In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of (...) truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that (...) result from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (shrink)

The social sciences playa variety of multifaceted roles in the policymaking process. So varied are these roles, indeed, that it is futile to talk in the singular about the use of social science in policymaking, as if there were one constant relationship between two fixed and stable entities. Instead, to address this issue sensibly one must talk in the plural about uses of dif ferent modes of social scientific inquiry for different kinds of policies under various circumstances. In some cases, (...) the influence of social scientific research is direct and tangible, and the connection between the find ings and the policy is easy to see. In other cases, perhaps most, its influence is indirect-one small piece in a larger mosaic of politics, bargaining, and compromise. Occasionally the findings of social scientific studies are explicitly drawn upon by policymakers in the formation, implementation, or evaluation of particular policies. More often, the categories and theoretical models of social science provide a general background orientation within which policymakers concep tualize problems and frame policy options. At times, the in fluence of social scientific work is cognitive and informational in nature; in other instances, policymakers use social science primarily for symbolic and political purposes in order to le gitimate preestablished goals and strategies. Nonetheless, amid this diversity and variety, troubling general questions persistently arise. (shrink)

I sketch the basic problem of vagueness - the sorites paradox and propose a new solution. I try to show that the paradoxical result of the sorites arguments arises from combining different language games or representation systems without sufficient care. I propose two solutions, two types of regimentating the sorites. They do not allow an inheritance of the vague property F in the whole sequence of objects. The first introduces some quantitatively determined predicates (quantitative regimentation) and the second (relational (...) regimentation) replaces the equivalence relation between successive objects with a suitable weaker asymmetrical relation ‘is at least as much F as’ (or ‘is at most as much F as’). (shrink)

This book develops a unique phenomenology of plurality by introducing Hannah Arendt’s work into current debates taking place in the phenomenological tradition. Loidolt offers a systematic treatment of plurality that unites the fields of phenomenology, political theory, social ontology, and Arendt studies to offer new perspectives on key concepts such as intersubjectivity, selfhood, personhood, sociality, community, and conceptions of the "we." _Phenomenology of Plurality_ is an in-depth, phenomenological analysis of Arendt that represents a viable third way between the "modernist" and (...) "postmodernist" camps in Arendt scholarship. It also introduces a number of political and ethical insights that can be drawn from a phenomenology of plurality. This book will appeal to scholars interested in the topics of plurality and intersubjectivity within phenomenology, existentialism, political philosophy, ethics, and feminist philosophy. (shrink)

As the foundation of our rationality, logic has traditionally been considered fixed, stable and constant. This conception of the discipline has been challenged recently by the plurality of logics and in this book, Pavel Arazim extends the debate to offer a new view of logic as dynamic and without a definite, specific shape. The Problem of Plurality of Logics examines the origins of our standard view of logic alongside Kant's theories, the holistic view, the issue of logic's pragmatic significance and (...) Robert Brandom's logical expressivism. Arazim then draws on proof-theoretical approaches to present a convincing argument for a dynamic version of logical inferentialism, which opens space for a new freedom to modify our own logic. He explores the scope, possibilities and limits of this freedom in order to highlight the future paths logic could take, as a motivation for further research. Marking a departure from logical monism and also from the recent doctrine of logical pluralism in its various forms, this book addresses current debates concerning the expressive role of logic and contributes to a lively area of discussion in analytic philosophy. (shrink)

