John Broome argues that fairness requires that claims are satisfied in proportion to their strength. Broome holds that, when distributing indivisible goods, fairness requires the use of weighted lotteries as a surrogate to satisfy proportionally each candidate's claims. In this article, we present two arguments against Broome's account of fairness. First, we argue that it is almost impossible to calculate the weights of the lotteries in accordance with the requirements of fairness. Second, we argue that Broome rules out those methods (...) whose use might provide some resolution to this problem. From these arguments, we conclude that, contra Broome, fairness does not require the proportional satisfaction of claims. (shrink)

Providing individuals with the information necessary to make informed decisions is now considered an ethical standard for health systems and general practitioners.

Legal reasoning requires identification through search of authoritative legal texts (such as statutes, constitutions, or prior judicial opinions) that apply to a given legal question. In this paper, using a network representation of US Supreme Court opinions that integrates citation connectivity and topical similarity, we model the activity of law search as an organizing principle in the evolution of the corpus of legal texts. The network model and (parametrized) probabilistic search behavior generates a Pagerank-style ranking of the texts that in (...) turn gives rise to a natural geometry of the opinion corpus. This enables us to then measure the ways in which new judicial opinions affect the topography of the network and its future evolution. While we deploy it here on the US Supreme Court opinion corpus, there are obvious extensions to large evolving bodies of legal text (or text corpora in general). The model is a proxy for the way in which new opinions influence the search behavior of litigants and judges and thus affect the law. This type of “legal search effect” is a new legal consequence of research practice that has not been previously identified in jurisprudential thought and has never before been subject to empirical analysis. We quantitatively estimate the extent of this effect and find significant relationships between search-related network structures and propensity of future citation. This finding indicates that “search influence” is a pathway through which judicial opinions can affect future legal development. (shrink)

This paper is about the cluster of issues that orbit a well-known thesis of Quine’s, as it applies to attitude ascriptions.

Background: Promoting patients’ rights is essential for defining the standards of clinical services within a country. Given their responsibilities, nurses can be the primary target for research to investigate the issue of patients’ rights within a healthcare system. As such, assessing the knowledge of nurses about patients’ rights is an essential step toward improving the quality of healthcare in limited resource settings like Sudan. Objectives: We aimed to assess the level of knowledge about patients’ rights among the nursing staff at (...) Friendship Teaching Hospital in Sudan. Methods: This hospital-based cross-sectional study was carried out at the Friendship Teaching Hospital in Sudan. We surveyed the totality of nurses (95) at the hospital using an amended survey. The data were analyzed in SPSS software using descriptive and inferential statistics. Ethical consideration: The study was approved by the Research Unit of Khartoum Ministry of Health and the Hospital administration. All respondents gave verbal consent prior to participating in the study. Results: Only 48.4% of the participants knew about the existence of the Sudanese Charter of patients’ rights. Nonetheless, our analysis found that 65.8% of nurses had acceptable level of knowledge (scored more than 75% of the total knowledge score) of patients’ rights, and none of the participant scored less than 50% of the total knowledge score. Finally, we found no statistical association between the knowledge score and demographic data, educational level, whether the participant knows about the existence of the Charter or not and a number of other factors. Conclusion: Nurses’ lack of knowledge about the existence of the Sudanese Charter of patients’ rights adopted in 2009 rights confirms the need for further efforts by Ministry of Health to promote the document. Furthermore, further research is needed to investigate the disconnect between nurses’ lack of knowledge about the existence of the charter and their awareness of the rights within the charter as well as the actual implementation of rights. (shrink)

I defend a neo-Lewisean form of contextualism about knowledge attributions. Understanding the context-sensitivity of knowledge attributions in terms of the context-sensitivity of universal quantifiers provides an appealing approach to knowledge. Among the virtues of this approach are solutions to the skeptical paradox and the Gettier problem. I respond to influential objections to Lewis’s account.

