 Lewis’s proposal is not ad hoc, as the notion of a natural property that it utilises is required, for example, by his account of laws of nature (see the entry on  David Lewis,  section 4.6). However, its application to the rule-following problem faces a number of challenges. First, it is not obvious how it extends to the mathematical examples that are the focus of Kripke’s Wittgenstein. Boghossian writes, 