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)

(1) Arnie, Bob and Carlos are shipmates.1 This is something true of the three of them together. We cannot say Arnie is a shipmate except perhaps as elliptical for something that connects Arnie to others. (Arnie is a..

Plurality, Conjunction and Events presents a novel theory of plural and conjoined phrases, in an event-based semantic framework. It begins by reviewing options for treating the alternation between `collective' and `distributive' readings of sentences containing plural or conjoined noun phrases, including analyses from both the modern and the premodern literature. It is argued that plural and conjoined noun phrases are unambiguously group-denoting, and that the collective/distributive distinction therefore must be located in the predicates with which these noun phrases combine. More (...) specifically, predicates must have a hidden argument place for events; the collective/distributive distinction may then be represented in the part/whole structure of these events. This allows a natural treatment of `collectivizing' adverbial expressions, and of `pluractional' affixes; it also allows a unified semantics for conjunction, in which conjoined sentences and predicates denote groups of events, much like conjoined noun phrases denote groups of individuals. (shrink)

Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.

Bare plurals (dogs) behave in ways that quantified plurals (some dogs) do not. For instance, while the sentence John owns dogs implies that John owns more than one dog, its negation John does not own dogs does not mean “John does not own more than one dog”, but rather “John does not own a dog”. A second puzzling behavior is known as the dependent plural reading; when in the scope of another plural, the ‘more than one’ meaning of (...) the plural is not distributed over, but the existential force of the plural is. For example, My friends attend good schools requires that each of my friends attend one good school, not more, while at the same time being inappropriate if all my friends attend the same school. This paper shows that both these phenomena, and others, arise from the same cause. Namely, the plural noun itself does not assert ‘more than one’, but rather the plural denotes a predicate that is number neutral (unspecified for cardinality). The ‘more than one’ meaning arises as an scalar implicature, relying on the scalar relationship between the bare plural and its singular alternative, and calculated in a sub-sentential domain; namely, before existential closure of the event variable. Finally, implications of this analysis will be discussed for the analysis of the quantified noun phrases that interact with bare plurals, such as indefinite numeral DPs (three boys), and singular universals (every boy). (shrink)

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.

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)

The paper argues that two distinct and independent notions of plurality are involved in natural language anaphora and quantification: plural reference (the usual non-atomic individuals) and plural discourse reference, i.e., reference to a quantificational dependency between sets of objects (e.g., atomic/non-atomic individuals) that is established and subsequently elaborated upon in discourse. Following van den Berg (PhD dissertation, University of Amsterdam, 1996), plural discourse reference is modeled as plural information states (i.e., as sets of variable assignments) in a new dynamic system (...) couched in classical type logic that extends Compositional DRT (Muskens, Linguistics and Philosophy, 19, 143-186, 1996). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics become available. The idea that plural info states are semantically necessary (in addition to non-atomic individuals) is motivated by relative-clause donkey sentences with multiple instances of singular donkey anaphora that have mixed (weak and strong) readings. At the same time, allowing for non-atomic individuals in addition to plural info states enables us to capture the intuitive parallels between singular and plural (donkey) anaphora, while deriving the incompatibility between singular (donkey) anaphora and collective predicates. The system also accounts for empirically unrelated phenomena, e.g., the uniqueness effects associated with singular (donkey) anaphora discussed in Kadmon (Linguistics and Philosophy, 13, 273-324, 1990) and Heim (Linguistics and Philosophy, 13, 131-177, 1990) among others. (shrink)

This paper develops an account of pluralities based on the following simple claim: some things are nothing over and above the individual things they comprise. For some, this may seem like a mysterious statement, perhaps even meaningless; for others, like a truism, trivial and inferentially inert. I show that neither reaction is correct: the claim is both tractable and has important consequences for a number of debates in philosophy.

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.

