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Philosophy
Logic

The Algebra of Logic Tradition

Profile image of JAVIER LEGRISJAVIER LEGRIS

Abstract

The algebra of logic, as an explicit algebraic system showing the underlying mathematical structure of logic, was introduced by George Boole (1815-1864) in his book The Mathematical Analysis of Logic (1847). The methodology initiated by Boole was successfully continued in the 19th century in the work of William Stanley Jevons (1835-1882), Charles Sanders Peirce (1839-1914), Ernst Schröder (1841-1902), among many others, thereby establishing a tradition in (mathematical) logic. Furthermore, this tradition motivated the investigations of Leopold Löwenheim (1878-1957) that eventually gave rise to model theory. The tradition of the algebra of logic played a key role in the notion of Logic as Calculus as opposed to the notion of Logic as Universal Language. This entry is divided into 10 sections: 0. Introduction 1. 1847—The Beginnings of the Modern Versions of the Algebra of Logic. 2. 1854—Boole's Final Presentation of his Algebra of Logic. 3. Jevons: An Algebra of Logic Based on Total Operations. 4. Peirce: Basing the Algebra of Logic on Subsumption. 5. De Morgan and Peirce: Relations and Quantifiers in the Algebra of Logic. 6. Schröder’s systematization of the Algebra of Logic. 7. Huntington: Axiomatic Investigations of the Algebra of Logic. 8. Stone: Models for the Algebra of Logic. 9. Skolem: Quantifier Elimination and Decidability.

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