The goal of this paper is a comprehensive analysis of basic reasoning patterns that are characteristic of vague predicates. The analysis leads to rigorous reconstructions of the phenomena within formal systems. Two basic features are dealt with. One is tolerance: the insensitivity of predicates to small changes in the objects of predication (a one-increment of a walking distance is a walking distance). The other is the existence of borderline cases. The paper shows why these should be treated as different, though (...) related phenomena. Tolerance is formally reconstructed within a proposed framework of contextual logic, leading to a solution of the Sorites paradox. Borderline-vagueness is reconstructed using certain modality operators; the set-up provides an analysis of higher order vagueness and a derivation of scales of degrees for the property in question. (shrink)

Semantic and soritical paradoxes display remarkable family resemblances. For one thing, several non-classical logics have been independently applied to both kinds of paradoxes. For another, revenge paradoxes and higher-order vagueness—among the most serious problems targeting solutions to semantic and soritical paradoxes—exhibit a rather similar dynamics. Some authors have taken these facts to suggest that truth and vagueness require a unified logical framework, or perhaps that the truth predicate is itself vague. However, a common core of semantic and soritical paradoxes has (...) not been identified yet, and no explanation of their relationships has been provided. Here we aim at filling this lacuna, in the framework of many-valued logics. We provide a unified diagnosis of semantic and soritical paradoxes, identifying their source in a general form of indiscernibility. We then develop our diagnosis into a theory of paradoxicality, which formalizes both semantic and soritical paradoxes as arguments involving specific instances of our generalized indiscernibility principle, and correctly predicts which logics can non-trivially solve them. (shrink)

Most ordinary objects - cats, humans, mountains, ships, tables, etc. - have indeterminate mereological boundaries. If the theory of mereology is meant to include ordinary objects at all, we need it to have some space for mereological indeterminacy. In this paper, we present a novel degree-theoretic semantics - Boolean semantics - and argue that it is the best degree-theoretic semantics for modeling mereological indeterminacy, for three main reasons: (a) it allows for incomparable degrees of parthood, (b) it enforces classical logic, (...) and (c) it is compatible with all the axioms of classical mereology. Using Boolean semantics, we will also investigate the connection between vagueness in parthood and vagueness in existence/identity. We show that, contrary to what many have argued, the connection takes neither the form of entailment nor the form of exclusion. (shrink)

Hartry Field has proposed a fundamental division of theories of linguistic and mental content into those that do, and those that don’t, give a central role to ‘that’-clause ascriptions. Here I investigate the commitments of theories that (in accord with Field’s position) deny ‘that’-clause ascriptions a central role, but (in contrast to Field’s position) give truth conditions a central role. Such non-oblique truth-conditionalism promises significant advantages. However, the stance is costlier than it may appear. Non-oblique truth-conditionalists, I argue, must renounce (...) a priori entitlement to schemas of disquotation that are presupposed when theories of content are put to metaphysical or epistemological use. As case studies, I discuss two theories that might seem to exemplify non-oblique truth-conditionalism: David Chalmers’s two-dimensionalist theory of content and Ruth Millikan’s teleosemantics. (shrink)

In this paper I develop a semantic theory of vagueness that is immune to worries regarding the use of precise mathematical tools. I call this view semantic quietism. This view has the advantage of being clearly compatible with the phenomenon of vagueness. The cost is that it cannot capture every robust semantic fact.

It is widely accepted that vagueness in law calls for a specific interpretation of the law—interpretation that changes the meaning of the law and makes it more precise. According to this view, vagueness causes gaps in the law, and the role of legal interpretation in the case of vagueness is to fill such gaps. I argue that this view is mistaken and defend the thesis that vagueness in law calls only for an application of the law to the case at (...) hand, leaving the meaning of the law intact. (shrink)

In this paper I argue that Gareth Evans’ famous proof of the impossibility of de re indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argument is straightforwardly invalid.

The goal of this paper is to develop a theory of content for vague language. My proposal is based on the following three theses: (1) language-mastery is not rulebased— it involves a certain kind of decision-making; (2) a theory of content is to be thought of instrumentally—it is a tool for making sense of our linguistic practice; and (3) linguistic contents are only locally defined—they are only defined relative to suitably constrained sets of possibilities. CiteULike Connotea Del.icio.us What's this?

