A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an IQ (...) of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided. (shrink)

This is a big-picture book, 2 written with a breadth of focus which I find admirable. It exhibits what's come to be known as the ‘intersubdiscplinary’ approach to philosophy, which is not restricted by traditional boundaries within the discipline but rather proceeds with an eye to all sorts of areas of philosophy where relevant arguments, results, analogies and strategies might be lurking. I approve of this way of doing philosophy; it seems to me that all too often that wheels are (...) reinvented, or crucial points missed, because of a lack of this sort of intersubdisciplinarity.To help guide us through such a broad landscape, this book needed to be well-signposted and clearly written, and it is. It cannot be denied, however, that the ambitious scale of The Nature of Normativity won't be to every taste. For one thing, not everyone likes big pictures. For another, this is a deep, dense and in many ways difficult book, which can only really be appreciated by sitting down with it for hours on end. It will not repay the casual skim-reader, nor is it likely to appeal to those who prefer dipping into philosophy books over reading them wholesale.The book is also long . The view under construction has a great many interlocking elements, including non-reductive normative naturalism, normative realism, a priorist intuitionism, normative internalism, the normativity of intentionality, conceptual-role semantics, contextualism, possible-worlds semantics, and certain ideas about ‘planning’ derived from the recent work of Allan Gibbard. It will be a tough read for specialists who do not share Wedgwood's familiarity with a wide range of subdisciplines, who will either have to content themselves with a superficial reading of many passages or else hunt down the necessary background material to …. (shrink)

ABSTRACT Our ascriptions of content to past utterances assign to them a level of conceptual continuity and determinacy that extends beyond what could be grounded in the usage up to their time of utterance. If one accepts such ascriptions, one can argue either that future use must be added to the grounding base, or that such cases show that meaning is not, ultimately, grounded in use. The following will defend the first option as the more promising of the two, though (...) this ultimately requires understanding the relation between use and meaning as ‘normative’ in two important ways. The first way is that the function from use to meaning must be of a sort that allows us to maintain a robust distinction between actual and correct use. The second sort of normativity is unique to theories that extend the grounding base into the future. In particular, if meaning is partially a function of future use, we can see our commitment to the ‘determinacy’ of meaning as a practical commitment that structures our linguistic practices rather than a theoretical commitment that merely describes them. (shrink)

Rampant non-factualism is the view that all non-fundamental matters are non-factual, in a sense inspired by Kit Fine (2001). The first half of this paper argues that if we take non-factualism seriously for any matters, such as morality, then we should take rampant non-factualism seriously. The second half of the paper argues that rampant non-factualism makes possible an attractive theory of vagueness. We can give non-factualist accounts of non-fundamental matters that nicely characterize the vagueness they manifest (if any). I suggest (...) that such non-factualist theories dissolve philosophical puzzlement about vagueness. In particular, the approach implies that philosophers should not try to say which of the sorites-paradox-forming claims are true; we should not try to solve the sorites paradox in that sense. (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 claims that there is a plausible sense in which validity is a matter of truth preservation relative to interpretations of the sentences that occur in an argument, although it is not the sense one might have in mind. §1 outlines three independent problems: the first is the paradox of the sorites, the second concerns the fallacy of equivocation, and the third arises in connection with the standard treatment of indexicals. §2 elucidates the claim about validity, while §§3-5 show (...) how the three problems outlined can be handled in accordance with it. §6 explains how the claim squares with the traditional idea that validity is related to formality, and in particular with a broadly accepted definition based on that idea, the model-theoretic definition of logical consequence. Unlike other works on the subject, this paper does not focus on necessity. It is not its intention to provide a characterization of necessity that conforms to some ideal of rigour or to some pre-theoretical understanding of validity. What follows can be taken as conditional on the assumption that such a characterization can be provided. (shrink)

This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided (...) which bear on three debated issues concerning quantification. (shrink)

The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...) and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. (shrink)

Varzi has recently joined a thread of arguments originating in an attempt by Sorensen (1985) to demonstrate that the predicate ‘vague’ is itself vague. Sorensen's conclusion is significant in that it has provided the basis for a subsequent effort by Hyde (1994) to defend the legitimacy of supposing higher-order vagueness. Varzi's contribution to this debate is twofold. First, contra earlier criticism by Deas (1989), he claims that Sorensen's result is sound so far as it goes. Second, he argues that despite (...) this it cannot be used as Hyde wishes on pain of circularity. I am not interested in the latter argument—it is examined in Hyde (2003)—but rather wish to defend and elaborate Deas's criticism of Sorensen against Varzi's repudiation. (shrink)

Epistemicists claim that if it is vague whether p, it is unknowable whether p. Some contest this on epistemic grounds: vague intuitions about vague matters need not fully preclude knowledge, if those intuitions are response-dependent in some special sense of enabling vague knowledge. This paper defends the epistemicist principle that vagueness entails ignorance against such objections. I argue that not only is response-dependence an implausible characterization of actual vague matters, its mere possibility poses no threat to epistemicism and is properly (...) accounted for by the epistemicist’s own principles. (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.

