The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...) 'Wright & Sudbury Argument,' and the 'Epistemic Blindspot Argument.' The reason that the Surprise Exam Paradox has persisted this long is not because any of these arguments is problematic. On the contrary, each of them is correct. The reason that it has persisted so long is because each argument is only part of the solution. The correct solution requires all three of them to be combined together. Once they are, we may see exactly why the No Friday Argument fails and therefore why we have a solution to the Surprise Exam Paradox that should stick. (shrink)

We give a general description of a class of contrastive constructions, intended to capture what is common to contrastive knowledge, belief, hope, fear, understanding and other cases where one expresses a propositional attitude in terms of “rather than”. The crucial element is the agent's incapacity to distinguish some possibilities from others. Contrastivity requires a course-graining of the set of possible worlds. As a result, contrastivity will usually cut across logical consequence, so that an agent can have an attitude to p (...) rather than q but not to r rather than q , where r is a logical consequence of p . We relate these ideas to some general issues about thought, such as the question of whether all possibilities that can be distinguished in emotion can be distinguished in belief. (shrink)

In their paper “Vagueness, Ignorance, and Margins for Error” Kenton Machina and Harry Deutsch criticize the epistemic theory of vagueness. This paper answers their objections. The main issues discussed are: the relation between meaning and use; the principle of bivalence; the ontology of vaguely specified classes; the proper form of margin for error principles; iterations of epistemic operators and semantic compositionality; the relation or lack of it between quantum mechanics and theories of vagueness.

The linchpin of Williamson (2000)'s radically externalist epistemological program is an argument for the claim that no non-trivial condition is luminous—that no non-trivial condition is such that whenever it obtains, one is in a position to know that it obtains. I argue that Williamson's anti-luminosity argument succeeds only if one assumes that, even in the limit of ideal reflection, the obtaining of the condition in question and one's beliefs about that condition can be radically disjoint from one another. However, no (...) self-respecting defender of the luminosity of the mental would ever make such an assumption. Thus Williamson can only secure his controversial claims in epistemology by taking for granted certain equally controversial claims in the philosophy of mind. What emerges is that the best bet for defending an internalist epistemology against Williamson's attack is to take there to be a tight, intimate connection between (to take one example) our experiences and our beliefs upon reflection about the obtaining of those experiences, or between (to take another example) the rationality of our beliefs and our beliefs upon reflection about the rationality of those beliefs. (shrink)

In natural language we rarely use relation-words with more than three argument places. This paper studies one systematic device, rooted in natural language, by which relations of greater adicity can be expressed. It is based on a higher-order relation between 1-place, 2-place, and 4-place relations (and so on) of which the relation between the positive and comparative degrees of a predicate is a special case. Two formal languages are presented in this connection, one of which represents the language of communication (...) and the other the contextual information against which the first language is interpreted. A semantical theory is described, which treats the two languages in an interdependent way. Logical consequence is non-compact. Connections with issues about vagueness are made. (shrink)

I address Peter Mott's 'Margins for Error and the Sorites Paradox' , pp. 494–503). Mott criticizes my account of inexact knowledge, on which it satisfies margin for error principles of the form 'If one knows in a given case, one avoids false belief in sufficiently similar cases'. Mott's arguments are shown to be fallacious because they ignore the fact that our knowledge of inexact knowledge is itself inexact. In the examples discussed, the first-level inexact knowledge is perceptual. Since my defense (...) of an epistemicist theory of vagueness explains our ignorance of truth-values in borderline cases as the result of knowledge the inexactness of which has a conceptual source, the paper also contributes to the defense of epistemicism about vagueness. (shrink)

We describe the three place relation of contrastive knowledge, which holds between a person, a target proposition, and a contrasting proposition. The person knows that p rather than that q. We argue for three claims about this relation. (a) Many common sense and philosophical ascriptions of knowledge can be understood in terms of it. (b) Its application is subject to fewer complications than non-contrastive knowledge is. (c) It applies over a wide range of human and nonhuman cases.

