In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)

In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use (...) these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ‘ p∨¬p ’ and ‘ p∧¬p ’ are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning. (shrink)

We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the (...) requisite of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference. (shrink)

This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.

Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic are (...) tightly connected since many of the arguments for and objections against one theory reappear in the other theory in dual form. The target of the paper is making explicit in exactly what way, if any, ST and TS are dual to one another. The connection will allow us to gain a more fine-grained understanding of these logics and of the theories based on them. In particular, we will obtain new insights on two questions concerning ST which are being intensively discussed in the current literature: whether ST preserves classical logic and whether it is LP in sheep’s clothing. Explaining in what way ST and TS are duals requires comparing these logics at a metainferential level. We provide to this end a uniform proof theory to decide on valid metainferences for each of the four logics. This proof procedure allows us to show in a very simple way how different properties of inferences (unsatisfiability, supersatisfiability and antivalidity) that behave in very different ways for each logic can be captured in terms of the validity of a metainference. (shrink)

One way in which we might approach the challenge posed by the Sorites Paradox is considering that Sorites-susceptible predicates have several candidate extensions, or several ways in which these expressions can be made precise. For example, a candidate extension for the predicate ‘is a baby’ is the set of humans of less than two years, but also the set of those less than two years and one second, and of those less than two years and two seconds. In this chapter (...) we present and discuss two theories for vague predicates based on this idea: supervaluationism and subvaluationism. The chapter is structured in three parts. The first presents the super- and subvaluationist theories: their similarities and differences in the semantics, the resulting logics with their most characteristic features. The second reviews the super- and subvaluationist solutions to the Sorites Paradox and provides discussion on several controversies surrounding these theories. The third part introduces proof procedures for s’valuationist logics. (shrink)

This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide complete (and (...) sound) systems of deduction for supervaluationist consequence in which proofs are completely classical with the exception of a single last step (involving the above mentioned inference). (shrink)

In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and (...) argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K3+. (shrink)

Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based (...) on a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new consequence-relation and discuss some of its properties. (shrink)

Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...) to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper). (shrink)

Building on early work by Girard ( 1987 ) and using closely related techniques from the proof theory of many-valued logics, we propose a sequent calculus capturing a hierarchy of notions of satisfaction based on the Strong Kleene matrices introduced by Barrio et al. (Journal of Philosophical Logic 49:93–120, 2020 ) and others. The calculus allows one to establish and generalize in a very natural manner several recent results, such as the coincidence of some of these notions with their classical (...) counterparts, and the possibility of expressing some notions of satisfaction for higher-level inferences using notions of satisfaction for inferences of lower level. We also show that at each level all notions of satisfaction considered are pairwise distinct and we address some remarks on the possible significance of this (huge) number of notions of consequence. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.

Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...) good as their paracomplete counterparts, than giving positive reasons to believe on a particular paraconsistent proposal. But it sometimes happens that the weakness of a theory turns out to be its mayor ally, and this is what (I claim) happens in a particular paraconsistent proposal known as subvaluationism. In order to make room for truth-value gluts subvaluationism needs to endorse a notion of logical consequence that is, in some sense, weaker than standard notions of consequence. But this weakness allows the subvaluationist theory to accommodate higher-order vagueness in a way that it is not available to other theories of vagueness (such as, for example, its paracomplete counterpart, supervaluationism). (shrink)

It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness . This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist (...) theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion. (shrink)

Though it is standardly assumed that supervaluationism applied to vagueness is committed to global validity, Achille Varzi (2007) argues that the supervaluationist should take seriously the idea of adopting local validity instead. Varzi’s motivation for the adoption of local validity is largely based on two objections against the global notion: that it brings some counterexamples to classically valid rules of inference and that it is inconsistent with unrestricted higher-order vagueness. In this discussion I review these objections and point out ways (...) to address them not considered in Varzi’s paper. (shrink)

This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...) consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic. (shrink)

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

If God knew I were going to write this paper, was I able to refrain from writing it this morning? One possible response to this question is that God's knowledge does not take place in time and therefore He does not properly fore-know. According to this response, God knows absolutely everything, it's just that He knows everything outside of time. The so-called timeless solution was one of the influential responses to the foreknowledge problem in classical Christian Theology. This solution, however, (...) seemed to lose support in the recent debate. For example, Pike claims that "the doctrine of God's timelessness entered Christian Theology because Platonic thought was stylish at the time" and Hasker catalogues this as one of the minor solutions to the problem. One possible source for this general attitude towards timelessness is the thought that the very idea of timelessness is incoherent. In this paper I argue that that the timeless solution to the foreknowledge problem is congenial with the supervaluationist theory of branching time and that this formal framework provides, in fact, a precise characterization of the timeless solution to the foreknowledge problem. The views presented in this paper are in line with those of Kretzmann and Stump, Leftow and De Florio and Frigerio. (shrink)

This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.

Inleidend overzicht van de wijsgerige ethiek.

