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 predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book (...) will be of great interest to philosophers of language, linguists, metaphysicians, and logicians. (shrink)

Natural language semanticists have often found it useful to assume that all expressions denote sets of values. The approach is most prominent in the study of questions and prosodic focus, but also common in work on indefinites, disjunction, negative polarity, and scalar implicature. However, the most popular compositional implementation of this idea is known to face technical obstacles in the presence of object-language binding constructs, including, chiefly, lambda abstraction. The problem has been well-described on several occasions in the literature, and (...) in fact several solutions have been explored. This paper seeks to formalize the challenge of defining an indeterminate semantics for binding operators, and to formally establish the intuition that the challenge is in fact insurmountable. The primary benefit to this exercise is that it offers an abstract characterization of what it means to lift an operation from one semantic space to another, a notion which may be applied to domains having nothing to do with sets of alternatives. (shrink)

This paper gives an analysis of the Chinese distributivity marker dou 'all', which can occur not only with definite plural NPs but also with NPs whose determiner is a quantifier word such as mei 'every' or dabufen-de 'most'. Besides normal distributive predicates, it can also occur with certain types of collective predicates. The difficulties of giving a compositional interpretation to constructions of these kinds are discussed in detail. I show that we can solve those difficulties if we treat dou (...) as a generalized distributivity marker in the sense of Schwarzschild (1991, 1996), which distributes over the members of a plurality cover. Apart from the above topic, which is more narrowly a semantics topic, this paper also discusses some syntax-semantics interface issues related to the distribution of dou's associates. (shrink)

There are predicates that I call “stubbornly distributive” based on what happens when they are combined with plural count noun phrases. I will use these stubbornly distributive predicates to identify and analyze a certain subset of mass nouns which I call “multi-participant nouns”. Traffic and rubble are multi-participant nouns but furniture and luggage turn out not to be. Importantly, ‘typical’ mass nouns like water are multiparticipant nouns.

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

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

The existence of complex predicates seems to support an abundant conception of properties. Specifically, the application conditions for complex predicates seem to be explained by the distribution of a sparser base of predicates. This explanatory link might suggest that the existence and distribution of properties expressed by complex predicates are explained by the existence and distribution of a sparser base of properties. Thus, complex predicates seem to legitimize the assumption of a wide array of properties. The additional properties are no (...) explanatory addition to the sparse base. I argue, however, that construing complex predicates as expressing properties undermines the explanatory links between simple and complex predications. The argument explores a variety of accounts of complex predicates currently on offer and develops a number of themes from the work of Herbert Hochberg. (shrink)

We investigate the relationship between two approaches to modeling physical systems. On the first approach, simplifying assumptions are made about the level of detail we choose to represent in a computational simulation with an eye toward tractability. On the second approach simpler, analogue physical systems are considered that have more or less well-defined connections to systems of interest that are themselves too difficult to probe experimentally. Our interest here is in the connections between the artifacts of modeling that appear in (...) these two approaches. We begin by outlining an important respect in which the two are essentially dissimilar and then propose a method whereby overcoming that dissimilarity by hand results in usefully analogous behavior. We claim that progress can be made if we think of artifacts as clues to the projectible predicates proper to the models themselves. Our degree of control over the connection between interesting analogue physical systems and their targets arises from determining the projectible predicates in the analogue system through a combination of theory and experiment. To obtain a similar degree of control over the connection between large-scale, distributed simulations of complex systems and their targets we must similarly determine the projectible predicates of the simulations themselves. In general theory will be too intractable to be of use, and so we advocate an experimental program for determining these predicates. the object of the natural history which I propose is...to give light to the discovery of causes and supply a suckling philosophy with its first food . Francis Bacon, The Great Instauration. (shrink)