Remember the story of the most-most? It’s the story of that club in New York where people are the most of every type. There is the hairiest bald man and the baldest hairy man; the shortest giant and the tallest dwarf; the smartest idiot and the stupidest wise man. They are all there, including honest thieves and crippled acrobats. On Saturday night they have a party, eat, drink, dance. Then they have a contest. “And if you can tell the hairiest (...) bald man from the baldest hairy man—we are told—you get a prize.”. (shrink)

It is generally agreed that vague predicates like ‘red’, ‘rich’, ‘tall’, and ‘bald’, have borderline cases of application. For instance, a cloth patch whose color lies midway between a definite red and a definite orange is a borderline case for ‘red’, and an American man five feet eleven inches in height is (arguably) a borderline case for ‘tall’. The proper analysis of borderline cases is a matter of dispute, but most theorists of vagueness agree at least in the thought that (...) borderline cases for vague predicate ‘ ’ are items whose satisfaction of ‘ ’ is in some sense unclear or problematic: it is unclear whether or not the patch is red, unclear whether or not the man is tall.1 For example, Lynda Burns cites a widespread view as holding that borderline cases “are not definitely within the positive or negative extension of the predicate. … Border- line cases are seen as falling within a gap between the cases of definite application of the predicate and cases of definite application of its negation” (1995, 30). Michael Tye writes that the “concept of a border- line case is the concept of a case that is neither definitely in nor defi- nitely out” (1994b, 18). (shrink)

The extensions of vague predicates like ‘is bald’, ‘is tall’, and ‘is a heap’ apparently lack sharp boundaries, and this makes such predicates susceptible to soritical reasoning, i.e. reasoning that leads to some version of the notorious sorites paradox. This essay is concerned with a certain kind of theory of vagueness, according to which the symptoms and puzzles of vagueness should be accounted for in terms of a particular species of context sensitivity exhibited by vague expressions. The basic idea is (...) that the extensions of vague predicates vary with certain contextual factors, and that this fact can explain why they appear to lack sharp boundaries. This kind of view is referred to as contextualism about vagueness. A detailed characterisation of contextualism about vagueness is given in chapter two and three. In chapter two, a generic version of contextualism about vagueness is developed, and some alternative forms of context sensitivity are introduced. In chapter three, the specific contextual factors appealed to by different contextualists are discussed. In chapter four, different contextualist diagnoses of the sorites paradox are considered, and found to be problematic in various ways. It is argued that contrary to what some of its proponents have claimed, contextualism about vagueness is not superior to other comparable theories of vagueness when it comes to explaining the appeal of soritical reasoning. In chapter five, a certain version of the sorites paradox, known as the forced march sorites, is discussed. It is argued that “data” about how speakers would behave in the forced march cannot lend any firm support to contextualism about vagueness. In chapter six, some problems concerning the instability of the contextual factors are considered. One problem is that contextualist diagnoses of the sorites which locate a fallacy of equivocation in the reasoning seem to render non-soritical reasoning fallacious as well. A model for treating this problem is suggested, but on closer consideration, it turns out to be problematic. Moreover, this model is of no help in solving the more general problem that even if classical logic remains valid for vague language on some contextualist views, the instability of the extensions of vague predicates makes it difficult to know when a certain piece of reasoning instantiates a valid argument form. Other difficulties arise with respect to speech reports and belief contents. Chapter seven concludes with a summary and some methodological remarks. (shrink)

In a recent paper, Barrio, Pailos and Szmuc (BPS) show that there are logics that have exactly the validities of classical logic up to arbitrarily high levels of inference. They suggest that a logic therefore must be identified by its valid inferences at every inferential level. However, Scambler shows that there are logics with all the validities of classical logic at every inferential level, but with no antivalidities at any inferential level. Scambler concludes that in order to identify a logic, (...) we at least need to look at the validities and the antivalidities of every inferential level. In this paper, I argue that this is still not enough to identify a logic. I apply BPS’s techniques in a super/sub-valuationist setting to construct a logic that has exactly the validities and antivalidities of classical logic at every inferential level. I argue that the resulting logic is nevertheless distinct from classical logic. (shrink)