In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial time. (...) Additionally, we suggest that plausible semantic theories of the everyday fragment of natural language can be formulated in the existential fragment of second-order logic. -/- In Chapter 2 we give an overview of the basic notions of generalized quantifier theory, computability theory, and descriptive complexity theory. -/- In Chapter 3 we prove that PTIME quantifiers are closed under iteration, cumulation and resumption. Next, we discuss the NP-completeness of branching quantifiers. Finally, we show that some Ramsey quantifiers define NP-complete classes of finite models while others stay in PTIME. We also give a sufficient condition for a Ramsey quantifier to be computable in polynomial time. -/- In Chapter 4 we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents. We show a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. Additionally, we argue that this difference should be acknowledged in the Strong Meaning hypothesis. -/- In Chapter 5 we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. The type-shifting approach cannot lead outside second-order logic and arguably some collective quantifiers are not expressible in second-order logic. As a result, we argue that algebraic (many-sorted) formalisms dealing with collectivity are more plausible than the type-shifting approach. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics. -/- In Chapter 6 we study the statement known as Hintikka's thesis: that the semantics of sentences like ``Most boys and most girls hate each other'' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading. -/- In Chapter 7 we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model. -/- In Chapter 8 we discuss some general open questions and possible directions for future research, e.g., using different measures of complexity, involving game-theory and so on. -/- In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science. (shrink)

This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. -/- Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of quantifier (...) expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in linguistics, philosophy, cognitive science, logic, AI, and computer science. (shrink)

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact definably equivalent (...) to the independence atom recently introduced by Väänänen and Grädel. (shrink)

Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a “quantifier” just in case it plays the right inferential role. Several critics argued that J.H. Harris’s “collapse” argument refutes variance by showing that identity of inferential role is incompatible with meaning variance. This standard, syntactic collapse argument has generated several responses. More recently, Cian Dorr proved semantic collapse theorems to generate a semantic collapse argument against variance. The argument is significantly (...) different from standard collapse, so it requires a new response. Here I clarify and analyze the semantic collapse argument, and explain how variantists can and should respond to it. The paper also includes an appendix showing the difficulties of positing identity variance without quantifier variance. The argument in the appendix has yet to appear in print, but is familiar to specialists. (shrink)

This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about (...) mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle of indefinite extensibility; section 2 develops and clarifies the metasemantics of quantifier variance; section 3 solves section 1's puzzle of indefinite extensibility by applying section 2's account of quantifier meanings; and section 4 compares the theory developed in section 3 to several other theories in the literature. (shrink)

Quantified expressions in natural language generally are taken to act like quantifiers in logic, which either range over entities that need to satisfy or not satisfy the predicate in order for the sentence to be true or otherwise are substitutional quantifiers. I will argue that there is a philosophically rather important class of quantified expressions in English that act quite differently, a class that includes something, nothing, and several things. In addition to expressing quantification, such expressions act like nominalizations, introducing (...) a new domain of objects that would not have been present in the semantic structure of the sentence otherwise. The entities those expressions introduce are of just the same sort as those that certain ordinary nominalizations refer to (such as John's wisdom or John's belief that S), namely they are tropes or entities related to tropes. Analysing certain quantifiers as nominalizing quantifiers will shed a new light on philosophical issues such as the status of properties and the nature of propositional attitudes. (shrink)

This work presents a model-theoretic approach to the study of first-order theories of classes of BL-chains. Among other facts, we present several classes of BL-algebras, generating the whole variety of BL-algebras, whose first-order theory has quantifier elimination. Model-completeness and decision problems are also investigated. Then we investigate classes of BL-algebras having (or not having) the amalgamation property or the joint embedding property and we relate the above properties to the existence of ultrahomogeneous models.

