In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall.

This paper motivates and explores an expressivist theory of vagueness, modelled on Allan Gibbard’s normative expressivism. It shows how Chris Kennedy’s semantics for gradable adjectives can be adjusted to fit into a theory on Gibbardian lines, where assertions constrain not just possible worlds but plans for action. Vagueness, on this account, is literally indecision about where to draw lines. It is argued that the distinctive phenomena of vagueness, such as the intuition of tolerance, can be explained in terms of practical (...) constraints on plans, and that the expressivist view captures what is right about several contending theories of vagueness. (shrink)

Ben-Yami presents Wittgenstein’s explicit criticism of the Platonic identification of an explanation with a definition and the alternative forms of explanation he employed. He then discusses a few predecessors of Wittgenstein’s criticisms and the Fregean background against which he wrote. Next, the idea of family resemblance is introduced, and objections answered. Wittgenstein’s endorsement of vagueness and the indeterminacy of sense are presented, as well as the open texture of concepts. Common misunderstandings are addressed along the way. Wittgenstein’s ideas, as is (...) then shown, have far-reaching implications for knowledge of meaning and the nature of logic, and with them to the nature of the philosophical project and its possible achievements. (shrink)

I argue that there can be no such thing as a borderline case of the predicate ‘phenomenally conscious’: for any given creature at any given time, it cannot be vague whether that creature is phenomenally conscious at that time. I first defend the Positive Characterization Thesis, which says that for any borderline case of any predicate there is a positive characterization of that case that can show any sufficiently competent speaker what makes it a borderline case. I then appeal to (...) the familiar claim that zombies are conceivable, and I argue that this claim entails that there can be no positive characterizations of borderline cases of ‘phenomenally conscious’. By the Positive Characterization Thesis, it follows that ‘phenomenally conscious’ can not have any borderline cases. (shrink)

What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics (...) from that model theory, one of which I will find to be more plausible than the other. (shrink)

This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...) that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection. (shrink)

Causal contextualism holds that sentences of the form ‘c causes e’ have context-sensitive truth-conditions. We consider four arguments invoked by Jonathan Schaffer in favor of this view. First, he argues that his brand of contextualism helps solve puzzles about transitivity. Second, he contends that how one describes the relata of the causal relation sometimes affects the truth of one’s claim. Third, Schaffer invokes the phenomenon of contrastive focus to conclude that causal statements implicitly designate salient alternatives to the cause and (...) effect. Fourth, he claims that the appropriateness of a causal statement depends on what is contextually taken for granted or made salient. We show that causal invariantism can explain these linguistic data at least as well as contextualism. We then argue that pace Schaffer, some causal sentences are always correct and can never be plausibly denied, regardless of the context. (shrink)

What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...) far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

Sex determines much about one's life, but what determines one's sex? The answer is complicated and incomplete: on close examination, ordinary notions of female and male are vague. In 2012, the International Olympic Committee further specified what they mean by woman in response to questions about who, exactly, is eligible to compete in women's Olympic events. I argue, first, that their stipulation is evidence that the use of vague terms is better described by semantic approaches to vagueness than by epistemic (...) approaches. In addition, the IOC's 2012 stipulation was made with sensitivity to its practical consequences. Linguistic actions often have morally relevant consequences, and I contend that, other things equal, we should adopt theories about language that acknowledge the responsibility we bear for what we say. Taking vagueness to be an epistemic phenomenon precludes the sense of agency needed for moral responsibility; taking it to be semantic does not. Thus I advance two arguments for semantic approaches to vagueness, as against epistemic approaches: one descriptive and one normative. (shrink)

Most words in natural language are vague, that is to say, they lack sharp boundaries and, hence, they have (actual or potential) borderline cases, where the word in question neither definitely applies nor definitely fails to apply. Vagueness gives rise to paradoxes, the best known of which is the sorites (concerned with how many grains of sand are needed to make a heap). Besides offering a solution to such paradoxes, a theory of vagueness should systematically describe how the truth conditions (...) of sentences with vague terms are determined; and it should also define the right logical principles for reasoning with such sentences. This article offers an introduction to the main theories of vagueness and to the problems they have to face. (shrink)