Following David Lewis, Ted Sider has famously argued that unrestricted first-order quantification cannot be vague. His argument was intended as a type of reductio: its strategy was to show that the mere hypothesis of unrestricted quantifier vagueness collapses into the claim that unrestricted quantification is precise. However, this short article considers two natural reconstructions of the argument, and shows that each can be resisted. The theme will be that each reconstruction of the argument involves assumptions which advocates of vague quantification (...) have independent reason to reject. (shrink)

Are moral terms semantically plastic—that is, would very slight changes in our patterns of use have shifted their meanings? This is a delicate question for moral realists. A 'yes' answer seems to conflict with the sorts of intuitions that support realism; but a 'no' answer seems to require a semantics that involves hefty metaphysical commitments. This tension can be illustrated by thinking about how standard accounts of vagueness can be applied to the case of moral terms, and also by considering (...) how realists should respond to the Moral Twin Earth problem. After presenting the puzzle, I will argue that moral realists can accept the semantic plasticity of moral expressions while accounting for contrary intuitions in a way that is nearly cost-free. (shrink)

Supervaluationism, traditionally conceived, is the conjunction of three theses: Vagueness in a language gives rise to there being a multitude of acceptable assignments of semantic values to some expressions of the language, These assignments correspond to possible completions of the meanings of vague expressions, Truth is truth under all acceptable assignments, and falsity is falsity under all acceptable assignments. Supervaluationism has three chief virtues. It preserves classical logic. It provides an account of what vagueness is. And it extends nicely to (...) the vagueness of singular terms. I argue, however, that the existence of vagueifiers ‐ expressions like‘roughly’– pose problems for thesis of Supervaluationism, and that the supervaluationist can get around these problems only at a serious cost. Toward the end of the paper, I present an alternative analysis of vagueness, which preserves the main virtues of Supervaluationism, but which identifies vagueness as semantic Overdetermination, rather than as semantic underdetermination. (shrink)

The problem of reconciling the philosophical denial of ontological vagueness with common-sense beliefs positing vague objects, properties and relations is addressed. This project arises for any view denying ontological vagueness but is especially pressing for transvaluationism, which claims that ontological vagueness is impossible. The idea that truth, for vague discourse and vague thought-content, is an indirect form of language-thought correspondence is invoked and applied. It is pointed out that supervaluationism provides one way, but not necessarily the only way, of implementing (...) the idea of indirect correspondence. (shrink)

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative (...) semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent. (shrink)

A number of recent accounts for vague terms postulate a kind of context-sensitivity, one that kicks in after the usual ‘external’ contextual factors like comparison class are established and held fixed. In a recent paper, ‘Vagueness without Context Change’: 275–92), Rosanna Keefe criticizes all such accounts. The arguments are variations on considerations that have been brought against context-sensitive accounts of knowledge, predicates of personal taste, epistemic modals, and the like. The issues are well known and there are variety of options (...) available in reply. More important, the arguments rely on an overly narrow conception of context-sensitivity, suggesting that one size fits all. If Keefe’s arguments were cogent, they would tell against the context-sensitivity of just about any expression, beyond the typical indexicals, including the variation of vague terms with comparison class. However, the criticisms raised by Keefe do highlight certain questions that must be answered by an advo... (shrink)

This is not an overly ambitious paper. What I would like to do is to take a thesis that most people would regard as wildly implausible, and convince you that it is, in fact, false. What's worse, the argument I shall give is by no means airtight, though I hope it's reasonably convincing. The thesis has to do with the fuzzy boundaries of terms that refer to familiar middle-sized objects, terms like ‘Kilimanjaro’ and ‘the tallest mountain in Africa.’ It is (...) intuitively clear that Kilimanjaro has a fuzzy boundary, so that there are some clods of earth at the base of the mountain for which there isn't anything, either in our practices in using the word ‘Kilimanjaro’ or in the facts of geography, that determines an answer to the question whether the clod is a part of Kilimanjaro. (shrink)

Title in English: "Being a certain way without being definitely that way: a problem for supervaluationism". I argue that the supervaluationist theory of vagueness, in its most common version, is committed to a thesis – viz., the incompatibility between being-F and not-being-definitely-F – which is doubtful, unjustified and in conflict with the definition of super-truth as truth in all admissible precisifications of a vague language.

