Łukasiewicz’ Theory of Truth, from the Quantum Logical Point of View

Abstract

In 1920 Łukasiewicz published a two-page article whose title was “On Three-valued Logic”. The paper proposes a semantic characterization for the logic that has been later called Ł³ (Lukasiewicz’ three-valued logic). In spite of the shortness of the paper, all the important points concerning the semantics of Ł³ are already there and can be naturally generalized to the case of a generic number n of truth-values (and also to the case of infinite many values). The conclusion of the article is quite interesting:

The present author is of the opinion that three-valued logic has above all theoretical importance as an endeavour to construct a system of non-aristotelian logic. Whether the new system of logic has any practical importance will be seen only when the logical phenomena, especially those in the deductive sciences, are thoroughly examined, and when the consequences of the indeterministic philosophy, which is the metaphysical substratum of the new logic, can be compared with empirical data.[6]