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)

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)

Statements about the behavior of biochemical entities (e.g., about the interaction between two proteins) abound in the literature on molecular biology and are increasingly becoming the targets of information extraction and text mining techniques. We show that an accurate analysis of the semantics of such statements reveals a number of ambiguities that have to be taken into account in the practice of biomedical ontology engineering: Such statements can not only be understood as event reporting statements, but also as ascriptions of (...) dispositions or tendencies that may or may not refer to collectives of interacting molecules or even to collectives of interaction events. (shrink)

In this work I first develop, motivate, and defend the view that mereological composition, the relation between an object and all its parts collectively, is a relation of identity. I argue that this view implies and hence can explain the logical necessity of classical mereology, the formal study of the part-whole relation. I then critically discuss four contemporary views of the same kind. Finally, I employ my thesis in a recent discussion of whether the world is fundamentally one in number.

In this paper I argue that we need to take irreducibly plural logic more seriously in metaphysical debates due to the fact that the verdict of many metaphysical debates hangs on it. I give two examples. The main example I focus on is the debate recently revived by Jonathan Schaffer over the fundamental cardinality of the world. I show how the three main arguments provided by Schaffer are unsound in virtue of an employment of plural logic. The second example I (...) give is a more general issue about the possibility of emergent properties of mereological wholes. Employing plural logic there is a new way to understand such cases. The upshot is that plural logic greatly matters to metaphysics and hence can no longer be ignored the way it has in this area. (shrink)

Survey of issues pertaining to the semantics of mass and plural nouns.

in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between (...) different contexts of utterance. I present an alternative response which involves the negation of that claim, and argue that it is preferable to van Inwagen’s. (shrink)

This paper argues that there is no possible structural way of drawing a distinction between objects of different types, such as individuals and properties of different adicities and orders. We show first that purely combinatorial information (information about how objects combine to form states of affairs) is not sufficient for doing this. We show that for any set of such combinatorial data there is always more than one way of typing them – that is, there are always several ways of (...) classifying the different constituents of states of affairs as individuals and properties. Therefore, contrary to received ontological opinion, no object is essentially of any specific type. In the second part we argue that taking into account logical information does not help either, since logic presupposes the very distinction we are trying to draw. Furthermore, this distinction is not even essential for logic, since logic can function perfectly well without it. We conclude that certain distinctions which have been traditionally regarded as ontologically basic (such as that between individuals and properties) cannot be as fundamental as is often supposed. (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)

Abstract: Friends of plural logic—like Oliver & Smiley (2001), Rayo (2002), Yi (2005), and McKay (2006)—have argued that a semantics of plurals based on mereological sums would be too weak, and they have adduced several examples in favor of their claim. However, they have not considered various possible counter-arguments. So how convincing are their own arguments? We show that several of them are easily answered, while some others are more problematic. Overall, the case against mereological singularism—the idea that mereological sums (...) can serve as the semantic values of plurals—turns out to be much less strong than what it is usually presented to be. (shrink)

Though there have been productive interactions between moral philosophers and deontic logicians, there has also been a tradition of neglecting the insights that the fields can offer one another. The most sustained interactions between moral philosophers and deontic logicians have notbeen systematic but instead have been scattered across a number of distinct and often unrelated topics. This chapter primarily focuses on three topics. First, we discuss the “actualism/possibilism” debate which, very roughly, concerns the relevance of what one will do at (...) some future time to what one ought to do at present (§2). This topic is also used to introduce various modal deontic logics. Second we discuss the particularism debate which, very roughly, concerns whether there can be any systematic general theory of what we ought to do (§3). This topic is also used to introduce various non-modal deontic logics. Third, we discuss collective action problems which concern the connection between the obligations of individuals and the behavior and obligations of groups of individuals (§4).This topic is also used to discuss formal systems that allow us to study the relationship between individuals and groups. The chapter also contains a general discussion of the relation between ethical theory and deontic logic (§1) and a brief consideration of other miscellaneous topics (§5). (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...) main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a “critical” alternative to traditional plural logic.

