Boolean algebra

Boolean algebra, or the algebra of logic, was devised by the English mathematician George Boole (1815–64) and embodies the first successful application of algebraic methods to logic.

Boole seems to have had several interpretations for his system in mind. In his earlier work he thinks of each of the basic symbols of his ‘algebra’ as standing for the mental operation of selecting just the objects possessing some given attribute or included in some given class; later he conceives of these symbols as standing for the attributes or classes themselves. In each of these interpretations the basic symbols are conceived as being capable of combination under certain operations: ‘multiplication’, corresponding to conjunction of attributes or intersection of classes; ‘addition’, corresponding to (exclusive) disjunction or (disjoint) union; and ‘subtraction’, corresponding to ‘excepting’ or difference. He also recognizes that the algebraic laws he proposes are satisfied if the basic symbols are interpreted as taking just the number values 0 and 1.

Boole’s ideas have since undergone extensive development, and the resulting concept of Boolean algebra now plays a central role in mathematical logic, probability theory and computer design.