QUANTIFIER VARIANCE AND THE COLLAPSE ARGUMENT. (26th November 2014) - Warren, Jared
Abstract: Recently, a number of works in meta-ontology have used a variant of J.H. Harris' collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz, the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. The central lesson I draw is that arguments against quantifier variance must pay strict attention to issues of translation and interpretation. The paper also has a substantial appendix in which I prove the equivalence of plural mereological nihilism and standard first-order atomistic mereology; results of this kind are often appealed to in the literature on quantifier variance but without many details on the nature or proof of the result.