This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

This paper examines the logical and metaphysical consequences of denying Leibniz's Law, the principle that if t1= t2, then φ(t1) if and only if φ(t2). Recently, Caie, Goodman, and Lederman (2020) and Bacon and Russell (2019) have proposed sophisticated logical systems permitting violations of Leibniz's Law. We show that their systems conflict with widely held, attractive principles concerning the metaphysics of individuals. Only by adopting a highly revisionary picture, on which there is no finest-grained equivalence relation, can a well-motivated metaphysics (...) for rejecting Leibniz's Law be developed. We sketch one such picture—a metaphysics of stuff. Stuff ontologies can be initially motivated through ordinary language: stuff stands to mass nouns as objects stand to count nouns. The stuff ontology we propose takes stuff to be fundamental and views the world as composed of an infinite descending hierarchy of kinds and portions of stuff. We defend the coherence of this picture and offer a model theory demonstrating that it can be consistently formalized. (shrink)

One prominent criticism of the abstractionist program is the so-called Bad Company objection. The complaint is that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some of them are inconsistent. The most notorious example, of course, is Frege’s Basic Law V. A common response to the objection suggests that an abstraction principle can be used to legitimately introduce a mathematical theory precisely when it is stable: when it can be made true on all sufficiently (...) large domains. In this paper, we raise a worry for this response to the Bad Company objection. We argue, perhaps surprisingly, that it requires very strong assumptions about the range of the second-order quantifiers; assumptions that the abstractionist should reject. (shrink)

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)

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)

Vendler’s :161–173, 1979) puzzle about imagination is that the sentences ‘Imagine swimming in that water’ and ‘Imagine yourself swimming in that water’ seem at once semantically different and semantically the same. They seem semantically different, since the first requires you to imagine ’from the inside’, while the second allows you to imagine ’from the outside.’ They seem semantically the same, since despite superficial dissimilarity, there is good reason to think that they are syntactically and lexically identical. This paper sets out (...) the puzzle and offers a novel solution. Our proposal is that, just as there is knowledge-wh, there is also imagining-wh and that the inside/outside distinction Vendler points to is properly understood as a distinction within imagining-wh. In particular, to imagine swimming from the inside is to imagine what it feels like to swim, while to imagine swimming from the outside is to imagine what it looks like to swim. We show that this proposal is well grounded in both the semantics and syntax of ‘imagine.’ We also argue it makes better sense than its rivals of the data Vendler found so puzzling. (shrink)

According to ‘composition as identity’, a composite object is identical to all its parts taken together. Thus, a plurality of composite objects is identical to the plurality of those objects’ parts. This has the consequence that, e.g., the bricks which compose a brick wall are identical to the atoms which compose those bricks, and hence that the plurality of bricks must include each of those atoms. This consequence of CAI is in direct conflict with the standard analysis of plural definite (...) descriptions. According to that analysis, the denotation of ‘the bricks’ can include only bricks. It seems, then, that if CAI is true, ‘the bricks’ doesn’t denote anything; more generally, if CAI is true, there are fewer pluralities than we ordinarily think. I respond to this argument by developing an alternative analysis of plural descriptions which allows the denotation of ‘the bricks’ to include non-bricks. Thus, we can accept CAI, while still believing in all the pluralities we could want. As a bonus, my approach to plural descriptions and plural comprehension blocks recent arguments to the effect that CAI entails compositional nihilism. (shrink)

The principal question addressed is whether there is a division among common nouns which is similar to a familiar division among noun phrases that designate particular-level individuals: the one which is captured in the relevant literature as the difference between de jure rigid and not de jure rigid singular terms. In relation with the previous philosophical literature relevant to noun rigidity it is argued that the extant positions on the matter are not defended on the basis of well-founded syntactic categories (...) and proper semantic arguments. Proper ways to argue for rigidity ascriptions to nouns are described. Then, such arguments are sought for the case of rigid/non-rigid division among count common nouns. It is shown that there are plausible, albeit inconclusive, reasons to hold that among common nouns (N-bar expressions) only simple common nouns are kind designators, and that if that is the case these simple common nouns will have to be reckoned as de jure rigid designators. (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)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars; they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple type theory while committing us to nothing more than the austere ontology (...) of First-Order Logic. Were this true, Higher-Level Plural Logic would be a useful tool, with various applications in philosophy and linguistics. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with a lot of scepticism. In this paper, I argue for the legitimacy of Higher-Level Plural Logic by providing evidence to the effect that natural languages contain higher-level plural expressions and showing that it is likely that they do so in an indispensable manner. Since the arguments I put forward are of the same sort advocates of Plural Logic have employed to defend their position, I conclude that the commonly held view that Plural Logic is legitimate, but not so its higher-level plural extensions is untenable. (shrink)

