PUB - Publikationen an der Universität Bielefeld

The dynamics of the historical growth of mathematics as well as natural science is reflected by the interaction of the continuity principle and the principle of the identity of indiscernibles. Aristotle, for example on the one side is responsible for introducing the continuity principle into natural history. On the other hand he is regarded as the great representative of a logic which rests upon the assumption of the possibility of clear divisions and rigorous classification. In modern times the Aristotelian antithesis presents itself in the problem of the concept of mechanical motion, and its mathematical formulation by means of the function concept. Leibniz' philosophy provides a differentiated and broad picture of the problem in which both principles play a major role. To talk of these means, according to Gueroult, "to take a central perspective from which one can perceive the unity of this colossal world of ideas as well as the sometimes contradictory components inherent in it". The contradictory elements alluded to here are I believe strongly related to the difference between philosophical and positive thought. Within positive scientific thought the continuity principle ranks very prominently, whereas the real importance of the principium indiscernibilium gets into view only from a philosophical perspective.