Numerical Quantification and Temporal Intervals

Abstract

Arthur Prior states that ‘It will be/was/is that p’ is true iff ‘p’ will be/was/is true, and that is all that needs to be said about the matter. This appears to avoid any need to invoke the existence of non-present entities and accounts for tensed truths with very little ontological cost. However, as David Lewis notes, this version of presentism gives the wrong results when applied to numerically quantified tensed propositions. I show how presentism can accommodate numerical quantification by introducing a more appropriate tense operator. Further, I argue that it is implausible to think that we can have a primitive understanding of it; the correct semantics involves quantification over past and future times. I go on to show what kind of ontology can complement this semantic story, whilst remaining presentist in nature.