LOGIC. This name denotes the science connected with the forms and methods of reasoning, and the establishment of truth by evidence. The science has come down to us from the Greeks, obtaining in great part the shape that we find it in from Aristotle, although lie did not apply to it the name " logic." This name, signifying originally both thought and the expression of thought, must have been applied soon atter the time of Aristotle. The most ancient name was " dialectic," meaning literally " conversation," " colloquy," or "dispute." (Hamilton's Logic, lect. 1.) "But it appears that Aristotle possessed no single term by which to designate the general science of which he was the principal author and finisher. Analytic, and apodeictic with topic (equivalent to dialectic, and including sophistic), were so many special names by which he denoted the particular parts or particular applications of logic." The definition of logic has never been, till lately, a matter of serious controversy. There was formerly a substantial unanimity, with some variations in the form of the phraseology employ-ed. We find it called usually the art of reasoning, or the science of reasoning, or both the one and the other. And by reasoning has been always under stood formal reasoning; that is, inferences stated in such general language that they apply to all kinds of matter alike, as wlmn in arithmetic we say three times four is twelve, without considering what the numbers are numbers of. A modification of this view has been adopted by sir W. Hamilton; he calls logic the " science of the laws of thought as thought." The introduction of the larger word " thought " is considered requisite, because " reasoning" is somewhat too limited, there being processes included in logic, and necessary to the establishment of truth, which that word does not cover; suck, for example, are conception—the forming of general notions--and judgment, the statement of propositions (see JUDGMENT), But the word " thought " having an accep tation co-extensive with all intelligence, including memory, imagination, etc., as well as the operations concerned about truth, must he held to its narrower meaning, bv which it shnply includes the three great operations, constituting the distinct stages or divisions of logic, coneeption, judgment, and reasoning.
3Ir. John Stuart Mill has p-ropounded a radical innovation in the definition and province of this subject. According to him, logic "is the science of the operations of the understanding which are subservient to the estimation of evidence; both the process itself of proceeding from known truths to unknown, and all other intellectual operations in so far a_s auxiliary to this. It includes, therefore, the operation of naming; for language is an instrument of thought, as well as a means of communicating our thoughts. It includes also, definition and classification." This definition has the merit of setting distinctly forth the end of the science, which is the essential point in every practical science, as logic is. That end is the estimation eviden,ce; in other words, it is not the ascertainment of all truth, but of those portions of truth that are authenticated by means of other truths, or by 2mference. The proper con
duct of the operation of inferring one thing from another is the final end of the whole science. And in laying down the true criteria of inference, a certain amount of study has to be bestowed upon some of the operations of the human understanding, not to the extent of converting logic into a system of mental philosophy, but simply so far as will conduce to the purpose in view. It is not, therefore, the "laws of thought as thought," but the laws of thought as bearin,g upon the arts of inference, that Mr. 31ill would esteem the matter of the science.
But inference is admitted on all hands to be of two or formal infer ence, and inductive or real inference. In the one, no more is inferred than is already contained in the premises; for example, "All men are mortal, therefore the present generation of Englishmen will die," is a formal inference; the conclusion is within, or less than, the premises. This is the kind of inference treated of in the deductive or syllogistic logic, which was till lately the whole of the science. In the other kind of inference, a conclusion is drawn wider than the premises, so that there is a real advance upon our knowledge: from certain things directly- ascertained we infer other things that have uot been ascertained by direct experiment, and which, but for such inference, we should have had to determine in that manner. Thus, " This, that, and the other piece of matter, in which actual observations have been made, gravitates," therefore, " inert matter, existing everywhere, known and unknown, gravitates," is an inductive inference. Of this last class of inferences, all the inductive sciences, including physics, chemistry, physiology', mental philosophy, etc., are made .up., Accordingly, Mr. Mill treats this as coming within the province of logic, no less 'than the deductive, formal, syllogistic, or necessary inference, which previous logicians had confined themselves to exclusively.
Sir 1V. Hamilton, in his system, admits the consideration of induction under what he terms " modified logic," in contradistinction to " pure logic," or formal inference; and it has not been unusual for writers on the science to devote a chapter to induction, after expounding the laws of the syllogism. But Mr. Mill has given to the inductive part the predominance over the other, as being the more fundamental, as well as prac itically the more irnportant of the two. Making logic co-extensive with proof, he endeav ors to show that the establishment of the prenuscs, front which the formal logician takes his start, is, after all, the main point, and that the other is subsidiary and subordi nate, although still important to be attended to, awl susceptible of being well or ill done. He further shows that there are rules, or methods of procedure, which may be set forth and followed in the inductive operation; that mankind often break those rules frorn ignorance or inadvertence (as well as from other causes); and that good may be done by explicitly calling attention to them, and niaking them a branch of education, as the old logic has for a long time been. See INDUCTION, SYLLOGISM.