Page:The American Cyclopædia (1879) Volume X.djvu/587

 LOGIC 581 German writings that have appeared under the name of logic have followed very much in the same direction, discussing questions which we are accustomed to regard as belonging to on- tology under the title logic, rather than what we expect to find in books on this subject. Archbishop Whately published his " Elements of Logic " in 1826, when this branch of study was at its lowest ebb in the English universi- ties. This work has had probably a wider circulation and more extensive use than any other ever written on the subject, and had the effect of recalling public attention to its im- portance. He maintained that induction as well as deduction should be regarded as a branch of logic, and consequently attempted to explain the philosophy of induction and to show its accordance with the deductive for- mulas; and while the writers of the German schools treated logic as chiefly or exclusively concerned with thought, Whately regarded it as chiefly concerned with words. His work gave rise to many other efforts in the same department, prominent among which was the " System of Logic, Eatiocinative and Induc- tive," by John Stuart Mill (1843), in which the author treats the grounds and fundamental Erinciples rather than the formulas of reason- ig. Being an eminent thinker of the sensa- tional school, he does not make logic an a pri- ori science, but aims to systematize the induc- tive method and reduce it to strict rules. The work abounds in valuable practical hints and reflections, and the concluding portion endeav- ors to solve the question whether from moral and social phenomena the instrument of logic may not derive a body of truths empirically acquired and universally assented to, like many of the laws of the physical' world. In 1847 Prof. De Morgan published his treatise on "Formal Logic," an attempt to construct the science on a new basis. A mathematician of high repute, his work is difficult of compre- hension to all except scholars in his own de- partment. The peculiarity of its fundamental principle is that it ignores the distinction be- tween a unit and an individual. Units, how- ever, are not, and individuals are distinguish- able from one another. Six men, for example, are not distinguished as mere units from any other six objects of thought ; but it is obvious that we may predicate of six men what would not be true of six individuals in any other spe- cies of objects ; and logic doee not deal with its objects as mere units, but as individuals making up species and genera. If the subject in any affirmative proposition denote an indi- vidual, the predicate will denote the species in which it is comprehended ; and if the subject denote a species, the predicate will denote the comprehending genus; but the argument nei- ther establishes nor affirms any numerical re- lation between them. Sir William Hamilton dissented from the views of Whately and his followers, who considered logic as chiefly con- cerned with language and as including the de- partment of dialectics. He maintained that it is exclusively occupied with the forms of rea- soning, that it takes no notice of the subject matter, and has no connection with psycho- logical processes. The peculiarity of his sys- tem results from what he calls the quantifica- tion of the predicate, a fact which in his view had hitherto been overlooked. Besides the four kinds of propositions designated by A, E, I, and O, he distinguishes four others. It had previously been held that all universal propo- sitions as such and of necessity distributed the subject, and negative propositions the predi- cate. Thus in the universal affirmative, "All men are animals," the subject only is taken into the scope of the proposition as a logical whole. We here speak of "all men" as a class, but not of "all animals," and we say or imply nothing concerning the latter except that some of them are men. The universal negative distributes both terms, and in like manner it has been held that the particular affirmative takes neither of its terms as a whole, and that the particular negative dis- tributes the predicate only. But Sir William Hamilton holds that we may have affirmative propositions with the subject distributed, and negatives with or without the predicate dis- tributed; and he proposes to designate the eight propositions which result as A, U, I, Y, E, ^, 0,. The scheme, presenting the quan- tity of the predicate, is as follows : U. Toto-total: All 8 is all P. A. Toto-partial: All 8 is some P. Y. Parti-total: Some 8 is all P. I. Parti-partial : Some 8 is some P. E. Toto-total: All 8 is not all P. TJ. Toto-partial: All 8 is not some P. O. Parti-total: Some 8 is not all P. <>. Parti-partial : Some S is not some P. This view, if it be accepted, revolutionizes the theory of the syllogism, and the whole system of logic as commenced by Aristotle and elabo- rated by his followers down to the time of Hamilton. De Morgan asserted that this theory of quantification was substantially the same as his own. George Boole, for many years math- ematical professor in Queen's college, Cork, published "Mathematical Analysis of Logic" (1847), and "Investigation of the Laws of Thought, on which are founded the Mathe- matical Theories of Logic and Probabilities" (1854). An elementary treatise on logic by Dr. W. D. Wilson, then professor in Geneva col- lege, K Y. (since 1868 in Cornell university), was published in 1856. In 1872 he reissued his " Logic," in a form which is rather a new trea- tise than a new edition of the former work. In this latter he takes the ground distinctly that logic deals, not with ideas or conceptions at all, but with things, using words only as represent- ing things under the various aspects in which they are contemplated by the mind. He holds that all the laws and formulas of reasoning are derived from one or another of the four rela- tions of things, namely : 1, individual to species,