Thesis 1 stipulating the apodictic nature of P-syllogism and its irreducibility to S-syllogism stays hitherto unfaslsified. Refutations of P-syllogism proposed by the opponents proved to be sophisms or contained mistakes in premises, while the proposed ways of reducing P-syllogism to S-syllogism, when not invalid, turned out impossible because S-syllogism needs a universal term in the major premise while P-syllogism is apodictic without a universally true premise. A hypothesis is proposed to explain apodictic nature of P-syllogism and its irreducibility to S-syllogism. The formal proof is interpreted as one of the links on an epistemic chain of cognitive acts based on the initial intuition of the subject-predicate agglutinate which displays itself at the level of sensual perception, ordinary language usage and formal theoretical thought. The basic multiplicity of human mind results from its capacity to produce diverse epistemic chains stemming from different basic subject-predicate agglutinate intuitions. To build an epistemic chain, human mind needs the ‘what’ and the ‘such,’ the ‘thing’ and its qualification, the subject and its predicates. In a process-based perspective, the ‘thing,’ the ‘what,’ the subject is a process flow, and not being of a substance. Traditional philosophic issues of universality, human mind unity and intercultural understanding are discussed from the point of view of the Thesis 1 and solutions proposed.