Timothy Williamson’s potentially most important contribution to epistemicism about vagueness lies in his arguments for the basic epistemicist claim that the alleged cut-off points of vague predicates are not knowable. His arguments for this are based on so-called ‘margin for error principles’. This paper argues that these principles fail to provide a good argument for the basic claim. Williamson has offered at least two kinds of margin for error principles applicable to vague predicates. A certain fallacy of equivocation seems to (...) underlie his justification for both kinds of principles. Besides, the margin for error principles of the first kind can be used in the derivation of unacceptable consequences, while the margin for error principles of the second kind can be shown to be compatible with the falsity of epistemicism, under a number of assumptions acceptable to the epistemicist. (shrink)

The epistemicist theory aims to explain ignorance due to vagueness by semantic plasticity: the shiftiness of intensions across close possible worlds resulting from shiftiness in usage. This explanation is challenged by the Omniscient Speaker Puzzle (Sennet in Philos Stud 161(2):273–285, 2012). Suppose that an omniscient speaker, Barney, who knows all the facts about usage and how these facts determine the intensions of expressions, cooks up a scheme to stabilise the intension of a normally semantically plastic term like ‘rich’. It seems (...) that ‘rich’ would display all the phenomena associated with vagueness without being semantically plastic, thus making the epistemicist explanation of ignorance due to vagueness insufficient. In this paper, I present a few choice points for epistemicism that arise as a result of the puzzle. (shrink)

Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property of balancedness, a significant (...) relaxation of introspective omniscience. I provide an example which shows that Geanakoplos’s statement is incorrect. I then introduce a new property, local balancedness, which allows us both to correct Geanakoplos’s result, and to extend it to cases where the truth axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic conditions for correlated and Nash equilibrium, both of which relax the assumption of introspective omniscience. In all three cases, the results are also extended to infinite state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.). (shrink)

You omega know something when you know it, and know that you know it, and know that you know that you know it, and so on. This paper first argues that omega knowledge matters, in the sense that it is required for rational assertion, action, inquiry, and belief. The paper argues that existing accounts of omega knowledge face major challenges. One account is skeptical, claiming that we have no omega knowledge of any ordinary claims about the world. Another account embraces (...) the KK thesis, and identifies knowledge with omega knowledge. This position faces counterexamples, and struggles to make sense of inexact knowledge. The paper then develops a new account of knowledge, by proposing the principle of Reflective Luminosity: if you know that you know something, then you omega know it. I argue that Reflective Luminosity allows for omega knowledge while avoiding the problems for KK. (shrink)

David Lewis—famously—never tasted vegemite. Did he have any knowledge of what it's like to taste vegemite? Most say 'no'; I say 'yes'. I argue that knowledge of what it’s like varies along a spectrum from more exact to more approximate, and that phenomenal concepts vary along a spectrum in how precisely they characterize what it’s like to undergo their target experiences. This degreed picture contrasts with the standard all-or-nothing picture, where phenomenal concepts and phenomenal knowledge lack any such degreed structure. (...) I motivate the degreed picture by appeal to (1) limits in epistemic abilities such as recognition, imagination, and inference, and (2) the semantics of ‘knows what it’s like’ expressions. I argue that approximate phenomenal knowledge cannot be explained merely via determinable or vague phenomenal concepts. I develop a framework for systematizing approximate knowledge of phenomenal character. And I explain how my view challenges some standard assumptions about the acquisition conditions, requirements for mastery, and referential mechanisms of phenomenal concepts. (shrink)

Williamson (2000) argues that the KK principle is inconsistent with knowledge of margin for error in cases of inexact perceptual observations. This paper argues, primarily by analogy to a different scenario, that Williamson’s argument is fallacious. Margin for error principles describe the agent’s knowledge as a result of an inexact perceptual event, not the agent’s knowledge state in general. Therefore, epistemic agents can use their knowledge of margin for error at most once after a perceptual event, but not more. This (...) insight blocks a crucial step in Williamson’s original argument. Along the way, the value of standard epistemic logic for analyzing margin for error reasoning is challenged. (shrink)

Kevin Dorst has recently pointed out an apparently puzzling consequence of denying epistemic luminosity: given some natural-sounding bridging principles between knowledge, credence, and indicative conditionals, the denial of epistemic luminosity licenses the knowledge and assertability of abominable-sounding conditionals of the form ⌜If I don’t know that ϕ, then ϕ⌝. We provide a general and systematic examination of this datum by testing Dorst’s claim against various semantics for the indicative conditional in the setting of epistemic logic. Our conclusion is that, regardless (...) of whether knowledge is luminous, the knowability of these conditionals is highly sensitive to the correct semantic analysis of the indicative conditional. Moreover, standard pragmatic resources can explain away the infelicity of such assertions. As it stands, the datum does not tell against epistemic non-luminosity. (shrink)

