"On how Lewis's natural properties fail to do all the "new work" they were called for"

Abstract:

Lewis (1983) offers an argument for adopting an objective distinction between natural and unnatural properties. He claims that with the addition of this distinction to his previous ontology—composed of possibilia and the iterative hierarchy of classes built up from them—he is now able to deal with several problems that his unamended ontology faced. Amongst these are what he calls "Putnam's Paradox" and Kripke's formulation of Wittgenstein's rule-following paradox (henceforth Rule-Following Paradox).
 
However, as I argue in this paper, Lewis's solutions to both paradoxes are ill-suited. The problem is that his characterization of the Rule-Following Paradox is misguided. Once the problem is rightly formulated, it becomes clear that his "solution" is not a real answer to it. Furthermore, without a solution to this first problem, his answer to Putnam's Paradox becomes unattractive. Thus, none of these paradoxes can be taken as reasons to accept Lewis's more heavily equipped ontology.