Plural first-person pronouns have often been ignored in the literature on indexicals and pronouns. The assumption seems to be that we is just the plural of I. So, we can focus on theorizing about singular indexicals and about non-indexical plurals then combine the results to yield a theory of plural indexicals. Here I argue that the “divide and conquer” strategy fails. By considering data involving plurals, generics, and complex demonstratives, I argue for a referential semantics on which we can refer (...) to two sorts of group-like entities. Further, by considering the nature of semantic theorizing, I argue that semantics must draw some metaphysical distinctions, including between groups of two sorts. (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)

The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting three necessary and independently motivated restrictions on (...) the metalinguistic predicates ‘atom’ and ‘non-atom’: both are sort, property, and context-relative. With these restrictions in place, Schein’s problematic assumption becomes evident: his presumed singularist analysis of ‘non-atom’ conflates the metalanguage with the meta-metalanguage, i.e. the language used to talk about the metalanguage. (shrink)

The primary argument against mereological singularism—the view that definite plural noun phrases like ‘the students’ refer to “set-like entities”—is that it is ultimately incoherent. The most forceful form of this charge is due to Barry Schein, who argues that singularists must accept a certain comprehension principle which entails the existence of things having the contradictory property of being both atomic and non-atomic. The purpose of this paper is to defuse Schein’s argument, by noting three necessary and independently motivated restrictions on (...) the metalinguistic predicates ‘atom’ and ‘non-atom’: both are sort, property, and context-relative. With these restrictions in place, Schein’s problematic assumption becomes evident: his presumed singularist analysis of ‘non-atom’ conflates the metalanguage with the meta-metalanguage, i.e. the language used to talk about the metalanguage. (shrink)

I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.

The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F Williams (1981, 1992). In what follows, I argue that this argument fails. I then defend an account according to which both predications of number and existence attribute properties to individuals.

Whether or not we achieve absolute generality in philosophical inquiry, most philosophers would agree that ordinary inquiry is rarely, if ever, absolutely general. Even if the quantifiers involved in an ordinary assertion are not explicitly restricted, we generally take the assertion’s domain of discourse to be implicitly restricted by context.1 Suppose someone asserts (2) while waiting for a plane to take off.

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)

Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.

Formal semantic theories are generally thought to make contact with pre-theoretic semantic notions of aboutness and reference. The nature of that contact is, however, not always straightforward. This paper addresses two debates where that issue assumes a significant role. I begin with Simchen’s recent argument that Lewisian Interpretationism succumbs to referential indeterminacy. I develop a proposal about the relationship between the theoretical notion of a term’s semantic value and the pre-theoretic notion of reference, and argue that the indeterminacy Simchen identifies (...) does not constitute a form of referential indeterminacy. In the second part, I apply these resources to the debate between singularist and pluralist approaches to the semantics of plural terms, arguing that a certain form of singularism that emerges from the dialectic ends up agreeing with the pluralist at the level of reference, if not semantic value. The paper concludes with some remarks on what a properly referential style of singularism might look like. (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)

A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but non-singular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based upon predicate logic (...) and mereological sums is too weak, since it cannot characterize the “intermediary” construals that sentences containing mass nouns may receive. We then develop an account where mass nouns are treated as non-singular terms, which may refer to several things at once. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: “The silverware that is on the table comes from Italy”. We show that this account provides a satisfactory semantics for a wide range of sentences, including cases often seen as difficult, like “The gold on the table weighs seven ounces” (Bunt 1985) and “All phosphorus is either red or black” (Roeper 1983). (shrink)

A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but plural logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets when characterizing their semantics, we arrive at a Russellian paradox. And if we use predicate logic and mereoogical ums, the semantics turns out (...) to be too weak. We then develop an account where mass nouns are treated as non-singular terms. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: "The silverware that is on the table comes from Italy." We show that this account provides a satisfactory semantics for a wide range of sentences. (shrink)

Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...) this, I argue that semantics can fail to deliver determinate ontological commitments and determinate answers to ontological questions, more generally. (shrink)

Anyone who admits the existence of composite objects allows a certain kind of coincidence, coincidence of a thing with its parts. I argue here that a similar sort of coincidence, coincidence of a thing with the stuff that constitutes it, should be equally acceptable. Acknowledgement of this is enough to solve the traditional problem of the coincidence of a statue and the clay or bronze it is made of. In support of this, I offer some principles for the persistence of (...) stuff that are general, not relying on the particular features of a kind of stuff in the way that principles for the persistence for a thing would. This provides a non-arbitrary grounding for stuff that is independent of the conditions on the nature and persistence of things the stuff composes. The principles also provide a general basis for responding to other questions about coincident stuff. (shrink)

Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular – universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the piecemeal investigation of this issue three interrelated conceptions of the particular – universal distinction are examined: universals, by contrast to particulars, are unigrade; particulars are related to universals by an asymmetric tie of exemplification; universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)

In arguing against a supposed ambiguity, philosophers often rely on the zeugma test. In an application of the zeugma test, a supposedly ambiguous expression is placed in a sentence in which several of its supposed meanings are forced together. If the resulting sentence sounds zeugmatic, that is taken as evidence for ambiguity; if it does not sound zeugmatic, that is taken as evidence against ambiguity. The aim of this article is to show that arguments based on the second direction of (...) the test are misguided: ambiguous expressions, and in particular philosophically contested ones, do not reliably lead to zeugmaticity, so an absence of zeugmaticity provides no meaningful evidence for an absence of ambiguity. (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)

Laura Gow, Uriah Kriegel, Hamid Taieb, and David Woodruff Smith raised help – and insightful points of criticism about my book Brentano’s Mind. In this paper, I will defend and expand on the main claims of the book. My responses are organized around four topics: Psychology without a Soul, Plural Intentionality (and Conceptual Parts), Intentionality and Intentionality Primitivism, Mark of Mental.

This paper replies to Himmelreich's ‘The Paraphrase Argument Against Collective Actions’ [2017], which presents three putative counterexamples to the multiple agents analysis of plural action sentences. The paper shows that the argument from the first example, the discursive dilemma, fails because it relies crucially on a simplification of the target analysis, and that the others don't bear on the question because they turn out on examination to be about individual rather than group action sentences.

I adapt an old example of Frank Jackson's, in order to show that it is not only possible that actions with different individual agents are sub-optimal when each is not, but that they are impermissible when each is not, and blameworthy when each is not.

This thesis advances and defends a novel two-category ontology of objects and dimensions, latterly conceived as respects of comparability. The proposed 'dimensionist' ontology is set out and brought to bear on discussions of determinables and determinates, the problem of universals, fact ontologies, and nomic governance. Dimensionism is argued to fare well in comparison to a range of rival ontological accounts of property possession. A metametaphysical framework is set out to undergird the discussion, which draws on both realist and pragmatist resources.

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)

Byeong-Uk Yi has argued that number words like ‘two’ primarily function as numerical predicates as in ‘Socrates and Hippias are two ’, and other grammatical uses of number words can be paraphrased in terms of the predicative use. This paper critically examines Yi’s paraphrase scheme and also some other alternative schemes, and argues that the adjectival use of number words as in ‘The Scots and the Irish are two peoples’ cannot be paraphrased in terms of the predicative use.

I address what I call the Number Issue, which is raised by our ordinary talk and beliefs about certain social groups and institutions, and I take the Hallé orchestra as my example. The Number Issue is that of whether the Hallé is one individual or several individuals. I observe that if one holds that it is one individual, one faces an accusation of metaphysical extravagance. The bulk of the paper examines the difficulty of reconciling the view that the Hallé is (...) several individuals with two prima facie plausible theses about the manner of its persistence through time. The paper is structured around some remarks made by Peter Simons about groups, and the Hallé in particular, in his 'Parts'. (shrink)

While writing this thesis, there were many things I wanted to get right. I wanted to get the data right. I wanted to get my analysis of the data right. I certainly wanted to get all my citations right, which can get pretty tricky when one is trying to finish a chapter at 2am. But if an error did creep in somewhere in the body of the thesis, that is not a disaster. Sooner or later, I will get a chance (...) to correct it in a future publication. However, this part of the thesis, which sits right at the beginning but was among the last to be written, is different. I only have one opportunity to express, in print, how thankful I am to the people whose assistance was so important to me over the past years. Which is unfortunate, since if I were to truly elaborate all I am thankful for, these acknowledgements would be the lengthiest chapter of the thesis. But I hope this brief version will suffice in its stead. (shrink)