Accidental propositions include, 1, those with a proper name for subject, since an individual has no essence (although the schoolmen, and rightly, according to their view of genera and species as entities inhering in the individuals, attributed to the individual the essence of his class); and, 2, all general or particular propositions in which the predicate connotes any attribute not connoted by the subject. Accidental propositions may be called real; they add to our knowledge. Their import may be expressed (according as the attention is directed mainly, either to what the proposition means, or to the way in which it is to be used), either, by the formula: The attributes of the subject are always (or never) accompanied by those signified by the predicate; or, by the formula: The attributes of the subject are evidence, or a mark, of the presence of those of the predicate. For the purposes of reasoning, since propositions enter into that, not as ultimate results, but as means for establishing other propositions, the latter formula is preferable.
CHAPTER VII.
THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.
It is merely an accident when general names are names of classes of real objects: e.g. The unity of God, in the Christian sense, and the non-existence of the things called dragons, do not prevent those names being general names. The using a name to connote attributes, turns the things, whether real or imaginary, into a class. But, in predicating the name, we predicate only the attributes; and even when a name (as, e.g. those in Cuvier's system) is introduced as a means of grouping certain objects together, and not, as usually, as a means of predication, it still signifies nothing but the possession of certain attributes.
Classification (as resulting from the use of general language) is the subject of the Aristotelians' Five Predicables, viz. Genus, Species, Differentia, Proprium, Accidens. These are a division of general names, not based on a distinction in their meaning, i.e. in the attributes connoted, but on a distinction in the class denoted. They express, not the meaning of the predicate itself, but its relation (a varying one) to the subject. Commonly, the names of any two classes (or, popularly, the classes themselves), one of which includes all the other and more, are called respectively genus and species. But the Aristotelians, i.e. the schoolmen, meant by differences in kind (genere or specie) something which was in its nature (and not merely with reference to the connotation of the name) distinct from differences in the accidents. Now, it is the fact that, though a fresh class may be founded on the smallest distinction in attributes, yet that some classes have, to separate them from other classes, no common attributes except those connoted by the name, while others have innumerable common qualities (from which we have to select a few samples for connotation) not referrible to a common source. The ends of language and of classification would be subverted if the latter (not if the former) sorts of difference were disregarded. Now, it was these only that the Aristotelians called kinds (genera or species), holding differences made up of certain and definite properties to be differences in the accidents of things. In conformity with this distinction—and it is a true one—any class, e.g. negro as opposed to white man, may, according as physiology shall show the differences to be infinite or finite, be discovered to be a distinct kind or species (though not according to the naturalist's construction of species, as including all descended from the same stock), or merely a subdivision of the kind or species, Man. Among kinds, a genus is a class divisible into other kinds, though it may be itself a species in reference to higher genera; that which is not so divisible, is an individual's proximate kind or infima species (species prædicabilis and also subjicibilis), whose common properties must include all the common properties of every other real kind to which the individual can be referred.
The Aristotelians said that the differentia must be of the essence of the subject. They vaguely understood, indeed, by the essence of a thing, that which makes it the kind of thing that it is. But, as a kind is such from innumerable qualities not flowing from a common source, logicians selected the qualities which make the thing be what it is called, and termed these the essence, not merely of the species, but, in the case of the infima species, of the individual also. Hence, the distinction between the predicables, Differentia, Proprium, and Accidens, is founded, not on the nature of things, but on the connotation of names. The specific difference is that which must be added to the connotation of the genus to complete the connotation of the species. A species may have various differences, according to the principle of the particular classification. A kind, and not merely a class, may be founded on any one of these, if there be a host of properties behind, of which this one is the index, and not the source. Sometimes a name has a technical as well as an ordinary connotation (e.g. the name Man, in the Linnæan system, connotes a certain number of incisor and canine teeth, instead of its usual connotation of rationality and a certain general form); and then the word is in fact ambiguous, i.e. two names. Genus and Differentia are said to be of the essence; that is, the properties signified by them are connoted by the name denoting the species. But both proprium and accidens are said to be predicated of the species accidentally. A proprium of the species, however, is predicated of the species necessarily being an attribute, not indeed connoted by the name, but following from an attribute connoted by it. It follows, either by way of demonstration as a conclusion from premisses, or by way of causation as effect from cause; but, in either case, necessarily. Inseparable accidents, on the other hand, are attributes universal, so far as we know, to the species (e.g. blackness to crows), but not necessary; i.e. neither involved in the meaning of the name of the species, nor following from attributes which are. Separable accidents do not belong to all, or if to all, not at all times (e.g. the fact of being born, to man), and sometimes are not constant even in the same individual (e.g. to be hot or cold).