46. DIVISION.-Division is an act of Analysis; Classification, of Synthesis. But the same principles govern both, and the elucidation of one will equally explain the other. In Logic, the analysis of terms is the more important process, and we will therefore adopt, as the subject of explanation, the process of Division. The term to be divided, or, rather, the class denoted by the term, is, as we have said, called the genus; the subordinate classes into which the genus is divided, species. The species must, of course, be exclusive of each other, i. e., they must not overlap; and taken together they must exhaust the genus. Thus, the term thing - meaning thereby things and quasi-things-may be divided, and subordinate classes subdivided, as follows:

Things

Real Things Quasi-Things

Bodies Not Bodies

Organic Inorganic

Animal Not Animal

Rational Not Rational

etc.

$47. DICHOTOMY. It will be observed that the above division is, in each case, two

fold,-i. e., into two classes, represented by a term and its negative. This is called Dichotomy, and, as in using it we are less liable to error than in other modes of division, it is most commonly used. The genus may, however, be divided into three or more species, provided the species taken together exhaust the genus, and be exclusive of each other, as, e. g., in the division of Bodies into (1) Inorganic, (2) Vegetable, and (3) Animal.

$48. NOMINAL DEFINITION OF TERMS.The definition (i. e., the real or nominal definition) of a term consists in assigning the class denoted by it to an appropriate genus, and giving its specific difference; by which is meant some mark or marks peculiar to it, by which it may be distinguished from other species. It is, therefore, a species of classification,-i. e., it consists simply in classifying the given class, or species, by assigning it to a genus, and in adding also the appropriate marks, or specific difference, by which it is distinguished from the other species contained in the genus. The definition of a term is, therefore, to be regarded simply as a complete classification of it; and the classification of it as an incomplete or imperfect definition. But the latter has the advantage that it can often be used where the former would be inconvenient or impossible.

$49. THE ESSENCE OF THE TERM.-A

quality at once common and peculiar to the individuals denoted by a term is called a property of the class denoted; a quality common to the class, but not peculiar to it, is called an accident. The definition of a term is made up by selecting from the accidents of the term one to serve as a mark for the purpose of determining the genus, and from the properties one to serve as specific difference. These together constitute the essence of the term; which will therefore vary with the definition, and be determined by it. Thus, e. g., if we define man as a rational animal, "animal" will be the genus; tional" the specific difference; talking, "laughing," "cooking," etc., properties; “mortal," "carnivorous,' mammal," etc., accidents. But we may, if we choose, define him variously as a talking, laughing, or cooking, mortal, carnivore, or mammal. The essence of a term is therefore but another name for the meaning of the term. Properties not used for specific difference, and accidents not used for genus, do not enter into the essence of the term.

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1 There is much confusion among logicians in the use of the term accident. The definition in the text is that of the best authorities, including Aristotle; and the term should be consistently thus used.

CHAPTER III

DOCTRINE OF THE PROPOSITION

I

RUDIMENTS OF THE DOCTRINE

§ 50. PROPOSITION DEFINED.-A proposition may be defined as the expression of a relation of signification between two terms; which, of course, implies the expression of the corresponding relation between the notions expressed in the terms.

851. THE GRAMMATICAL PROPOSITION.But here there is a difference between Logic and Grammar, or, we may say, between the logical and the grammatical proposition. In the latter, any of the innumerable relations existing between terms, or, what is the same thing, between the things denoted by them, whether past, present, or future, may be expressed as existing between the terms; and the relation may be expressed by any copula or connecting word, or the same word may be

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used to express both copula and predicate, as, e. g., John struck William "; " The sun will rise at six o'clock to-morrow"; It rains" "The Carthaginians did not conquer Rome," etc. But in Logic the only copula used is the present tense of the verb "to be," with or without the negative particle; and the only interterminal relation considered is that of species and genus; which may be either affirmed or denied.

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52. THE LOGICAL PROPOSITION.-ACcordingly the logical proposition is of two forms, the affirmative and the negative. In the former the relation of species and genus between the terms is affirmed,-as, e. g., Man is mortal, Y is X," etc.; in the latter it is denied, as, e. g., " Man is not perfect," "Y is not X," etc. The affirmative proposition may be read, either, “ Y is X," or " Every Y is X," or " All Y's are X's ; or, to take the concrete example, “Man is mortal," or

-

Every man is mortal," or “All men are mortal," these expressions being all equivalent, and signifying equally that the subject class or class denoted by the subject is a species of the predicate class. The negative proposition may be read either as above or as follows: "No man is perfect," "No Y is X," etc. It is a cardinal postulate in Logic that all propositions may, and indeed for purposes