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)

Recent scholarship provides the opportunity for an assessment of the underexplored but promising marriage between science and technology studies and Internet governance research. This article seeks to provide such an assessment by reviewing and discussing, in particular, three volumes: Laura DeNardis’s The Global War for Internet Governance, The Power of Networks: Organizing the Global Politics of the Internet by Mikkel Flyverbom, and Governance, Regulations and Powers on the Internet edited by Eric Brousseau, Meryem Marzouki, and Cécile Méadel. Approaching IG through (...) an STS lens, these authors bring to the fore a number of related issues that political and legal sciences have addressed only incompletely so far, but are crucial to understand today’s governance of the Internet as a complex sociotechnical system of systems. In their research, STS scholars of IG highlight the day-to-day, mundane practices that constitute IG; the plurality and “networkedness” of hybrid devices and arrangements that populate, shape, and define IG processes; the performative function of these arrangements vis-à-vis the virtual, yet very material, worlds they seek to regulate; the invisibility, pervasiveness, and agency of infrastructure. (shrink)

In the wake of recent attempts at alternate history (Bowler 2013), this paper suggests several avenues for a pluralistic approach to Charles Darwin and his role in the history of evolutionary theory. We examine in what sense Darwin could be described as a major driver of theoretical change in the history of biology. First, this paper examines how Darwin influenced the future of biological science: not merely by stating the fact of evolution or by bringing evidence for it; but by (...) discovering natural selection, and giving it pre-eminence over any other mechanism for evolution; and also by proposing a masterful and quite unique synthesis of many scientific fields. Contrasting Darwin’s views with those of A.R. Wallace, I conclude that “natural selection” is clearly an original contribution, that it had no forerunners or co-discoverers, and could barely have appeared after Darwin conceived of it. This specificity of Darwin’s contribution is an invitation to be strongly presentist (Loison 2016) and to adopt only weak counter-factuals. In contrast, there are possible ways to use strong counter-factuals as attempts to “pluralize” the history of biological theory: i.e. imagine new possible avenues for the development of evolutionary biology. The idea that evolution was a theory “in the air” suggests that evolutionary theory could have developed in a world without Darwin, especially if we accept to delete not only “Darwin” but “England”. France and Germany are examined as possible countries where evolutionary ideas would have thrived even with no contribution from the English scientists. Finally, the paper suggests another counter-factual hypothesis: deleting not Darwin and his Origin but the Darwin Industry itself. This may allow us to read the Origin of Species with fresh eyes and to discover Darwin’s life-long interest in variation and its laws, as many of his early readers did. (shrink)

This paper defends 'plural reference', the view that definite plurals refer to several individuals at once, and it explores how the view can account for a range of phenomena that have been discussed in the linguistic literature.

Amartya Sen; XII*—Plural Utility, Proceedings of the Aristotelian Society, Volume 81, Issue 1, 1 June 1981, Pages 193–216, https://doi.org/10.1093/aristotelian/.

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...) their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ, which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions. (shrink)

The paper addresses the evaluation of climate models and gives an overview of epistemic uncertainties in climate modeling; the uncertainties concern the data situation as well as the causal behavior of the climate system. In order to achieve reasonable results nonetheless, multimodel ensemble studies are employed in which diverse models simulate the future climate under different emission scenarios. The models jointly deliver a robust range of climate prognoses due to a broad plurality of theories, techniques, and methods in climate research; (...) the range reliably indicates the future development of the global climate. Nevertheless, the uncertainties are widely used by skeptics to challenge the IPCC’s prognoses. Such skeptical allegations can well be distinguished from points of fruitful epistemological criticism: in spite of the enduring range of prognoses, the epistemic uncertainties should not play a role in finding agreements on climate change mitigation. (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)

In this Critical Notice on Oliver and Smiley's Plural Logic, I defend the dominant paradigm in the semantics of plurals among linguists against several objections Oliver and Smiley raise, focusing especially on the proper treatment of plural definite descriptions, the threat posed by Russell's paradox, and the notion of objecthood.

