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.

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)

Various syntacticians have argued that coordinate structures involve a three-dimensional syntactic structure. This paper proposes an interpretation of three-dimensional syntactic structures in terms of plural reference and argues that such structures give further support for plural reference, the view that plural terms refer to several entities at once, rather than referring to a single plural individual.

A plural referring expression (‘the Fs’ or ‘Tom, Dick and Harriet’) may be used to refer either distributively, saying something which applies to each of the Fs individually, or collectively, to the Fs taken as a single totality. Predicate Logic has to analyse both uses in terms of singular reference, treating them quite differently in so doing; but we think of such an expression as functioning in basically the same way in both kinds of use. This understanding can (...) be vindicated if we recognise that what a plural referring expression picks out is not either an aggregate simpliciter or a set, but a plurality– an aggregate taken relative to a principle for individuating its constituents; this admits of being seen either as many things or as one. In any given case, it is the nature of what is being said about the plurality which tells us whether the reference to it is to be taken as distributive, collective, or a combination of the two. Talk about pluralities is extensional. Augmenting Predicate Logic to accommodate the distinctive inference‐pattern associated with distributive plural reference is simple – and arguably necessary, to cope with cases in which distributive and collective reference are essentially combined (e.g., attributions of concerted action). (shrink)

In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, (...) the alleged innocence of mereology and plural quantification is highly controversial and has been criticized by several authors. In the present paper we propose a new approach to megethology based on the theory of plural reference developed in To be is to be the object of a possible act of choice. Our approach shows how megethology can be grounded on plural reference without the help of mereology. (shrink)

This book surveys the thesis that all religions are alike in referring and relating to a single, common transcendent and sacred reality. It treats this thesis as one in the philosophy of religion. In the first chapter pluralism is defined and its core is distinguished from its particular character and defence in the writings of John Hick and others. The underpinnings of pluralism are held to lie in an understanding of reference in religion, the definition of religion, the nature (...) of salvation, the character of religious language, an appropriate epistemology for the philosophy of religion, and, crucially, the nature of a realist perspective on the religions. A notion of referential realism is set out which when applied to religion makes the pluralist thesis plausible. A chapter is devoted to each of these main themes. The conclusion offers a brief survey of the implications of pluralism for our general view of religion. (shrink)

In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as (...) a theory of logical concepts. Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism. (shrink)

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic charac.

This chapter deals with (apparent) reference to universals. A common view is that terms like _wisdom_ and _the property of being wise_ both refer to abstract objects. There is a range of linguistic evidence, however, that this view is mistaken. Bare adjective nominalizations like _wisdom_ have the status of kind terms and as such are best considered terms plurally referring to the various instances. Only _the property of being wise_ is a term referring to an abstract property, but as (...) such it is best viewed as a term that introduces a property on the basis of a corresponding predicate. This chapter also gives an introduction to plural reference and discusses parallels between plural terms and kind terms. (shrink)

A fundamental part of the process of referring to an entity is to categorise it (for instance, as the woman). Where multiple categorisations exist, this implicitly involves the adoption of a conceptual perspective. A challenge for the automatic Generation of Referring Expressions is to identify a set of referents coherently, adopting the same conceptual perspective. We describe and evaluate an algorithm to achieve this. The design of the algorithm is motivated by the results of psycholinguistic experiments.

A fundamental part of the process of referring to an entity is to categorise it (for instance, as the woman). Where multiple categorisations exist, this implicitly involves the adoption of a conceptual perspective. A challenge for the automatic Generation of Referring Expressions is to identify a set of referents coherently, adopting the same conceptual perspective. We describe and evaluate an algorithm to achieve this. The design of the algorithm is motivated by the results of psycholinguistic experiments.

This chapter begins by trying to describe, without assuming any specific formalism, how quantifier phrases differ from other noun phrases. Then we will be better able to appreciate what it means to say that they can be used to refer, as a variety of examples to be given in the second section will illustrate. The third section surveys plural pronouns. The next two sections take up the interaction of quantifier phrases with pronouns. So-called ‘bound’ pronouns are often likened to (...) variables bound by quantifiers. However, despite the impressive influence of the Fregean tradition and of Chomsky's recent (1981) theory, it is argued that the bound variable approach to pronouns is unsatisfactory and unnecessary. The chapter then extends the argument of the previous chapter — that the relation between a pronoun and its so-called antecedent is a not grammatical one — to so-called bound pronouns: the fact that the use of such a pronoun mayor may not be referentially dependent on the use of a quantifier phrase does not make the pronoun ambiguous. It is denied that when a pronoun functions as a ‘bound’ rather than as a ‘free’ pronoun it plays a different semantic role. Rather, the difference can be explained pragmatically with the help of the notion of referential dependence. The final section offers a pragmatic account of E-type pronouns used in environments containing quantifier phrases. (shrink)