This paper revisits intervention effects in Mandarin Chinese why-questions. I present a novel empirical generalization, in which it is shown that the ability for quantifiers to induce intervention hinges upon their monotonicity and their ability to be interpreted as topics. I then propose a semantic account of intervention that correlates topicality with the monotone properties of intervening operators. A crucial assumption in this account is that why-questions in Chinese are idiosyncratic, in that the Chinese equivalent of why directly merges at (...) a high scope position that stays above a propositional argument. Combining the semantic idiosyncrasies of why-questions with the theory of topicality, I conclude that a wide range of intervention phenomena can be explained in terms of interpretation failure. (shrink)

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)

This paper argues that lexical and operator-based analyses of distributivity are not in conflict, but are both necessary components of any theory of distributivity that aims to account for all the relevant data. I use several contrasts between plural definites and group NPs to show that we need an operator-based analysis of distributivity; this kind of distributivity is available with plural definites but not with group subjects, which can be explained under the common assumption that group NPs denote atoms rather (...) than sums and hence do not allow quantification over their individual parts. At the same time, we need a lexical theory of distributivity to account for the various distributive interpretations that we do find with groups; a formalisation of such a theory is outlined in the final section of this paper. (shrink)

The present paper discusses two interesting phenomena concerning phi-features on plural pronouns: plural pronouns that denote atomic individuals, and plural pronouns with more than one binder. A novel account of these two phenomena is proposed, according to which all occurrences of phi-features are both semantically and morphologically relevant. For such a ‘uniformly semantic account’ of phi-features, dependent plural pronouns constitute a theoretical challenge, while partial binding is more or less straightforwardly accounted for. In order to make sense of the semantic (...) effects of the phi-features on dependent plural pronouns, the following idea is pursued: the phi-features on a dependent plural pronoun reflect the range of values that the pronoun takes, rather than the particular value it denotes at a time. This idea is implemented in a compositional semantics by making use of choice functions. An appealing feature of the present account is that, unlike its predecessors, it accounts for dependent plural pronouns without c-commanding antecedents in essentially the same way as for those with c-commanding antecedents. It is also shown how this account of dependent plural pronouns can straightforwardly be augmented with set indices to account for partial binding. (shrink)

This paper is concerned with the relationship between the semantics of specificational and predicational sentences and the Connectivity effects they display. It discusses the advantages and disadvantages of semantic and syntactic approaches to Connectivity (the ‘unconstrained-be theory’, the ‘question-in-disguise theory’, and the ‘unclefting theory’), concluding that a semantic theory of Connectivity is not only preferable, but necessary. The paper also discusses the implications of such a move regarding Binding phenomena (i.e., Principle A, B, and C effects): adopting a semantic theory (...) of Connectivity requires a theory of Binding which is different from the standard GB Binding Theory. (shrink)

This paper is devoted to the study of bare nominal arguments (i.e., determinerless NPs occurring in canonical argumental positions) from a crosslinguistic point of view. It is proposed that languages may vary in what they let their NPs denote. In some languages (like Chinese), NPs are argumental (names of kinds) and can thus occur freely without determiner in argument position; in others they are predicates (Romance), and this prevents NPs from occurring as arguments, unless the category D(eterminer) is projected. Finally, (...) there are languages (like Germanic or Slavic) which allow both predicative and argumental NPs; these languages, being the ‘union’ of the previous two types, are expected to behave like Romance for certain aspects of their nominal system (the singular count portion) and like Chinese for others (the mass and plural portions). This hypothesis (the ‘Nominal Mapping Parameter’) is investigated not just through typological considerations, but also through a detailed contrastive analysis of bare arguments in Germanic (English) vs. Romance (Italian). Some general consequences of this view, which posits a limited variation in the mapping from syntax into semantics, for current theories of Universal Grammar and acquisition are considered. (shrink)

