Gonzalo Rodriguez-Pereyra (1997) has refined an argument due to Thomas Baldwin (1996), which claims to prove nihilism, the thesis that there could have been no concrete objects, and which apparently does so without reliance on any heavy-duty metaphysics of modality. This note will show that on either reading of its key premiss, the subtraction argument Rodriguez-Pereyra proposes is invalid. [A sequel to this paper, 'The Subtraction Argument(s)', was published in Dialectica in 2006.].

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after (...) all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory. (shrink)

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after (...) all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory. (shrink)