Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to order should be accounted for (...) without altering the standard formulation of plural logic. In particular, sensitivity to order does not call for a fine-grained notion of plural reference. We point out that the phenomenon in question is quite broad and that current proposals are not equipped to deal with the full range of cases in which order plays a role. Then we develop an alternative and unified account, which locates the phenomenon not in the way in which plural terms can refer, but in the meaning of special expressions such as 'in that order' and 'respectively'. (shrink)

According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which dispenses with (...) plural properties and thus undermines the semantic argument in favor of the plural conception of reality. (shrink)

In 1903, in _The Principles of Mathematics_ (_PoM_), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before _PoM_ even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...) why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

I formulate a theory of groups based on pluralities and counterparts: roughly put, a group is a plurality of entities at a time. This theory comes with counterpart-theoretic semantics for modal and temporal sentences about groups. So this theory of groups is akin to the stage theory of material objects: both take the items they analyze to exist at a single time, and both use counterparts to satisfy certain conditions relating to the modal properties, temporal properties, and coincidence properties of (...) those items. (shrink)

Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This (...) makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars. Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

Institutions, if unjust, ought to be reformed or even abolished. This radical Rawlsian thought leads to the question of whether the family ought to be abolished, given its negative impact on the very possibility of delivering equality of life chances. In this article, we address questions regarding the justice of the family, and of marriage, and reflect on rights, equality, and the provision of social goods by institutions. There is a temptation to justify our social institutions in terms which highlight (...) their universal accessibility and benefits. But we may best understand the claim of some of our most important institutions where we recognize that they are forms of social good which may legitimately benefit some without having to benefit all. Their abolition is unjustified where there is sufficient value in them given our collective needs that it is unreasonable for some to refuse the means to maintain and promote these goods. (shrink)

I give shape to a neglected debate in metaphysics, the debate over the ontological priority between individuality and collectivity. I distinguish the debate from more familiar ones in the recent literature and articulate what I call ontological collectivism, the view that collectivity is prior to individuality. I defend the in-principle intelligibility of the view from forceful general objections and argue that not only is it coherent but also of significant interest to the literature: it allows for overlooked alternatives on a (...) variety of central discussions. (shrink)

In the semantic debate about plurals, pluralism is the view that a plural term denotes some things in the domain of quantification and a plural predicate denotes a plural property, i.e. a property that can be instantiated by many things jointly. According to a particular version of this view, untyped pluralism, there is no type distinction between objects and properties. In this article, I argue against untyped pluralism by showing that it is subject to a variant of a Russell-style argument (...) put forth by Timothy Williamson and that it clashes with a plural version of Cantor’s theorem. I conclude that pluralists should postulate a type distinction between objects and properties. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

In recent literature on plurals the claim has often been made that the move from singular to plural expressions can be iterated, generating what are occasionally called higher-level plurals or superplurals, often correlated with superplural predicates. I argue that the idea that the singular-to-plural move can be iterated is questionable. I then show that the examples and arguments intended to establish that some expressions of natural language are in some sense higher-level plurals fail. Next, I argue that these and some (...) other expressions should instead be classified as plurals whose reference is articulated, an idea explained and elaborated in the paper. I also show that the related categories of plural and superplural predicates collapse to that of ordinary predicates. In the process we also see that the law of substitutivity salva veritate should be elaborated for cases involving expressions more complex than singular ones. (shrink)

1. ExpositionRichard Sharvy's ‘A more general theory of definite descriptions’ was published in 1980. Its aim was to replace Russell's paradigm by " a general theory of definite descriptions, of which definite mass descriptions, definite plural descriptions, and Russellian definite singular count descriptions are species. … We have an account of the generic ‘the’ along these same lines. " By now his theory has attained the status of a new paradigm. Even a casual trawl of the literature throws up over (...) a score of citations and endorsements, and no rebuttals of its central contention that the primary use of ‘the’ is to indicate totality . We shall argue that it is wrong for mass description, wrong for singular description, wrong for plural description and wrong for generic ‘the’. Sharvy would have approved: his obituary says that his car displayed the slogan ‘Subvert the Dominant Paradigm’.He follows Russell in treating descriptions as incomplete symbols, but nothing in his paper turns on this aspect of it, and we can bypass the issue by considering them in the context of complete sentences. Where Russell translates F into the predicate calculus as Formula Sharvy translates it as Formula Here ≤ is supposed to stand for some or other species of part of relation. His other governing idea is of a predicate's being cumulative. G is cumulative if any number of things that satisfy G have a sum, i.e. a least upper bound with respect to ≤ which also satisfies G. The meanings of ≤, sum and cumulativity vary according to the different kinds of description, which we take in the order in which Sharvy presents them. Meanwhile, we note that he originally defined ‘sum’ to mean simply the l.u.b. , but subsequently redefined …. (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)

Descriptions are phrases of the form ‘an F’, ‘the F’, ‘Fs’, ‘the Fs’ and NP's F (e.g. ‘John's mother’). They can be indefinite (e.g., ‘an F’ and ‘Fs’), definite (e.g. ‘the F’ and ‘the Fs’), singular (e.g., ‘an F’, ‘the F’) or plural (e.g., ‘the Fs’, ‘Fs’). In English plural indefinite descriptions lack an article and are for that reason also known as ‘bare plurals’. How to account for the semantics and pragmatics of descriptions has been one of the central (...) topics in philosophy for centuries. This entry focuses on the historical and contemporary philosophical debate about Bertrand Russell’s theory of descriptions and the theories that developed as responses to this theory. (shrink)

We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of (...) quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items. (shrink)

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. (shrink)

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

This thesis explores the development of Bertrand Russell‘s theory of definite descriptions. It aims at demonstrating the connection between Russell‘s views on the subject of denoting and his attempt, in the period 1903-05, to develop a solution to 'the Contradiction'. The thesis argues that the discovery of the theory of descriptions, and the way in which it works, are best understood against the backdrop of Russell‘s work on the paradoxes. A new understanding of Russell‘s seminal paper 'On Denoting' is presented, (...) including a novel interpretation of the notorious 'Gray‘s Elegy Argument', in which Russell argues against his earlier theory of denoting. That Russell‘s work on denoting is connected to his work on the paradoxes is reasonably well-known: the nature of the connection has not, however, been adequately brought out in the literature. This is addressed through demonstrating the relationship between Russell‘s work on denoting and his development of the 'substitutional theory' of classes and relations. This theory eliminates classes and propositional functions in favour of matrices and substitutions. The role of the theory of descriptions in the development of the substitutional theory is commonly supposed to be merely that the theory of descriptions facilitates the ontological elimination of classes. But this elimination was equally possible on Russell‘s earlier theory of denoting. In the thesis it is suggested that the theory of descriptions brings with it a new conception of analysis, and that it is through the introduction of this new form of analysis—rather than through the elimination of classes—that the theory of descriptions facilitates the substitutional approach. (shrink)