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The traditional mode of dividing logic, into "formal" and "material", is maintained in many modern treatises on the subject. In formal logic the processes of thought are studied independently of, or without consideration of, their content. In material logic the chief question is the truth of the content of mental processes. An example from arithmetic will serve to illustrate the function of formal logic. When we add two and two, and pronounce the result to be four, we are dealing with a process of addition in its formal aspect, without paying attention to the content. The process is valid whatever the content may be, whether the "two and two "refer to books, horses, trees, or circles. This is precisely how we study judgments and arguments in logic. From the judgment "All A is B" we infer "Therefore some B is A"; and the process is valid whether the original proposition be "All circles are round" or "All lions are carnivorous ". In material logic, on the contrary, we inquire into the content of the judgments or premises and endeavour to determine whether they are true or false. Material logic was styled by the old writers "major logic", "critical logic", or simply" criticism". In recent times the word epistemology (science of knowledge), meaning an inquiry into the value of knowledge, has come into general use, and designates that portion of philosophy which inquires into the objective value of our concepts, the import and value of judgments and reasoning, the criteria of truth, the nature of evidence, certitude, etc. Whenever this new term is adopted there is a tendency to restrict the term logic to mean merely formal logic. Formal logic studies concepts,and other mental images, for the purpose of securing clearness and order among those contents of the mind. It studies judgments for the purpose of showing when and how they are consistent or inconsistent, that is, when one may be inferred from another (conversion), and when they are opposed (opposition) . It studies the two kinds of reasoning, deductive and inductive, so as to direct the mind to use these processes validly. Finally, it studies sophisms (or fallacies) and method for the purpose of showing what errors are to be avoided, and what arrangement is to be followed in a complex series of reasoning processes. But, while it is true in general that in all these tasks formal logic preserves its purely formal character, and does not inquire into the content of thought, nevertheless, in dealing with inductive reasoning and in laying down the rules for definition and division, formal logic does take account of the matter of thought. For this reason, it seems desirable to abandon the old distinction between formal and material, to designate as logic what was formerly called formal logic, and to reserve the term epistemology for that portion of philosophy which, while inquiring into the value of human knowledge in general, covers the ground which was the domain of material logic.
There remain certain kinds of logic which are not included under the heads formal and material. Transcendental logic (Kant) is the inquiry into human knowledge for the purpose of determining what elements or factors in human thought are a priori, that is, independent of experience. Symbolic logic (Lambert, Boole) is an application of mathematical methods to the processes of thought. It uses certain conventional symbols to represent terms, propositions, and the relations among them, and then, without any further reference to the laws of thought, applies the rules and methods of the mathematical calculus (Venn, "Symbolic Logic", London, 1881). Applied logic, in the narrower sense, is synonymous with material logic in the wider sense, it means logic applied to the study of the natural sciences, Logic applied to education, logic applied to the study of law, etc. Natural logic is that native power of the mind by which most persons are competent to judge correctly and reason validly about the affairs and interests of everyday life; it is contrasted with scientific logic, which is logic as a science and cultivated art.
Editor: Haselhurst
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