Valentina Luporini


Impure Sets as Abstract Objects Modelized Using Zalta’s Individual Concepts


In this talk, I aim to investigate the nature and the epistemology of impure sets whose use is very common in contemporary analytic philosophy. What is the nature of impure sets? Are they abstract, concrete or hybrid objects? I will argue that impure sets are fully abstract objects. Before stressing my own account, I will point out a difficulty affecting the standard idea according to which impure sets are abstract objects containing concrete ones (see, for instance, Parsons [2008] Mathematical Thought and its Objects, Lowe [1995] “The Metaphysics of Abstract Objects”, and Katze [1998] Realistic Rationalism). Then, I will explore the claim according to which impure sets are fully concrete objects (see Maddy [1991] Realism in Mathematics). I will consider certain objections raised in Chihara [1991] Constructibility and Mathematical Existence and finally reject her account proposing further and still unexplored objections. I will finally argue that impure sets are successfully formalized as fully abstract objects by extending Zalta’s Object Theory formulated in Zalta [1983] Abstract Objects: An Introduction to Axiomatic Metaphysics. More specifically, impure sets can be conceived as abstract entities whose Urelements can be modelized using Zalta’s notion of Individual Concept.

Date / Time / Place

June 21st / 12:05 / Aula Magna