This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.

Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book will be (...) of great interest to philosophers of language, linguists, metaphysicians, and logicians. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

I propose a `stage theory’ of groups: a group is a fusion of group-stages, where a group-stage is a plurality of individuals at a world and a time. The stage theory consists of existence conditions, identity conditions, and parthood conditions for groups.

Many explanations rely on identity facts. In this paper, I propose an account of how identity facts explain: roughly, the fact that A is identical to B explains another fact whenever that other fact depends, counterfactually, on A being identical to B. As I show, this account has many virtues. It avoids several problems facing accounts of explanatory identities, and when precisified using structural equations, it can be used to defend interventionist accounts of causation against an objection.

I propose an account of probability in the Everett interpretation of quantum mechanics. According to the account, probabilities are objective chances of centered propositions. As I show, the account solves a number of problems concerning the role of probability in the Everett interpretation. It also challenges an implicit assumption, concerning the aim and scope of fundamental physical theories, that is made throughout the philosophy of physics literature.

Groups are ubiquitous in our lives. But while some of them are highly structured and appear to support a shared intentionality and even a shared agency, others are much less cohesive and do not seem to demand much of their individual members. Queues, for example, seem to be, at a given time, nothing over and above some individuals as they exemplify a certain spatial arrangement. Indeed, the main aim of this paper is to develop the more general thought that at (...) a given time, a group is nothing over and above some individual members as they exemplify a certain complex condition. The general conception of groups that emerges is able to accommodate a variety of constraints on a reasonable answer to the question of what are groups. (shrink)

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (shrink)

Construing ontology as an inventory of what genuinely and nonredundantly exists, this paper investigates two questions: Do all – or any – social phenomena belong in ontology? and What difference does it make what is, and is not, in ontology? First, I consider John Searle’s account of social ontology, and make two startling discoveries: Searle’s theory of social reality conflicts with his ontological conditions of adequacy; and although ontology concerns existence, Searle’s theory of social reality is wholly epistemic. Then, I (...) offer my own view of social reality, on which social phenomena are ontologically significant. Since ontology concerns what genuinely and nonredundantly exists, anyone interested in what there is ought to care about ontology. (shrink)

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer—that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the (...) criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, “What are groups?”. (shrink)

Social groups—like teams, committees, gender groups, and racial groups—play a central role in our lives and in philosophical inquiry. Here I develop and motivate a structuralist ontology of social groups centered on social structures (i.e., networks of relations that are constitutively dependent on social factors). The view delivers a picture that encompasses a diverse range of social groups, while maintaining important metaphysical and normative distinctions between groups of different kinds. It also meets the constraint that not every arbitrary collection of (...) people is a social group. In addition, the framework provides resources for developing a broader structuralist view in social ontology. (shrink)

Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...) if only because mathematicians take many-valued functions seriously. We assess the objection (by Russell, Frege and others) that many-valued functions are illegitimate because the corresponding terms are ambiguous. We also assess the various methods proposed for getting rid of them. Finding the objection ill-founded and the methods ineffective, we introduce a logical framework that admits plural reference, and use it to answer some earlier questions and to raise some more. (shrink)

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.. (shrink)

I present two puzzles about the metaphysics of stores, restaurants, and other such establishments. I defend a solution to the puzzles, according to which establishments are not material objects and are not constituted by the buildings that they occupy.

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

ABSTARCT When people go shopping, they enter a building. But the shop cannot be identified with the building, because it would remain the same shop if it moved to another building or if it became an e-store. Daniel Korman [2019] uses these two observations to argue that establishments are immaterial objects. However, all that follows is that establishments are not buildings. I argue that establishments are organisations or corporate agents that are constituted by people. This entails that they are material (...) objects. Korman’s observations can be accommodated in terms of the further observation that corporate agents can but need not own or rent buildings. (shrink)

