§ 312. The chief advantage claimed for the quantification of the predicate is that it reduces every affirmative proposition to an exact equation between its subject and predicate. As a consequence every proposition would admit of simple conversion, that is to say, of having the subject and predicate transposed without any further change in the proposition. The forms also of Reduction (a term which will be explained later on) would be simplified; and generally the introduction of the quantified predicate into logic might be attended with certain mechanical advantages. The object of the logician, however, is not to invent an ingenious system, but to arrive at a true analysis of thought. Now, if it be admitted that in the ordinary form of proposition the subject is used in extension and the predicate in intension, the ground for the doctrine is at once cut away. For, if the predicate be not used in its extensive capacity at all, we plainly cannot be called upon to determine whether it is used in its whole extent or not. CHAPTER VI. _Of the Heads of Predicables_. § 313. A predicate is something which is stated of a subject. § 314. A predicable is something which can be stated of a subject. § 315. The Heads of Predicables are a classification of the various things which can be stated of a subject, viewed in their relation to it. § 316. The treatment of this topic, therefore, as it involves the relation of a predicate to a subject, manifestly falls under the second part of logic, which deals with the proposition. It is sometimes treated under the first part of logic, as though the heads of predicables were a classification of universal notions, i.e. common terms, in relation to one another, without reference to their place in the proposition. § 317. The heads of predicables are commonly reckoned as five, namely, (1) Genus. (2) Species. (3) Difference. (4) Property. (5) Accident. § 318. We will first define these terms in the sense in which they are now used, and afterwards examine the principle on which the classification is founded and the sense in which they were originally intended. (1) A Genus is a larger class containing under it smaller classes. Animal is a genus in relation to man and brute. (2) A Species is a smaller class contained under a larger one. Man is a species in relation to animal. (3) Difference is the attribute, or attributes, which distinguish one species from others contained under the same genus. Rationality is the attribute which distinguishes the species, man, from the species, brute. N.B. The genus and the difference together make up the Definition of a class-name, or common term. (4) A Property is an attribute which is not contained in the definition of a term, but which flows from it. A Generic Property is one which flows from the genus. A Specific Property is one which flows from the difference.