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LOOIO

for, speaking of St. Mark, Papias says that the Evange- list recorded " what had been said and done by Christ", and what he had heard from Peter, and not "as if he were composing an orderly account of the X67U1 ", so that the X67to are equivalent to the recorded " words and deeds " of Christ. Again, the title of Papias's work is Aoylay KvpiaKutw 'E^ifyiya-ti, thou^ the writer does not confine himself to the explanation of the "say- ings " of the Lord. (3) The X67ta of Papias must refer to the Gospel of St. Matthew: (a) No writing of St. Matthew except his Gospel was generally known in the second century; (b) there is no record of a work of the Evan^list that contained the Lord's words only; (c) even Eusebius found no trace of the 'K6yia m/pioicd, though he diligently collected all that had been writ^ ten about Christ by the Apostles and the disciples; (d) all antiquity could not have remained ignorant of a work of such importance, if it had existed; (e) the First Gospel contains so many discourses of the Lord that it might well be called \6yia KvpiaKd (cf . Hilgen- feld, "EinL", 456; Lightfoot in "Contemp. Review", Aug., 1867, 405 sqq.; Aug., 1875, 399 sqq., 410 sq.). The Logia, or the document Q of the critics, rests therefore on no historical authority, but only on

critical induction.

See literature under Agrapua; also the works quoted in this article. A. J. Maas.

Logic is the science and art which so directs the mind in the process of reasoning and subsidiary pro- cesses as to enable it to attain clearness, consistency, and validity in those processes. The aim of logic is to secure clearness in the definition and arriingement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference.

I. The Name. — ^The Greek word XA70J, meaning vpayfrnrela, or ixurr'^fifjf understood), as the name of a science or art, first occurs in the writings of the Stoics (see Stoic Philosophy). Aristotle, the foim- der of the science, designates it as "analytic ", and the Epicureans (see Epicureanism) use the term canonic. From the time of Cicero, however, the word logic is used almost without exception to designate this science. The names dialectic and analytic are also used.
 * reason", is the origin of the term logic — \oyiK'^ (j^x^t

II. The Definition. — ^It is a curious fact that, al- though logic is the science which treats of definition, logicians are not agreed as to how logic it«elf should be defined. There are, in all, about two hundred differ- ent definitions of logic. It would, of course, be im- possible to enumerate even the principal definitions here. It will be sufficient to mention and discuss a few typical ones.

A. The Port Royal Lopic ("L* Art de penser", pub- lished 1662) defines logic as **ihe art of using reason well in the acquisition of the knowledge of things, both for one's own instruction and that of others *'. More briefly, " Logic is the art of reasoning ". The latter is Amauld's definition. Definitions of this type are con- sidered too narrow, both because they define logic in terms of art, not leaving room for its claim to be con- sidered a science, and because, by the use of the term reasoning^ they restrict the scope of logic to one class of mental processes.

B. He^el (see Heqelianism) goes to the other ex- treme when he defines logic as " the science of the pure idea ". By idea he understands all reality, so that for him logic includes the science of subjective reality Gogic of mental concepts) and the science of objective reality Oo^c of being, metaphysics). In like manner the definitions which fail to distinguish between logic and psychology, defining logic as the science of men- tal processes, or "the science of the operations of the mind ", are too wide. Definitions which characterize logic as " the science of sciences ", " the art of arts ", are 0SO too wide : they set up too large a claim for logic.

C. 8U Thotnas, in his commentary on Aristotle's logical tr^itises (" In Post. Anal.", lect. i, Leonine ed., I, 138), says: "Ars qusedam necessaria est, qu» sit directiva ipsius actus rationis, per quam scilicet homo in ipso actu rationis ordinate faciliter et sine errore procedat. Et hsec ars est logica, id est rationaliB scientia." Combining those two sentences, we m&j render St. Thomas's definition as follows: "Logic is the science and art which directs the act of the reason, by which a man in the exercise of his reason is enabled to proceed without error, confusion, or unnecessaiy difficulty ". Taking reason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation of mental images, judgment, and ratiocination, we may expand St. Thomas definition and define logic as *' t£te science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness (or order), consistency, and validity in those processes". Logic is essentially directive. Therein it differs from psychology, which is essentially speculative, or theoretical, and which concerns itself only in an incidental and secondary manner with the direction of mental processes. Logic deals with pro- cesses of the mind. Therein it differs from metaphy- sics, which has for its field of inquiry and specula- tion the whole universe of being (see MirrAPHTSics). Logic deals with mental processes in relation to truth or, more particularly, in relation to the attainment and exposition of truth by processes which aim at being valid, clear, orderly, and consistent. Therein it differs from ethics, which treats of human actions, external deeds as well as thoughts, in relation to man's final destiny. Validity, clearness, consistency, and order are logical qualities of thought; goodness and evil are ethical qualities. Finally, logic is not to be confoimded with rhetoric. Rhetoric, in the old meanr ing of the word, was the art of persuasion; it used all the devices, such as emotional appeal, verbal arrange- ment, etc., in order to bring about a state of mind which had reference to action primarily, and to con- viction only in a secondary sense. Logic is the science and art of conviction ; it uses only arguments, discarding emotional appeal and employing merely words as the symbols of thoughts.

The question whether logic is a science or an art is now generally decided by asserting that it is both. It is a science, in so far as it not merely formulates rules for ri^ht thinking, but deduces those rules from general principles which are based on the nature of mind and of truth. It is an art, in so far as it is directly and im- mediately related to performance, namely, to the acts of the mind. As the fine arts direct the painter or the sculptor in the actions by which he aims at producing a beautiful picture or a beautiful statue, so logic directs the thinker in the actions by which he aims at attaining truth, or expoimding truth which he has attained.

III. Division op Logic. — The traditional mode of dividing logic, into " formal " and ** material "^ is main- tained in many modern treatises on the subject. In formal logic the processes of thought are studied inde- pendently of, or without consideration of, their con- tent. In material logic the chief question is the truth of the content of mental processes. An example from arithmetic will serve to illustrate the function of for- mal logic. When we add two and two, and pronounce the result to be four, we are dealing with a process of addition in its formal aspect, without paying attention to the content. The process is valid whatever the content may be, whether the "two and two" refer to books, horses, trees, or circles. This is precisely how we study judgments and arguments in logic. From the judgment "All A is B" we infer "Therefore some B is A"; and the process is valid whether the original proposition be "All circles are round" or " All umis are carnivorous "• In material logic, on the oontrwy,