Sets as Mereological Tropes

Abstract

Either from concrete examples such as tomatoes on a plate, an egg carton full of eggs and so on, or simply because of the braces notation, we come to have some intuitions about the sorts of things sets might be. (See Maddy 1990) First we tend to think of a set of particulars as itself a particular thing. Second, even after the distinction between set-theory and mereology has been carefully explained we tend to think of the members of a set as in some sense parts. And third we tend to think that there is something represented by the braces.Now if there were experts who got their intuitions from elsewhere then we could discard these rather crude ideas about egg cartons and so on. But I suspect the intuitions of experts are, just like those of the rest of us, based on notation and simple examples.Doing full justice to our homely intuitions about sets might well require that we abandon classical mereology and treat the members of a set as quite literally parts of the set. In this paper, however, I explore an alternative, in which sets are identified with mereological tropes.