In western philosophy and beyond, a tension between pluralism and monism has sparked many developments and debates. Pluralism of norms, of forms of knowledge, of aesthetic and moral values, of interests etc. has often been pitted against monism. Monism usually implies a hierarchical order of such norms etc. After having traced the origin of this tension between pluralism and monism in ancient tragedy and philosophy, I’m asking in this article whether a rejection of monism and embrace of pluralism necessarily raises (...) the specter of inconsistency and contradiction. The threat of inconsistency need not be associated with pluralism as even with regard to logic an argument can be made for a ‘multiplicity of logics’, as van Lambalgen and Stenning argue in several places. They refer to the varieties in reasoning that can be observed in humans and which are partly due to there being ‘dual systems’ of reasoning: System 1 processes information fast, automatized, and emotional, while System 2 is rather slow, more deliberative, and more rational. In contrast to a widely held view, the authors argue that System 1 processing is not without logic, even though it is a different form of logic from System 2. In addition, the multiplicity of logics they discuss is related to the multiple semantics required for distinct domains of reasoning. This perspective raises the subsequent question how this pluralism can be available while maintaining consistency, how should the available options be configured or related to each other? In the remainer of this chapter I’m addressing several such options for configurating pluralism like: non-foundational pluralism and foundational pluralism, moderate or temporary pluralism, antagonistic pluralism, incompatible pluralism, incommensurable pluralism, ‘Anything goes’ pluralism, complementary pluralism, integrative pluralism, and interactive pluralism. The discussion and examples of these options show that irrespective of its domain, the encounter with different configurations of pluralism shows how some forms of pluralism are likely to be productive, whereas others are less so - which is an important lesson given the prominent pluralism of pluralisms in philosophy and beyond. (shrink)

English has plural terms as well as singular terms. But our standard formal languages, e.g., the predicate calculus, feature only singular terms. How can the plural idiom be formalized?‘Changing the subject’ is by far the most common plurals strategy among both philosophers and linguists: a plural term is replaced by a singular term standing for some complex object that ‘contains’ the individuals to which the plural term alludes. For example, one might simply replace ‘A, B imply C’ with ‘{A, (...) B} implies [singular] C’. We uncover a surprising variety of ways to change the subject, of ever‐increasing complexity and ingenuity. Our question is whether any can made to work. (shrink)

The one-page 1978 informal proof of Goodman and Myhill is regimented in a weak constructive set theory in free logic. The decidability of identities in general (⁠|$a\!=\!b\vee\neg a\!=\!b$|⁠) is derived; then, of sentences in general (⁠|$\psi\vee\neg\psi$|⁠). Martin-Löf’s and Bell’s receptions of the latter result are discussed. Regimentation reveals the form of Choice used in deriving Excluded Middle. It also reveals an abstraction principle that the proof employs. It will be argued that the Goodman–Myhill result does not provide the constructive (...) set theorist with a dispositive reason for not adopting (full) Choice. (shrink)

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

According to the counterfactual comparative account, an event harms a person if and only if it makes things worse for her. Cases of overdetermination and preemption pose a serious challenge to CCA since, in these cases, although it is evident that people are harmed, there are no individual events that harm them. However, while there are no individual events that make people worse off in cases of overdetermination and preemption, there are pluralities of events that do so. In light of (...) this feature of these cases, several philosophers have suggested that it is these pluralities that do the harming. In this article, I will argue that although the most prominent accounts of plural harm – e.g., Neil Feit’s account – fare better than one might initially think, they fail to deal adequately with a number of intriguing cases of preemption first introduced by Alastair Norcross. I will also introduce a new view on plural harm and argue that this view, apart from dealing with the cases of overdetermination and preemption that the other accounts of plural harm handle, also deals adequately with Norcross’s cases. (shrink)

According to the counterfactual comparative account, an event harms a person if and only if it makes things worse for her. Cases of overdetermination and preemption pose a serious challenge to CCA since, in these cases, although it is evident that people are harmed, there are no individual events that harm them. However, while there are no individual events that make people worse off in cases of overdetermination and preemption, there are pluralities of events that do so. In light of (...) this feature of these cases, several philosophers have suggested that it is these pluralities that do the harming. In this article, I will argue that although the most prominent accounts of plural harm – e.g., Neil Feit’s account – fare better than one might initially think, they fail to deal adequately with a number of intriguing cases of preemption first introduced by Alastair Norcross. I will also introduce a new view on plural harm and argue that this view, apart from dealing with the cases of overdetermination and preemption that the other accounts of plural harm handle, also deals adequately with Norcross’s cases. (shrink)