According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with tools for dispelling (...) the threat of a version of referential indeterminacy, according to which nothing in our use of a singular term, even when it is guided by an associated criterion of identity, could determine which particular object it refers to. I end by examining the bearing of the indeterminacy challenge to Linnebo's treatment of Frege's Caesar Problem: in the absence of an argument against the indeterminacy of reference, it is unclear how numerical expressions could qualify as genuine singular terms. (shrink)

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that (...) nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken. (shrink)

I argue that some perceptual experiences are vague. To do so, I identify a characteristic feature of vagueness and show that some perceptual experiences have this feature. These include blurry experiences, experiences of color under low lighting, and experiences of number, as in the case of the speckled hen. The conclusion that these experiences are vague has two noteworthy consequences. First, it presses us to see whether and how existing theories of vagueness can be extended to perceptual experience. Second, it (...) sheds light on several puzzles in the philosophy of perception. (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.

The modal fictionalist faces a problem due to the fact that her chosen story seems to be incomplete—certain things are neither fictionally true nor fictionally false. The significance of this problem is not localized to modal fictionalism, however, since many fictionalists will face it too. By examining how the fictionalist should analyze the notion of truth according to her story, and, in particular, the role that conditionals play for the fictionalist, I develop a novel and elegant solution to the incompleteness (...) problem. (shrink)

According to contextualism about vagueness, the content of a vague predicate is context sensitive. On this view, when item a is in the penumbra of the vague predicate ‘F’, speakers may utter ‘Fa’, or they may utter ‘not-Fa’, without contravening the literal meaning of ‘F’. Unlike its more popular variants, the version of contextualism I defend rejects the principle of tolerance, a principle according to which small differences should not affect the applicability of a vague predicate. My goal is to (...) show how such a rejection allows for a plausible treatment of higher-order vagueness, and for a dissolution of paradoxes of higher-order vagueness. (shrink)

Vagueness is understood as the problem of associating imprecise application criteria with ordinary predicates such as ‘bald’ or ‘blue’. It is often construed as due to one’s tolerance to a minute difference in forming a verdict on the application of a vague predicate. This paper reports an experiment conducted to test the effect of tolerance, using as paradigm categorisation tasks performed with respect to transitional series, e.g., a series of tomatoes from red to orange. The findings suggest a negative effect (...) of tolerance on categorisation with vague predicates. The implication of the findings for certain commonly-held assumptions about tolerance is discussed. (shrink)

It is argued that truth value of a sentence containing free variables in a context of use, just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. (...) On letting, say, x be such that \, the sentence ‘Either \ or \’ is true but the sentence ‘\’ has an indeterminate truth value: it is determinate that the variable x refers to either 2 or \, but it is indeterminate which of the two it refers to, as a result ‘\’ has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a ‘radically’ supervaluational semantic framework closely analogous to the treatment of vagueness in McGee and McLaughlin and Smith, which saves bivalence, the T-schema and the truth-functional analysis of the boolean connectives. It is shown that on such an analysis the modality ‘determinately’ is quite clearly not an epistemic modality, avoiding a potential objection raised by Williamson against such ‘radically’ supervaluational treatments of vagueness, and that determinate truth is the semantic value preserved in classically valid arguments. The analysis is contrasted with the epistemicist proposal of Breckenridge and Magidor which implies that ‘\’ has a determinate but unknowable truth value. (shrink)

This paper is a tribute to Delia Graff Fara. It extends her work on failures of meta-rules for validity as truth-preservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vagueness-related operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a context-dependent background. This paper extends her argument to: quantifier meta-rules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist attempts to qualify the (...) meta-rules impose unreasonable cognitive demands on reasoning and underestimate her challenge. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe's response to combat both paradoxes. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe's response to combat both paradoxes. (shrink)