‘If I were to toss a coin 1000 times, then it would land heads exactly n times’. Is there a specific value of n that renders this counterfactual true? According to an increasingly influential view, there is. A precursor of the view goes back to the Molinists; more recently it has been inspired by Stalnaker, and versions of it have been advocated by Hawthorne, Bradley, Moss, Schulz, and Stefánsson. More generally, I attribute to these authors what I call Counterfactual Plenitude:For (...) any antecedent A, there is a world wisuch that A ☐→ wiis true.Moreover, some of these authors are also committed to Primitive Counterfacts Realism:There exist primitive modal facts that serve as truth-makers for counterfactual claims.Call the conjunction of these italicized theses counterfactism. I clarify it and suggest some of its virtues, while ultimately rejecting it.Stefánsson’s counterfactism is motivated by and targeted at my “counterfactual skepticism”—I argue that most counterfactuals are false—and counterfactism has various other sources of support. I briefly defend that skepticism, and I seek to undercut those sources of support. I then argue more directly against counterfactism, especially on grounds of its ontological profligacy, and its leading to another kind of skepticism about counterfactuals that I believe is more problematic than my kind. In the process, I discuss how Bradley’s multidimensional semantics bears on counterfactism; I offer some new considerations against some central theses regarding conditionals ; and I reflect more generally on the epistemology of modality and the choice of primitives in our theorizing. (shrink)

For a very long time truth-value gaps were under a cloud of suspicion because they were considered logically unmanageable. So Frege declared that:“as regards concepts we have a requirement of sharp delimitation; if this were not satisfied it would be impossible to set forth logical laws about them”.Three-valued logic promised to dispel the cloud but in the eyes of many it had promised more than it could deliver. So in response to Reichenbach's plea for a three-valued quantum logic Russell replied:“This (...) is one of a number of questions as to which I am prevented from accepting a certain view by difficulties in carrying it out, but am prepared to alter my opinion if technical skill supplies an answer to my difficulties”.‘By now technical skill has supplied many alternative systems of three-valued logic, but few answers and numerous additional difficulties.’. (shrink)

This article presents an approach to how to make reasonable social choices when independent criteria (e.g., prioritarianism, religious freedom) fail to fully determine what to do. The article outlines different explanations of why independent criteria sometimes fail to fully determine what to do and illustrates how they can still be used to eliminate ineligible alternatives, but it is argued that the independent criteria cannot ground a reasonable social choice in these situations. To complement independent criteria when they fail to fully (...) determine what to do, it is suggested that society must engage in public deliberation by way of generating new reasons that can determine how to rank the alternatives. It is suggested that the approach to social choice presented here reveals a way of accepting the relevance of independent criteria for social choice without letting go of the idea that the attitudes of affected parties matter. (shrink)

This paper argues that cost-effectiveness analysis in the healthcare sector introduces a discrimination risk that has thus far been underappreciated and outlines some approaches one can take toward this. It is argued that appropriate standards used in cost-effectiveness analysis in the healthcare sector fail to always fully determine an optimal option, which entails that cost-effectiveness analysis often leaves decision makers with large sets of permissible options. Larger sets of permissible options increase the role of decision makers’ biases, whims, and prejudices, (...) which means that the discrimination risk increases. Two ways of mitigating this are identified: tinkering with standards used in the cost-effectiveness analysis and outlining anti-discrimination guidelines for decision makers. (shrink)

A number of epistemologists have recently concluded that a piece of reasoning may be epistemically permissible even when it is impossible for the reasoning subject to present her reasoning as an argument without begging the question. I agree with these epistemologists, but argue that none has sufficiently divorced the notion of begging the question from epistemic notions. I present a proposal for a characterization of begging the question in purely pragmatic terms.

This paper presents an new epistemicist account of vagueness, one that avoids standard arbitrariness worries by exploiting a plenitudinous metaphysic.