This paper presents a new system of conditional logic B2, which is strictly intermediate in strength between the existing systems B1 and B3 from John Burgess (1981) and David Lewis (1973a). After presenting and motivating the new system, we will show that it is characterized by a natural class of frames. These frames correspond to the idea that conditionals are about which worlds are nearly closest, rather than which worlds are closest. Along the way, we will also give new characterization (...) results for B1 and B3, along with two other new systems B1.1 and B1.2. (shrink)

The Free Choice effect—whereby \\) seems to entail both \ and \—has traditionally been characterized as a phenomenon affecting the deontic modal ‘may’. This paper presents an extension of the semantic account of free choice defended by Fusco to the agentive modal ‘can’, the ‘can’ which, intuitively, describes an agent’s powers. On this account, free choice is a nonspecific de re phenomenon that—unlike typical cases—affects disjunction. I begin by sketching a model of inexact ability, which grounds a modal approach to (...) agency in a Williamson -style margin of error. A classical propositional semantics combined with this framework can reflect the intuitions highlighted by Kenny ’s dartboard cases, as well as the counterexamples to simple conditional views recently discussed by Mandelkern et al.. In Section 3, I turn to an independently motivated actual-world-sensitive account of disjunction, and show how it extends free choice inferences into an object language for propositional modal logic. (shrink)

Many of our sources of knowledge only afford us knowledge that is inexact. When trying to see how tall something is, or to hear how far away something is, or to remember how long something lasted, we may come to know some facts about the approximate size, distance or duration of the thing in question but we don’t come to know exactly what its size, distance or duration is. In some such situations we also have some pointed knowledge of how (...) inexact our knowledge is. That is, we can knowledgeably pinpoint some exact claims that we do not know. We show that standard models of inexact knowledge leave little or no room for such pointed knowledge. We devise alternative models that are not afflicted by this shortcoming. (shrink)

According to the KK-principle, knowledge iterates freely. It has been argued, notably in Greco, that accounts of knowledge which involve essential appeal to normality are particularly conducive to defence of the KK-principle. The present article evaluates the prospects for employing normality in this role. First, it is argued that the defence of the KK-principle depends upon an implausible assumption about the logical principles governing iterated normality claims. Once this assumption is dropped, counter-instances to the principle can be expected to arise. (...) Second, it is argued that even if the assumption is maintained, there are other logical properties of normality which can be expected to lead to failures of KK. Such failures are noteworthy, since they do not depend on either a margins-for-error principle or safety condition of the kinds Williamson appeals to in motivating rejection KK. “Introduction: KK and Being in a Position to Know” Section formulates two versions of the KK-Principle; “Inexact Knowledge and Margins for Error” Section presents a version of Williamson’s margins-for-error argument against it; “Knowledge and Normality” and “Iterated Normality” Sections discuss the defence of the KK-Principle due to Greco and show that it is dependent upon the implausible assumption that the logic of normality ascriptions is at least as strong as K4; finally, “Knowledge in Abnormal Conditions” and “Higher-Order Ignorance Inside the Margins” Sections argue that a weakened version of Greco’s constraint on knowledge is plausible and demonstrate that this weakened constraint will, given uncontentious assumptions, systematically generate counter-instances to the KK-principle of a novel kind. (shrink)

Some people commonly know a proposition just in case they all know it, they all know that they all know it, they all know that they all know that they all know it, and so on. They commonly believe a proposition just in case they all believe it, they all believe that they all believe it, they all believe that they all believe that they all believe it, and so on. A long tradition in economic theory, theoretical computer science, linguistics (...) and philosophy has held that people have some approximation of common knowledge or common belief in a range of circumstances, for example, when they are looking at an object together, or when they have just discussed something explicitly in conversation. In this paper, I argue that people do not have any approximation of common knowledge or common belief in these circumstances. The argument suggests that people never have any approximation of common knowledge or common belief. (shrink)

This paper offers a new solution to the Surprise Test Paradox. The paradox arises thanks to an ingenious argument that seems to show that surprise tests are impossible. My solution to the paradox states that it relies on a questionable closure principle. This closure principle says that if one knows something and competently deduces something else, one knows the further thing. This principle has been endorsed by John Hawthorne and Timothy Williamson, among others, and I trace its motivation back to (...) work by Alvin Goldman. I provide counterexamples to the principle and explain the flaw in the reasoning of those who defend it. (shrink)

