Boole, George, 1815-64, English mathematician and logician. He became professor at Queen's College, Cork, in 1849. Boole wrote An Investigation of the Laws of Thought (1854) and works on calculus and differential equations. He developed a form of symbolic logic, called Boolean algebra, that is of fundamental importance in the study of the foundations of pure mathematics and is also at the basis of computer technology.

(born Nov. 2, 1815, Lincoln, Eng.—died Dec. 8, 1864, Ballintemple, Ire.) British mathematician. Though basically self-taught and lacking a university degree, in 1849 he was appointed professor of mathematics at Queen's College in Ireland. His original and remarkable general symbolic method of logical inference is fully stated in Laws of Thought (1854). Boole argued persuasively that logic should be allied with mathematics rather than with philosophy, and his two-valued algebra of logic, now called Boolean algebra, is used in telephone switching and by electronic digital computers.

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(born Nov. 2, 1815, Lincoln, Eng.—died Dec. 8, 1864, Ballintemple, Ire.) British mathematician. Though basically self-taught and lacking a university degree, in 1849 he was appointed professor of mathematics at Queen's College in Ireland. His original and remarkable general symbolic method of logical inference is fully stated in Laws of Thought (1854). Boole argued persuasively that logic should be allied with mathematics rather than with philosophy, and his two-valued algebra of logic, now called Boolean algebra, is used in telephone switching and by electronic digital computers.

Learn more about Boole, George with a free trial on Britannica.com.

Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values.

In Boolean logic, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and not-P"; "no S is P", that "there is nothing that is both S and P". For example, since there is nothing that is a round square, it is true both that nothing is a round square and purple, and that nothing is a round square and not-purple. Therefore, both universal statements, that "all round squares are purple" and "no round squares are purple" are true.

Similarly, the subcontrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent.

Thus, the subaltern relationship between universal and existential also does not hold, since for a nonexistent S, "All S is P" is true but does not entail "Some S is P", which is false. Of the Aristotelian square of opposition, only the contradictory relationships remain intact.

See also

• Boolean logic
• Propositional logic
• list of Boolean algebra topics