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given (...) that the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

Based on a qualitative study about expert musicianship, this paper distinguishes three ways of interacting by putting them in relation to the sense of agency. Following Pacherie, it highlights that the phenomenology of shared agency undergoes a drastic transformation when musicians establish a sense of we-agency. In particular, the musicians conceive of the performance as one single action towards which they experience an epistemic privileged access. The implications of these results for a theory of collective intentionality are discussed by addressing (...) two general questions: When several individuals share an intention, does this fact secure plural self-knowledge? And is it possible to have non-observational knowledge about a collective action? It is claimed that the results drawn from the study about expert musicianship supports negative answers to both questions. (shrink)

This paper begins with a discussion ofcumulativity (e.g., ‘P(a) & P(b) implies P(a+b)’), formalized using a verb phrase operator. Next, the meanings of distributivity markers such aseach and non-distributivity indicators such astogether are considered. An existing analysis ofeach in terms of quantification over parts of a plurality is adopted. However,together is problematic, for it involves a cancellation or negation of the quantification associated witheach. (The four boys together owned exactly three cars could not be true if each of the boys (...) owned three cars, though the same sentence withouttogether could be.) A refinement of this idea of negated quantification over parts is proposed as an analysis for non-distributivity operators. It is then worked out in the system described in Cooper (1983), in which positive and negative extensions are assigned. Presuppositions connected with plural reference are considered at this point as well. Finally, the cumulativity operator is argued to be quantificational and therefore sensitive to contextual domain selection. This context sensitivity is claimed to be the source of distributive readings that appear in the absence of modifiers likeeach and non-distributive or collective readings that arise withouttogether. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

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)

I would like to discuss the claim that the resources of plural reference and plural quantification are sufficient for the purpose of paraphrasing all ordinary statements apparently concerned with composite material objects into plural statements concerned exclusively with simples.

he paper examines the thesis that participants in shared intentional activities have first-person plural ‘practical knowledge’ of what they are jointly doing, in the sense of ‘practical knowledge’ articulated by G.E.M Anscombe. Who is supposed to be the subject of such knowledge? The group, or members of the group, or both? It is argued that progress with this issue requires conceiving of collective activities as instances, not of supra-personal agency, but of interpersonal agency; specifically: as involving communication. There is a (...) sense, it is suggested, in which the basic form of plural practical knowledge is relational: ‘I am doing x with you.’. (shrink)

Plural and conflicting values are often held to be conceptually problematic, threatening the very possibility of ethics, or at least rational ethics. Rejecting this view, Stocker first demonstrates why it is so important to understand the issues raised by plural and conflicting values, focusing on Aristotle's treatment of them. He then shows that plurality and conflict are commonplace and generally unproblematic features of our everyday choice and action, and that they do allow for a sound and rational ethics.

This paper responds to an argument of Hilary Putnam to the effect that the plurality of modern sciences shows us that any natural kind has a plurality of essences. In the past, he has argued that no system of representations, mental or linguistic, could have an intrinsic relationship to the world. Though he has granted that the Thomistic notion of form and its application to the identity of concepts may avoid these earlier objections, he has maintained that the advance of (...) the sciences has shown us that there are too many substantial forms in any particular kind of thing to provide the unity of conceptual identity required by the Thomist’s account. Given the resemblance of Putnam’s position to the “pluralists” against whom Aquinas argued in the Summa Theologiae a consideration of Aquinas arguments is undertaken. Following this, the paper examines a particular case of recent scientific practice, in order to suggest whose position, Putnam’s or the Thomist’s, more adequately captures the practice of the natural sciences of today, and their bearing upon the metaphysical question of the nature of essence in natural kinds. The paper concludes that the Thomist position on the unity of form or essence, with qualifications made about distinct conceptual approaches to some object of investigation, and the use of analogy in sorting through these distinct approaches, is better capable of accounting for the actual goals and practices of scientific understanding as we see it practiced today than is Putnam’s transcendental nominalism and neopragmatism. (shrink)

