Tre modi di intendere le categorie: Aristotele, Kant, Mac Lane

The present paper introduces to a comparative analysis of the concept of category. First, we examine the two most known views about categories, with their associated systems of categories: the system proposed by Aristotle to frame his metaphysics and the system by which Kant intended to provide the list of epistemic categories with a rational criterion. The reasons behind their difference are briefly considered and some logical problems of both doctrines are emphasised as pointing at long-lasting theoretical gaps, which are independent of the divide between an ontological perspective and an epistemological one. Then attention shifts at the philosophical turn which led to acknowledge an irreducible plurality of categorical systems, their context-relative nature and the need of a system open to change. We sketch an argument which shows that the problems resulting from this view, often thought of as inevitable in the light of either the present-day scientific image or theorems of logic, are no less unsolvable than the problems left by the two ‘classical’ doctrines, as far as the formal architecture of a system of category is not (properly) analysed. Finally, we suggest the consideration of the mathematical theory of categories, introduced by Mac Lane and Eilenberg in 1945, as a tool to solve the above-mentioned problems and to raise new problems which prepare the ground for a more precise design of any categorical system.