Logic:
§ Logic is a system of laws governing the process of valid reasoning; it is the systematic study of valid inference.20 "The vulgar notion of logic," as the OED points out, "has been largely that it is a system of rules for convincing or confounding an opponent by argument." Logic is to be distinguished from rhetoric, in that logic deals in truth and "rhetoric is planted in popular opinions and manners."21
Classical, or Aristotelian logic, is concerned with the formal properties of an argument, not its factual accuracy. Aristotle (in his syllogistic approach) posited that there are 3 propositions basic to all logical thought: the law of identity (A is A), the law of contradiction (A cannot be both A and not A) and the law of the excluded middle (A must be either A or not A). Though Aristotelian logic has basically held sway in the Western world for 2,000 years, it is not the only logic. John Stuart Mill in the 19th century helped to formulate the scientific method of induction, i.e., movement from specific perceptions to generalizations. Most systems of logic have been, since the 19th century, largely supplanted as a field of study by symbolic logic, which replaces ordinary language with mathematical symbols. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to the development of the foundations of mathematics.
