In this paper I discuss some ideas of Andrey V. Smirnov, presented in his paper «Process-based Logic and Two Kinds of Apodictic Proofs», and in other works. I accentuate the importance of his hypothesis about two kinds of irreducible apodictic proofs for cultural studies and for our worldview in general. I try to assess the key premises of A. V. Smirnov’s conclusions and claim that their success is mostly dependent on the possibility of plausible interpretation of construction “because, and only because”, by which the premises of process-based syllogism of non-Aristotelian kind are connected, according to A. V. Smirnov, who have discovered such a syllogism in some works of Arabic philosophers. I claim that if we interpret this construction as a necessary condition, we would open a way for counterexamples, blocking a possibility of treating such a syllogism as an apodictic proof. But if we interpret it as a sufficient condition, we would open a way for reducing this syllogism to the Aristotelian one. Another option is to treat that construction in terms of causation of processes. The problem is, however, that causation is typically interpreted in terms of necessary or sufficient conditions as well. So it seems that to avoid serious problems A. V. Smirnov has to adopt such a definition of causation that wouldn’t include any reference to those conditions.