This chapter explores the case for referentialism about plurals. It presents a version of referentialism characterized by the following theses: (i) semantic predicates, such as ‘designate’ and ‘satisfy’, remain constant in sense whether they attach to a plural subject or a singular subject; (ii) in the principles that state the designations of plural terms the expressions that follow the verb ‘designates’ (or ‘refers to’) are themselves plural expressions; and (iii) the designation relation does not distribute, so there (...) is no entailment from ‘α refers to _x_ & _y_ & _z_’ to ‘α refers to _x_’. The chapter deploys Boolos's second-order account of the logic of plurals to explore how plurals behave in modal contexts. (shrink)

This chapter argues that a certain weaker use of mereology, compared to Lewis’s, supports an innocence thesis similar to plural reference. We propose a theory of virtual mereology (VM), where agents play both the role of choosers and of chosen. Using our semantics of plural choices, we interpret a formal first-order mereological language, like Goodman’s calculus of individuals.

How do plurals and mass nouns refer? What kind of logic should be used in order to account for the truth-conditions of the sentences they appear in? For linguists, first-order predicate logic is adequate, provided it is supplemented by a notion of mereological sum for plurals and for mass nouns. On the contrary, according to some philosophers, new logics must be used, plural logic for plurals and mass logic for mass nouns. We survey these debates in this entry.

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)

Reference is a central topic in philosophy of language, and has been the main focus of discussion about how language relates to the world. R. M. Sainsbury sets out a new approach to the concept, which promises to bring to an end some long-standing debates in semantic theory.There is a single category of referring expressions, all of which deserve essentially the same kind of semantic treatment. Included in this category are both singular and plural referring expressions ('Aristotle', 'The (...) Pleiades'), complex and non-complex referring expressions ('The President of the USA in 1970', 'Nixon'), and empty and non-empty referring expressions ('Vulcan', 'Neptune'). Referring expressions are to be described semantically by a reference condition, rather than by being associated with a referent. In arguing for these theses, Sainsbury's book promises to end the fruitless oscillation between Millian and descriptivist views. Millian views insist that every name has a referent, and find it hard to give a good account of names which appear not to have referents, or at least are not known to do so, like ones introduced through error ('Vulcan'), ones where it is disputed whether they have a bearer ('Patanjali') and ones used in fiction. Descriptivist theories require that each name be associated with some body of information. These theories fly in the face of the fact names are useful precisely because there is often no overlap of information among speakers and hearers. The alternative position for which the book argues is firmly non-descriptivist, though it also does not require a referent. A much broader view can be taken of which expressions are referring expressions: not just names and pronouns used demonstratively, but also some complex expressions and some anaphoric uses of pronouns.Sainsbury's approach brings reference into line with truth: no one would think that a semantic theory should associate a sentence with a truth value, but it is commonly held that a semantic theory should associate a sentence with a truth condition, a condition which an arbitrary state of the world would have to satisfy in order to make the sentence true. The right analogy is that a semantic theory should associate a referring expression with a reference condition, a condition which an arbitrary object would have to satisfy in order to be the expression's referent.Lucid and accessible, and written with a minimum of technicality, Sainsbury's book also includes a useful historical survey. It will be of interest to those working in logic, mind, and metaphysics as well as essential reading for philosophers of language. (shrink)

In this paper, I outline and defend a novel approach to alethic pluralism, the thesis that truth has more than one metaphysical nature: where truth is, in part, explained by reference, it is relational in character and can be regarded as consisting in correspondence; but where instead truth does not depend upon reference it is not relational and involves only coherence. In the process, I articulate a clear sense in which truth may or may not depend upon (...) class='Hi'>reference: this involves distinguishing semantic denotation from pragmatic speaker reference and claiming that there may or may not exist a metasemantic connection between these two notions. Finally, I argue that reference is not in general inscrutable—that this metasemantic connection does exist in the case of our ordinary discourse about present macroscopic concrete objects—but that it is in pure mathematics, where reference cannot be secured, and which therefore plays no role in accounting for truth. In this manner, alethic pluralism is upheld. (shrink)

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

Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. (...) Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517). (shrink)