In chapter 5 of Knowledge and its Limits, T. Williamson formulates an argument against the principle (KK) of epistemic transparency, or luminosity of knowledge, namely “that if one knows something, then one knows that one knows it”. Williamson’s argument proceeds by reductio: from the description of a situation of approximate knowledge, he shows that a contradiction can be derived on the basis of principle (KK) and additional epistemic principles that he claims are better grounded. One of them is a reflective (...) form of the margin for error principle defended by Williamson in his account of knowledge. We argue that Williamson’s reductio rests on the inappropriate identification of distinct forms of knowledge. More specifically, an important distinction between perceptual knowledge and non-perceptual knowledge is wanting in his statement and analysis of the puzzle. We present an alternative account of this puzzle, based on a modular conception of knowledge: the (KK) principle and the margin for error principle can coexist, provided their domain of application is referred to the right sort of knowledge. (shrink)

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

My concern in this paper is with the claim that knowledge is a mental state – a claim that Williamson places front and centre in Knowledge and Its Limits. While I am not by any means convinced that the claim is false, I do think it carries certain costs that have not been widely appreciated. One source of resistance to this claim derives from internalism about the mental – the view, roughly speaking, that one’s mental states are determined by one’s (...) internal physical state. In order to know that something is the case it is not, in general, enough for one’s internal physical state to be a certain way – the wider world must also be a certain way. If we accept that knowledge is a mental state, we must give up internalism. One might think that this is no cost, since much recent work in the philosophy of mind has, in any case, converged on the view that internalism is false. This thought, though, is too quick. As I will argue here, the claim that knowledge is a mental state would take us to a view much further from internalism than anything philosophers of mind have converged upon. (shrink)

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. (...) Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence. (shrink)

Williamson (2000a) has argued that posi- tive introspection is incompatible with in- exact knowledge. His argument relies on a margin-for-error requirement for inexact knowledge based on a intuitive safety prin- ciple for knowledge, but leads to the counter- intuitive conclusion that no possible creature could have both inexact knowledge and posi- tive introspection. Following Halpern (2004) I put forward an alternative margin-for-error requirement that preserves the safety require- ment while blocking Williamson’s argument. I argue that the infallibilist conception of knowledge (...) that underlies the new require- ment provides a better account of inexact knowledge and higher-order knowledge than both Williamson’s and Halpern’s. (shrink)

The paper discusses some ways in which vagueness and its phenomena may be thought to impose certain limits on our knowledge and, more specifically, may be thought to bear on the traditional philosophical idea that certain domains of facts are luminous, i.e., roughly, fully open to our view. The discussion focuses on a very influential argument to the effect that almost no such interesting domains exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts (...) that are best candidates for being luminous plays an illicit role in such argument. The paper centres around the idea that vagueness brings with itself the prima facie plausibility of soritical principles. Using the diagnostics of sharpenings, it is first pointed out that, despite certain considerations to the contrary, the margin‐for‐error principle required by the anti‐luminosity argument may well derive all of its plausibility from an underlying soritical principle. The notion of confidence that is relevant to the argument is then isolated and sharply distinguished from the notion of subjective probability. Against this background, it is argued that the reasoning about confidence involved in the argument in favour of the problematic margin‐for‐error principle is fallacious in the same way in which sorites reasoning is. This reveals the possibility of having reliable knowledge even at the penumbral limit with falsity, a possibility for which a concrete formal model is constructed. The model in turn permits a deeper appreciation of the role played in the dialectic by the distinction between confidence and subjective probability as well as by confidence requirements on knowledge. It is concluded that careful heeding of vagueness and its phenomena, far from forcing new and surprising limits on our knowledge, actually removes one of the main barriers – unreliability – often thought to stand in its way. (shrink)

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...) argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge. (shrink)

We provide a full characterization of computational error states for information systems. The class of errors considered is general enough to include human rational processes, logical reasoning, scientific progress and data processing in some functional programming languages. The aim is to reach a full taxonomy of error states by analysing the recovery and processing of data. We conclude by presenting machine-readable checking and resolve algorithms.

I present three invented languages, in order to support a claim that vagueness and demonstrativity are related. One of them handles vagueness like English handles demonstratives, the second handles demonstratives like English handles vagueness, and the third combines the resources of the first two. The argument depends on the claim that all three can be learned and used by anyone who can speak English.

