Groups, Sets, and Paradox

Abstract: Perhaps the most pressing challenge for singularism – the view that definite plurals like ‘the students’ singularly refer to a particular collective entity, such as a mereological sum or set – is that it threatens paradox. Indeed, this serves as a primary motivation for pluralism – the opposing view that definite plurals refer to multiple individuals simultaneously through the primitive relation of plural reference. Groups represent one domain in which this threat is immediate. After all, groups resemble sets in having a kind of membership-relation and iterating: we can have groups of groups, and groups can be members of each other. Yet there cannot be a group of all non-self-membered groups. In response, we develop a potentialist theory of groups according to which we always can, but do not have to, form a group from any sum. Modalizing group-formation makes it a species of potential, as opposed to actual or completed, infinity. This allows for a consistent, plausible, and empirically adequate treatment of natural language plurals, one which is motivated by the iterative nature of syntactic and semantic processes more generally.

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