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LOGIO

inquire into the content of the judgments or premltoB and endeavour to determine whether they are truc^or false. Material logic was styled by the old writers ''major logic'^ "critical logic", or simply "criticism". In recent times the word epistemoiowj (science of knowledge), meaning an inquiry into the value of knowledge, has come into general use, and designates that portion of philosophy which inquires into tiie objective value of our concepts, the import and value of judgments and reasoning, the criteria of truth, the nature of evidence, certitude, etc. When- ever this new term i^ adopted there is a tendency to restrict the term logic to mean merely formal logic. Formal logic studies concepts, and other mental images, for the purpose of securing clearness and order among those contents of the mind. It studies judgments for the purpose of showing when and how they are con- sistent or inconsistent, that is, when one may be in- ferred from another (conversion), and when they are opposed (opposition). It studies the two kinds of rea- soning, deductive and inductive, so as to direct the nund to use these processes validly. Finally, it studies sophisms (or fallacies) and method for the purix)sc of showing what errors are to be avoided, and what arrangement is to be followed in a complex series of reasoning processes. But, while it is true in general that in all these tasks formal logic preserves its purely for- mal character, and docs not inquire into the content of thought, nevertheless, in dealing with inductive reasoning and in laying down the rules for definition and division, formal logic does take accoimt of the matter of thought. For this reason, it seems desirable to abandon the old distinction between formal and material, to designate as logic what was formerly called formal logic, and to reserve the term epistcmology for that portion of philosophy which, while inquiring into the value of human knowledge in general, covers the ground which was the domain of material logic.

There remain certain kinds of logic which are not included under the heskdafontial and material. Trans- cendental logic (Kant) is the in(}uiry into human knowledge for the purpose of determining what ele- ments or factors in human thought are a priori, that is, independent of experience. Symbolic logic (Lam- b^, Boole) is an application of mathematical methods to the processes of thought. It uses certain conven- tional symbols to represent terms, projjositions, and the relations among them, and then, without any further reference to the laws of thought, applies the rules and methods of the mathematical calculus (Venn, "Symbolic Logic", London, 1881). Applied logic, in the narrower sense, is synonymous with material logic; in the wider sense, it means logic applied to the study of the natural sciences, logic applied to education, logic applied to the study of law, etc. Natural logic is that native power of the mind by which most persons are competent to jud^e correctly and reason validly about the affairs and mterests of everyday life; it fs osntrasted with scientific logic, which is logic as a science and cultivated art.

IV. HiSTORT OP Logic. — ^The history of logic pos- a more than ordinary interest, because, on the

one hand, every change in the point of view of the metaphysician and the psychologist tended to produce a corresponding change in logical' theory and practice, while, on the other hand, changes in logical method and procedure tended to affect the conclusions as well as the method of the philosopher. Notwithstanding th^ tendencies towards variation, the science of logic has undergone very few ra<lical changes from the be- ginning of its history.

A. The Nyaya, — A system of philosophy which was studied in India in the fifth century b. c, though it is, perhaps, of much older date, takes its name from the word nyaya, meaning logical argument, or syllogism. This philosophy, like all the Indian Hystems. f)usied it- self with the problem of the deliverance of the- soul

from bondage, and its solution was that the soul is to be freed from the trammels of matter by means of systematic reasoning. This view of the question 1^ naturally to an analysis of the methods of thinking, and to the construction of a type of reasoning whicn bears a remote resemblance to the s\'lIogism. The nyaya, or Indian syllogism, as it is sometimes called, consists of five propositions. If, for instance, one wishes to prove that the hill is on fire, one begins with the assertion: "The hill is on fire." Next, the reason is given: "For it smokes." Then comes an instance, "Like the kitchen fire"; which is followed by the application, * ' So also the hill smokes." Finally comes the conclusion, "Therefore it is on fire." fietween this and the clear-cut Aristotelean s>^lIogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking. It is hardly necessary to say that there is no historical evidence that Aristotle was in any way influenced in his logic by Gotama, the reputed author of the nyaya,

B. Pre-AHstotelean Logic in Greece. — ^The first pliilosophers of Greece devoted attention exclusively to the problem of the origin of the imiverse (see Ionian School of Philosophy). The Eleatics, especially Zeno of Elea, the Sophists, and the Megarians devel- oped the art of argumentation to a high degree of perfection. Zeno was especially remarkable in this respect, and is sometimes styled the Founder of Dialec- tic. None of these, however, formulated laws or rules of reasoning. The same is true of Socrates and Plato, although the former laid great stress on definition ana induction, and the latter exalted dialectic, or dis- cussion, into an important instrument of philosophical knowledge.

C. Aristotle, the Founder of Logic. — In the six trea- tises which he devoted to the subject, Aristotle ex- amined and analysed the thinking processes for the purpose of formulating the laws of thought. These treatises are (1) "The Categories", (2) "Interpreta- tion", (3) " Prior Analytics", (1) " Posterior Analytics", (5) " Topics", and (G) " Sophisms". These were after- wards given the title of " Organon", or " Instrument of Knowledge"; this designation, however, did not come into common use until the iifteenth century. The first four treatises contain, with occasional excursions into the domain of grammar and metaphysics, the science of formal logic essentially the same as it is taught at the present day. The "Topics" and the "Sophisms" contain the applications of logic to argu- mentation and the refutation of fallacies. In con- fonnity with the fundamental principle of his theory of knowledge, namely, that all our knowledge comes from experience, Aristotle recognizes the importance of inductive reasoning, that is to say, reosonmg from particular instances to general principles. If he and nis followers did not develop more fully this portion of logic, it was not l>ecause they did not recognize its importance in principle. His claim to the title of Founder of Logic has never been seriously disputed; the most that his opponents in the modern era could do was to set up rival systems in which induction was to supplant syllogistic reasoning. One of the devices of the opponents of scholasticism is to identify the Schoolmen and Aristotle with the advocacy of an ex- clusively deductive logic.

D. Post-Aristotelean Logicians Among the Greeks. — Among the immediate disciples of Aristotle, Theo- phrastus and Eudemus devoted special attention to logic. To the former is sometimes attributed the in- vention of the hypothetical syllogism, although the same claim is sometimes made for the Stoics. The latter, to whom, probably, we owe the name logic, recognized this science vls one of the constitutive parts of philosophy. They included in it dialectic and rhetoric, or the science of argumentation and the science of persuasion. They busied themselves also