Recent research in philosophy of science has shown that scientists rely on a plurality of strategies to develop successful explanations of different types of phenomena. In the case of biology, most of these strategies go far beyond the traditional and reductionistic models of scientific explanation that have proven so successful in the fundamental sciences. Concretely, in the last two decades, philosophers of science have discovered the existence of at least two different types of scientific explanation at work in the biological (...) sciences, namely: mechanistic and structural explanations. Despite the growing evidence about the radically different nature of these two types of explanation, no inquiry has been conducted to date to determine the ontological reasons that might underlie these differences, nor the way in which these types of explanations can be systematically related with each other. Here, we aim to cover this gap by connecting this plurality of research strategies with the existence of emergent levels of reality. We argue that the existence of these different—and apparently incompatible—explanatory strategies to account for biological phenomena derives from the existence of “ontological jumps” in nature, which generate different regimes of causation that in turn demand the development of different explanatory frameworks. We identify two of these strategies—mechanistic modelling and network modelling—and connect them to the existence of two ontological regimes of causation. Finally, we relate them with each other in a systematic way. In this vein, our paper provides an ontological justification for the plurality of explanatory strategies that we see in the life sciences. (shrink)

The book Phenomenology of Plurality: Hannah Arendt on Political Intersubjectivity is a contribution not only to the phenomenological tradition of thought and Hannah Arendt studies, but also political science and, most importantly, political philosophy. Sophie Loidolt advances an intervention that stands in contrast to contemporary phenomenological research which in certain times have had the tendency to perform depoliticized examination of the self and sociality, actually revealing the intention of Phenomenology of Plurality to articulate the numerous elements that comprise the methodological (...) novelty with which Arendt changes the theory of the political. (shrink)

PG (Plural Grundgesetze) is a predicative monadic second-order system which exploits the notion of plural quantification and a few Fregean devices, among which a formulation of the infamous Basic Law V. It is shown that second-order Peano arithmetic can be derived in PG. I also investigate the philosophical issue of predicativism connected to PG. In particular, as predicativism about concepts seems rather un-Fregean, I analyse whether there is a way to make predicativism compatible with Frege’s logicism.

Say that some things form a set just in case there is a set whose members are precisely the things in question. For instance, all the inhabitants of New York form a set. So do all the stars in the universe. And so do all the natural numbers. Under what conditions do some things form a set?

The Strongest Meaning Hypothesis of Dalrymple et al (1994,1998), which was originally proposed as a principle for the interpretation of reciprocals, is extended in this paper into a general principle of plural predication. This principle applies to complex predicates that are composed of lexical predicates that hold of atomic entities, and determines the pluralities in the extension of the predicate. The meaning of such a complex predicate is claimed to be the truth-conditionally strongest meaning that does not contradict lexical properties (...) of the simple predicates it contains. Weak interpretations of reciprocals (as in the books are stacked on top of each other), plural predicate conjunction (e.g. the books are old and new) and ’atomic’ distributivity in general are derived by a unified mechanism, which ’weakens’ the basic universal meanings of strong reciprocals, boolean conjunction and quantification over atomic entities. (shrink)

Genuine agents are able to engage in activity because they find it worth pursuing—because they care about it. In this respect, they differ from what might be called “mere intentional systems”: systems like chess-playing computers that exhibit merely goal-directed behavior mediated by instrumental rationality, without caring. A parallel distinction can be made in the domain of social activity: plural agents must be distinguished from plural intentional systems in that plural agents have cares and engage in activity because of those cares. (...) In this paper, I sketch an account of what it is for an individual to care about things in terms of her exhibiting a certain pattern of emotions. After extending this account to make sense of an individual's caring about other agents, I then show how a certain sort of emotional connectedness among a group of people can make intelligible the group's having cares and thereby constitute that group as a plural agent. Alternative accounts of social action, by ignoring the difference between mere intentional systems and genuine agents, and so by leaving out these emotional entanglements from their accounts of social action, thereby fail to capture a whole range of social phenomena involving plural agents. (shrink)