The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (...) (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.). (shrink)

In this paper I consider the surprise examination paradox from a practical perspective, paying special attention to the communicative role of the teacher’s promise to the students. This perspective, which places the promise within a practice, rather than viewing it in the abstract, imposes constraints on adequate solutions to the paradox. In the light of these constraints, I examine various solutions which have been offered, and suggest two of my own.

This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches – solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy (...) and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes. (shrink)

Good’s theorem is the apparent platitude that it is always rational to ‘look before you leap’: to gather information before making a decision when doing so is free. We argue that Good’s theorem is not platitudinous and may be false. And we argue that the correct advice is rather to ‘make your act depend on the answer to a question’. Looking before you leap is rational when, but only when, it is a way to do this.

Forthcoming in S. Artemov and R. Parikh, Proceedings of the ESSLLI 2006 Workshop on Rationality and Knowledge.

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is (...) emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

Forthcoming in D.H. Pritchard & V. Hendricks, New Waves in Epistemology,.

Epistemicism seems to be the most dominating approach to vagueness in the recent twenty years. In the logical and philosophical tradition, e.g. Peirce, vagueness does not depend on human knowledge. Epistemicists deny this fact and contend that vagueness is merely the result of our imperfect mind, our dearth of knowledge, sort of phantom, finally, that it simply does not exist. In my opinion, such a stance not only excludes vagueness comprehended in terms of human knowledge, but which is worse, stems (...) from spurious logical arguments. The part of arguments called Sorensen’s Arguments or even Proofs were the subject of my analysis in the book Paradoksy and in the paper “Epistemicism and Roy Sorensen Arguments” published in the Bulletin of the Section of Logic. Here I shall only briefly refer to these works and focus mainly on the arguments launched by Tymothy Williamson. One of them is to uncover why we are not able to recognize the alleged sharp boundary between positive and negative extensions of any vague predicates. Williamson’s reasoning is based on his margin for error principle. Another argumentation of Williamson aims at the refutation of the principle I know that I know. It should be emphasized that all the aforementioned arguments are fundamental for epistemicism and all of them are fallacious because of either formal or false-premise fallacy. There is the circumstance that we cannot deem epistemicism logical. Finally, we show that within the epistemic frame the following thesis is valid: if what epistemicism states is the case, then what epistemicism states is not the case. This immediately implies → ¬p’) that it is not the case what epistemicism states. So, either epistemicism or logic. (shrink)

The paper discusses some ways in which the phenomenon of borderline cases may be thought to bear on the traditional philosophical idea that certain domains of facts are fully open to our view. The discussion focusses on a very influential argument (due to Tim Williamson) to the effect that, roughly, no such domains of luminous facts exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts that are best candidates for being luminous plays an (...) illicit role in the argument. The paper investigates this issue by centring around the idea that vagueness brings with itself borderline cases, and that these in turn generate absence of a fact of the matter and hence epistemically benign lack of knowledge. It is argued that, given the possibility of absence of a fact of the matter, the idea of luminosity should be reformulated using the notion of determinacy, and that the resulting reformulation is not immediately subject to the original anti-luminosity argument. However, it is shown that the specific understanding of determinacy required by this strategy validates a new argument against the reformulated version of luminosity. Moreover, reflection on the connection between mistake and absence of a fact of the matter offers another argument against such version, with the surprising upshot that, granting the soundness of the original anti-luminosity argument, not even the determinacy of a certain fact would guarantee its knowability. (shrink)

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These (...) explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox. (shrink)

This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and (...) rationality, in a number of central axes in dynamic epistemology: temporal, social, probabilistic and even deontic dynamics. (shrink)

Classically, vagueness has been considered something bad. It leads to the Sorites paradox, borderline cases, and the (apparent) violation of the logical principle of bivalence. Nevertheless, there have always been scholars claiming that vagueness is also valuable. Many have pointed out that we could not communicate as successfully or efficiently as we do if we would not use vague language. Indeed, we often use vague terms when we could have used more precise ones instead. Many scholars (implicitly or explicitly) assume (...) that we do so because their vagueness has a positive function. But how and in what sense can vagueness be said to have a function or value? This paper is an attempt to give an answer to this question. After clarifying the concepts of vagueness and value, it examines nine arguments for the value of vagueness, which have been discussed in the literature. The (negative) result of this examination is, however, that there is not much reason to believe that vagueness has a value or positive function at all because none of the arguments is conclusive. A tenth argument that has not been discussed so far seems most promising but rests on a solely strategic notion of function. (shrink)

Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)