Classical logicClassical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Each logical system in this class shares characteristic properties: Law of excluded middle and double negation elimination Law of noncontradiction, and the principle of explosion Monotonicity of entailment and idempotency of entailment Commutativity of conjunction De Morgan duality: every logical operator is dual to another While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.
Gödel's incompleteness theoremsGödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.
Bertrand RussellBertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology, and metaphysics.
