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L ogic The algebraic treatment of logic, first discussed by the Irish mathematician and logician George Boole in The Mathematical Analysis of Logic (1847). He translated symbols expressing logical relations into algebraic equations, and then manipulated them in accordance with a set of algebraic laws that he took as axioms governing the operations. This has become the central idea in modern mathematical logic. The characteristic axioms Boole's system contains are as follows: for every term there exists a complement; for any two terms there exists a sum; for any two terms there exists a product; for any term there exists a universal class; for any term there exists a null class; any two classes are commutative with regard to disjunction and conjunction; and any three classes are distributive with regard to disjunction and conjunction. The variables in this algebra are unquantified and can be read as schematic one-place predicate letters. Boolean algebra has been developed and applied to many areas. Any abstract structure constitutes such an algebra if its appropriate operations satisfy these axioms. “The Boolean algebra of unions, intersections, and complements merely does in another notation what can be done in that part of the logic of quantification which uses only one-place predicate letters.” Quine, Philosophy of Logic ... log in or subscribe to read full text