...in Synthese (Open Access). Thanks to Oystein Linnebo for discussion and comments.
Title: Plural quantifiers: a modal interpretation Abstract: One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability.
I generally admire the work of Geoffrey Hellman, so I was excited to read his preprint titled Mereology in Philosophy of Mathematics, to be included in Handbook of Mereology. While the paper is well-written and quite informative, I find it highly disappointing in terms of whom it gives credit to.
When talking about using mereology in metatheory in order to describe the syntax of a given system, Hellman writes: In their "Steps Toward a Constructive Nominalism", Goodman and Quine
usedmereology along with a short list of syntactic primitive predicates of concrete marks or inscriptions intended to reconstruct enough formal syntax of mathematical language to serve as the basis of a formalist, nominalistic account of
mathematics as a symbolic, rule-governed activity... thus crediting Goodman and Quine with this approach. (Goodman and Quine are also often wrongly credited with the formulation of Mereology). Nowhere in his paper does Hellman mention Stanislaw Lesniewski, a Polish log…