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The curiously sweeping assumption that all reference is ‘ultimately’ singular — even in the case of plural or non-count reference — is presented and examined. In the case of plural reference, especially when associated with collective predication, the assumption takes the form of the thought that this is reference to collective entities, plural objects, or sets. Perhaps the most suggestive and profound, albeit notorious idea of this genre is Russell’s doctrine of the ‘class as many’. George Boolos’ explicitly ‘no-class’ approach to the logic of plurality is then compared favourably with ‘reductive’ approaches.

This chapter discusses the mereology of three kinds of object for which it is reasonable to suppose the extensionality principle PPP holds: occurrents, classes, and masses. Classes and masses provide the most plausible concrete interpretations of classical extensional meteology. The ontological categories of class and mass have been relatively neglected by comparison with that of individuals, and they are introduced in the present chapter. The concept of class is not that found in contemporary set theory, but what is argued to be the old-fashioned notion of a plurality of individuals; this view is also explained in this chapter. Activities and performances are also discussed, along with plural reference, pluralities, analogies between ontology and mereology, mass reference and masses, parts of groups, and further possible applications of extensional mereology.

This chapter deals with (apparent) reference to universals. A common view is that terms like wisdom and the property of being wise both refer to abstract objects. There is a range of linguistic evidence, however, that this view is mistaken. Bare adjective nominalizations like wisdom have the status of kind terms and as such are best considered terms plurally referring to the various instances. Only the property of being wise is a term referring to an abstract property, but as such it is best viewed as a term that introduces a property on the basis of a corresponding predicate. This chapter also gives an introduction to plural reference and discusses parallels between plural terms and kind terms.

This chapter discusses two approaches to the semantics of (definite) plurals: Reference to a Plurality and Plural Reference. Reference to a Plurality takes a definite plural noun phrase like “the children” to stand for a single entity that is a plurality of some sort (a sum, set, or class). Plural Reference takes “the children” to refer to each child at once. The chapter will defend Plural Reference, rejecting both the extensional-mereological version of Reference to a Plurality and the information-based version in my earlier work, especially “Parts and Wholes in Semantics” (OUP 1997). In the semantics of natural language, pluralities are never treated as “single” entities or as particular types of entities. In a given context, though, pluralities may be structured and divided into lower-level pluralities. This requires carrying over some of the insights of the information-based theory for a full account of plurals within the Plural Reference approach.

The extensional view that predicates are general terms that refer severally to the members of a set of objects that satisfy them is rejected. Instead, it is argued that predicates refer to properties, and are thus singular terms like names. The distinction between names and predicates is upheld, but it is argued that what accounts for it is not the spurious distinction between singularity and plurality of reference, but rather grammatical position, and the ontological type of the reference.

The chapter clarifies the conclusion of Brentano’s Duplication Argument. On Brentano’s view, a conscious mental act is directed on two objects, one of them being the act itself, but its plural reference is primitive, not due to the fact that the mental act has parts which each have reference on their own. Because of the plural reference the act can be brought under different partial concepts that are arrived at by abstraction. Brentano’s view is compared with contemporary versions of self-representationalism and shown not to admit of higher orders, double presentations, or indirect presentation of complexes. Brentano’s Duplication Argument makes plausible that awareness of perceiving can’t be such a complex that integrates independently existing mental acts; instead one simple act can have multiple objects.

Arbitrariness arguments turn on the claim that there is no ontologically significant difference between certain of the objects that conservatives do believe in and certain of the ones they don’t. This chapter shows how conservatives can identify ontologically significant differences in a wide range of cases. It argues that certain arbitrariness arguments can be defused by treating grammatically singular terms like ‘the Supreme Court’ as referentially plural, referring not to a single scattered object, but to nine objects (the nine justices), and shows that others can be defused by holding that the presence of creative intentions can make a difference to which objects exist.

The common view, at least since Frege, is that terms like ‘the number of planets’ refer to numbers as abstract objects. On the basis of a range of linguistic evidence, I will argue that this view is mistaken. Instead I will argue that ‘the number of planets’ refers to a number trope, the instantiation of the property of being eight in the plurality of the planets.

This chapter starts with a discussion of Parmenides’ view that there is just one object with no parts. Parmenides’ arguments are rejected. It then moves to Plato’s critique of Parmenides’ view in the Sophist. Plato draws a crucial distinction between a true unity and a sum of parts. This raises the question of how to understand mereological wholes, and the matter is examined in the rest of the chapter. It is argued that we may take an object to be identical with the sum of its parts, but not the plurality of its parts. Various objections are considered and rejected. It is also argued that nothingness may be seen as the mereological sum of the empty set. The idea is spelled out in technical detail in a formal appendix to the chapter.

This chapter gives a detailed presentation of the permissivist, eliminativist, and conservative theses under discussion. It distinguishes among a variety of different permissive and eliminative theses (e.g., universalism, plenitude, nihilism, and organicism) and explains how the arguments from the previous chapter are meant to motivate the different revisionary theses. It address a variety of attempts to show that there is a trivial answer to whether universalism and/or eliminativism is true. Finally, it includes some remarks about methodology and other background assumptions.