Cognitive forms vary considerably as a human being detaches herself from what is closest and most personal and moves to communicate — in the broad sense of taking part in a common matter — across increasing relational distances. The article proposes to deal with the variety of cognitive formats which cannot `commonize' cognition to an equal degree, relating them to a set of regimes of engagement with the world that are identified in terms of the dependency between the human agent (...) and her environment. The good that engagement aims to guarantee orients how reality is grasped and specifies the format of what constitutes relevant information. This analysis offers new insight into the composition of communities as well as persons who have to cope with the plurality of cognitive formats and engagements from the very familiar to the most public. (shrink)

My thesis consists of three self-contained but interconnected papers. In the first one, 'Word and Objects', I assume that it is possible to quantify over absolutely everything, and show that certain English sentences containing collective predicates resist paraphrase in first-order languages and even in first-order languages enriched with plural quantifiers. To capture such sentences I develop a language containing plural predicates . ;The introduction of plural predicates leads to an extension of Quine's criterion of ontological commitment. I argue that theories (...) containing plural predicates can have plural ontological commitments in addition to singular ones. In this sense, I argue that the subject-matter of ontology is richer than one might have thought. ;Plural predicates turn out to be tremendously fruitful. For example, they provide us with natural formalizations for English plural definite descriptions and generalized quantifiers. They also allow us to state important set theoretic propositions, and give a formal semantics for second-order languages. Such a formal semantics is developed in the second paper, 'Toward a Theory of Second-Order Consequence', which is a collaboration with Gabriel Uzquiano. ;In the third paper, 'Frege's Unofficial Arithmetic', I consider an application of plural predicates to the philosophy of mathematics. By developing a suggestion of the later Frege, I show that any arithmetical predicate can be transformed into a plural predicate in such a way that the arithmetical predicate is true of the number of the Fs just in case the plural predicate is true of the Fs themselves. ;The transformation is important both because it can be put to use by nominalists about arithmetic and neo-Fregeans, and because it provides the foundations for an account of applied arithmetic. (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.

Margaret Gilbert has defended the claim that her plural subject theory can give a reasonable account of retrospective (or backward-looking) collective responsibility. On one occasion, publishing in this periodical, she writes that she deliberately left out the discussion of prospective (or forward-looking) collective responsibility, or the “responsibilities” of a collective. In the present paper, I want to show that plural subject theory, in fact, also allows accounting for prospective responsibilities of groups and institutions. In order to do so, I will (...) first sketch the social ontological background of my discussion which is, in fact, an amended version of Gilbert’s theory of plural subjects (§ 2). Based on the assumption that a prospective responsibility accrues from some kind of commissioning, I will then discuss a variety of possible sources of prospective collective responsibilities: self-commissioning, third-party commissioning and what I will call commissioning by unique capability (§ 3). Having done so, I will discuss some consequences of this account and defend it against objections (§ 4). (shrink)

In this paper, I distinguish three claims, which I label individual intentional autonomy, individual intentional autarky, and intentional individualism. The autonomy claim is that under normal circumstances, each individual's behavior has to be interpreted as his or her own action. The autarky claim is that the intentional interpretation of an individual's behavior has to bottom out in that individual's own volitions, or pro-attitudes. The individualism claim is weaker, arguing that any interpretation of an individual's behavior has to be given in (...) terms of individual intentional states. I argue that individual intentional autonomy implies neither individual intentional autarky, nor intentional individualism, with which it is usually lumped together. I further argue that this insight is the key to an adequate view of an important class of actions, i.e., plural actions. (shrink)

