Tarski did research on set theory and also used set theory in many of his emblematic writings. Yet his notion of set from the philosophical viewpoint was almost unknown. By studying mostly the posthumously published evidence, his still unpublished materials, and the testimonies of some of his collaborators, I try to offer here a first, global picture of that intuitive notion, together with a philosophical interpretation of it. This is made by using several notions of universal languages as framework, and by taking into consideration the evolution of Tarski’s thoughts about set theory and its relationship with logic and mathematics. As a result, his difficulties to reconcile nominalism and methodological Platonism are precisely located, described and much better understood.