Saunders Mac Lane: logika, matematika eta filosofia

Abstract

This is a survey paper on Saunders Mac Lane's contributions to logic, mathematics, and philosophy of mathematics. I give in the introduction Mac Lane's basic biography. Then, I present Mac Lane's first works on mathematical logic, under the special influence of Paul Bernays, his Ph. D. advisor. I want to emphasize the fact that Mac Lane's functionalism was grounded in his early contacts with Hilbertian formalism at Göttingen. The second part of the paper is devoted to Mac Lane's fieldwork in mainstream mathematics, particularly in algebra, geometry and topology. As a result of that work, his close collaboration with Samuel Eilenberg gave birth to category theory, at least in the original American form. The third and last part of the paper shows Mac Lane's functionalist philosophy of mathematics, which was presented late in his life, but developed all along his active mathematical life. It is worth indicating that Mac Lane gave us not only a systematic picture of the totality of classical mathematics, but also a normative philosophy for understanding and doing good mathematics.