The paper puts forward a modifi ed defi nition of the notion “following”, which can be used to solve the paradoxes of material implication in a new way. The classical truth-functional defi nition of implication is criticized as a purely “scalar” one, i.e. not containing the proper vector aspect. According to the author’s hypothesis, inclusion of the vector aspect to make the defi nition of implication more complete and precise (in comparison with the classical one) would provide new opportunities for eliminating the paradoxes of following. The author goes on to propose a new generalized formulation of the laws of contraposition of logical operations “implication” and “correction”, which takes into account their vector aspect. The described approach is further applied to analyze Schopenhauer’s remark about the fundamental analogy between formal logic and а priori knowledge of nature. In relation to the interconnection between logic and metaphysics of nature, the structural-functional analogy between two-valued algebra of logic and two-valued algebra of metaphysics as formal axiology is exemplifi ed by Newton’s third law.