Classical logic

Classical 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. In other words, the overwhelming majority of time spent studying classical logic has been spent studying specifically propositional and first-order logic, as opposed to the other forms of classical logic. Most semantics of classical logic are bivalent, meaning all of the possible denotations of propositions can be categorized as either true or false. History of logic Classical logic is a 19th and 20th-century innovation. The name does not refer to classical antiquity, which used the term logic of Aristotle. Classical logic was the reconciliation of Aristotle's logic, which dominated most of the last 2000 years, with the propositional Stoic logic. The two were sometimes seen as irreconcilable. Leibniz's calculus ratiocinator can be seen as foreshadowing classical logic. Bernard Bolzano has the understanding of existential import found in classical logic and not in Aristotle. Though he never questioned Aristotle, George Boole's algebraic reformulation of logic, so-called Boolean logic, was a predecessor of modern mathematical logic and classical logic. William Stanley Jevons and John Venn, who also had the modern understanding of existential import, expanded Boole's system. The original first-order, classical logic is found in Gottlob Frege's Begriffsschrift. It has a wider application than Aristotle's logic and is capable of expressing Aristotle's logic as a special case.

Orthologic with Axioms

Orthologic with Axioms