This chapter introduces a new approach to plural quantification through the concept of plural arbitrary reference. It highlights the implicit presupposition in mathematical reasoning that any individual in the universe of discourse can be referred to. By introducing a team of ideal agents capable of direct access to any individual, plural arbitrary reference is achieved through simultaneous acts of choice by each agent. This idealized notion of reference provides a basis for understanding plural (...) quantification without second-order entities, maintaining the ontological innocence of second-order logic by distinguishing between acts and entities. (shrink)

D.K. Lewis, in his “Mathematics is Megethology,” combines mereology with plural quantification to reconstruct set theory, creating a megethology with enough expressive power to explore hypotheses about the size of reality. This chapter presents a new approach to megethology based on the theory of plural arbitrary reference developed earlier in the book. Our approach demonstrates how megethology can be founded on plural arbitrary reference without relying on mereology.

This paper explores the idea that scalar implicatures are computed with respect todiscourse referents. Given the general consensus that a proper account of pronominal anaphora in natural language requires discourse referents separately from the truth-conditional meaning, it is naturally expected that the anaphoric information that discourse referents carry play a role in the computation of scalar implicatures, but the literature has so far mostly exclusively focused on the truth-conditional dimension of meaning. This paper offers a formal theory of scalar implicatures (...) with discourse referents couched in dynamic semantics, and demonstrates its usefulness through a case study on the plurality inferences of plural nouns in English. (shrink)

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)

This book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolosʼ interpretation of second order logic in terms of plural quantification and a sketched (...) structuralist reconstruction of second-order arithmetic based on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linneboʼs objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded. In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that – for a certain use of mereology – a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract (...) objects, but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (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)

In this book, Alan Berger further develops the new theory of reference -- as formulated by Kripke and Putnam -- applying it in novel ways to many philosophical problems concerning reference and existence. Berger argues that his notion of anaphoric background condition and anaphoric links within a linguistic community are crucial not only to a theory of reference, but to the analysis of these problems as well. The book is organized in three parts. In part I, Berger (...) distinguishes between two styles of rigid designation. Based on this distinction, he develops a theory of reference change for rigid designator terms and shows how this distinction sheds light on identity statements. In part II, he offers an account of belief attribution containing vacuous names within the belief context, of intentional identity statements, and of true negative existential statements. In part III, he analyzes anaphoric expressions and presents a formalization of anaphora and plural quantification. (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)

In this chapter, building on the previous chapters’ approach to plural quantification through plural arbitrary reference grounded on the semantics of plural acts of choice, we develop a theory of concepts termed as a theory of logical concepts. Within this framework, we propose a novel logicist approach to natural numbers.

Legal pluralism refers to the idea that in any one geographical space defined by the conventional boundaries of a nation state, there is more than one law or legal system. This article examines several aspects of legal pluralism focusing on the relationship between the empirical facts of pluralism and its conceptual foundations. Variety of factors produce the perception of legal pluralism, which is reflected in intensified interest in the concept in contemporary scholarship. Legal philosophy and sociological approaches to law often (...) still occupy quite separate scholarly terrains. Legal pluralism has been identified as a fruitful area for constructive engagement between legal philosophy and the sociology of law. This article emphasizes the fact that with the decline of nation states as the locus of political and legal power, it seems inevitable that traditional state-centered legal philosophy must give way to a different paradigm, which recognizes the plurality of law. (shrink)

The Moral Twin Earth challenge to ethical naturalism threatens to undermine an otherwise promising metaethical view by showing that typical, naturalist-friendly theories of reference determination predict diverging reference in Twin Earth scenarios, making it difficult to account for substantive moral disagreement. Several theorists have recently invoked David Lewis’s doctrine of reference magnetism as a solution, claiming that a highly elite moral property—a moral “joint in nature”—could secure shared reference between ourselves and our twins on Twin Earth, (...) despite our diverging usages of moral terms. This paper argues that this move has significant methodological implications: namely, it entails that a certain sort of simplicity is truth-conducive. Consequently, when applied to moral theories, this gives certain views, specifically monist ones like utilitarianism and contractualism, an advantage over their more complicated rivals, forms of pluralism and particularism. Thus, ethical naturalists cannot invoke reference magnetism without a substantial impact on first-order theorizing. (shrink)