The view that plural reference is reference to a set is examined in light of George Boolos's treatment of second-order quantification as plural quantification in English. I argue that monadic second-order logic does not, in Boolos's treatment, reflect the behavior of plural quantifiers under negation and claim that any sentence that properly translates a second-order formula, in accordance with his treatment, has a first-order formulation. Support for this turns on the use of certain partitive constructions to assign values to variables (...) in a way that makes Boolos's reading of second-order variables available for a first-order language and, with it, the possibility of interpreting quantification in an unrestricted domain.A first-order theory, T(D), is developed on the basis of Boolos's treatment of simple plural definite descriptions extended to Richard Sharvy's general theory of definite plural and mass descriptions. I introduce a primitive predicate, o, for the relation of the referent of a singular description to that of its plural. If o is simply added to T(D), is definable in T(D), and the result is inconsistent. If o is added to a theory with axioms for the fragment of T(D) I call D-mereology, the result is a natural basis for the development of a pluralized Zermelo set theory. This theory, however, is inconsistent in an unrestricted domain, unless it is recast as a second-order theory of sets interpreted in Boolos's way. (shrink)

This paper introduces some of the main components of a novel type theoretical semantics for quantifi- cation with plural noun phrases. This theory, unlike previous ones, sticks to the standard generalized quantifier treatment of singular noun phrases and uses only one lifting operator per semantic category (predicate, quantifier and determiner) for quantification with plurals. Following Bennett (1974), plural individuals are treated as functions of type ¢¡ . Plural nouns and other plural predicates accordingly denote £ ¢¡¥¤¦¡ functions. Such predicates (...) do not match the standard £ ¢¡¥¤ £§£ ¢¡¨¤©¡¥¤ type of determiners. Following Partee and Rooth (1983), type mismatches are resolved using type shifting operators. These operators derive collectivity with plurals, keeping the analysis of singular noun phrases, where no type mismatch arises, as in Barwise and Cooper (1981). A single type shifting operator for determiners combines into one reading the existential shift and the counting (neutral) shift of Scha (1981) and Van der Does (1993). This operator combines the conservativity principle of generalized quantifier theory with Szabolcsi’s (1997) existential quantification over witness sets. The unified lift prevents unmotivated ambiguity as well as the monotonicity ill of existential lifts pointed out by Van Benthem.. (shrink)

Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if (...) class='Hi'>plurals presuppose complexes: but an Appendix shows that reference to complexes is not required in the semantics of plurals. (shrink)

This paper raises the question under what circumstances a plurality forms a set. My main point is that not always all things form sets. A provocative way of presenting my position is that, as a result of my approach, there are more pluralities than sets. Another way of presenting the same thesis claims that there are ways of talking about objects that do not always collapse into sets. My argument is related to expressive powers of formal languages. Assuming classical logic, (...) I show that if all plurality form a set and the quantifiers are absolutely general, then one gets a trivial theory. So, by reductio, one has to abandon one of the premiss. Then, I argue against the collapse of the pluralities into sets. What I am advocating is that the thesis of collapse limits important applications of the plural logic in model theory, when it is assumed that the quantifiers are absolutely general. (shrink)

Extension of the logical language to deliver plural reference and the logical relations that constitute knowledge of the singular and plural acquires empirical bite just in case it conforms with increasing precision to the syntax of the natural language and affords explanation of what speakers know about the distribution and meaning of plural expressions in their language. As for the syntax of natural language, this discussion, being none too precise, is guided throughout by just two considerations and their immediate consequences, (...) which is discussed at greater length in this article. The first, morpheme univocality, is that a morpheme despite its various syntactic and morphological contexts has a single meaning that supports all its occurrences. (shrink)

In a recent article published in this journal, Kris McDaniel proposes a variant of Peter van Inwagen’s argument against the principle of sufficient reason that makes crucial use of plural grounding. In this response paper I object to McDaniel’s argument. I argue that there is no notion of plural grounding available that is both irreflexive in the sense required for the argument to go through and general enough to formulate the principle of sufficient reason as proposed by McDaniel.