Russell Reductio Redux

Abstract

By far and away the strongest argument against there being an absolutely comprehensive domain of quantification comes from the set-theoretic paradoxes. The argument from indefinite extensibility can be rigorously regimented with the help of schematic or modal resources. After dispensing with the charge that the argument relies on an incoherent conception of set, this chapter offers a defence of its premisses. Advocates of the orthodox absolutist means to defend absolute generality have yet to give a non-ad-hoc response to the paradoxes. A heterodox absolutist view, which seeks to give an absolutist-friendly account of indefinite extensibility, leads to severe problems with impure set theory. The chapter closes by considering a revenge problem for hybrid relativists, who take modalized quantifiers to achieve absolute generality.