Scientific realists have suggested that changes in our scientific communities over the course of their history have rendered those communities progressively less vulnerable to the problem of unconcieved alternatives over time. I argue in response not only that the most fundamental historical transformations of the scientific enterprise have generated steadily mounting obstacles to revolutionary, transformative, or unorthodox scientific theorizing, but also that we have substantial independent evidence that the institutional apparatus of contemporary scientific inquiry fosters an exceedingly and increasingly theoretically (...) conservative form of that inquiry. I conclude that contemporary scientific communities are actually more vulnerable to the problem of unconceived alternatives than their historical predecessors, and I briefly suggest how we might seek to pursue scientific inquiry in a less theoretically conservative way. (shrink)

The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid pat- terns of inference even in the absence of a definitely-operator (or similar device). As a (...) consequence, the supervaluationist theory itself is in trou- ble. This paper discusses the objection. (shrink)

인간의 이성적 의식과 법의 관계를 밝히고 법의 해석 과 판단에 인간의 의식이 어떻게 작용하는가를 고찰 한 저술. 제1부에서는 법의 형이상학적인 측면에서 법의 실체, 그리스의 법, 데카르트의 법, 로크와 법, 칸트와 법, 헤겔과 법, 아담스미스의 법의 경제, 중국의 도덕과 법사상을 다루었다. 제2부에서는 심리학적 분석으로 헌법의 심리학적 해석, 법의 판결절차, 증거법, 형법과 죄, 청소년과 가족법, 조세법, 플라톤의 법, 칸트의 도덕론의 경험적 확인, 헤겔의 자아와 노동법, 법의 4차원에 대해 다뤘다.

George Berkeley is one of the greatest and most influential modern philosophers. In defending the immaterialism for which he is most famous, he redirected modern thinking about the nature of objectivity and the mind's capacity to come to terms with it. Along the way, he made striking and influential proposals concerning the psychology of the senses, the workings of language, the aims of science, and the scope of mathematics. In this Companion volume a team of distinguished authors not only examines (...) Berkeley's achievements but also his neglected contributions to moral and political philosophy, his writings on economics and development, and his defense of religious commitment and religious life. The volume places Berkeley's achievements in the context of the many social and intellectual traditions - philosophical, scientific, ethical, and religious - to which he fashioned a distinctive response. (shrink)

One diagnosis of what is wrong with the Knowledge Argument rests on the Ability Hypothesis. This couples an ability analysis of knowing what an experience is like together with a denial that phenomenal propositions exist. I argue against both components. I consider three arguments against the existence of phenomenal propositions and find them wanting. Nevertheless I deny that knowing phenomenal propositions is part of knowing what an experience is like. I provide a hybrid account of knowing what an experience is (...) like which is the coherent expression of a single idea: knowing what an experience is like is knowing what it would be like to have the phenomenal content of the experience as the content of an experience one is currently having. I explain how my conclusions indicate that the focus of discussion should be on the alleged explanatory gap between phenomenal facts and physical facts and not on the Knowledge Argument. The latter is a poor expression of the difficulty Physicalists face. (shrink)

Typical discussions of virtual reality (VR) fixate on technology for providing sensory stimulation of a certain kind. They thus fail to understand reality as the place wherein we live and work, misunderstanding it instead as merely a sort of presentation. The first half of the paper examines popular conceptions of VR. The most common conception is a shallow one according to which VR is a matter of simulating appearances. Yet there is, even in popular depictions, a second, more subtle conception (...) according to which VR is a matter of facilitating new kinds of interaction. The latter half of the paper turns to questions about the contemporary technology of Internet chatrooms. The fact that chatrooms can be used in certain ways suggests something about the prospects for VR. The penultimate section asks whether chatrooms may legitimately be thought of as places. (In a sense, they may.) The final section asks whether cybersex may legitimately be thought of as sex. (Again, yes.) Chatroom technology thus provides an argument for the second conception of VR over its much ballyhooed rival. (shrink)

There has been an increase in recent years in the use of empirical methods in healthcare ethics. Appeals to empirical data cannot answer moral questions, but insights into the knowledge, attitudes, experience, preferences and practice of interested parties can play an important part in the development of healthcare ethics. In particular, while we may establish a general ethical principle to provide explanatory and normative guidance for healthcare professionals, the interpretation and application of such general principles to actual practice still requires (...) interpretation and judgement. And many situations in healthcare practice are complex and may involve a variety of principles, each of which may conflict with the others. Simple surveys or interview studies may not be sufficient if we wish to develop a nuanced approach to ethical practice that can be set out in guidelines, codes or directives. We do not resolve moral questions by plebiscite. In this paper, the authors argue for the use of consensus methods to develop shared understanding of ethical practice, and they argue further for the combination of the Delphi method with the use of vignettes to illustrate the kind of situations that may occur in practice. They develop their argument in part by reference to their experience of using this approach in their recent research. (shrink)

As family physicians, general practitioners play a key role in safeguarding children. Should they suspect child abuse or neglect they may experience a conflict between responding to the needs and interests of the child and those of an adult patient. English law insists on the paramountcy of the interests of the child, but in family practice many other interests may be at stake. The authors argue that uncritical adoption of the paramountcy principle is too simplistic and can lead, paradoxically, to (...) greater harm. They argue for a more subtle and nuanced view of interests and of conflicts of interest in safeguarding children. (shrink)

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in (...) the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

On-line, just as off-line, there are ways of assessing the credibility of information sources. The Internet, although it arguably makes for nothing wholly new in this regard, complicates the ordinary task of assessing credibility. In the first section, I consider a specific example and argue that Internet content providers have no clear interest in resolving these comlications. In the second, I consider four general ways that we might assess credibility and explore how they apply to life online. Finally, I argue (...) that even careful information gathering may pose subtle pitfalls but that some of these may be mitigated on-line. (shrink)