I argue for two major claims in this paper. First, I argue that the linguistic evidence best supports a certain form of contextualism about predicates of personal taste (PPTs) like ?fun? and ?tasty?. In particular, I argue that these adjectives are both individual-level predicates (ILPs) and anaphoric implicit argument taking predicates (IATPs). As ILPs, these naturally form generics. As anaphoric IATPs, PPTs show the same dependencies on context and distributional behavior as more familiar anaphoric IATPs, for example, ?local? and ?apply?. (...) Moreover, they are subject to important binding-related phenomena, for example, various kinds of anaphora, binding arguments, and strict-sloppy ambiguities. The latter are particularly problematic for relativism, contextualism's major competitor. I argue that relativism cannot account for these binding facts in a non-ad hoc manner. Second, I argue that disagreement is a predictable feature of dialogues involving PPTs in conjunction with the contextualist semantics defended. Appealing to ?off the shelf? analyses of genericity, I show how disagreement arises in just the cases we would expect, licensing just the kinds of responses we would expect. They also suggest promising explanations, unavailable to relativists, of various otherwise puzzling features of disagreements involving PPTs. (shrink)

Increasingly visible global distributive inequalities and famine pose considerable challenges for policy-makers and political philosophers alike. A recent proposal forwarded by Thomas Pogge has taken on the challenge of outlining a concept of global justice according to which redistribution is not merely predicated on the beneficiaries being in a state of need. The scheme, which he calls the Global Resources Dividend, aims to compensate people who are excluded from the benefits of the common stock of natural resources, by taxing (...) those who unilaterally exploit it and by subsequently redistributing the revenues to the globally poor. This article assesses the GRD's moral standing once it is institutionalized in the real world. It analyses the causal link between a country's resource endowments and its economic prosperity and identifies the beneficiaries of, and contributors to, the monetary transfers under two possible tax-shifting scenarios. The article concludes that in order to offset the morally questionable results that Pogge's scheme produces, some moral demands need to be relaxed and the GRD scheme be divided into separate stages that operate with distinct moral rationales. (shrink)

“Feminicity” is the term for a predicate register that enables feminist work be accounted for as relational “active-points” that collectively can be seen through what they have achieved. But going further, it marks where those active-points contribute to the dynamic field of feminist epistemologies and where change occurs. This article contributes to my larger project’s discussion of this concept. Broadly, feminicity argues that the active-points of feminist practices need to be understood within their situated fields as materialist informatics. In (...) the digital era, examples of the affects of digital feminicity are as identified in works such as those by Wajcman ; Haraway, Hayles, VNSMatrix, Adam, Plant. Collectively, such authors and artists opened a creative, and sometimes radical discourse of the digital field as multidirectional, multidimensional, multitemporal platform of “gender actions”. Taken as a predicated field sense of the term “predicate”), this work contributes to the feminist materialist reappraisal of feminist epistemology, and larger radical feminist deconstructive projects. Thus conceived, the genealogy of digital feminicity problematizes the monopolitical terms of feminism in its collation of actions, enabling a re-situation of feminist practices as positive material interventions and expressions of the ontological constitution of the political sphere. Feminicity does not propose a chronological account of the active-points, but processually and systemically addresses the terms of generational epistemological political change. This article describes the ways in which a materialist constructed register – “feminicity”– can be used to think about encounters between the domains of gender, politics and technology, as manifested by materialist informatics. For reasons of brevity, this article focuses on just two aspects of feminicity: the terms of predication of the female as gendered, and the issue of the image, as digital informatics, comprised of activitypoints of feminist practice. Consequently, these are measurable and offer practical resources for the general problem of gendering politics that operate in governance, resource distribution and a non-equal opportunity social/cultural power structure, under which minorities are disadvantaged. Feminist practice here refers to forms produced through feminist activities, ie, forms generated through relations with the matter of life through specific modalities of needs-based practices. (shrink)

This work, the first book-length study of its topic, is an important contribution to the literature of philosophical logic and philosophy of language, with implications for other branches of philosophy, including philosophy of mathematics. However, five of the book's ten chapters , including many of the author's most original contributions, are devoted to issues about natural language, and lie pretty well outside the scope of this journal, not to mention that of the reviewer's competence. For this reason I will here (...) largely confine my attention to the other half of the book, and so will be far from doing full justice to the book as a whole; indeed, there is such a wealth of detail in the book that I will be unable to do full justice even to the five chapters selected for comment.Non-distributive predicates.To begin with some points that have often been remarked, formulas in classical first-order logic are built up from predicates by means of a limited range of logical operators . Natural language involves many other such operators, beginning with temporal and modal operators, that are of great philosophical interest, but these are ignored by classical first-order logic. The reasons why it ignores them are surely that classical first-order logic was developed primarily for analyzing mathematical arguments, and that such grammatical categories as tense and mood play no significant role in mathematics.It has been less often remarked that the range of predicates considered in classical first-order logic is also limited. From Frege onwards, predicates have been taken to be essentially sentences with one or more gaps or places suitable to be filled in by singular noun phrases. Natural language involves also plural predicates, as well as mixed predicates with some …. (shrink)