According to the discontinuity view, people recognize a deep discontinuity between phenomenal and intentional states, such that they refrain from attributing feelings and experiences to entities that do not have the right kind of body, though they may attribute thoughts to entities that lack a biological body, like corporations, robots, and disembodied souls. We examine some of the research that has been used to motivate the discontinuity view. Specifically, we focus on experiments that examine people's aptness judgments for various mental (...) state ascriptions to groups. These studies seem to reveal that people are more inclined to think of groups as having intentionality than as having phenomenology. Combined with the fact that groups obviously lack a single biological body, this has been taken as evidence that people operate according to the relevant discontinuity. However, these studies support discontinuity only on the assumption that the experimental participants are interpreting the relevant group mental state ascriptions in a specific way. We present evidence that people are not interpreting these ascriptions in a way that supports discontinuity. Instead, we argue that people generally interpret group mental state ascriptions distributively, as attributions of mental states to various group members. (shrink)

This paper argues that several leading theories of subjunctive conditionals are incompatible with ordinary intuitions about what credences we ought to have in subjunctive conditionals. In short, our theory of subjunctives should intuitively display semantic humility, i.e. our semantic theory should deliver the truth conditions of sentences without pronouncing on whether those conditions actually obtain. In addition to describing intuitions about subjunctive conditionals, I argue that we can derive these ordinary intuitions from justified premises, and I answer a possible worry (...) for my derivation by refuting a subjunctive triviality result modeled on (Lewis 1976). I conclude that the debate over the correct theory of subjunctive conditionals requires settling meta-philosophical questions about the relative value of various virtues of first-order theories of subjunctive conditionals. (shrink)

The mass/count distinction attracts a lot of attention among cognitive scientists, possibly because it involves in fundamental ways the relation between language (i.e. grammar), thought (i.e. extralinguistic conceptual systems) and reality (i.e. the physical world). In the present paper, I explore the view that the mass/count distinction is a matter of vagueness. While every noun/concept may in a sense be vague, mass nouns/concepts are vague in a way that systematically impairs their use in counting. This idea has never been systematically (...) pursued, to the best of my knowledge. I make it precise relying on supervaluations (more specifically, ‘data semantics’) to model it. I identify a number of universals pertaining to how the mass/count contrast is encoded in the languages of the world, along with some of the major dimensions along which languages may vary on this score. I argue that the vagueness based model developed here provides a useful perspective on both. The outcome (besides shedding light on semantic variation) seems to suggest that vagueness is not just an interface phenomenon that arises in the interaction of Universal Grammar (UG) with the Conceptual/Intentional System (to adopt Chomsky’s terminology), but it is actually part of the architecture of UG. (shrink)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

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

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)

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)

Epistemology and epistemic logic At first sight, the modern agenda of epistemology has little to do with logic. Topics include different definitions of knowledge, its basic formal properties, debates between externalist and internalist positions, and above all: perennial encounters with sceptics lurking behind every street corner, especially in the US. The entry 'Epistemology' in the Routledge Encyclopedia of Philosophy (Klein 1993) and the anthology (Kim and Sosa 2000) give an up-to-date impression of the field. Now, epistemic logic started as a (...) contribution to epistemology, or at least a tool in its modus operandi, with the seminal book Knowledge and Belief (Hintikka's 1962, 2005). Formulas like Ki for "the agent i knows that " Bi for "the agent i believes that " provided logical forms for stating and analyzing philosophical propositions and arguments. And more than that, their model-theoretic semantics in terms of ranges of alternatives provided an appealing extensional way of thinking about what agents know or believe in a given situation. In particular, on Hintikka's view, an agent knows those propositions which are true in all situations compatible with what she knows about the actual world; i.e., her current range of uncertainty. (shrink)

This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.

