Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. (...) This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

This essay explores the thesis that for vague predicates, uncertainty over whether a borderline instance x of red/large/tall/good is to be understood as practical uncertainty over whether to treat x as red/large/tall/good. Expressivist and quasi-realist treatments of vague predicates due to John MacFarlane and Daniel Elstein provide the stalking-horse. It examines the notion of treating/counting a thing as F , and links a central question about our attitudes to vague predications to normative evaluation of plans to treat a thing as (...) F . The essay examines how the account applies to normatively defective or contested terms. The final section raises a puzzle about the mechanics of MacFarlane’s detailed implementation for the case of gradable adjectives. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

In this paper, we present a simple overview of the main non classical logics proposed for dealing with the Sorites paradox, that is, weakly paracomplete logics, weakly paraconsistent, and type 1 fuzzy logics. We note some of their advantages and problems and we suggest that the problems can be at least partially overcome by adopting a solution which relies on interval based type 2 fuzzy logics.

Wright holds that the following two theses are jointly incoherent: Rules determine correct language use. These rules are discoverable via internal reflection on language use. I argue that incoherence is derivable from alone and examine two types of probabilistic accounts that model a modification of, one in terms of inexact knowledge, the other in terms of viewing semantic rules as reasons for linguistic actions. Both accommodate tolerance by breaking the link between justified assertion and truth, but incoherence threatens their conception (...) of justified assertion. I argue that the rules-as-reasons approach can relocate sharp boundaries to a place where they are not only more tolerable, but to be expected. (shrink)

According to the plurivaluationist, our vague discourse doesn’t have a single meaning. Instead, it has many meanings, each of which is precise—and it is this plurality of meanings that is the source of vagueness. I believe plurivaluationist positions are underdeveloped and for this reason unpopular. This paper attempts to correct this situation by offering a particular development of plurivaluationism that I call supersententialism. The supersententialist leverages lessons from another area of research—the Problem of the Many—in service of the plurivaluationist position. (...) The Problem reveals theoretical reasons to accept that there are many cats where we thought there was one; the supersententialist claims that we are in a similar situation with respect to languages, propositions and sentences. I argue that the parallel suggested by the supersententialist reveals unappreciated advantages and lines of defense for plurivaluationism. (shrink)

According to the form of logical pluralism elaborated by Beall and Restall there is more than one relation of logical consequence. Since they take the relation of logical consequence to reside at the very heart of a logical system, different relations of logical consequence yield different logics. In this paper, we are especially interested in understanding what are the consequences of endorsing Beall and Restall’s version of logical pluralism vis-à-vis the normative guidance that logic is taken to provide to reasoners. (...) In particular, the aim of this paper is threefold. First, in Sections 2 and 3, we offer an exegesis of Beall and Restall’s logical pluralism as a thesis of semantic indeterminacy of our concept of logical consequence – i.e. understood as indeterminacy logical pluralism. Second, in Sections 4 and 5, we elaborate and critically scrutinize three models of semantic indeterminacy that we think are fit to capture Beall and Restall’s indeterminacy logical pluralism. Third, in Section 6, following Beall and Restall’s assumption that the notion of logical consequence has normative significance for deductive reasoning, we raise a series of normative problems for indeterminacy logical pluralism. The overall conclusion that we aim to establish is that Beall and Restall’s indeterminate logical pluralism cannot offer an adequate account of the normative guidance that logic is taken to provide us with in ordinary contexts of reasoning. (shrink)

Vagueness is an extremely common feature of natural language, but does it actually play a positive, efficiency enhancing, role in communication? Adopting a probabilistic interpretation of vague terms, we propose that vagueness might act as a source of randomness when deciding what to assert. In this context we investigate the efficacy of multiple sender channels in which senders choose assertions stochastically according to vague definitions of the relevant words, and a receiver then aggregates the different signals. These vague channels are (...) then compared with Boolean channels in which assertions are selected deterministically based on classical definitions. We show that given a sufficient number of senders, a linear stochastic channel outperforms Boolean channels when performance is measured by the expected squared error between the actual value described by the senders and the receiver’s estimate of it based on the signals they receive. The number of senders required for vague channels to be at least as accurate as Boolean channels is shown to be a decreasing function of the size of the language i.e. the number of description labels available to the senders. Vague channels are then shown to be robust to transmission error provided the error rate is not too large. In addition, we investigate the behaviour of both Boolean and vague channels for a parametrised family of distributions on the input values. Finally, we consider optimal vague channels assuming a fixed number of senders and show that, provided there are more than two senders, a vague channel can be found that outperforms the optimal Boolean channel. In this context, we show that for channels with relatively low numbers of senders S-curve production functions are optimal. (shrink)