Owing to the problem of inescapable clashes, epistemic accounts of might-counterfactuals have recently gained traction. In a different vein, the might argument against conditional excluded middle has rendered the latter a contentious principle to incorporate into a logic for conditionals. The aim of this paper is to rescue both ontic mightcounterfactuals and conditional excluded middle from these disparate debates and show them to be compatible. I argue that the antecedent of a might-counterfactual is semantically underdetermined with respect to the counterfactual (...) worlds it selects for evaluation. This explains how might-counterfactuals select multiple counterfactual worlds as they apparently do and why their utterance confers a weaker alethic commitment on the speaker than does that of a would-counterfactual, as well as provides an ontic solution to inescapable clashes. I briefly sketch how the semantic underdetermination and truth conditions of mightcounterfactuals are regulated by conversational context. (shrink)

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address (...) arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use. (shrink)

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)

The purpose of this paper is to generalize Kripke semantics for propositional modal logic by geometrizing it, that is, by considering the space underlying the collection of all possible worlds as an important semantic feature in its own right, so as to take the idea of accessibility seriously. The resulting new modal semantics is worked out in a setting coming from Riemannian geometry, where Kripke semantics is shown to correspond to a particular case, namely, the discrete one. Several correspondence results, (...) established between variants of well-known modal systems and corresponding geometric properties, illustrate the import of this new framework. (shrink)

In an alleged counter-example to the completeness of rational preferences, a career as a clarinettist is compared with a career in law. It seems reasonable to neither want to judge that the law career is at least as preferred as the clarinet career nor want to judge that the clarinet career is at least as preferred as the law career. The two standard interpretations of examples of this kind are, first, that the examples show that preferences are rationally permitted to (...) be incomplete and, second, that the examples show that preferences are rationally permitted to be indeterminate. In this paper, I shall argue that the difference between these interpretations is crucial for the money-pump argument for transitivity, which is the standard argument that rational preferences are transitive. I shall argue that the money-pump argument for transitivity fails if preferences are rationally permitted to be incomplete but that it works if preferences are rationally permitted to be indeterminate and rationally required to be complete. (shrink)

In this paper, we present a new account of teleological reasons, i.e. reasons to perform a particular action because of the outcomes it promotes. Our account gives the desired verdict in a number of difficult cases, including cases of overdetermination and non-threshold cases like Parfit’s famous _Drops of water._ The key to our account is to look more closely at the metaphysics of causation. According to Touborg (_The dual nature of causation_, 2018), it is a necessary condition for causation that (...) a cause increases the security of its effect. Building on this idea, we suggest, roughly, that you have a teleological reason to act in a certain way when doing so increases the security of some good outcome. This represents a middle way between the proposal that you have a reason to act in a certain way just in case this _would_ cause a good outcome and the proposal that you have a reason to act in a certain way just in case this _could_ cause a good outcome. (shrink)

The tolerance principle, the idea that vague predicates are insensitive to sufficiently small changes, remains the main bone of contention between theories of vagueness. In this paper I examine three sources behind our ordinary belief in the tolerance principle, to establish whether any of them might give us a good reason to revise classical logic. First, I compare our understanding of tolerance in the case of precise predicates and in the case of vague predicates. While tolerance in the case of (...) precise predicates results from approximation, tolerance in the case of vague predicates appears to originate from two more specific sources: semantic indeterminacy on the one hand, and epistemic indiscriminability on the other. Both give us good and coherent grounds to revise classical logic. Epistemic indiscriminability, it is argued, may be more fundamental than semantic indeterminacy to justify the intuition that vague predicates are tolerant. (shrink)

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. -/- The present article defends Harsanyi against the Sen–Weymark critique. (...) I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann–Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann-Morgenstern utilities, he has done nothing to establish any con- nection between the notion of von Neumann-Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. The present article defends Harsanyi against the Sen-Weymark cri- (...) tique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann-Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

A basic intuition we have regarding the nature of time is that the future is open whereas the past is fixed. For example, whereas we think that there are things we can do to affect how the future will unfold, we think that there are not things we can do to affect how the past unfolded. However, although this intuition is largely shared, it is not a straightforward matter to determine the nature of the asymmetry it reflects. So, in this (...) paper, I survey various philosophical ways of characterizing the asymmetry between the ‘open future’ and the ‘fixed past’ in order to account for our intuition. In particular, I wonder whether the asymmetry is to be characterized in semantic, epistemic, metaphysical or ontological terms. I conclude that, although many of these characterizations may contribute to a global understanding of the phenomenon, an ontological characterization of the asymmetry is to be preferred, since it is superior to the alternatives in explanatory power, intelligibility, and in how it coheres with interesting senses of openness. (shrink)

