Systematic study of valid inference. Classical, or Aristotelian, logic is
concerned with the formal properties of an argument, not its factual accuracy. Aristotle, in his Organon, held that any logical argument could be reduced to a
sequence of 3 propositions (2 premises and a conclusion), known as a Syllogism, and posited 3 laws as 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). Aristotle assumed a
correspondence linking the structures of reality, the mind, and language, a position
known in the Middle Ages as Realism. The opposing school of thought, Nominalism,
represented by William Of Occam, maintains that language and logic correspond to
the structure of the mind only, not to that of reality. John Stuart MILL in
the 19th century helped to formulate the scientific method of Induction, i.e.,
movement from specific perceptions to generalizations. Aristotelian logic
basically held sway in the Western world for 2,000 years, but since the 19th century
it has been 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. In the early 20th
century. Bertrand Russell and Alfred North Whitehead attempted to develop
logical theory as the basis for mathematics.