A theory of vagueness gives a model of vague language and of reasoning within the language. Among the models that have been offered are Degree Theorists’ numerical models that assign values between 0 and 1 to sentences, rather than simply modelling sentences as true or false. In this paper, I ask whether we can benefit from employing a rich, well-understood numerical framework, while ignoring those aspects of it that impute a level of mathematical precision that is not present in the (...) modelled phenomenon of vagueness. Can we ignore apparent implications for the phenomena by pointing out that it is just a model and that the unwanted features are mere artefacts? I explore the distinction between representors and artefacts and criticise the strategy of appealing to features as mere artefacts in defence of a theory. I focus largely on theories using numerical resources, but also consider other, related theories and strategies, including theories appealing to non-linear structures. (shrink)

A framework of degrees of belief, or credences, is often advocated to model our uncertainty about how things are or will turn out. It has also been employed in relation to the kind of uncertainty or indefiniteness that arises due to vagueness, such as when we consider “a is F” in a case where a is borderline F. How should we understand degrees of belief when we take into account both these phenomena? Can the right kind of theory of the (...) semantics of vagueness help us answer this? Nicholas J.J. Smith defends a unified account, according to which “degree of belief is expected truth-value”; this builds on his Degree Theory of vagueness that offers an account of the semantics and logic of vagueness in terms of degrees of truth. I argue that his account fails. Degree theories of vagueness do not help us understand degrees of belief and, I argue, we shouldn’t expect a theory of vagueness to yield a detailed uniform story about this. The route from the semantics to psychological states needn’t be straightforward or uniform even before we attempt to combine vagueness with probabilistic uncertainty. (shrink)

A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be (...) supplemented; the role of simulations of such infinite games; the role of small probabilities, and of idealization, in decision theory; tolerance about practical norms; and alternative ways of understanding decision theory's job description. (shrink)

This paper looks at the phenomenon of ethical vagueness by asking the question, how ought one to reason about what to do when confronted with a case of ethical vagueness? I begin by arguing that we must confront this question, since ethical vagueness is inescapable. I then outline one attractive answer to the question: we ought to maximize expected moral value when confronted with ethical vagueness. This idea yields determinate results for what one rationally ought to do in cases of (...) ethical vagueness. But what it recommends is dependent on which substantive theory of vagueness is true; one can't draw conclusions about how to reason about vagueness in ethics in the absence of concrete assumptions about the nature of vagueness. (shrink)

Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...) other. Building on work by Kamp and Partee, this paper further shows how verities, thus conceived of, may plausibly be assumed to have probabilistic structure. The new interpretation of verities is argued to also help answer the question of what the verities of indicative conditionals are, a question which Edgington leaves open. Finally, the question of how to accommodate higher-order vagueness, given this interpretation, is addressed. (shrink)

It has seemed natural to model phenomena related to vagueness in terms of graded membership. However, so far no satisfactory answer has been given to the question of what graded membership is nor has any attempt been made to describe in detail a procedure for determining degrees of membership. We seek to remedy these lacunae by building on recent work on typicality and graded membership in cognitive science and combining some of the results obtained there with a version of the (...) conceptual spaces framework. (shrink)

In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (in (...) celestial mechanics). Thinking of logic, epistemology, and decision theory as normative models employing various idealisations of these kinds, changes the way we approach the justification of the models in question. (shrink)

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)

Neutralism is the broad view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory, treatment, or methodology is adopted. The broad goal here is to articulate a distinct, specific kind of sorites paradox (The Observational Sorites Paradox) and show that it can be effectively treated via Neutralism.

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)

In this thesis, I will defend a new kind of compatibilist account of free action, indirect conscious control compatibilism (or indirect compatibilism for short), and argue that some of our actions are free according to it. My argument has three components, and involves the development of a brand new tool for experimental philosophy, and the use of cognitive neuroscience. The first component of the argument shows that compatibilism (of some kind) is a conceptual truth. Contrary to the current orthodoxy in (...) the free will literature, which is that our concept of free will is an incompatibilist concept - a concept according to which we have free will only if determinism is false - I will show that our concept of free will is in fact a compatibilist concept - a concept according to which we can have free will even if determinism is true - and I do so using a new experimental philosophy methodology inspired by two-dimensional semantics. -/- Of course, even if our concept of free will is a compatibilist concept, this does not mean that there are any free actions in the world: the current empirical evidence from the brain sciences appears to show that there might be no, or very few, free actions in the world, even on many compatibilist understandings of what it would take for there to be free will. The second component of the argument addresses this concern by extending our understanding of compatibilism. Agents act freely either when their actions are caused by compatibilistically acceptable psychological processes, or are indirectly caused by those same processes. Hence the name of my account: indirect compatibilism. -/- The final component of the argument defends my new account against some interesting objections and provides evidence from cognitive neuroscience that some of our actions count as free by the lights of indirect compatibilism. (shrink)

This paper focuses on two interrelated issues about the prospects for research projects in experimental philosophical logic. The first issue is about the role that logic plays in such projects; the second involves the role that experimental results from the cognitive sciences play in them. I argue that some notion of logic plays a crucial role in these research projects, and, in turn, the results of these projects might inform substantive debates in the philosophy of logic.

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)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)