Every general idea is technically a concept, and may be simple or complex; i.e. it may or may not he incapable of analysis. Thus intensity of a color sensation is unanalyzable. while bility. as qualifying an object, is analyzable into the various attributes of visual sensations. Tf an object, is visible, it is colored or bright, and besides it has an intensity, a duration, and a spatial extension of these sensations. Thus visi bility is analyzable; intensity, one of the results of the analysis. as yet has not been analyzed. The results of an analysis of a concept are col lectively called its connotation (q.v.). and are severally called its marks; the objects which such a concept qualifies are its denotation (q.v.). The statement of the connotation of a term is called definition (q.v.) ; a systematic statement of its denotation is called division (q.v.). In general. but not with a mathematical accuracy, denota tion and connotation vary inversely; the larger the number of marks in a concept, the fewer will hi all probability be the number of real objects which are qualified by the concept. Traditional logic has distinguished between concrete and ab stract terms. A term is concrete when it names a total percept or image with its full comple ment of features; it is abstract if it names only certain of these features. The test of a full com plement of features is the ability of these fea tures to function as percept or image without need of supplementation by further features. Thus animal is the name of various percepts or images; the term is therefore concrete. Ani mality is the name of a certain feature or emu pies of features characterizing those percepts or images, but the feature or emnplex of features known as animality is unable to function in consciousness as a percept or imago; hence animality is an abstract term. It will be noticed that while animal is a name applied to complete percepts or images, it is thus applicable only because of the attribute of animality which they possess. It names. or technically it denotes. the percepts or images; it makes reference to, or technically it connotes, the attribute of ani mality. by virtue of the possession of which the percepts or images have a right to be denoted by the term. Hence, contrary to the traditional opinion. concrete terms are not names of con cepts at all; they are names of percepts or images. while at the same time they usually con note concepts. Some concrete terms are said to be non-connotative: i.e. they do not specifically refer to any definite concept which characterizes the objects they name. Proper names. strictly so called, • arc to all intents and purposes non connotative. Thus Saint Louis is it name given to a city which is identifiable by various charac teristics, not one of which is referred to directly by the name it bears and not one of which is singled out for purposes of identification. Many so-called proper names are not absolutely 'proper' in that they indicate sex or family relationships or nationality or other traits; hence they arc to a certain extent connotative. This distinction between connotative and non-connotative tennis is really a matter of language, not of logic; for although the name Saint Louis does not refer explicitly to any mark possessed by the object it denotes, no thinker can employ the term without thinking that object as characterized by some mark. In his thought it is a city, situated on the Mississippi. etc. If not characterized in same way, it is not an object of thought at all. Again, traditional logic divides terms into positive and negative. Corresponding to this distinction in terms. there is in consciousness a two-fold eharae ter belonging to every concept. As we have seen, a concept is obtained by analysis of a percept. Analysis always involves distinction of one ele ment of a complex from another, and 'distinction is negation" (Spinoza). To distinguish one thing from another is to recognize that it is what the other is not. Concepts thus owe their origin to a primitive negative aspect in the original judg ment that breaks a percept up into its constit uents. The result of sueli an analyzing judgment is a complex of differentiated perpetual features or concepts. Now a concept in proportion as emphasis is laid on the difference between it and another concept becomes negative. In order to have any significance at all as part of an object of consciousness, it must indeed have sonic positively experienced content. either sensational. affectional, or relational. Bid this content may he practically neglected, and attention may rest almost entirely on its mere difference from other contents of consciousness. A negative term is one whose connotation is an idea negatively con ceived. Thus 'inhuman' began as a negative term, because, although in order to have any meaning it must connote some positive feature of experience, still attention was given to its difference from another positive feature. A posi tive term, on the contrary, connotes an idea, conceived with stress on its perceptual or atTec tional or relational content rather than on its mere difference from other contrasted contents. 'Thus 'inhuman as now used generally means •cruel, and the perceptual and emotional features connoted by the term are more prominent in thought than those perceptual and emotional fea tures with which this connotation is contrasted. 'Thus we see that the philological form of a term is no infallible index to its positive or negative quality in logic.
The traditional distinction between absolute and relative terms is related to the distinction we have just discussed. Negative terms are from the very nature of the case relative. But not all positive terms are absolute, for there is posi tiveness as well as negativity in all relation.
