Page:The American Cyclopædia (1879) Volume X.djvu/588

 582 LOGIC species to genus, &c. ; 2, comparison of quan- tity, time, place, &c. ; 3, cause and effect; 4, the relation of parts to their wholes, and vice versa. In his " Introduction to the Study of Metaphysics" Dr. Wilson has pointed out a new form of logic, applicable to the investiga- tion and criticism of metaphysical facts and phenomena. In this he starts with the prin- ciple that language consists of nouns which denote things, and that all other words are used as subsidiary to the nouns in making sen- tences ; thus, while the nouns denote the things we are speaking of, the other words indicate the relation which we suppose to exist between the things denoted by the nouns. Again, as language is but an expression of the facts and states of consciousness, we may use the words that constitute any sentence as a means of de- veloping what was contained or even implied in the thought or mental state which gave rise to the sentence, and thus obtain a more rigor- ous and exact analysis of the phenomena of consciousness than we have been accustomed to. On the other hand, Dr. McCosh, president of Princeton college, has published a work, "The Laws of Discursive Thought" (New York, 1870), in which he holds that logic is based upon and deals chiefly with " the notion." His first part treats of " the notion," and oc- cupies nearly half of the entire work. In this the author treats with great clearness and pre- cision of the nature and relation of terms as the foundation of all reasoning. Thomson's " Outline of the Necessary Laws of Thought " is based on Sir William Hamilton's theory of what is called "the quantification of predi- cate." It has been extensively used, and is a very valuable treatise. Prof. Francis Bowen, of Harvard university, published in 1864 a " Treatise on Logic," in which the two sys- tems, which may perhaps be best designated as the Aristotelian and the Hamiltonian, are both given with great clearness and impartial- ity, in such a way as to enable the learner to compare them easily and judge of their respec- tive merits. Other important works produced in this country on the subject are : " The Ele- ments of Logic," by Prof. Levi Hedge (1816), founded on the Scotch philosophy, and there- fore omitting all metaphysical discussions of formulas and a priori conditions of thought ; " The Elements of Logic," by Prof. Henry P. Tappan (1844), founded on the philosophy of Kant, and occupied rather with the conditions and laws of thought than with the application of logical formulas; "The Science of Logic," by Prof. A. Mahan (1857) ; and " System of Logic," by P. McGregor (New York, 1862). Prof. Bain, of the university of Aberdeen, published in 1870 (new ed., 1874) "Logic, De- ductive and Inductive," a work which aims at embracing a full course of the science as it is usually taught, and also in the wider sense in which it is conceived and treated by Mill. The author also treats of the principles of psycho- logy so far as he considers a knowledge of them necessary to a right understanding of logic. A peculiar and useful feature of the book is its treatment of the great generaliza- tion of the 19th century, variously designated as the correlation, conservation, persistence, or indestructibility of force or energy. It also contains an account of the various modifica- tions of the science and additions to it recom- mended by Hamilton, De Morgan, Boole, and others, and examples of its application to the other sciences. The work is valuable not only as a treatise on logic, but as explaining and illustrating the methods employed in modern scientific investigations. In 1872 Prof. Jevons, of Owens college, Manchester, England, pub- lished a small work, " Elementary Lessons in Logic," in which he gave a plain and fair state- ment of the theories of Hamilton, De Morgan, and Boole, although he regarded them as too recent to be generally adopted, and still pre- ferred the old or Aristotelian system. Sub- sequently Prof. Jevons issued a larger and more comprehensive work, "The Principles of Science : a Treatise on Logic and Scientfic Method" (London, 1874), in which he pro- poses a new system of representing the logical formulas. It is in a measure based upon the systems of Hamilton, De Morgan, and Boole, though different from them, supplying their deficiencies and correcting some errors which had been found to be involved in each of them. He assumes what is called the entire quantifi- cation of the terms, and treats the " some " which has been regarded as the sign of a par- ticular or partial proposition, as in the state- ment " Some men are wise," as an adjective differentiating a class as completely as any other adjective, as "good men." Then, rep- resenting each noun and each adjective by a letter, supposing S to stand for u some," M for "men," and W for "wise," we should have S M = M W, " Some men are men wise;" or in the ordinary form of expression, where the recurring noun in the predicate is omitted by ellipsis, we have " Some men are wise." Or if we take the following syllogism in Barbara, " All metals are elements, and all elements are incapable of decomposition," and, consid- ering " incapable of decomposition " as a sin- gle word, " indecomposable," use the initials of each word for symbols, we have M = M E, and ME = I. Replacing the subject of the last proposition by M, which is shown by the first to be equivalent (logically) to the subject of the last, we have M = I, namely, " Metal is inde- composable," for our conclusion. The author then proceeds at great length to discuss the two methods of reasoning, deductive and in- ductive. He holds that deduction is first in order, and that even induction is but a method and form of deduction, inasmuch as induction always presupposes an assumed principle or hypothesis as its major premise, although he does not call it by that name. He dissents entirely from Bacon's view of induction, and agrees, as he affirms, with the method pur-