El objetivo de este artículo es entender ciertas cuestiones que surgen cuando reconocemos que un buen número de predicados del lenguaje natural son indeterminados de dos maneras diferentes. Por ejemplo, el predicado ‘es una montaña’ es vago y susceptible al problema de los muchos. A lo largo de este artículo me enfocaré en cómo distinguir estos dos tipos de indeterminación, y en un problema que el supervaluacionismo iene cuando reconoce que un predicado puede ser vago y susceptible al problema de (...) los muchos. La dificultad es que el supervaluacionismo pierde su habilidad para capturar nuestras intuiciones acerca de cortes precisos. Finalmente, ofrezco una solución a dicho problema. (shrink)

A standard approach to indeterminacy treats ‘determinately’ and ‘indeterminately’ as modal operators. Determinacy behaves like necessity; indeterminacy like contingency. This raises two questions. What is the appropriate modal system for these operators? And how should we interpret that system? Ken Akiba has developed an account of ontic indeterminacy that interprets possible worlds as worldly precisifications. He argues that this account vindicates S4 as the logic of indeterminacy. In this paper I explore one significant and surprising consequence of this view. I (...) do this in two stages. First, I prove a technical result, which I call the Infinite Indeterminacy Theorem. Roughly put, this theorem states that, at any given precisification w, either every instance of indeterminacy admits of never-ending higher-order indeterminacy, or else there's indeterminacy in an infinite amount of distinct atomic formulas. In slogan form: either all indeterminacy is infinitely ascending or else there's infinitely wide indeterminacy. Second, I unpack the metaphysical consequences of this technical result (under its intended interpretation) and assess their plausibility. I conclude that these consequences commit Akiba's theory to highly contentious – and arguably untenable – views about the metaphysics of indeterminacy and related matters. (shrink)

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)

e presenta el debate entre reduccionismo y no reduccionismo respecto de la probabilidad objetiva y se identifican las cargas dialécticas adquiridas por cada posición: el problema de la motivación y el problema de la explicación. Se argumenta que, mientras que el problema de la motivación no presenta ningún desafío para los no reduccionistas, los reduccionistas no son capaces de responderlo exitosamente. Contrariamente a lo que se ha sugerido, ambos lados comparten el problema de la explicación. Se argumenta que los no (...) reduccionistas pueden responderlo exitosamente, mientras que los reduccionistas no son capaces de hacerlo. Por lo tanto, el lado no reduccionista tiene una ventaja dialéctica importante. (shrink)

This dissertation examines some of ways of evaluating beliefs, relevant to epistemology and to metaphysics. Some problems in normative epistemology are solved by properly relating justified belief, rational belief, and knowledge. Chapter 1 uses this strategy to defend externalism about justified belief. Chapters 3 and 4 defend the view that knowledge is the epistemic standard we aim for our beliefs to meet. Chapter 2 investigates which beliefs are improper because formed in an objectionably circular way. The findings support the Moorean (...) response to Brain-In-a-Vat skepticism, by rebutting the objection from ‘easy knowledge’. The theory of justified belief developed in chapter 1 underwrites the Moorean reply. Chapters 5 and 6 make a non-epistemic way of evaluating beliefs central to metaphysics. To understand relativity or vagueness in a subject-matter, we must hold that being true or false is not the metaphysically serious evaluation of how a belief answers to reality. Either verdict on a borderline case is ‘acceptable’ in the metaphysically serious sense. For a matter to be relative is for the ‘acceptability’ of affirming the proposition to vary between judges. Chapters 5 and 6 sketch an approach to metaphysics built from the notion of ‘metaphysically acceptable judgment’, with chapter 6 concentrating on vagueness, and chapter 5 focusing on relativism about knowledge. Chapter 5 argues that the lottery and preface puzzles manifest central features of our concept of knowledge. The proposed version of relativism about knowledge is the only theory to respect those features. The view of knowledge presented in chapter 5 is not an isolated metaphysical extravagance, as the same framework is needed for the right metaphysics of everything that’s vague. It is worth noting that my solution to the lottery puzzle is metaphysical relativism about knowledge, but my rebuttal of Brain-In-a-Vat skepticism concerns epistemic circularity and belongs to normative epistemology. Much recent work incorrectly assumes that the two puzzles receive the same treatment. (shrink)