II

OF THE SEVERAL KINDS OF TERMS

$35. SINGULAR, AND COMMON, OR UNIVERSAL, TERMS. Grammatically speaking, terms are said to be either singular or common, or, as otherwise expressed, singular or universal. A singular term is one that denotes an individual or single thing, as, e. g., any particular thing, animal, or man. A common or universal term is one that denotes either a class of individuals or a class made up of other classes. But in the latter case, the subordinate classes may be regarded as individuals constituting the superior class; and conversely the individual may always be regarded as a class, — i. e., a class of one.' In this work, therefore, the distinction between singular and common or universal terms will be regarded as logically immaterial; all terms will be regarded as universals, or, in other words, as denoting classes of significates.

§ 36. ADJECTIVES.- Hence also adjectives used as terms will be regarded as nouns or sub

1" By a class is usually meant a collection of individuals .; but in this work the meaning of the term will be extended so as to include the case where but a single individual exists, as well as cases denoted by the terms 'nothing' and universe'; which as 'classes' should be understood to comprise respectively no beings' and 'all beings.'"— Boole, Laws of Thought, p. 28.

stantives; that is to say, where a term is in adjective form (which can occur only with the predicate) it is either regarded as a substantive, or converted into one by adding the substantive understood. Thus, e. g., the proposition, "Man is mortal," is to be read: "Man is a mortal," or "a mortal being."'

1

$37. ABSTRACT AND CONCRETE NAMES.A concrete name is one that denotes a class of real individuals. An abstract name is one that denotes qualities or attributes conceived as existing apart from the things in which they inhere, or, in other words, fictitiously regarded as things,―as, e. g., whiteness, strength, goodness, humanity, etc. Abstract names are commonly singular in form, but in their essential nature they are always universal. Thus, when we speak of virtue, the name is to be regarded as

1 "If we attach to the adjective the universally understood subject, 'being' or 'thing,' it becomes virtually a substantive, and may for all the essential purposes of reasoning be replaced by the substantive. Whether or not in every particular of the mental regard it is the same thing to say, 'water is a fluid thing,' as to say, 'water is fluid,' it is at least equivalent in the expression of the processes of reasoning."-Boole, Laws of Thought, p. 27.

2 The distinction between concrete and abstract names corresponds precisely to the distinction made by old logicians between names of first intention and names of second intention. The former are names that denote real significates; the latter, names that denote fictitious significates, or quasithings. See further on this point Appendix I.

denoting, not a quality existing in any particular man, or in itself, but the class of qualities by which all virtuous men are distinguished. So, though we may consider the color red, or redness, in the abstract,- dismissing from the mind the individuals in which it is manifested, - yet, upon analyzing the concept, we cannot fail to perceive that there are as many individual instances of red, or, we may say, as many individual reds or rednesses, as there are individual things in which the color is manifested; and that red, or redness, is simply the denomination of the class of colors thus manifested. Hence, abstract names, though grammatically singular, are to be regarded as plural, and as differing from concrete names only in this, that the individuals constituting the class are qualities,—i. e., quasi-things, or fictitious, not actual existences, and that among the marks by which the class is distinguished are the actual individuals in whom alone the qualities exist. An abstract name is therefore to be regarded as denoting a class of qualities; and as connoting the individuals in which they inhere.

38. THE DISTINCTION OF FUNDAMENTAL IMPORTANCE.- The distinction between concrete and abstract names, or names of first, and of second intention, is one of fundamental importance. In dealing with the former, the things denoted by the names we use are ever

present to the mind, and we may therefore, as is asserted by Mill, be said—without violent absurdity to deal with things, rather than with notions or names. But where we deal with abstract terms, the things present to the mind are mere abstractions, fictitiously regarded as things; and we are, in fact, dealing not with things, but with quasi-things only.'

$ 39. POSITIVE AND NEGATIVE TERMS.The distinction between positive and negative terms is also one of fundamental importance in Logic. By this division of terms the whole universe of things, real and fictitious, is divided into two classes, the one marked by having, the other by not having, a certain quality or qualities, as e. g., white things, and things that are not white; and it is obvious that to each positive there must be a corresponding negative term.

$40. OF THE UNIVERSE OF THE PROPOSITION. But ordinarily in speech we have in view a more limited class, and must be understood to refer, not to the universe of things, but to some class less than the universe, but superior to the classes denoted by the subject and predicate; and this superior class is said to constitute the universe of the proposition in which the terms are used. Thus, when we speak of "mortal” and “immortal," the class 1 See Appendix K.

of" living things" or beings" is obviously referred to as the superior class, and is, therefore, said to constitute the universe of the proposition; and the division is to be understood to be into "mortal" and immortal" beings. So, in the proposition, Brutes are irrational," the superior class we have in view is that of animals, and this class is to be regarded as the universe of the proposition; as (denoting "not" by the Greek privative, a) may be illustrated by the following diagrams, either of which may be used:

UNIVERSE

UNNERSE

XaX

III

OF THE ANALYSIS OF TERMS

$41. APPREHENSION.-As it is the function of Logic to compare the notions denoted by terms, with the view of determining their relations, a preliminary process is essential: namely, that of apprehending or understanding the significations of terms; which is called by logicians," Simple Apprehension."'

1 The operations of the mind involved in reasoning are (1) Simple Apprehension, (2) Judgment, and (3) Inference (see