Øystein Linnebo

where ‘aa’ is a plural term, and ‘F’ a plural predicate. Following George Boolos (1984) and others, many philosophers and logicians also think that plural expressions should be analysed as not introducing any new ontological commitments to some sort of ‘plural entities’, but rather as involving a new form of reference to objects to which we are already committed (for an overview and further details, see Linnebo 2004). For instance, the plural term ‘aa’ refers to Alice, Bob and Charlie simultaneously, and the plural predicate ‘F’ is true of some things just in case these things cooperate. A natural question that arises is whether the step from the singular to the plural can be iterated. Are there terms that stand to ordinary plural terms the way ordinary plural terms stand to singular terms? Let’s call such terms superplural. A superplural term would thus, loosely speaking, refer to several ‘pluralities’ at once, much as an ordinary plural term refers to several objects at once.1 Further, let’s call a predicate superplural if it can be predicated of superplural terms. It is reasonably straightforward to devise a formal logic of superplural terms, superplural predicates, and even superplural quantifiers (see Rayo 2006). But does this formal logic reflect any features of natural languages? In particular, does ordinary English contain superplural terms and predicates? The purpose of this article is to address these questions. We examine some earlier arguments for the existence of superplural expressions in English and find them to be either..

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects

The neo-Fregean project of basing mathematics on abstraction principles faces “the bad company problem,” namely that a great variety of unacceptable abstraction principles are mixed in among the acceptable ones. In this paper I propose a new solution to the problem, based on the idea that individuation must take the form of a well-founded process. A surprising aspect of this solution is that every form of abstraction on concepts is permissible and that paradox is instead avoided by restricting what concepts there are.

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.