From Leibniz’s Labyrinths and Kant’s Antinomies to Science Metaphysics

Leibniz suggested two labyrinths where human reason “goes astray”: one about the two kinds of infinity and another about law and freedom1; the latter characterizes the subjective experience of an organization of a whole system. In 1781 Kant applied them to four metaphysical subjects as they are considered by empiricists and idealists2. He then produced four couples of ad absurdum proofs, each couple giving an “antinomy” between the empirical result and the idealist result. Yet, Kant’s interpretation was incorrect because the empirical thinking, being essentially of an inductive nature, relies on intuitionist logic whose negation is weaker than the classical one. Each couple of Kant’s proofs represents two parallel ways of arguing within different kinds of logic about the two the kind of the infinity and the two kinds of a theoretical organization. Remarkably, the same two dichotomies emerged in theoretical physics from Einstein’s 1905 paper on quanta, declared by him its “most revolutionary” paper. They emerged also from an accurate inspection of the past classical scientific theories. In retrospect, Kant’s merit is to have worked at the level of the categories of our knowledge. Leibniz’ and Kant’s philosophies of knowledge suggested the best hints for recognizing and approaching the two dichotomies as the foundations of science and hence the categories of the metaphysics of science.