This paper considers a now familiar argument that the ubiquity of context -dependence threatens the project of natural language semantics, at least as that project has usually been conceived: as concerning itself with `what is said' by an utterance of a given sentence. I argue in response that the `anti-semantic' argument equivocates at a crucial point and, therefore, that we need not choose between semantic minimalism, truth-conditional pragmatism, and the like. Rather, we must abandon the idea, familiar from Kaplan and (...) others, that utterances express propositions `relative to contexts' and replace it with the Strawonian idea that speakers express propositions by making utterances in contexts. The argument for this claim consists in a detailed investigation of the particular case of demonstratives, which I argue demand such a Strawsonian treatment. I then respond to several objections, the most important of which allege that the Strawsonian account somehow undermines the project of natural language semantics, or threatens the semantics -pragmatics distinction. Please note that the paper posted here is an extended version of what was published. (shrink)

Stewart Shapiro has objected to the epistemicist theory of vagueness on grounds that it gives counterintuitive predictions about cases involving conditional obligation. This paper details a response on the epistemicist’s behalf. I first argue that Shapiro’s own presentation of the objection is unsuccessful as an argument against epistemicism. I then reconstruct and offer two alternative arguments inspired by Shapiro’s considerations, and argue that these fail too, given the information-sensitive nature of conditional obligations.

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

In this paper I explore the implications of moral vagueness (viz., the vagueness of moral predicates) for non-naturalist metaethical theories like those recently championed by Shafer-Landau, Parfit, and others. I characterise non-naturalism in terms of its commitment to 7 theses: Cognitivism, Correspondence, Atomism, Objectivism, Supervenience, Non-reductivism, and Rationalism. I start by offering a number of reasons for thinking that moral predicates are vague in the same way in which ‘red’, ‘tall’, and ‘heap’ are said to be. I then argue that (...) the moral non-naturalist seeking to countenance moral vagueness faces a dilemma: are moral properties vague, or perfectly sharp? On either horn of the dilemma, serious problems arise for some of the central tenets of non-naturalism: vague properties seem to threaten Objectivism, Supervenience, and Non-reductivism; on the other hand, sharp properties raise problems for Supervenience and Rationalism. The difficulties on each horn of the dilemma are real, and while they may not be insuperable, they do, at the very least, drastically limit the things non-naturalists can consistently say about moral properties, facts, and reasons. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by their flexibility. (...) Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)

On Richard’s When Truth Gives Out Content Type Journal Article Pages 1-9 DOI 10.1007/s11098-011-9796-0 Authors Kevin Scharp, Department of Philosophy, The Ohio State University, 350 University Hall, 230 North Oval Mall, Columbus, OH 43210, USA Stewart Shapiro, Department of Philosophy, The Ohio State University, 350 University Hall, 230 North Oval Mall, Columbus, OH 43210, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

The Pyrrhonian sceptic Favorinus of Arelata personified indeterminacy, cultivating his (or her) borderline status to undermine dogmatism. Inspired by the techniques of Favorinus, I show, by example, that ‘vague’ has borderline cases. These concrete steps lead to a more abstract argument that ‘vague’ has borderline borderline cases and borderline borderline borderline cases. My specimens are intended supplement earlier non-constructive proofs of the vagueness of ‘vague’.

The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories (...) of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language. Here, I first briefly review claims made by various theorists about these borderline contradictions, attempting to draw out some predictions about the behavior of ordinary speakers. Second, I present an experiment intended to gather relevant data about the behavior of ordinary speakers. Finally, I discuss the experimental results in light of several different theories of vagueness, to see what explanations are available. My conclusions are necessarily tentative; I do not attempt to use the present experiment to demonstrate that any single theory is incontrovertibly true. Rather, I try to sketch the auxiliary hypotheses that would need to be conjoined to several extant theories of vague language to predict the present result, and offer some considerations regarding the plausibility of these various hypotheses. In the end, I conclude that two of the theories I consider are better-positioned to account for the observed data than are the others. But the field of logically-informed research on people’s actual responses to vague predicates is young; surely as more data come in we will learn a great deal more about which (if any) of these theories best accounts for the behavior of ordinary speakers. (shrink)

ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition.

