Naturalness and Convex Class Nominalism

Abstract

In this paper I argue that the analysis of natural properties as convex subsets of a metric space in which the distances are degrees of dissimilarity is incompatible with both the definition of degree of dissimilarity as number of natural properties not in common and the definition of degree of dissimilarity as proportion of natural properties not in common, since in combination with either of these definitions it entails that every property is a natural property, which is absurd. I suggest it follows that we should think of the convex class analysis of natural properties as a variety of resemblance nominalism.

Does everything resemble everything else to the same degree?

“…152-158), for example, present a sparse conception of properties which is like Armstrong's in accepting that all conjunctions of sparse properties are properties, but differs from Armstrong's in only denying that some negative and disjunctive properties are. ButBlumson (2019b) proves this conception does not overcome the problems with Armstrong's.…”

“…22-35), Oliver (1996, p. 52), Rodriguez-Pereyra (2002, Paseau (2012, p. 365), Blumson (2014b, pp. 179-193), Paseau (2015, p. 110), Blumson (2018), andBlumson (2019b). Yi (2018) criticises some of these analyses.…”

ZF-Class Nominalism and the Küng-Armstrong Trilemma

“…Thus I already have at my disposal a theory of properties as classes of possibilia. (Lewis, 1983, p. 343) More recently Busse (2016) has expressed sympathy with this general perspective by proposing a defense of Class Nominalism from Wolterstorff (1970)'s argument to the effect that properties cannot be identical to classes, while Blumson (2019) has put forward a novel proposal, Convex Class Nominalism, which brings together Resemblance Nominalism and Gärdenfors (2000)'s conception of natural properties as convex subsets of a conceptual space.…”