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Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short (...) |
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The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...) |
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In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) |
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This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework. |
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The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid pat- terns of inference even in the absence of a definitely-operator (or similar device). As a (...) |
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Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...) |
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Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on (...) |
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It is often supposed that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical (...) |
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In the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical (...) |
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Fallibilists about looks deny that the relation of looking the same as is non-transitive. Regarding familiar examples of coloured patches suggesting that such a relation is non-transitive, they argue that, in fact, indiscriminable adjacent patches may well look different, despite their perceptual indiscriminability: it’s just that we cannot notice the relevant differences in the chromatic appearances of such patches. In this paper, I present an argument that fallibilism about looks requires commitment to an empirically false consequence. To succeed in deflecting (...) |
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Contemporary Anglophone scholarship on the Zhuangzi 莊子 tends to reject intellectualism, the view that all knowledge is propositional. Scholars usually state that Zhuangzi values practical knowledge more than propositional knowledge. This valuation, however, seems to presuppose that the Zhuangzi or its interpreters must recognize the distinction between these two kinds of knowledge. In this article, I argue that Zhuangzi sees all knowledge as practical, and if we situate him in the contemporary philosophical field we can extract several ideas from the (...) |
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The mass/count distinction attracts a lot of attention among cognitive scientists, possibly because it involves in fundamental ways the relation between language (i.e. grammar), thought (i.e. extralinguistic conceptual systems) and reality (i.e. the physical world). In the present paper, I explore the view that the mass/count distinction is a matter of vagueness. While every noun/concept may in a sense be vague, mass nouns/concepts are vague in a way that systematically impairs their use in counting. This idea has never been systematically (...) |
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The philosophical interest of verbal disputes is twofold. First, they play a key role in philosophical method. Many philosophical disagreements are at least partly verbal, and almost every philosophical dispute has been diagnosed as verbal at some point. Here we can see the diagnosis of verbal disputes as a tool for philosophical progress. Second, they are interesting as a subject matter for first-order philosophy. Reflection on the existence and nature of verbal disputes can reveal something about the nature of concepts, (...) |
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How to handle vagueness? One way is to introduce the machinery of acceptable sharpenings, and reinterpret truth as truth-in-all-sharpenings or truth-in-some-sharpenings. A major selling point has been the conservativism of the resulting systems with respect to classical theoremhood and inference. Supervaluationism and subvaluationism possess interesting formal symmetries, a fact that has been used to argue for the subvaluationist approach. However, the philosophical motivation behind each is a different matter. Subvaluationism comes with a standard story that is difficult to sign up (...) |
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John Broome has argued that incomparability and vagueness cannot coexist in a given betterness order. His argument essentially hinges on an assumption he calls the ‘collapsing principle’. In an earlier article I criticized this principle, but Broome has recently expressed doubts about the cogency of my criticism. Moreover, Cristian Constantinescu has defended Broome’s view from my objection. In this paper, I present further arguments against the collapsing principle, and try to show that Constantinescu’s defence of Broome’s position fails. |
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David Lewis (1986) criticizes moderate views of composition on the grounds that a restriction on composition must be vague, and vague composition leads, via a precisificational theory of vagueness, to an absurd vagueness of existence. I show how to resist this argument. Unlike the usual resistance, however, I do not jettison precisificational views of vagueness. Instead, I blur the connection between composition and existence that Lewis assumes. On the resulting view, in troublesome cases of vague composition, there is an object, (...) |
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Symposium on Insensitive Semantics. Replies to Kent Bach, John Hawthorne, Kepa Korta and John Perry, and Robert J. Stainton. |
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This paper addresses four issues: 1. What is nonsense? 2. Is nonsense possible? 3. Is nonsense actual? 4. Why do the answers to (1)–(3) matter, if at all? These are my answers: 1. A sentence (or an utterance of one) is nonsense if it fails to have or express content (more on ‘express’, ‘have’, and ‘content’ below). This is a version of a view that can be found in Carnap (1959), Ayer (1936), and, maybe, the early Wittgenstein (1922). The notion (...) |
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Machery’s book is an effort to show how experimental philosophy can be valuable without the perephenelia of intuitions. I argue that the effort fails. |
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I attempt to accommodate the phenomenon of vagueness with classical logic and bivalence. I hold that for any vague predicate there is a sharp cut-off between the things that satisfy it and the things that do not; I claim that this is due to the greater naturalness of one of the candidate meanings of that predicate. I extend the thought to the problem of the many and Benacerraf cases. I go on to explore the idea that it is ontically indeterminate (...) |
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In Calosi and Wilson (Phil Studies 2019/2018), we argue that on many interpretations of quantum mechanics (QM), there is quantum mechanical indeterminacy (QMI), and that a determinable-based account of metaphysical indeterminacy (MI), as per Wilson 2013 and 2016, properly accommodates the full range of cases of QMI. Here we argue that this approach is superior to other treatments of QMI on offer, both realistic and deflationary, in providing the basis for an intelligible explanation of the interference patterns in the double-slit (...) |
