Page:The New International Encyclopædia 1st ed. v. 12.djvu/463

* LOGIC. 411 LOGIC. emphasis is laid on the difference between it and another coiR-opt becomes negative. In order to have any significance at all as part of an object of consciousness, it must indeed have some positively experienced content, either sensational, affectional, or relational. But this content may be 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 affec- tional nr 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 some 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 father. 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 branch 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 aflirmative 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 singvilarity of judgment (q.v. for the distinction bet-ween singularity, particular- ity, and universality). Vol. XII— 27. Traditional logic has scarcely so much as recog- nized tlie distinction between singularity and uni- versality, much 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 Judgmen'T for definition of these terms.) The subject, in this scheme, was the term, either connotative or non - connotativc, which denoted the logical subject ; hut frcm the logical subject was excluded all consideration of logical quantity. Hence provision had to be made for logical quantity elsewhere, and it was made very mechanically. The subject was regarded as either a single object, or as single mutually inde- pendent olijects, of which there were a fixed num- ber. Now the question was whether the predicate (see .Ji"UGME>T for definition of the pre<licate) was affirmed (or denied) of every one of these objects or only of a part of them. In the former case the judgment was considered universal ; in the latter, particular. Xow, 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 'AH men are mortal,' were both regarded as universal, because, just as, in the latter, the speaker means all men, without exception, so, in tlie former, he means aU 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 wi^re 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: (I) Universal allirmative (A) : (2) universal negative (E) ; (.3) particular affirmative (I); and (4) particu- lar negative (O). The symbols. A, E, I, O, came down to us from Latin logicians, who took the first two vowels of the verb affirmo, I affirm, to symbolize the two classes of affirmative judgment, and the two vowels of the verb, ncf/o, 1 deny, to symbolize the two classes of negative judgments, in each case giving precedence to the vmiversal judgment. These symbols form the basis of the nonsense-names given in traditional logic to fhe moods of the syllogism (q.v.). This same tra- ditional logic divides inference (q.v.) into two kinds — direct, or immediate, ancl indirect, or mediate. Direct inference is any method of trans- forming a given single judgment into (apparent- ly) another judgment equally true, or into a jiulgment known to be false if the given judg- ment is true, or vice versa. Indirect or mediate 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 inunediate inference was divided into inference by opposition (q.v.), conversion (q.v.). obvor- sion (q.v.), and contraposition. See Cox'ERsion. Of recent years attempts have been made to reduce logic to a mathematical discipline. George Boole in his works. The Mathematical Analiisis of Thouqht (Cambridge. 1847), and An Anahjsis of the Lawfi of Thoiiriiit (London. 1S.54), promul- gated the theorv that judgments are equations. Jevons, De Morgan, C. S. Pierce, and E. Schroe- der have carried this algebraic treatment of logic