The term “law” appears in different contexts with different meanings. We are used to speaking of natural laws, legal laws, moral laws, aesthetic laws, historical laws. Such a linguistic convention has represented a constant phenomenon through the history of civilization. Is there any deep common root among all these different uses and meanings?

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 . 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 . 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. (shrink)