Elements related to each other are indeed each what the other is not, but also each is in sonic respect or feature what it is by virtue of what the other is. A relative term is one which con notes in an object those features that are recog nized as belonging to it because some other object is what it is. Thus in the relation of father and son there is negativity; father is not son, and son is not fath(;r. But this negativity does not exhaust the relation. There is a positive charac ter possessed by each because the other possesses a positive character. This mutual determina tion is relatively positive, and any term like `father' or 'son' which names either of mutually determining objects by connoting some feature given to that object in virtue of such mutual determination is a relative term. And also any abstract term which names such a feature is also relative.
It must be borne in mind that all these dis tinctions between concepts are distinctions be tween integral components of judgment. The doctrine of concepts, or, as it is often called, the doctrine of terms, is not an independent branell of logic. It is part of the doctrine of judgment, although tradition has given it an independent treatment, and has included within the doctrine of judgment only a discussion of the quality and quantity of judgments. Quality is a term ap plied to judgment to express the character it has as affirmative or negative. A judgment is affirmative if it is the recognition of the fact that an object possesses a certain qualifying feature; it is negative if it is the recognition of the fact that an object does not possess a certain qualifying feature. Quantity is a term applied to judgments to express the universality or par ticularity or singularity of judgment (q.v. for the distinction between singularity, particular ity, and universality).
Traditional logic has scarcely so much as recog nized the distinction between singularity and versality, mueh less has it done any justice to the distinction. It took a proposition and di vided it into three parts, subject, predicate, and copula. (See JUDGMENT for definition of these terms.) The subject, in this scheme. was the term, either connotative or non - connotative, denoted the logical subject ; but fr?du the logical subject was excluded all consideration of logical quantity. [Lome provision had to be made for logical quantity elsewhere. and it was very mechanically. The subject. was regarded as either a single object, or as single mutually inde pendent objects, of which then- were a fixed num ber. Now the question was whether the predicate (see JiDGMENT for definition of the predicate) was affirmed (or denied) of every one cf those objects or only of a part of them. In the former ease the judgment was considered universal: in the particular. Now, if the subject was only one object, then the predicate was considered as true of the whole subject, and therefore the ,judgment was in this case regarded as universal. Hence it came about that two so very different judgments as 'Garfield died of an assassin's bullet.' and 'All men are mortal,' were both regarded as universal, because, just as, in the latter, the speaker means all men, without. exception. so. in the former, lie means all Garfield without excep tion. Following this artificial method of identi fying singular and universal judgments, logical quantity was regarded as either particular or uni versal. Now, as there were two possible quan tities, particular and universal, and two possible qualities, affirmative and negative, there were, as regards quantity and quality together. four possible kinds of judgments: (1) Universal affirmative (A) ; (2) universal negative ( El ; (3) particular affirmative (I); and (4) particu lar negative (0). The symbols, A, E. I, 0, came down to us from Latin logicians, who took the first two vowels of the verb affirm°. I affirm, to symbolize the two classes of affirmative judgment. and the two vowels of the verb, sego, I deny, to symbolize the two classes of negative judgments, in each case giving precedence to the universal judgment. These symbols form the basis of the nonsense-names given in traditional logic to the moods of the syllogism (q.v.). This same tra ditional logic divides inference (q.v.) into two kinds—direct, or immediate. and indirect, or mediate. Direct inference is any method of t rans forming a given single judgment into (apparent ly) another judgment equally true, or into a judgment known to be false if the given judg ment is true, or vice versa. Indirect or m•liate inference is a syllogism (q.v.). True induction had originally no place in this scheme. and even now a place can be found for it only by consider ing induction as a species of syllogism. Direct or immediate inference was divided into inference by opposition (q.v.). conversion (q.v.). obver sion (q.v.). and contraposition. CONVERSION.
Of recent years attempts have been made to reduce logic to a mathematical discipline. George Boole in his works, The Ilathemettical .1 nalysis of Thought I l;1, and .t n .1 mil yRis of the Lairs of Thought (London. Is1341, promul gated the theory that are (Illations:. Jevons, De Morgan. C. S. Pierce, and E. Schroe der have carried this algebraic treatment of logic out in great detail, and some of them at least claim that there is no really scientific logic ex cept of this algorismic sort. But they have not succeeded in converting ninny logicians to their way of thinking. The tendency has been to con sider logic as an independent science which can only in a very artificial and inadequate way be reduced to algebraic expression.