The manuscripts of Harriot discussed in this paper are essentially rough notes marginal to his systematic treatment of algebra, of which a small part was published posthumously. The central theme is the sign-rule for multiplication; but the incidentals open up an aspect of symbolism in mathematics entirely new for the time. A more restricted aspect of the same theme was touched on by Commandino in his Euclid, quoted by Harriot as rightly blaming ‘those that thinke that minus per minus shal (...) produce plus’; Commandino's authority was Cardano, in a similarly marginal departure from his great Ars magna, the de Aliza, which Harriot also cites in the same reference. The ostensible motivation, to preserve intact the Euclidean tradition in geometry, plays a very minor role in Harriot's notes. The basic aim, to elude the fatal link with imaginaries, they do touch on. More dimly underlying the arguments are the crucial logical facets of the problem, which Harriot faced with a greater conceptual clarity, formulating in words, however, only his own conclusion: the choice of sign-rule is the user's—a fact not fully recognised by mathematicians generally until the 19th century. (shrink)

May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a single vote (...) from each voter, then plurality rule is the uniquely compelling electoral procedure. To illustrate the conditional nature of this claim, we also identify a richer informational environment in which approval voting, not plurality rule, is supported by a May-style argument. (shrink)

Argues against a Gillon-style covers-based analysis of plural noun phrases.

Innovative modes of collaboration between archaeologists and Indigenous communities are taking shape in a great many contexts, in the process transforming conventional research practice. While critics object that these partnerships cannot but compromise the objectivity of archaeological science, many of the archaeologists involved argue that their research is substantially enriched by them. I counter objections raised by internal critics and crystalized in philosophical terms by Boghossian, disentangling several different kinds of pluralism evident in these projects and offering an analysis of (...) why they are epistemically productive when they succeed. My central thesis is that they illustrate the virtues of epistemic inclusion central to proceduralist accounts of objectivity, but I draw on the resources of feminist standpoint theory to motivate the extension of these social -cognitive norms beyond the confines of the scientific community. (shrink)

In this paper I provide a decompositional analysis of three kinds of plural indefinites in two related languages, European Spanish and Brazilian Portuguese. The three indefinites studied are bare plurals, the unos (Spanish)/uns (Portuguese) type, and the algunos (Spanish)/alguns (Portuguese) type. The paper concentrates on four properties: semantic plurality, positive polarity, partitivity, and event distribution. The logic underlying the analysis is that of compositionality, applied at the subword level: as items become bigger in form (with the addition of morphemes), (...) they also acquire more semantic properties. The paper proposes the “indefinite hierarchy", which establishes a set of components for languages to build their indefinites with, in a particular order. (shrink)

The study of social values has its origins in the study of both cross cultural and within cultural differences in latent or manifest definitions of the right social order to achieve the good life. To this extent, the social scientific literature is replete with references to them. Yet, researchers either use the term values Social values are often used interchangeably with that of attitudes or treated as a post-hoc explanatory concept. When values are the focal research point, such endeavours predominantly (...) depart from universal and reductionist understandings of their functions, meanings and structures. Through tracing the roots of key theoretical and empirical investigations in values, originating in the work of Charles Morris, Gordon Allport, Florence Kluckhohn and Fred Strodtbeck, Milton Rokeach and Shalom Schwartz, we reveal the common as well as the different tenets underpinning their work. It will be shown that these accounts have lost sight of the importance of plurality and context. We claim that a renewed program of research in values is needed, which should be characterised by methodological pluralism in order to investigate a) value plurality, b) value specificity and c) values as properties and as processes. (shrink)

Groups are ubiquitous in our lives. But while some of them are highly structured and appear to support a shared intentionality and even a shared agency, others are much less cohesive and do not seem to demand much of their individual members. Queues, for example, seem to be, at a given time, nothing over and above some individuals as they exemplify a certain spatial arrangement. Indeed, the main aim of this paper is to develop the more general thought that at (...) a given time, a group is nothing over and above some individual members as they exemplify a certain complex condition. The general conception of groups that emerges is able to accommodate a variety of constraints on a reasonable answer to the question of what are groups. (shrink)

Priority monism (hereafter, ‘monism’) is the view that there exists one fundamental entity—the world—and that all other objects that exist (a set of objects typically taken to include tables, chairs, and the whole menagerie of everyday items) are merely derivative. Jonathan Schaffer has defended monism in its current guise, across a range of papers. Each paper looks to add something to the monistic picture of the world. In this paper we argue that monism—as Schaffer describes it—is false. To do so (...) we develop an ‘island universe’ argument against Schaffer's monistic theory. (shrink)