It is known that a multiple-_wh_ question can inquire about a dependency between _wh_-expressions, termed “_wh_-dependency”, admitting a pair-list answer. In discourse, the dependency can even support a “plural” interpretation of a singular pronoun. Consider _Which_$$^u$$ _girl bought which_$$^{\nu }$$ _book and how much did_ $$she_u$$ _pay for it_$$_{\nu }$$_?_ The multiple-_wh_ question is asking about a dependency between girls and books. In the subsequent question, the dependency is referred to and the resolution of the singular pronouns varies among (...) the girls and the books they bought. While van Rooy (In: Hulstijn and Nijholt (eds.) Modal subordination in questions, Twendial, 1998) and Dotlačil & Roelofsen (Dynamic inquisitive semantics, Amsterdam, 2019) have noticed this phenomenon, it is still understudied. Based on their insights, this paper argues that reference to _wh_-dependencies is facilitated in two types of subordination constructions: quantificational subordination, where reference to _wh_-dependencies is facilitated through quantificational structure, and question subordination, where reference to _wh_-dependencies is facilitated through conjoining questions. Building on Hamblin-Karttunen semantics of questions and Dynamic Plural Logic (DPlL), this paper proposes a dynamic family-of-questions approach to multiple-_wh_ questions. In particular, a multiple-_wh_ question generates a set of sub-questions, i.e., a family of questions, and then the set is transformed into a set of possible pair-list answers. Both encode the relevant _wh_-dependency in a different manner. As a consequence, the dependency encoded in a family of questions is retrievable in question subordination, while the one encoded in a pair-list answer is retrievable in quantificational subordination. (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 article proposes a conceptual shift in the understanding of scientific theo- ries: from representational realism, which views theories as mappings onto a mind- independent reality, to a framework grounded in constraint convergence. Rather than aiming to mirror the world, scientific theories are understood as architectures of interlocking constraints, structural, empirical, and projective, that collectively stabilize scientific practice. This account reframes key debates in the philosophy of science, including theory change, objectivity, and theory-ladenness, by emphasizing functional coherence over semantic correspondence. (...) Through analyses of dualities, limiting cases, and inter-theoretic transitions, the constraint-based approach ex- plains how theories evolve not by replacing referents but by reorganizing constraint compatibility. The result is a model of scientific progress that is realist without metaphysical commitment, pluralist without fragmentation, and operationally ro- bust. This framework opens the possibility of a general research program structured around constraint architectures, supported by tools from category theory, varia- tional modeling, and computational metamodeling. Scientific knowledge, on this view, gains its epistemic legitimacy not through referential accuracy, but through the convergence and stability of constraint regimes across diverse domains. (shrink)

The aim of this chapter is to argue that: (a) our semantics of acts of choices (SAC), as developed in Chap. 2, defends second-order logic from claims of ontological commitment; (b) understanding our semantics does not require any prior mathematical concepts; and (c) although SAC is not universally applicable, it still offers significant applicability, especially in mathematics. We conclude the chapter arguing that second-order logic, as interpreted through our semantics, can indeed be considered a genuine logic. One might object that, (...) since only concrete objects can be referred to by arbitrary acts of choice, SAC lacks the logical requirement of universal applicability. However, such limitation is superseded by the structuralist conception of mathematics, according to which arbitrary entities, independently of their very nature, can play the role of mathematical objects. (shrink)

Starts by showing that semantic complexity is not as such a barrier to being a referring expression, using the example of compound names. Goes on to consider whether definite descriptions, at least in some uses, should be counted as referring expressions and concludes that they should be, even if one endorses Russellian truth conditions for sentences containing definite descriptions.

The need for the definite article to express a singular kind ("the cat") in the Germanic languages is predicted by Borer's (2005) structural approach to the mass-count distinction. Chierchia's (1998) "down" operator can apply to nPs to derive mass kinds ("rice") and to DivPs to derive plural kinds ("cats"), but there is no determinerless structure that exclusively denotes properties of atomic individuals to which this same operator can apply to derive singular kinds. The only alternative is the process that (...) Chierchia proposes for plural kinds in Romance, where the definite article returns a maximal individual that can be intensionalized into a kind. In articleless languages like Mandarin, this account allows for a universal property-denoting denotation of nP and simultaneously captures the fact that singular kinds have the same distribution as mass kinds. (shrink)

PG (Plural Grundgesetze) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. George Boolos’ plural semantics is replaced with Enrico Martino’s Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. Also, substitutional quantification is exploited to interpret quantification into predicate position. ACS provides a form of (...) logicism which is radically alternative to Frege’s and which is grounded on the existence of individuals rather than on the existence of concepts. (shrink)