1. Definition. Logic is the study of reasoning --- the nature of good (correct) reasoning and of bad (incorrect) reasoning. Its focus is the method or process by which an argument unfolds, not whether any arbitrary statement or series of statements is "true" or accurate. Logicians study and analyze arguments, premises, inferences, propositions, conditional statements, and symbolic forms.
As a "branch" of philosophy, logic is often broken down into many subsets: for instance, modal logic, many-valued logic, modern logic, symbolic logic, formal and informal logic, deductive and inductive logic.
See also logical fallacies.
"Logic. The systematic study and discipline dealing with the principles of valid inference. Its distinction from psychology is in its matter, i.e., logic concerns itself solely with the validity of thought, psychology with the nature of thought and its relationship with other vital processes. Aristotle was the founder of logic; and later investigation has not superseded his work but extended the field. From the beginning it has been recognized that in all thinking there are certain presuppositions, three of which have been known as the laws of thought. They are the law of identity: whatever is, is (A is A); the law of contradiction: a thing cannot both be and not be (A cannot be B and not-B); the law of the excluded middle: a thing must either be or not be (A is either B or not-B). Deductive thinking is largely reducible to a form such as: All men are mortal. Socrates is a man, therefore Socrates is mortal (all S is P, M is S, therefore M is P); or more exactly: If all men are mortal, and if Socrates is a man, Socrates must then be mortal. Such a form is known as a syllogism. The investigation of deduction and the elaboration of the syllogism are the work of Aristotle, and the Aristotelian logic has been the logic of schools and men in general; this has been certainly assisted by its application in the Euclidean geometry and in the scholastic philosophy. Induction lends itself to no such analysis as deduction, and it has been often neglected. This is the process by which general propositions are established: it involves the passing from the particular to the general. Its application in the world rests on the assumption that there are invariable effects produced by natural causes; and a general induction is made by discovering apparent uniformities which afford the basis of generalizations. It can achieve only probability, never mathematical certainty.
J.S. Mill's canons of inductive method sought to formulate the principles of experimental procedure. The theory of probability belongs to induction as well as to mathematics. The process of induction has been the great method of modern science, and by it many of the most notable of scientific achievements have been made. Thus it was by induction that Newton enunciated the principle of gravity and Darwin the theory of evolution. The importance of induction in science led for a time to a common acceptance of it as giving certainty and to a kind of compensatory neglect of deduction. That there was a certain inadequacy in the Aristotelian logic was long felt. Thus, some metaphysicians have held that the law of contradiction may not be true at all times, that A may be both B and not-B. Similarly some claimed that, though it is true, it is not strictly capable of syllogistic statement that: if A is to the right of B and C is to the right of A, then C is to the right of B. Most of the principal philosophers of the post-Renaissance period attempted to add to logic or to develop a logic of their own, some of them going so far as to apply the term to fields which were quite unrelated.
In the 19th century arose a new logical field which has had wide attention and cultivation. It is called logistic or symbolic logic and owes much to the work of George Boole and Augustus de Morgan. Its characteristic form is the application of mathematical symbols to logic, and its substance is analysis of relation. The fundamental inadequacy of Aristotelian logic, according to the logicians, arises in the use of language rather than symbols. An example of how language can fail the logician is the alleged ambiguity of the copula, e.g., in the statements "A is B" and "All A are B" the "is" and "are" seem to express different relations. The application of mathematical symbols to logic not only removes any such possible ambiguity but also greatly simplifies logical processes and admits of extending their application far beyond the province of the Aristotelian logic. The development of symbolic logic in the hands of A.N. Whitehead and Bertrand Russell has made it cover the same ground in its extension as the higher mathematics.
3. Reasons To Study Logic. Nothing might seem as dry, as technical, and as boring as plowing through old logic texts such as those of Aristotle and John Stuart Mill. Who but a very ambitious and select breed would look upon the experience with eagerness and excitement? The old tomes aren't as bad as one might think, and the study of logic needn't center on memorizing them. There are countless odd textbooks for college freshmen and sophomores that are quite good. Many of these provide good recapitulations, interesting problems to solve, and a hefty list of common fallacies. Leafing through numerous such guides can be immensely helpful.
Why should anyone bother to study at least a little logic? To sharpen the mind in a world saturated by streams of propaganda and advertising. To know when a pitchman is conning you, when some "expert" or pundit is propounding a dubious doctrine, when someone is making an apocryphal claim about miracles or divinity or the afterlife. To chasten one's own thinking, to develop an appreciation for tenable arguments and a respect for good reasoning. To become more adept at solving problems, whether they're encountered in business, science, politics, or the law.