Williamson's Barber
In Timothy Williamson's thought-provoking paper 'Everything' (2003) a variant of Russell's paradox is presented as a challenge for the defenders of absolute quantification, i.e. quantification over absolutely everything there is. Among those philosophers engaged in the debate on absolute quantification, two main reactions to the paradox may be identified: either one thinks that the paradox shows that absolute quantification is unten able, or that it merely shows that some underlying principle is faulty, and hence, that absolute quantification is tenable once this flaw is fixed.1 We argue, however, that both positions result from a misapprehension of the paradox, taking it too seriously. Instead, we claim that there is no paradox but merely a reductio of the claim that a definition succeeds. In fact, we find Williamson's argument more similar to the pseudo-paradox of the barber than to the paradox of Russell. Accordingly, rather than speaking of Williamson's paradox, we shall call it Williamson's argument. We first give a brief account of the argument as Williamson presents it. Some of the reactions found in the literature are then presented. Finally, we formalize the allegedly paradoxical argument to see where and why, pre cisely, it fails to be a paradox, and also what this entails for the reactions to the argument.