History
Algebraic logic is, perhaps, the oldest approach to formal logic, arguably beginning with a number of memoranda Leibniz wrote in the 1680s, some of which were published in the 19th century and translated into English by Clarence Lewis in 1918. But nearly all of Leibniz's known work on algebraic logic was published only in 1903 after Louis Couturat discovered it in Leibniz's Nachlass. Parkinson (1966) and Loemker (1969) translated selections from Couturat's volume into English.
Brady (2000) discusses the rich historical connections between algebraic logic and model theory. The founders of model theory, Ernst Schröder and Leopold Loewenheim, were logicians in the algebraic tradition. Alfred Tarski, the founder of set theoretic model theory as a major branch of contemporary mathematical logic, also:
- Co-discovered Lindenbaum-Tarski algebra;
- Invented cylindric algebra;
- Wrote the 1941 paper that revived relation algebra, which can be viewed as the starting point of abstract algebraic logic.
Modern mathematical logic began in 1847, with two pamphlets whose respective authors were Augustus DeMorgan and George Boole. They, and later C.S. Peirce, Hugh MacColl, Frege, Peano, Bertrand Russell, and A. N. Whitehead all shared Leibniz's dream of combining symbolic logic, mathematics, and philosophy. Relation algebra is arguably the culmination of Leibniz's approach to logic. With the exception of some writings by Leopold Loewenheim and Thoralf Skolem, algebraic logic went into eclipse soon after the 1910-13 publication of Principia Mathematica, not to be revived until Tarski's 1940 re-exposition of relation algebra.
Leibniz had no influence on the rise of algebraic logic because his logical writings were little studied before the Parkinson and Loemker translations. Our present understanding of Leibniz as a logician stems mainly from the work of Wolfgang Lenzen, summarized in Lenzen (2004). To see how present-day work in logic and metaphysics can draw inspiration from, and shed light on, Leibniz's thought, see Zalta (2000).
Read more about this topic: Algebraic Logic
Famous quotes containing the word history:
“No cause is left but the most ancient of all, the one, in fact, that from the beginning of our history has determined the very existence of politics, the cause of freedom versus tyranny.”
—Hannah Arendt (1906–1975)
“We have need of history in its entirety, not to fall back into it, but to see if we can escape from it.”
—José Ortega Y Gasset (1883–1955)
“Every library should try to be complete on something, if it were only the history of pinheads.”
—Oliver Wendell Holmes, Sr. (1809–1894)