Eternalists say that non-present entities (for instance dinosaurs) exist; presentists say that they do not. But some sceptics deny that this debate is genuine, claiming that presentists simply represent eternalists' quantifiers over non-present entities in different notation. This scepticism may be refuted on purely logical grounds: one of the leading candidate ‘presentist quantifiers’ over non-present things has the inferential role of a quantifier. The dispute over whether non-present objects exist is as genuine and non-verbal as the dispute over whether there (...) is life on other planets. (shrink)

We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of (...) all singular arguments, allows us to represent PC quantification in Quarc and translate PC into Quarc, preserving validity. Introducing a weak existential quantifier into PC allows us to translate Quarc into PC, also preserving validity. However, unlike the translated systems, neither extended system can have a sound and complete proof system with Cut, supporting the claim that these are basically different calculi. (shrink)

The cofinality quantifiers were introduced by Shelah as an example of a compact logic stronger than first-order logic. We show that the classes of models axiomatized by these quantifiers can be turned into an Abstract Elementary Class by restricting to positive and deliberate uses. Rather than using an ad hoc proof, we give a general framework of abstract Skolemizations. This method gives a uniform proof that a wide rang of classes are Abstract Elementary Classes.

ABSTRACT In this paper, I ask whether quantifiers are intensional operators, with variable assignments playing the role of indices. Certain formulations of extensional type theory suggest an affirmative answer, but the most satisfactory among them suffer from a contamination of their semantic ontology with syntactic material. I lay out ‘Fregean’ versions of extensional type theory that are free from syntactic contamination and suggest a negative answer to our question.

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...) and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)

Let DDQ be the thesis that definite descriptions are quantifiers. Philosophers often deny DDQ because they believe that quantifiers do not depend on context in certain ways, ways in which definite descriptions do depend on context. In this paper, we examine one such argument, which, if sound, would entail the negation of DDQ.We show that this argument fails, and draw some consequences from its failure.

In this article, I argue that as a theoretical matter, a population's health-level is best quantified via averagism. Averagism asserts that the health of a population is the average of members’ health-levels. This model is better because it does not fall prey to a number of objections, including the repugnant conclusion, and because it is not arbitrary. I also argue that as a practical matter, population health-levels are best quantified via totalism. Totalism asserts that the health of a population is (...) the sum of members’ health-levels. Totalism is better here because it fits better with cost-benefit analysis and such an analysis is the best practical way to value healthcare outcomes. The two results are compatible because the theoretical and practical need not always align, whether in general or in the context of population health. (shrink)

A quantified universe is a set M equipped with a Riesz space equation image of real functions on Mn, for each n, and a second order operation equation image. Metric structures 4, graded probability structures 9 and many other structures in analysis are examples of such universes. We define ultraproduct of quantified universes and study properties preserved by this construction. We then discuss logics defined on the basis of classes of quantified universes which are closed under this construction.

Natural languages exhibit manysemantic universals, that is, properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal, the monotonicity universal. While the existing work has shown that quantifiers satisfying the monotonicity universal are easier to learn, we provide a more complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, we show that quantifiers satisfy the monotonicity universal evolve reliably in an iterated learning paradigm (...) with neural networks as agents. (shrink)

The gene regulation function (GRF) provides an operational description of a promoter behavior as a function of the concentration of one of its transcriptional regulators. Behind this apparently trivial definition lies a central concept in biological control: the GRF provides the input/output relationship of each edge in a transcriptional network, independently from the molecular interactions involved. Here we discuss how existing methods allow direct measurement of the GRF, and how several trade‐offs between scalability and accuracy have hindered its application to (...) relatively large networks. We discuss the theoretical and technical requirements for obtaining the GRF. Based on these requirements, we introduce a simplified and easily scalable method that is able to capture the significant parameters of the GRF. The GRF is able to predict the behavior of a simple genetic circuit, illustrating how addressing the quantitative nature of gene regulation substantially increases our comprehension on the mechanisms of gene control. (shrink)

I develop a device for simulating quantification over merely possible objects from the perspective of a modal actualist ---someone who thinks that everything that exists actually exists.

We identify the locally finite graphs that are quantifier-eliminable and their first order theories in the signature of distance predicates. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.