes.
The genus may be subdivided into species; the species together form the genus.
To illustrate: The term man stands for five subordinate classes or species, as white, black, brown, yellow and red. “Man” is, therefore, a genus, while “white man” and “black man,” etc., are species. The term “polygon” is a genus with reference to “trigon,” “tetragon,” “pentagon,” etc., while “trigon” is a species of “polygon.”
Any given genus may be a species of some higher class. That is, “man,” which is a genus with reference to the kinds of men, is a species of the higher class “biped,” while “biped” is a species of “animal,” “animal” a species of “organized being,” “organized being” of “material being,” “material being” of “being.” But herewe stop, as there is no higher grade to which “being” can be referred. This highest genus takes the name of summum genus.
Similarly any given species may be a genus of some lower class. “White man,” for example, which is a species of “man,” is a genus of “American,” “Englishman,” “German,” “Frenchman,” etc. “American” is a genus of “New Yorker,” “Californian,” etc., while “New Yorker” is a genus of “Smith of Jamaica.” This last term is an individual and cannot be subdivided. It represents the lowest possible species and is referred to in logic as infima species.
It is obvious that the highest genus cannot become a species, neither can the lowest species become a genus.
PROXIMATE GENUS.
The proximate genus is the next class above. To illustrate: “Animal” is a genus of “man,” but “biped” is the proximate genus of “man.” “Quadrilateral” is the genus of “square,” but “rectangle” is the proximate genus. The next class above “trigon” is polygon not figure. Hence “polygon” is the proximate genus of “trigon.”
GENUS AND SPECIES OF NATURAL HISTORY.
In natural history the following terms are used to denote the various grades of kinship in any scheme of classification: (1) kingdom, (2) class, (3) order, (4) family, (5) genus, (6) species, (7) variety, (8) the individual thing. Here “genus” and “species” are absolute not relative and occupy a fixed place in the scheme, while from a logical viewpoint any of the grades indicated between the lowest and highest would be the speciesof the next higher grade or a genus of the next lower; e. g., order is a species of “class,” while it is the genus of “family.”
GENUS, A DOUBLE MEANING.
We recall that any class name or genus has a double use, extensional and intensional. When considered from the standpoint of its extension, a genus represents a group of objects or is mathematical in its application, but when used in an intensional sense it represents a group of qualities or is logical in its application.
Considered extensionally the genus refers to a larger number of objects than the species. But when viewed intensionally the species refers to more qualities than the genus. This was made clear when discussing the law of variation in the extension and intension of terms.
(3) Differentia.
The differentia of a term is that attribute which distinguishes a given species from all the other species of the genus.
It has been observed that the species refers to more qualities than the genus. In fact, it represents all the attributes of the genus plus those which distinguish the particular species from the other species of the genus. These additional qualities are the differentiæ of the particular species.
TO ILLUSTRATE:
The attribute which distinguishes man from the other bipeds of the world is his rationality. That which distinguishes the rectangle from the other parallelogramsis its four right angles. The attributes rationality and right angles are differentiae.
(4) Property.
A property of a term is any attribute which helps to make the term what it is. Thus “consciousness” is a property of man, “binding” a property of book, “angles” a property of triangle. Deprive the terms of these attributes and their true nature is altered.
A differentia is a property according to the foregoing definition. However, Jevons defines “property” as “Any quality which is common to the whole of a class, but is not necessary to mark out the class from other classes.” This viewpoint excludes “differentia” from the notion of property. The difference in opinion is of slight importance.
(5) Accident.
An accident of a term is any attribute which does not help to make the term what it is. It may indifferently belong or not belong to the term. Deprive a term of an accident and the nature of the term remains unchanged. Thus, a teacher’s position, a man’s watch, the fact that the angle is one of 80° are all accidents.
It is obvious that a property is a constant attribute while an accident is variable. This gives to the former a universal validity while the latter is more or less shifting and uncertain. All triangles must have three angles (property) while the value of each angle in degrees (accident) admits of unlimited variation.
Some logicians divide accidents into separable and inseparable. A man’s hat would be a separable accident while his birthplace would be an inseparable accident.
FIVE PREDICABLES ILLUSTRATED.
In the following brief descriptions the five predicables are designated:
(1) This (species)
rectangle is a (genus)
parallelogram with (differentia)
four right angles its longer sides being (accident)
ten inches.
(2) This (species)
man is a (differentia)
rational (prox. genus)
biped with the (property)
power of locomotion and a (accident)
ruddy complexion.
(3) A (species)
trigon is a (genus)
polygon of (differentia)
three sides and (property)
three angles, (accident)
the sum of the angles being equal to two right angles.