There has been considerable recent interest in the “collective moral autonomy” thesis (CMA), that is, the notion that we can predicate moral successes, failures, and duties of collectives even if there are no comparable successes, failures, and duties among members. One reason why this position looks appealing is because the opposing individualist position seems to have what we might call an accounting problem. Individualists maintain that only individuals can be subjects of moral success, failure, or duty; however, many reasonable (...) judgments about collective actions include moral information on a scale and of a stringency that it does not seem possible to predicate even of the duties of members who have steering power in the actions of the collective. Here I offer a paradigm for thinking about responsibility judgments in organized collective cases to help individualism solve its accounting problem, and allow us to account within a strict individualist perspective for moral information that ostensibly favors CMA. (shrink)

Two objections are raised against Oliver and Smiley’s analysis of the collective–distributive opposition in their 2016 book: They take it as a basic premise that the collective reading of ‘baked a cake’ corresponds to a predicate different from its distributive reading, and the same applies to all predicate expressions that admit both a collective and a distributive interpretation. At the same time, however, they argue that inflectional forms of the same lexeme reveal a univocity that (...) should be preserved in a formal representation of English. These two assumptions sit uneasily. In developing their analysis, Oliver and Smiley come to the conclusion that even a singular predication such as ‘Tom baked a cake’ must be regarded as ambiguous between a collective and a distributive reading. This is so artificial that it hardly makes sense, and yet there seems to be no way out of the difficulty unless we are prepared to give up the basic premise just mentioned. (shrink)

This paper discusses Crawley completions of residuated lattices. While MacNeille completions have been studied recently in relation to logic, Crawley completions (i.e. complete ideal completions), which are another kind of regular completions, have not been discussed much in this relation while many important algebraic works on Crawley completions had been done until the end of the 70’s. In this paper, basic algebraic properties of ideal completions and Crawley completions of residuated lattices are studied first in their conncetion with the join (...) infinite distributivity and Heyting implication. Then some results on algebraic completeness and conservativity of Heyting implication in substructural predicate logics are obtained as their consequences. (shrink)

The paper contends that the heart of Aristotle's theory of justice is the desert-based principle of proportional equality schematically described in the _Nicomachean Ethics and applied to the organization of the state in the _Politics. It argues against the view that for Aristotle distributive justice is only a means to promoting the common good (Thomas Hurka's maximizing perfectionism interpretation of the _Politics) and against the view of Martha Nussbaum that Aristotle understands the common good in a special way that (...) leads to egalitarian conclusions. (shrink)

In this paper we propose a unified semantics for singular and plural superlative expressions that makes use of the ‘**’ (“double star”) distributivity operator (an operator whose role is to pluralize 2-place predicates). The analysis aims to solve two problems: (a) the distributivity problem (the fact that a superlative expression doesn’t distribute over the atomic parts of the plural individual it is predicated of); and (b) the cut-off problem (the fact that a plural superlative expression cannot simultaneously be predicated of (...) two distinct yet overlapping plural individuals). We argue that any solution to these problems that posits two distinct superlative morphemes, one corresponding to a superlative operator for singular individuals and one corresponding to a superlative operator for plural individuals, is challenged by the lack of cross-linguistic morphological evidence. We provide a unified analysis, and account for the differences between plural and singular superlative expressions by appealing to pragmatic principles. (shrink)

This paper presents a diagnostic for identifying distributive constructions and shows that it applies to pseudopartitives and for -adverbials. On this basis, a unified account is proposed for the parallels between the constructions involved. This account explains why for -adverbials reject telic predicates (*run to the store for five hours), why pseudopartitives reject count nouns (*five pounds of book ), and why both reject certain measure functions like temperature and speed (*30 of water, *drive for 5 mph). These restrictions (...) all follow from a general constraint on distributive constructions. Related concepts such as the D operator (Link, 1987), the subinterval property (Bennett and Partee, 1972), and divisive reference (Cheng, 1973) can be understood as formalizing special cases of this constraint. (shrink)

