Non‐Catastrophic Presupposition Failure

Abstract

Abstract Is there always a fact of the matter about the existence of events, sets, worlds, and arbitrary mereological sums? A prior question is, how could there fail to be a fact of the matter? This chapter proposes a model, drawing on recent work in linguistics on sentences that strike us as true or false despite the failure of existential presuppositions, e.g., ‘The King of France lives in my basement’. If a term's referential properties are determined by its sentence-level effects, and these are the same whether the term refers or not, then whether a referent exists is left undetermined.

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