This paper presents a theory of situated part structures involving the notion of an integrated and not just a part-of relation. The theory is applied in particular to the semantics of the modifiers 'whole' and 'individual', as in 'the whole collection' and 'the individual students'. The adnominal modifiers 'whole' and 'individual' have been entirely been ignored in the linguistic and philosophical literature, even though they pose significant challenges for standard views of reference, of the semantics of referential NPs, and for (...) ontology (the exception being medieval philosophy of language where 'whole' has received significant attention). 'Whole' strikingly displays two opposite readings: 'The whole collection is expensive' can mean - 'as a whole' or 'every part'. The paper proposes that the two readings be traced to two different conceptions of part structures of objects: one according to which the parts of an objects are just the material parts and another, Aristotelian conception according to which the parts of an object include properties of form. (shrink)

This paper explores the link between number marking and(in)definiteness in nominals and their interpretation. Differencesbetween bare singulars and plurals in languages without determinersare explained by treating bare nominals as kind terms. Differencesarise, it is argued, because singular and plural kinds relatedifferently to their instantiations. In languages with determiners,singular kinds typically occur with the definite determiner, butplural/mass kinds can be bare in some languages and definite inothers. An account of singular kinds in terms of taxonomic readingsis proposed, with number marking playing (...) a crucial role inexplaining the obligatory presence of the determiner. The variationbetween languages with respect to plural/mass kinds is explained bypositing a universal scale of definiteness, with individual languageschoosing different cut-off points for lexicalization of the definitedeterminer. The possibility of further cross-linguistic variation isalso considered. (shrink)

In this paper, we discuss some rather puzzling facts concerning the semantics of Warlpiri expressions of cardinality, i.e. the Warlpiri counterparts of English expressions like one,two, many, how many. The morphosyntactic evidence, discussed in section 1, suggests that the corresponding expressions in Warlpiri are nominal, just like the Warlpiri counterparts of prototypical nouns, eg. child. We also argue that Warlpiri has no articles or any other items of the syntactic category D(eterminer). In section 2, we describe three types of readings— (...) "definite", "indefinite" and "predicative"—which are generally found with Warlpiri nouns, including those which correspond to English common nouns and cardinality expressions. A partial analysis of these readings is sketched i n section 3. Since Warlpiri has no determiner system, we hypothesize that the source of (in)definiteness in this language is semantic. More specifically, we suggest that Warlpiri nominals are basically interpreted as individual terms or predicates of individuals and that their three readings arise as a consequence of the interaction of their basic meanings, which are specific to Warlpiri, with certain semantic operations, such as type shifting (Rooth and Partee 1982, Partee and Rooth 1983, Partee 1986, 1987), which universally can or must apply in the process of compositional semantic interpretation. (shrink)

Generic sentences involving phrasal conjunctions present a prima facie problem for the standard theory of generics according to which they express quasi-universal generalisations about what is characteristic for members of a particular kind. For example, the sentence ‘Elephants live in Africa and Asia’ is true, even though it is uncharacteristic for an elephant to live in both Africa and Asia. In response to this problem, theorists have recently proposed radical departures from the standard view. This paper argues that such departures (...) are unwarranted: not only do they fail to fully accommodate the data involving generic conjunctions, their scope is overly narrow, since the phenomena in question also arise in non-generic contexts. I propose a new theory of generics that aims to account for generic conjunctions in a principled manner and which sheds new light on the mereological commitments of natural language. (shrink)

Perhaps the most pressing challenge for singularism—the predominant view that definite plurals like ‘the students’ singularly refer to a collective entity, such as a mereological sum or set—is that it threatens paradox. Indeed, this serves as a primary motivation for pluralism—the opposing view that definite plurals refer to multiple individuals simultaneously through the primitive relation of plural reference. Groups represent one domain in which this threat is immediate. After all, groups resemble sets in having a kind of membership-relation and iterating: (...) we can have groups of groups, groups of groups of groups, etc. Yet there cannot be a group of all non-self-membered groups. In response, we develop a potentialist theory of groups according to which we always can, but do not have to, form a group from any sum. Modalizing group-formation makes it a species of potential, as opposed to actual or completed, infinity. This allows for a consistent, plausible, and empirically adequate treatment of natural language plurals, one which is motivated by the iterative nature of syntactic and semantic processes more generally. (shrink)

Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...) as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects. (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)

The purpose of this paper is to provide a simple type-free set theory which can be used to give the various readings of collective/distributive sentences.

