The Algebra of Logic Tradition

STANLEY BURRIS; JAVIER LEGRIS

Stanford Encyclopedia of Philosophy

Metaphysics Research Lab - Center for the Study of Language and Information

Lugar: Stanford, CA; Año: 2015

The algebra of logic, as an explicit algebraic system showing the underlyingmathematical structure of logic, was introduced by George Boole (1815-1864)in his book The Mathematical Analysis of Logic (1847). The methodologyinitiated by Boole was successfully continued in the 19th century in the work ofWilliam Stanley Jevons (1835-1882), Charles Sanders Peirce (1839-1914), ErnstSchröder (1841-1902), among many others, thereby establishing a tradition in(mathematical) logic. From Boole?s first book until the influence after WWI ofthe monumental work Principia Mathematica (1910?1913) by Alfred NorthWhitehead (1861-1947) and Bertrand Russell (1872 ? 1970), versions of thealgebra of logic were the most developed form of mathematical above allthrough Schröder's three volumes Vorlesungen über die Algebra der Logik(1890?1905). Furthermore, this tradition motivated the investigations ofLeopold Löwenheim (1878-1957) that eventually gave rise to model theory. Inaddition, in 1941, Alfred Tarski (1901-1983) in his paper ?On the calculus ofrelations? returned to Peirce's relation algebra as presented in Schröder'sAlgebra der Logik. The tradition of the algebra of logic played a key role in thenotion of Logic as Calculus as opposed to the notion of Logic as UniversalLanguage. Beyond Tarski?s algebra of relations, the influence of the algebraictradition in logic can be found in other mathematical theories, such as categorytheory. However this influence lies outside the scope of this entry, which isdivided into 10 sections.