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I argue, pace Timothy Williamson, that one cannot provide an adequate account of what it is for a case to be borderline by appealing to facts about our inability to discriminate our actual situation from nearby counterfactual situations in which our language use differs in subtle ways. I consider the two most natural ways of using such resources to provide an account of what it is for a case to be borderline and argue that both face crippling defects. I argue (...) |
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Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...) |
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Derek Parfit has offered numerous arguments in an attempt to establish that identity is not what matters. Jens Johannson has recently argued that Parfit's various arguments for the claim that identity is not what matters fail to establish what Parfit takes such arguments to establish. Johannson contends that this is due in part to the invalidity of one of Parfit's key arguments, and the fact that Parfit ignores a position that is compatible with the conclusions of his successful arguments and (...) |
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We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over (...) |
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A common objection to Russell's theory of descriptions concerns incomplete definite descriptions: uses of (for example) ‘the book is overdue’ in contexts where there is clearly more than one book. Many contemporary Russellians hold that such utterances will invariably convey a contextually determined complete proposition, for example, that the book in your briefcase is overdue. But according to the objection this gets things wrong: typically, when a speaker utters such a sentence, no facts about the context or the speaker's communicative (...) |
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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 (...) |
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The distinction between true belief and knowledge is one of the most fundamental in philosophy, and a remarkable effort has been dedicated to formulating the conditions on which true belief constitutes knowledge. For decades, much of this epistemological undertaking has been dominated by a single strategy, referred to here as the modal approach. Shared by many of the most widely influential constraints on knowledge, including the sensitivity, safety, and anti-luck/risk conditions, this approach rests on a key underlying assumption — the (...) |
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Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations such as ‘Let n be an arbitrary number’ or ‘Let John be an arbitrary Frenchman’. Yet the semantics underlying such stipulations are far from clear. What, for example, does ‘n’ refer to following the stipulation that n be an arbitrary number? In this paper, we argue that ‘n’ refers to a number—an ordinary, particular number such as 58 or 2,345,043. Which one? We do (...) |
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According to an old and attractive view, vagueness must be eliminated before semantic notions — truth, implication, and so on — may be applied. This view was accepted by Frege, but is rarely defended nowadays.1 This.. |
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Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must (...) |
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ABSTRACTBy means of critical reflection on the current situation of Chinese philosophy, this article aims to clarify two different approaches to philosophy. One is for scholars to focus on original texts and thought tradition, concerned with interpretation and inheritance; even in this way, scholars can achieve theoretical innovation through creative interpretation. The other is for researchers to face up questions from academics and from reality, and mainly to do theoretical creation in philosophy on a profound theoretical background, strictly following academic (...) |
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If a brain is duplicated so that there are two brains in identical states, are there then two numerically distinct phenomenal experiences or only one? There are two, I argue, and given computationalism, this has implications for what it is to implement a computation. I then consider what happens when a computation is implemented in a system that either uses unreliable components or possesses varying degrees of parallelism. I show that in some of these cases there can be, in a (...) |
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Most event-referring expressions are vague; it is utterly difficult, if not impossible, to specify the exact spatiotemporal location of an event from the words that we use to refer to it. We argue that in spite of certain prima facie obstacles, such vagueness can be given a purely semantic (broadly supervaluational) account. |
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In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness. |
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Most speakers experience unclarity about the application of predicates like tall and red to liminal cases. We formulate alternative psychological hypotheses about the nature of this unclarity, and report experiments that provide a partial test of them. A psychologized version of the ‘vagueness-as-ignorance’ theory is then advanced and defended. |
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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. |
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The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have two contradictory pictures of reality but also compelled to abandon the objectiveness of the truth values, “true” and “false”. Yet, even if we could accept wave-like behavior of quantum particles as the best explanation for the build-up of an interference pattern in (...) |
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According to Douglas Walton, the concept of presumption relates to both logical and dialogical components. Logically, a presumption is the conclusion of a presumptive defeasible inference. Dialogically, the function of a presumptions to shift the burden of proof to the respondent in order to move the dialogue forward when the proponent, due to an objective lack of evidence, cannot present a sufficiently persuasive proposition. Presumptive status, assigned only at the argumentation stage of dialogue, is provisional: a particular presumption stands until (...) |
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ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes. |
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This paper shows that the following common assumption is false: that in modal-logical representations of higher-order vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal). |
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Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It corresponds (...) |
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This paper analyzes communication with a language that is vague in the sense that identical messages do not always result in identical interpretations. It is shown that strategic agents frequently add to this vagueness by being intentionally vague, i.e. they deliberately choose less precise messages than they have to among the ones available to them in equilibrium. Having to communicate with a vague language can be welfare enhancing because it mitigates conflict. In equilibria that satisfy a dynamic stability condition intentional (...) |
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The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful (...) |
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