A basic intuition we have regarding the nature of time is that the future is open whereas the past is fixed. For example, whereas we think that there are things we can do to affect how the future will unfold (e.g. acting in an environmentally responsible manner), we think that there are not things we can do to affect how the past unfolded (“what is done is done”). However, although this intuition is largely shared, it is not a straightforward matter (...) to determine the nature of the asymmetry it reflects. So, in this paper, I survey various philosophical ways of characterizing the asymmetry between the ‘open future’ and the ‘fixed past’ in order to account for our intuition. In particular, I wonder whether the asymmetry is to be characterized in semantic, epis‐ temic, metaphysical or ontological terms. I conclude that, although many of these characterizations may contribute to a global understanding of the phenomenon, an ontological characterization of the asymmetry is to be preferred, since it is superior to the alternatives in explanatory power, intelligibility, and in how it coheres with interesting senses of openness. (shrink)

Among those living systems, which are cognizers? Among the behaviours of, and causes of behaviour in, living systems, which are cognitive? Such questions sit at the heart of a sophisticated, ongoing debate, of which the recent papers by Corcoran et al. ( 2020 ) and Sims and Kiverstein ( 2021 ) serve as excellent examples. I argue that despite their virtues, both papers suffer from flawed conceptions of the point of the debate. This leaves their proposals ill-motivated—good answers to the (...) wrong question. Additionally, their proposals are unfit to serve the legitimate roles for characterizations of cognition. (shrink)

My proposed mechanism of reference fixing for ordinary natural kind terms in the book Roads to Reference appeals to the ordinary notion of substance. In this note I reply to an objection by Martín Abreu Zavaleta that that notion is too vague to allow for a sufficiently constrained property to become the referent of a given ordinary substance term. I argue that the notion of substance is far less vague than Abreu Zavaleta claims.

This paper argues against relativism, focusing on relativism based on the semantics of predicates of personal taste. It presents and defends a contextualist semantics for these predicates, derived from current work on gradable adjectives. It then considers metasemantic questions about the kinds of contextual parameters this semantics requires. It argues they are not metasemantically different from those in other gradable adjectives, and that contextual parameters of this sort are widespread in natural language. Furthermore, this paper shows that if such parameters (...) are rejected, it leads to an unacceptably rampant form of relativism, that relativizes truth to an open-ended list of parameters. (shrink)

The need for a ‘many-valued logic’ in linguistics has been evident since the 1970s, but there was lack of clarity as to whether it should come from the family of fuzzy logics or from the family of probabilistic logics. In this regard, Fine [14] and Kamp [26] pointed out undesirable effects of fuzzy logic (the failure of idempotency and coherence) which kept two generations of linguists and philosophers at arm’s length. (Another unwanted feature of fuzzy logic is the property of (...) truth functionality.) While probabilistic logic is not fraught by the same problems, its lack of constructiveness, i.e. its inability to compose complex truth degrees from atomic truth degrees, did not make it more attractive to linguists either. In the absence of a clear perspective in ‘many-valued logic’, scholars chose to proliferate ontologies grafted atop the classical bivalent logic: ontologies for truth, individuals, events, situations, possible worlds and degrees. The result has been a collection of incompatible classical logics. In this paper, I present sample logic, in particular its semantics (not its axiomatization). Sample logics is a member of the family of probabilistic logics, which is constructive without being truth functional. More specifically, I integrate all the important linguistic data on which the classical logics are predicated. The concepts of (in)dependency and conditional (in)dependency are the cornerstones of sample logic. (shrink)

Following Hartry Field in distinguishing disquotational truth from a conception that grounds truth conditions in a community's usage, it is argued that the notions are materially inequivalent (since the latter allows truth-value gaps) and that both are needed. In addition to allowing blanket endorsements ("Everything the Pope says is true"), disquotational truth facilitates mathematical discovery, as when we establish the Gödel sentence by noting that the theorems are all disquotationally true and the disquotational truths are consistent. We require a more (...) substantial notion, however, if we intend to use truth values and truth conditions in explaining communication by language. (shrink)

On standard versions of supervaluationism, truth is equated with supertruth, and does not satisfy bivalence: some truth-bearers are neither true nor false. In this paper I want to confront a well-known worry about this, recently put by Wright as follows: ‘The downside . . . rightly emphasized by Williamson . . . is the implicit surrender of the T-scheme’. I will argue that such a cost is not high: independently motivated philosophical distinctions support the surrender of the T- scheme, and (...) suggest acceptable approximations. (shrink)

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...) the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (shrink)

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)

Proponents of supervaluationism claim super-truth, i. e., truth on every admissible precisification, is identical to truth or, at least, is a suitable truth proxy. I object that super-truth is neither identical to nor a suitable proxy for truth. I argue that to claim a statement is super-true is simply to maintain that a certain counterfactual holds, and that a claim is true, counterfactually, is no reason to treat it as true. I further argue that, with super-truth undermined, Roy Sorensen’s objection (...) that supervaluationism cannot accommodate vague directly referential terms presents supervaluationism’s defenders with a significant challenge. (shrink)