Fri Dec 1, 2006
60 Evans Hall, 4:10–6 PM
Jose Ferreiros (UC-Berkeley)
Is the Concept of Set Intuitive?
Talk of the concept of set as intuitive or commonsense has been widespread since the emergence of set theory, and it has been given much weight by such influential authors as Kurt Gˆdel. The aim of this talk is to criticize the view that our conception of sets may have intuitive origins a la Godel or be an outgrowth of common sense, while at the same time offering some suggestions as to where the impression of intuitiveness comes from. To that end I shall consider: the complex origins of set theory (especially the conflicting views of Cantor, Dedekind, Frege, and Zermelo); the role of intuitive images vs. axiomatic principles in shaping the concept of set; and the intimate connections, indeed the essential equivalence, of the concepts of set and function. This last topic will take us to reflect on what I regard as limitations of the ZFC system in relation to one of its key motivations, the idea of arbitrary subsets. If time allows, I shall end with some suggestions about the role of analogies and inter-theory relations in building up an “intuitive” understanding of sets.