  At first, Łukasiewicz called his three-valued logic “Non-Aristotelian”, but later he preferred the qualification “Non-Chrysippean”. According to Łukasiewicz, the Stagirite himself doubted the validity of the principle of excluded middle in the domain of future contingents. On the other hand, the Stoics believed that every proposition is true or false, independently of its temporal reference. Thus, the Stoics accepted the principle of bivalence in its unrestricted form. Now, the foundation of two or many-valued logic lies not in this or that logical theorem, but in metalogic; in particular, it is determined by accepting or rejecting the principle of bivalence. Whoever, as Chrisippus did, accepts the validity of the principle of bivalence, opts for two-valued logic; whoever even partially rejects this principle, as Aristotle did, thereby opens the door to many-valued logic. Łukasiewicz took the side of Aristotle. However, this did not close the problem of the interpretation of other logical values. Łukasiewicz tried to go though indeterminism and causality. A typical difficulty is the following. Take p as valued by ½. Its negation also has the value ½. The same holds for KpNp, contrary to the firm intuition that any pair of contradictory sentences is false. Difficulties with interpretation changed Łukasiewicz’s primary view concerning the relation of many-valued logic to reality. At first, guided by a realistic epistemology of logic, he maintained that one of the rival logics could be proved to be the correct description of the physical world. Later, he was rather inclined to look at logical systems as formalisms having their own problems deserving research and as useful devices for solving various questions but not as something leading to the only “true” ontological scheme. Yet he believed that many-valued logic would play a considerable role in the foundations of mathematics.