Williamson on Wittgenstein’s “Family Resemblances” and the Sorites Paradox

In a short section of his book Vagueness, Timothy Williamson attempts to resolve a paradox regarding the expansion of Wittgenstein’s ‘family resemblance’ concepts, as they are described in his Philosophical Investigations Williamson contends that certain ‘family resemblance’ concepts such as “game” seem to have the capability to expand through a network of resemblances to become applicable to everything – an undesirable and perhaps paradoxical conclusion In short, if Wittgenstein’s theory is to be plausible, argues Williamson, there must be some sort of block, conceptual or otherwise, to extensions of concepts that are susceptible to sorites paradoxes Williamson finds the best such block to be that the negation of a family resemblance concept expands in tandem with that family resemblance concept, eliminating the possibility of paradox through a sort of tension between assertion and denial This paper argues that this solution, along with Williamson’s framing of the problem, is untenable because it misunderstands the nature of Wittgenstein’s investigations and provides no relief from the problem it sets out to correct An alternative solution is presented through an exegesis of Wittgenstein’s text, which, while not addressing the problem directly, gives guidance on how to approach paradoxes like Williamson’s