580 LOGIC cation when it was intended for only a limit- ed one. 9. The ignoratio elenchi occurs when we either fail to -give for any particular con- clusion the premises required, or draw from given premises a conclusion not legitimately following from them, or employ a legitimate syllogism which does not give the conclusion that the occasion demanded. 10. The a non causa, pro causa, occurs when we reason from a premise that is true, but not a premise to the conclusion which we profess to draw from it. 11. The fallacy of consequences consists in employing a conclusion not derived from the premises. 12. The petitio principii, or begging the question, assumes as true that which should be proved. 13. The fallacy of many questions occurs when several interrog- atories are either expressly or implicitly so combined into one that they must all receive the same answer, though truth requires that some be answered affirmatively and others negatively. Aristotle was the creator of the science of logic (though he says that Zeno the' Eleatic was the founder of dialectics), and his writings have been the basis of most of the treatises on logic that have since appeared. Six separate works constitute his Organon. In his "Categories" he treats of the highest generic ideas, which he reduces to ten, and of the nature of terms. In his " Prior Analytics " he examines the nature of propositions and the theory of conclusions; in his "Posterior An- alytics," of demonstrable knowledge and the methods of reasoning. His " Topics " embrace dialectics and the discussion of first principles ; his SopJiistica are devoted to fallacies ; and he also wrote a work on the art of expression. The whole system of Aristotle is crude and perplexed, as is usually the case with the first draft or statement of anything that lies far beyond the ordinary thought of men. There has, however, until a late period been little done in the department of logic more than to simplify and rearrange the materials furnished by the Stagirite. He recognized and discussed only the first three figures, and the discovery of the fourth is ascribed to Galen. Moreover, he scarcely regards the hypothetical syllogisms as modes of reasoning at all ; the discovery of these is ascribed to Theophrastus. It was clearly seen by Aristotle that reasoning de- pends in some way on the relations of the logical wholes (individual, species, and genus) to one another. Porphyry in his "Introduc- tion to Aristotle" explained more fully and clearly than his master had done the predica- bles, as they were called, namely, genus, spe- cies, differentia, property, and accident. Logic was extensively studied during the middle ages, though no important advance was made in its development. Its use gave rise to the scholastic method, which consists in applying the formulas of reasoning to terms, or to gen- eral principles deduced by definition or other- wise from terms. This method is of course legitimate, and the only one that is at all le- gitimate, in mathematics, and in all a priori or demonstrative sciences. But in the natural sciences the first principles or topics are the facts of nature; and a careful observation, analysis, and classification of them, together with an induction from them, must precede any useful deduction. The discovery of this great principle led to a disregard of the proper sphere and use of formal logic, and brought the whole subject into neglect and contempt ; and the inductive was generally proclaimed to be of vastly more use than the scholastic method. Induction, however, had not wholly escaped the attention of Aristotle, who defined it as "the method by which we pass from par- ticular instances to general truths." The natu- ral sciences all begin with induction. The philosophy of the method has not, however, been explained to universal satisfaction. The Novum Organum of Bacon was designed to show its necessity and practical application, rather than the philosophic grounds on which its validity rests. The works of Herschel, "Preliminary Discourse on the Study of Natu- ral Philosophy," and Whewell, "History and Philosophy of the Inductive Sciences," have greatly improved the matter since Bacon's time. But the " System of Logic " by John Stuart Mill is regarded as the best exposition of the inductive method that has yet been pro- duced. During the general neglect of logic, one of the most important works produced in its interest was La logique, ou VArt de pemer (1662), usually called the Port-Eoyal logic, by- several authors, among whom Arnauld, Ni- cole, and Sacy were most prominent. It was really in the interest of the scholastic meth- od, though intended otherwise, and though the scholastic rules and formulas were illustra- ted by new and well chosen examples, which constitute the great merit of the work. It was widely read, and gave a new impulse to the study. At the beginning of the next cen- tury Wolf published his great treatise on logic, in which he attempted to incorporate the pe- culiarities of the Leibnitzian philosophy, and which gave the direction to speculations on this subject in Germany, leading the German writers to regard the fundamental laws of thought which underlie and give validity to logical formulas, rather than their practical value or application. In 1816 Hegel comple- ted the publication of his "Logic," in which the term is used with a breadth of meaning peculiar to his philosophical system. The He- gelian logic is the law of absolute being, the scientific exposition of the pure conceptions of reason, of the absolute idea ; its domain is the absolute truth as it is in itself, apart from its manifestations ; it represents God as he is in his eternal being, before the creation of the world or of any finite mind ; it is the analysis of the successive stages of history in their ab- stract form. It thus constitutes the first and highest part of the Hegelian scheme of abso- lute idealism, and since the time of Hegel the
