Logic (Gk. logos, "reason," "argument") may be roughly defined as the study of the laws or forms of correct thinking. Since thought is at bottom the instrument of all knowledge, it soon became necessary to determine whether all conclusions of thought were equally correct. Logic, in other words, begins with the beginning of science. The problem as to what are the laws or forms to which correct thinking must conform presented itself at an early date to the Greeks and obtained a provisional solution from both Parmenides and Plato. With them, however, logic is not yet separated from general philosophy. Aristotle is the first to systematise logic, and to assign it a department of its own. The real question which Aristotle attempts to solve in his Analytics (the term Logic is due to Zeno the Stoic) is what are the conditions of science. Science exists as systematised knowledge. What presuppositions are necessary to explain'its existence ? And this question has remained the problem of logic for most succeeding thinkers. This aim of Aristotle's logic was obscured in succeeding ages by the attention which was concentrated on the account which he gives of the formal laws of thought. The whole mechanism of deductive logic, depending on the doctrine of syllogism (q.v.), was taken over by the schoolmen from Aristotle, and little attention was paid to the other parts of his logical system. This deductive logic was well suited to mediaeval thought. Science in the modern sense did not exist, and all that was required of logic was to evolve the correct consequences of the propositions of the faith, which according to the theory of the mediaeval Church' were given by revelation. Hence the syllogistic logic did not lay down a method of arriving at knowledge, but merely analysed conceded general propositions, and rendered explicit what was implied in them. Bacon's Novum Organmn is a revolt against this deductive logic, and is, in the main, a return to the real views of Aristotle. Logic is to be the instrument of scientific discovery, and, as no general proposition can be taken for granted, it must be obtained by experiment in accordance with the new inductive method, which assembles a number of particular allied instances, and discovers the law which underlies them. Inductive logic, which begins with Bacon, is most fully worked out by J. S. Mill in his System, of Logic. Since Bacon two principal views have obtained as to the office of logic. (1) There are the formal logicians (e.g. Hamilton, Mansel), who have rehabilitated the scholastic logic. Under the influence of Kant, Mansel elevates formal logic into a speculative science, which would exist and investigate the laws of unerring thought, even if all men were unerring thinkers. (Cf. for criticism, T. H. Green, 11 'orks, ii. 158.) (2) There are also other logicians who hold that logic is the science of the method of knowledge (e.g. J. S. Mill, Kuno, Fischer, Sigwart, Wundt). As to what the method of knowledge is, each inquirer will differ according to his view as to what the object of knowledge is; and this is a question for metaphysic to those who believe in metaphysic, and for psychology to those who, like Mill, believe that nothing is required to render reasoning possible but the senses and association. An exception must be claimed from both these two classes for Hegel, who, with his theory of the world as a process of thought from the abstract to the concrete, identifies logic with metaphysic.
[For the whole subject see Jevons' Elements of Logic; for deduction, Mansel's edition of Aldrick, Oxford (1862); for induction, Mill's System of Logic. For an attempt to reduce logic to an algebraical notation see J. Venn, Symbolic Logic (1881); also see Syllogism, Induction, Deduction.]