My concern in this paper is how to reconcile a central tension in Hannah Arendt’s thinking, one that – if left unresolved – may make us reluctant to endorse her political theory. Arendt was profoundly and painfully aware of the horrors of political evil; in fact, she is almost unparalleled in 20 th century thought in her concern for the consequences of mass political violence, the victims of political atrocities, and the most vulnerable in political society – the stateless, the (...) pariahs, the outcasts. At least, this is the case in her discussions of concrete, historical political situations. Yet in her philosophical writings, she continues to argue that the political realm ultimately redeems human existence, and furthermore, that politics should remain distinct and autonomous from moral evaluation. Political action must be evaluated according to “greatness,” not goodness or any other explicitly moral or even ethical standard. She goes so far as to suggest that politics and morality may be deeply hostile to one another, and can only be reconciled in situations of extreme emergency. This can leave many feeling both perplexed and deeply uncomfortable with the theory of human action that Arendt proposes. Drawing on her notions of political conscience, judgment and - in particular - her account of forgiveness, in this paper I argue that Arendt offers an ethics of plurality, in which what is good is developed from what is most politically important: amor mundi, or love of our shared political world. (shrink)

In chapter one I will try to reconstruct a plot, or a hidden agenda, in the discussion in ethics between the beginning of the twentieth century and 1958, the year of a decisive turning point in ethics, both Anglo-Saxon and Continental, and strangely enough also the year of the beginning of the end of the Cold War, of post-Tridentine Catholicism, and perhaps something else. My hypothesis will be that there are two similar starting points for the Anglo-Saxon and the Continental (...) twentieth-century discussion, the philosophies of Henry Sidgwick and Friedrich Nietzsche, both expressions of some kind of ethical scepticism, and that a third, somewhat analogous starting-point could be found in Émile Durkheim, the proponent of the dream of the morale laïque. I will discuss how far the diagnosis formulated by Karl-Otto Apel of a kind of ‘parallel convergence' between existentialism and analytic philosophy, based on the shared division of facts and values that eventually justified two kinds of 'decisionism' is useful in making sense of the agenda of the discussion. In the second chapter I will discuss the reasons for two parallel U-turns around 1958 which brought back traditional schools of normative ethics, 'deontologism' and utilitarianism, as well as the reasons for criticism to both schools from the heterogeneous alignment of virtue ethics. In the third chapter I will discuss the remarkable phenomenon of the emergence, starting with the Sixties or the early Seventies, of ‘applied’ ethics. I examine the reasons, both theoretical and political, for the revival, the point to which applied ethics may look as a grand return of a casuistic and natural law way of thinking, or in Alan Donagan’s words a case of “reverse subversion” of the modern secular world by traditional Scholastic ways of thinking, and the difficult coexistence between general normative ethics and procedures for settling issues in a ‘reasonable’ way while dissent on issues of principle is as alive as ever. Then I try to draw a provisional moral. My suggestions are that (i) casuistry is more alive than ever; (ii) natural law thinking is more alive than ever; (iii) moral dilemmas never arise; (iv) moral dissent is treatable, with the right strategy; (v) practical philosophy does not need the same degree of exactness as the theoretical sciences but this is no obstacle to its working in practice. (shrink)

This volume explores challenges posed by plurality, as understood by Hannah Arendt, but also the opportunities it offers. It is an interdisciplinary collection of chapters, including contributions from different traditions of philosophy, political science, and history. The book offers novel perspectives on central issues in research on Arendt, reconfiguring the existing interpretations and reinforcing the line of interpretation illuminating the phenomenological facets of Arendt’s theory. The authors of the contributions to this volume decisively put the notion of plurality in the (...) center of the collected interpretations, pointing out that plurality in its dialectic form of commonality, and difference is not only, as assumed by default, one of the most important notions in Arendt’s theory, but the very central one. At the same time, plurality is a central issue in many current debates, from populism and hate speech to migration and privacy. This collection therefore connects the theoretical advancements regarding Arendt and other political thinkers with some of the most pressing contemporary issues. This book will be of interest to scholars and advanced students from philosophy, political theory and related fields studying contemporary challenges of plurality as well as scholars interested in the work of Hannah Arendt. (shrink)