Open texture is a kind of semantic indeterminacy first systematically studied by Waismann. In this paper, extant definitions of open texture will be compared and contrasted, with a view towards the consequences of open-textured concepts in mathematics. It has been suggested that these would threaten the traditional virtues of proof, primarily the certainty bestowed by proof-possession, and this suggestion will be critically investigated using recent work on informal proof. It will be argued that informal proofs have virtues that mitigate the (...) danger posed by open texture. Moreover, it will be argued that while rigor in the guise of formalisation and axiomatisation might banish open texture from mathematical theories through implicit definition, it can do so only at the cost of restricting the tamed concepts in certain ways. (shrink)

On a simple and neat view, sometimes called the Relational Analysis of Attitude Ascriptions, a belief ascription on the form ‘S believes that x is F’ is correct if, and only if, S stands in the belief-relation to the proposition designated by ‘that x is F’, i.e., the proposition that x is F. It follows from this view that, for a person to believe, say, that x is a boat, there is one unique proposition that she has to believe. This (...) paper argues against this view. It fails, I contend, to make sense of peripheral concept variation. As we attribute and individuate concepts, two people’s concepts C1 and C2 count as e.g., concepts of boats even if their concepts have different extensions in peripheral, or borderline, cases of boats. Thus, A and B can believe that x is a boat through believing peripherally different propositions. It follows that there is no unique proposition that a person has to believe in order to believe e.g., that x is a boat. (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)

Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...) battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. Thus, supervaluationists (...) can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

This paper develops and defends the view that substantively normative uses of words like “good”, “right” and “ought” are irresolvably indeterminate: any single case of application is like a borderline case for a vague or indeterminate term, in that the meaning-fixing facts, together with the non-linguistic facts, fail to determine a truth-value for the target sentence in context. Normative claims, like vague or indeterminate borderline claims, are not meaningless, though. By making them, the speaker communicates information about the precisifications that (...) s/he accepts. The analogy with vague/indeterminate language, I argue, lays out a new and interesting foundation for a subjectivist approach to normativity. (shrink)

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic, that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two (...) uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation. (shrink)

Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics. This paper offers a detailed assessment of this suggestion. I argue that an interesting version of logical pluralism is hard, if not impossible, to achieve. I first outline an intuitive understanding of the notions of rivalry and correctness. (...) I then discuss a natural account of rivalry in terms of disagreement about validity claims and the argument from meaning variance that has been raised against it. I explore a more refined picture of the meaning of validity claims that makes use of the character-content distinction of classical two dimensional semantics. There are three ways in which pluralists can use that framework to argue for the view that different logics may be rivals but could nevertheless be equally correct. I argue that none of them is convincing. (shrink)

This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility (...) of mereological vagueness and indeterminacy in quantum mechanics and they offer various arguments both for and against ontic vagueness; onticism is also compared with other, competing theories of vagueness such as semanticism, the view that vagueness exists only in our linguistic representation of the world. Gareth Evans’s influential paper of 1978, “Can There Be Vague Objects?” gave a simple but cogent argument against the coherence of ontic vagueness. Onticism was subsequently dismissed by many. However, in recent years, researchers have become aware of the logical gaps in Evans’s argument and this has triggered a new wave of interest in onticism. Onticism is now widely regarded as at least a coherent view. Reflecting this growing consensus, the present anthology for the first time puts together essays that are focused on onticism and its various facets and it fills in the lacuna in the literature on vagueness, a much-discussed subject in contemporary philosophy. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...) so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...) to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory. (shrink)

Problems of logical theory choice are current being widely dis- cussed in the context of anti-exceptionalist views on logic. According to those views, logic is not a special science among others, so, in particular, the methodology for theory choice should be the same in logic as for other scientific disciplines. Richard Routley advanced one such methodology which meshes well with anti-exceptionalism, and argued that it leads one to choosing one single logic, which is a kind of ultralogic. We argue that (...) the choice for only one correct system of logic may be rejected on the basis of the methodology proposed by Routley and, furthermore, that taking anti-exceptionalism about logic seriously recommends that a pluralist view of logic should be accepted. We call this view “full-blooded anti-exceptionalism”, and the resulting view on logic, lacking a proper name, “local pluralism”. (shrink)

It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit Fine calls penumbral (...) connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context , Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. (shrink)

I discuss the interest-relative account of vagueness and argue for a distinction between relational vague predicates and non-relational vague predicates depending on the kind of properties expressed by them. The strategy rests on three arguments arising from the existence of clear cases of a vague predicate, from contexts in which a different answer is required for questions about whether a vague predicate applies to an item, and whether such an item satisfies the interest of an agent, and from cases where (...) an object changes up to the point of becoming P, where P is a vague predicate. In the second part of the paper, I distinguish between relational properties and non-relational properties, and I argue for the view that some vague predicates can express non-relational properties, comparative relational properties and interest-relative properties. On the basis of these arguments, I conclude that vagueness cannot be reduced to interest-relativity. (shrink)

We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions.

