Lukasiewicz Jan (1878–1956), Polish philosopher and logician, the most renowned member of the Warsaw School. The work for which he is best known is the discovery of many-valued logics, but he also invented bracket-free Polish notation; obtained original consistency, completeness, independence, and axiom-shortening results for sentential calculi; rescued Stoic logic from the misinterpretation and incomprehension of earlier historians and restored it to its rightful place as the first formulation of the theory of deduction; and finally incorporated Aristotle’s syllogisms, both assertoric and modal, into a deductive system in his work Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Reflection on Aristotle’s discussion of future contingency in On Interpretation led Lukasiewicz in 1918 to posit a third truth-value, possible, in addition to true and false, and to construct a formal three-valued logic. Where in his notation Cpq denotes ‘if p then q’, Np ‘not p’, Apq ‘either p or q’, and Kpq ‘both p and q’, the system is defined by the following matrices (½ is the third truthvalue): Apq is defined as CCpqq, and Kpq as NANpNq. The system was axiomatized by Wajsberg in 1931. Lukasiewicz’s motivation in constructing a formal system of three-valued logic was to break the grip of the idea of universal determinism on the imagination of philosophers and scientists. For him, there was causal determinism (shortly to be undermined by quantum theory), but there was also logical determinism, which in accordance with the principle of bivalence decreed that the statement that J.L. would be in Warsaw at noon on December 21 next year was either true or false now, and indeed had been either true or false for all time. In three-valued logic this statement would take the value ½, thus avoiding any apparent threat to free will posed by the law of bivalence.
See also MANY-VALUED LOGIC, POLISH LOGI. S.Mc.