How do groups of people persist through time? Groups can change their members, locations, and structure. In this paper, I present puzzles of persistence applied to social groups. I first argue that four-dimensional theories better explain the context sensitivity of how groups persist. I then exploit two unique features of the social to argue for the stage theory of group persistence in particular. First, fusion and fission cases actually happen to social groups, and so cannot be marginalized as “pathological.” Second, (...) it is implausible that groups spatially coincide pre-fission. This means that theories that depend on pre-fission spatial coincidence, such as some endurance theories and the worm theory, cannot explain fission cases. All things considered, the stage theory offers the best explanation of how groups persist. (shrink)

This paper presents a systematic approach for analyzing and explaining the nature of social groups. I argue against prominent views that attempt to unify all social groups or to divide them into simple typologies. Instead I argue that social groups are enormously diverse, but show how we can investigate their natures nonetheless. I analyze social groups from a bottom-up perspective, constructing profiles of the metaphysical features of groups of specific kinds. We can characterize any given kind of social group with (...) four complementary profiles: its “construction” profile, its “extra essentials” profile, its “anchor” profile, and its “accident” profile. Together these provide a framework for understanding the nature of groups, help classify and categorize groups, and shed light on group agency. (shrink)

If you are a realist about groups there are three main theories of what to identify groups with. I offer reasons for thinking that two of those theories fail to meet important desiderata. The third option is to identify groups with sets, which meets all of the desiderata if only we take care over which sets they are identified with. I then canvass some possible objections to that third theory, and explain how to avoid them.

Four-dimensionalism, or perdurantism, the view that temporally extended objects persist through time by having (spatio-)temporal parts or stages, includes two varieties, the worm theory and the stage theory. According to the worm theory, perduring objects are four-dimensional wholes occupying determinate regions of spacetime and having temporal parts, or stages, each of them confined to a particular time. The stage theorist, however, claims, not that perduring objects have stages, but that the fundamental entities of the perdurantist ontology are stages. I argue (...) that considerations of special relativity favor the worm theory over the stage theory. (shrink)

If a bit of perceptual behavior is a trope, so is any response to a stimulus, and so is the stimulus, and so therefore, more generally, is every effect and its cause. When we say that the sunlight caused the blackening of the film we assert a connection between two tropes; when we say that Sunlight in general causes Blackening in general, we assert a corresponding relation between the corresponding universals. Causation is often said to relate events, and generally speaking (...) any event is a trope: a smile, a sneeze, a scream, an election, a cold snap, a storm, a lightning flash, a conspiracy, perhaps a wave, and so on up to such big and important events that they have proper names, like the Passover and Lulu the H-bomb explosion. We have called a trope a "case" of its universal, while the universal is the "kind" of the trope, so it is no surprise that a medical "case" is a trope--in the sense, at any rate, in which a person is said to have a case of typhoid fever rather than to be a case of it. A high-school boy, uncoached, has assured me, "Of course there's such a thing as Redness--this pencil has a case of it." When a scientist reports a temperature or a velocity or a viscosity he is reporting a trope--not a universal, because it is a once-for-all occurrence, but not a concrete thing either, though doubtless a component of one. He is likely to call it an "aspect" of the thing or, preferably, a "state," and generally speaking a "state" of a thing or a nation is a trope. Recent developments in sub-atomic physics, a none too reliable oracle, suggest that an electron, e.g., just is an existent state, and that the common-sense philosophy of concreta here abdicates altogether in favor of the trope. (shrink)

I have two main objectives. The first is to get a better understanding of what is at issue between friends and foes of higher-order quantification, and of what it would mean to extend a Boolos-style treatment of second-order quantification to third- and higherorder quantification. The second objective is to argue that in the presence of absolutely general quantification, proper semantic theorizing is essentially unstable: it is impossible to provide a suitably general semantics for a given language in a language of (...) the same logical type. I claim that this leads to a trilemma: one must choose between giving up absolutely general quantification, settling for the view that adequate semantic theorizing about certain languages is essentially beyond our reach, and countenancing an open-ended hierarchy of languages of ever ascending logical type. I conclude by suggesting that the hierarchy may be the least unattractive of the options on the table. (shrink)