logic, logics

[Fr. logique, from Lat. log ica ( ars ) = (the art) of logic; logic us = logical; Gr. logike techne = (the art) of logic; logikos = pertaining to speech or logic; logos = a speech; lego = to read.] Hist. & Phil.: Logic, as known in the present day, is a development and modification of the technë dialektikē =art of reasoning, which Aristotle, utilizing the labors of his predece ors, and not ably those of Zeno of Elea, molded into something like consistent shape. The first development of Aristo tel i an Logic was by the Scholastics (q. v.); and Lewes ( Hist . Phil . (1880), ii. 22) mentions it with praise of Abelard, that "he brought forward Logic as an independent power in the great arena of theological debate." At the time of the Reformation, probably as a protest, Scholasticism was depreciated, and at some of the Scotch Universities it was discarded for Ramism (q. v.). The subtle distinctions and keen disputations of the Schoolmen led in the next century to Bacon's condemnation of the perversion-not of the cultivation of logical pursuits. Locke was not so moderate, as may be seen in his E ay (ch. xxii., Of Reason ). [For German Logic, see HEGELIANISM, KANTIAN-PHILOSOPHY, and TRANSCENDENTALISM.] Generally speaking, down to the first half of the present century, there was little dispute as to how Logic should be defined. The Port Royalists had certainly called it the Art of Thinking; but the Art or Science of Reasoning, or the Art and Science of Reasoning met with little opposition as a definition. This is how Whately defines it ( Logic , Introd., § 1), and a writer of such opposite opinions as Tongiorgi, S. J. ( Inst . Phil .) has substantially the same words; and a parallel pa age to Whately's explanation, as to how Logic is at once a science and an art, occurs in Liber a tore, who is read in many of the ecclesiast i tical colleges in Rome. Sir W. Hamilton says that: " Logic is the Science of the Laws of Thought as Thought or the Science of the Formal Laws of Thought, or the Science of the Laws of the Forms of Thought; for all these are merely various expre ions of the same thing." - Lectures on Logic (ed. 1874), i. 26. Mill's definition is far wider in its inclusion, for he makes Logic coextensive with proof: " Logic , then, is the science of the operations of the understanding which are subservient to the estimation of evidence; both the proce itself of advancing from known truths to unknown, and all other intellectual operations in so far as auxiliary to this. It includes, therefore, the operation of Naming; for language is an instrument of thought, as well as a means of commu nicating our thoughts." -Logic (Introd. § 7). Sayce ( Prin . Comp . Philol ., Pref. ix.) has a pa age, which is an admirable glo upon the latter part of this definition. (See also Lewes: Hist. Phil. (1880), i. 301, sqq.) 1. Applied logic : (1) [ Modified logic .] (2) The term is sometimes loosely used for logical method employed in some particular branch of investigation. logistic 2. Deductive logic : Syllogistic Logic; in which no more is inferred in the conclusion than is implicitly contained in the premises. [SYLLOGISM.] 3. Equational logic : A system of logical notation in which propositions are expre ed in the form of equations. (See Jevons : Principles of Science , and Studies in Deductive Logic .) 4. Inductive logic : The science which treats of inductive reasoning, by which, broadly speaking, a general proposition is inferred from a number of particular propositions. [INDUCTIVE-METHOD.] 5. Modified logic : That logic which is concerned in the investigation of Truth and its contradictory opposite, Error; of the causes of Error, and the impediments to Truth and their removal, and of the subsidiaries by which human thought may be strengthened and guided in its functions. "What I have called Modified Logic is identical with what Kant and other philosophers have denominated Applied Logic."- Sir W. Hamilton: Logic (ed. 1874), i. 60. 6. Pure logic : (See extracts.) "Pure logic arises from a comparison of things as to their samene or difference in any quality or circumstance whatever."-W. Stanley Jevons: Pure Logic , p. 17. "Pure logic teaches both the laws of immediate knowledge or Perception, and those of mediate knowledge or Thought."-Ueberweg: Logic , p. 17. 7. Syllogistic logic: [ Deductive logic.] 8. Symbolic logic: IMG:content-0690.jpg:[graphic] (1) (See extract.) "Symbolic logic is not a generalization of the Common Logic in all directions alike. It confines itself to one side of it, viz., the cla or denotation side-probably the only side which admits of much generalization-and this it pushes to the utmost limits, withdrawing attention from everything which does not develop in this direction."-Venn: Symbolic Logic , ch. ii. (2) The term is also loosely applied to the illustration of logical relations by mathematical signs or by diagrams. log-ic-al, a. [Eng. logic; -al.] 1. Of or pertaining to logic; taught or used in logic. "But they are put off by the names of vertues, and natures, and actions, and pa ions, and such other log ical words."- Bacon: Nat. Hist., § 98. 2. According to the rules or principles of logic; sound in reasoning. "He, by sequel logical , Writes best, who never thinks at all." Prior : Epistle to Fleet wood Shephard. 3. Skilled in logic; furnished with logic. "A man who sets up as a judge in criticism, should have a clear and logical head."- Add is on . log-1-căl-1-ty, s. [Eng. logical; -ity.] The state or quality of being logical. "It [Cynicism] required a great rude energy, a fan at ical logicality of mind."-Lewes: History of Philosophy, i. 191. *log-i-căl-i-zā-tion, s . [English logic a liz ( e ); -ation.] The act of making logical. "The mere act of writing tends in a great degree to the logical i zati on of thought."-E. A. Poe: Marginalia, xvi. *log'-1-cal-ize, v . t . [Eng. logical ; -ize .] To make logical. "Thought is logical i zed by the effort at expre ion."E. A. Poe: Marginalia , xvi. log-ic-al-ly, adv. [Eng. logical; -ly.] In a logical manner; according to the rules or principles of logic. "This danger we avoid if we logically follow out the principles of the constitution to their consequences." Macaulay : Hist . Eng ., ch. x.