When voters’ preferences on candidates are mutually coherent, in the sense that they are at all close to being perfectly single-peaked, perfectly single-troughed, or perfectly polarized, there is a large probability that a Condorcet Winner exists in elections with a small number of candidates. Given this fact, the study develops representations for Condorcet Efficiency of plurality rule as a function of the proximity of voters’ preferences on candidates to being perfectly single-peaked, perfectly single-troughed or perfectly polarized. We find that the (...) widely used plurality rule has Condorcet Efficiency values that behave in very different ways under each of these three models of mutual coherence. (shrink)

Collective entities and collective relations play an important role in natural language. In order to capture the full meaning of sentences like The Beatles sing Yesterday, a knowledge representation language should be able to express and reason about plural entities — like the Beatles — and their relationships — like sing — with any possible reading (cumulative, distributive or collective).In this paper a way of including collections and collective relations within a concept language, chosen as the formalism for representing the (...) semantics of sentences, is presented. A twofold extension of theA–C concept language is investigated: (1) special relations introduce collective entities either out of their components or out of other collective entities, (2) plural quantifiers on collective relations specify their possible reading. The formal syntax and semantics of the concept language is given, together with a sound and complete algorithm to compute satisfiability and subsumption of concepts, and to compute recognition of individuals. (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)

I argue that Leibniz’s well-known Argument from Unity is equally an argument from plurality. I detail two main claims about plurality that drive the argument, and I provide evidence that they structure Leibniz’s argument from the late 1670s onwards. First, there is what I call Mereological Nihilism (i.e., the claim that a plurality cannot be made into a true unity by any available means). Second, there is what I call the Plurality Thesis (i.e., the claim that matter is a plurality (...) in need of unity in the first place). I suggest that the Plurality Thesis offers a general analysis of materiality that, in some sense, is the most important aspect of Leibniz’s argument. Finally, I connect these claims about plurality to the common 17th & 18th century commitment known as the actual parts doctrine. (shrink)

This volume is a tribute to Roger Schwarzschild's immense contributions in the formal semantics of nouns, focus, degrees and space, and tense and aspect. Collectively, the papers in the volume reveal parallels across ontological domains, in particular in the context of elements with internal structure, like plural sets, alternative sets, degree intervals, temporal intervals, and vectors. This research suggests that the structure of an entity could inform the semantic behavior of that entity just as much than its semantic type or (...) lexical category. And because these structures dictate the formation of semantic alternatives, it can help inform focus semantics and scalar implicature as well. Old questions on plurals, focus and degree expressions get new answers in this collection of papers in honor of Roger Schwarzchild. Roger Schwarzschild is one of the leading scholars in semantics, and the editors have been highly successful in requesting contributions by his teachers, peers and former students. Some papers have circulated in draft form for many years, and find their final home in this edited volume, which well reflects the state of the art in the field. Prof. dr. Henriëtte de Swart, Utrecht University, The Netherlands. (shrink)

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...) that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

What do we do when we say ‘We’? This paper pursues a response from analytic pragmatism. The guiding idea of analytic pragmatism is to look to what one must implicitly know how do to be able to use expressions to say something, including how to make that implicit know-how explicit. Accordingly, the question we are tasked to answer is what one must know how to do to say ‘We’ – that is, what practical know-how saying ‘We’ requires and can be (...) employed to make explicit. The concept normative ascent is introduced in developing an answer. On this approach, the know-how in question turns out to be a distinctively normative capacity. Both being and saying ‘We’ turns out to involve being able to do and say something normative. (shrink)

In his recent essay, Mark Wenman highlighted parallels between Connolly’s theory of pluralism and earlier iterations of pluralism in the postwar period and the early twentieth century. Focusing on his account of postwar pluralism and especially his interpretation of Dahl, I argue that Dahl’s vision of democracy as polyarchy is fundamentally at odds with Connolly’s. A close reading of Dahl’s text and a consideration of the historical context suggest that Dahl’s theory effectively creates a depoliticized world where citizens are unresponsive (...) to claims about alternative possibilities of democratic life. (shrink)