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)

Personal and demonstrative pronouns are notorious for challenging any theory of natural language. Singular pronouns have received much attention from linguists and philosophers alike during the last three decades. Plural pronouns, on the other hand, have been neglected, especially by philosophers. I want to fill this gap and suggest accounts of ‘we,’ the plural ‘you,’ and ‘they.'Intuitively, singular and plural personal pronouns are ‘counterparts.' Any account of personal pronouns should make sense of this intuition. However, the latter is not very (...) sophisticated and, as we move along, it will be reexamined and relativized. As we shall see, plural pronouns are much more than mere counterparts of the familiar singular ones. It is well known that third person singular pronouns have puzzling behaviors, acting as co-referential terms, bound variables, or unbound anaphora. But co-reference, binding, and unbound anaphora are not confined to the usual examples and extend, in a way, to plural pronouns. My discussion of the latter is partly motivated by this particular behavior. (shrink)

In this paper, I shall explore a determiner in natural language which is ambivalent as to whether it should be classified as quantificational or objectdenoting: the determiner both. Both in many ways appears to be a paradigmatic quantifier; and yet, I shall argue, it can be interpreted as having an individual—an object—as semantic value. To show the significance of this, I shall discuss two ways of thinking about quantifiers. We often think about quantifiers via intuitions about kinds of thoughts. Certain (...) terms are naturally used to express singular thoughts, and appear to do so by contributing objects to the thoughts expressed. Other terms are naturally used to express general thoughts, and appear to do so by contributing higher-order properties to the thoughts expressed. Viewed this way, the main condition on whether a term is a quantifier or not is whether its semantic value is an object or a higher-order property. At least, these provide necessary conditions. Both can be interpreted as contributing objects to thoughts, and in many cases appears to express genuine singular thoughts. Thinking about quantifiers this way, both can appear object-denoting and non-quantificational. We also often think about quantifiers in terms of a range linguistic features, including semantic value, presupposition, scope, binding, syntactic distribution, and many others. Viewed this way, I shall argue, both can appear quantificational. In particular, it displays scope behavior that is one of the hallmarks of quantification. But, I shall show, it can do so even if given a semantics on which it denotes an object. Thus, both appears quantificational by some linguistic standards, and yet appears object-denoting by standards based on intuitions about the kinds.. (shrink)

English mass noun phrases & count noun phrases differ only minimally grammatically. The basis for the difference is ascribed to a difference in the features +/-CT. These features serve the morphosyntactic function of determining the available options for the assigment of grammatical number, itself determined by the features +/-PL: +CT places no restriction on the available options, while -CT, in the unmarked case, restricts the available options to -PL. They also serve the semantic function of determining the sort of denotation (...) associated with demonstrative & quantified noun phrases. The feature -CT requires that the associated denotation be the set whose sole member is the greatest aggregate of which the noun phrase or noun is true; the feature +CT requires that the associated denotation be the set whose members are all & only those minimal aggregates of which the noun phrase or noun is true. At the same time, neither mass NPs nor count NPs that are arguments of a predicate have their predicate evaluated with respect to their denotations. Rather, the predicate is evaluated with respect to an aggregation, a set of aggregates constructed from the denotation of the noun phrase that is an argument of the predicate. 3 Tables, 4 Figures, 74 References. AA. (shrink)

A number of natural language constructions seem to provide access to structured pluralities — that is, pluralities of pluralities. A body of semantic work has debated how to model this additional structure and the extent to which it depends on pragmatics. In this article, after controlling for the distinction between ambiguity and underspecification, we present new data showing that structured pluralities are sometimes but not always available, depending on the form of the plural noun phrase used. We show that these (...) results challenge two longstanding theories of plurality. We sketch two different ways to account for these data and describe some of the diverging predictions they make. (shrink)