Against a broad consensus within contemporary analytic philosophy, Hattiangadi (Mind and Language 21(2):220–240, 2006 , 2007 ) has recently argued that linguistic meaning is not normative, at least not in the sense of being prescriptive. She maintains, more specifically, that standard claims to the effect that meaning is normative are usually ambiguous between two readings: one, which she calls Prescriptivity , and another, which she calls Correctness . According to Hattiangadi, though meaning is normative in the uncontroversial sense specified in (...) the principle Correctness , it is not normative in the sense specified by Prescriptivity . In this paper, I instead show that meaning is normative in the sense of being prescriptive. My argument for this claim takes the form of a classical disjunctive syllogism. I argue that either Correctness implies (because it presupposes) Prescriptivity , or linguistically meaningful items are ‘intrinsically intentional.’ But linguistically meaningful items are not intrinsically intentional, and thus Correctness implies (because it presupposes) Prescriptivity. (shrink)

The primary appeal of stakeholder theory in business ethics derives from its promise to help solve two large and often morally difficult problems: (1) how to manage people fairly and efficiently and (2) how to determine the extent of a firm's moral responsibilities beyond its obligations to enhance its profits and economic value. This article investigates a variety of conceptual quandaries that stakeholder theory faces in addressing these two general problems. It argues that these quandaries pose intractable obstacles for stakeholder (...) theory which prevent it from delivering on its large promises. Acknowledging that various versions of stakeholder theory have made a contribution in elucidating the complex nature of firms and business decision making, the article argues that it is time to move on. More precise explications of the nature of modern firms focusing on the application of basic moral principles to different business contexts and situations are likely to prove more accurate and useful. (shrink)

I examine the radical contextualists’ two main arguments for the semantic underdeterminacy thesis, according to which all, or almost all, English sentences lack context-independent truth conditions. I show that both arguments are fallacious. The first argument, which I call the fallacy of the many understandings , mistakenly infers that a sentence S is semantically incomplete from the fact that S can be used to mean different things in different contexts. The second argument, which I call the open texture fallacy , (...) wrongly concludes that a sentence S lacks context-independent truth conditions from the fact that there are circumstances in which the truth value of S would be indeterminate. I do however defend the claim that a certain class of sentences not containing any indexicals do lack context-independent truth conditions, and put forward an argument to that effect. But this argument, as I show, does not generalize to all sentences, and thus fails to support the semantic underdeterminacy thesis. (shrink)

Scott Soames argues that consideration of the practice of legal judgement gives us good reason to favor the partial-definition/context-sensitive theory of vagueness against epistemicism. Despite the fact that the value of power-delegation through vagueness is evidenced in practice, Soames says, epistemicism cannot account for it theoretically, while the partial-definition/context-sensitive theory is capable of it. In this paper, I examine the two possible arguments against epistemicism that can be extracted from Soames’s account: (i) an argument based on unknown obligations, and (ii) (...) an argument based on power-delegation through vagueness. The first argument tries to convince us that, as based on epistemicism, the law has already decided the borderline cases, so that judges have obligatory decisions even in such cases: therefore epistemicism is inconsistent with the discretion of judges in borderline cases. I show that even if we sympathize with Soames’s intuitions concerning the legal practice, the argument he offers is not conclusive since it is either invalid, unsound, or paradoxical. The second argument holds that only the gaps which the partial-definition/context-sensitive theory predicts give judges the possibility of lawmaking in borderline cases. However, by categorizing the vague laws as imperfect laws, the judges can claim the right of lawmaking without any need to refer to gaps in the law. By neutralizing these arguments, I argue that epistemicism is able to explain the phenomena just as well as the partial-definition/context-sensitive theory. (shrink)

Epistemicism is the view that seemingly vague predicates are not in fact vague. Consequently, there must be a sharp boundary between a man who is bald and one who is not bald. Although such a view is often met with incredulity, my aim is to provide a defense of epistemicism in this essay. My defense, however, is backhanded: I argue that the formal commitments of epistemicism are the result of good practical reasoning, not metaphysical necessity. To get to that conclusion, (...) I spend most of the essay arguing that using a formal system like classical logic to manage seemingly vague situations requires practical principles to mediate between the formalism and what it aims to represent. (shrink)

Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)