Despite the incremental nature of Dynamic Syntax, the semantic grounding of it remains that of predicate logic, itself grounded in set theory, so is poorly suited to expressing the rampantly context-relative nature of word meaning, and related phenomena such as incremental judgements of similarity needed for the modelling of disambiguation. Here, we show how DS can be assigned a compositional distributional semantics which enables such judgements and makes it possible to incrementally disambiguate language constructs using vector space semantics. Building (...) on a proposal in our previous work, we implement and evaluate our model on real data, showing that it outperforms a commonly used additive baseline. In conclusion, we argue that these results set the ground for an account of the non-determinism of lexical content, in which the nature of word meaning is its dependence on surrounding context for its construal. (shrink)

While accepting that distribution is a coherent notion, I argue that it is nevertheless irrelevant to the working of the syllogism. Instead, I propose: (i) that a term's being distributed or undistributed in a proposition is its capacity to be replaced in a truth-preserving substitution with a narrower or a wider term; (ii) that which capacity the term has is determined by whether it occurs as the predicate of a negative or of an affirmative statement of the proposition; and (...) (iii) that it is only the term's occurrence as the predicate of a negative or an affirmative statement–rather than its distribution value–that is relevant to syllogistic entailment. (shrink)

On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. In effect, this solution rejects the reasoning of the sorites argument. This paper discusses a thorny problem afflicting this approach to vagueness. (...) In particular, it is shown that, on the foregoing view, whether an object is a heap will sometimes depend on factors extrinsic to that object, such as whether its components came from other heaps. More generally, the paper raises the issue of how to count heaps in a tolerance-friendly framework. (shrink)

Covaluation is the generalization of coreference introduced by Tanya Reinhart. Covaluation distributes in patterns that are very similar yet not entirely identical to those of binding. On a widespread view, covaluation and binding distribute similarly because binding is defined in terms of covaluation. Yet on Reinhart's view, binding and covaluation are not related that way: binding pertains to syntax, covaluation does not. Naturally, the widespread view can easily explain the similarities between binding and covaluation, whereas Reinhart can easily explain the (...) dissimilarities. Reciprocally, the widespread view finds it harder to explain the dissimilarities, whereas Reinhart finds it harder to explain the similarities. Reinhart and others have proposed more than one explanation of the similarities, but as I argue, these explanations do not work. Hence although I adopt Reinhart's view, I propose a new explanation of the similarities and dissimilarities between binding and covaluation: While Reinhart has invoked semantic structure only to explain dissimilarities, I do so to explain both similarities and dissimilarities at once. Finally, I examine in light of this approach the topics of language acquisition, only-constructions, the identity predicate, the Partee/Bach/Higginbotham problem, the Dahl puzzle and its recent versions by Roelofsen. (shrink)

The theory of rough sets starts with the notion of an approximation space , which is a pair ( U , R ), U being the domain of discourse, and R an equivalence relation on U . R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U . The focus then is on approximations of concepts (...) on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base , which is a tuple , where N is a set of sources and P ranges over all finite subsets of N . Each R P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS D is proposed. In LMSAS D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS D are discussed and it is shown that the modal system KTB is embedded in LMSAS D . The epistemic logic is also embedded in LMSAS D , and cannot replace the latter to serve our purpose. The relationship of LMSAS D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed. (shrink)

This paper advances the Hunt–Vitell General Theory of Marketing Ethics as a framework for enriching current understanding of both long-term marketing relationships in general, and principal-agent associations specifically. Under economic models of agency theory, manufacturer-distributor relationships are conceptualized as principal-agent associations where both parties are assumed be motivated exclusively by short-term financial self-interest within the logical constraints of zero-sum game conditions. As a general model of ethical decision making and behavior in marketing, the Hunt–Vitell theory illustrates how ethical decisions are (...) predicated not only upon estimations of potential benefits or outcomes (using teleological criteria), but also deontological evaluations which invoke norms and values. Furthermore, the recent ideas advanced in "relationship marketing" perspectives suggest that distribution channel associations premised upon non-zero-sum or symbiotic assumptions may be more effective and more jointly profitable. Based upon the Hunt–Vitell model, propositions are formulated that complement the understanding of agency theory within the context of marketing channel relationships, and thus, may represent a basis for more effective agency selection and interaction in marketing practice. (shrink)