Paul Egre

We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises of X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisite of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

Eubulide de Milet est connu comme l’auteur d’un ensemble considérable d’arguments logiques déconcertants, encore appelés sophismes ou paradoxes. Parmi ceux-ci figurent l’antinomie du Menteur et le paradoxe du Sorite. Peut-on donner une solution unifiée de ces paradoxes? La réponse examinée dans cet essai est positive et vise à faire connaître la théorie stricte-tolérante, développée à l’origine pour résoudre le Sorite avant d’être transposée au Menteur. Selon cette théorie, la conclusion d’un argument suit logiquement des prémisses quand la vérité stricte des prémisses implique la vérité tolérante de la conclusion. Si les notions de vérité stricte et tolérante coïncident dans un cadre bivalent, elles se recouvrent seulement partiellement dans un cadre trivalent. Nous expliquons en quel sens la théorie stricte-tolérante confère aux notions mêmes de vérité et de conséquence logique un caractère d’équivocité. Or l’identification d’une équivocité préside à la solution d’autres paradoxes, comme dans l’argument du Cornu également dû à Eubulide.

This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: one pairs de Finetti’s conditional with validity as the preservation of non-false values, but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table proposed by Cooper and Cantwell. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties.

In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects.

We present an investigation of the ways in which speakers' subjective perspectives are likely to affect the meaning of gradable adjectives like tall or heavy. We present the results of a study showing that people tend to use themselves as a yardstick when ascribing these adjectives to human figures of varied measurements: subjects' height and weight requirements for applying tall and heavy are found to be positively correlated with their personal measurements. We draw more general lessons regarding the definition of subjectivity and the ways in which a standard of comparison and a significant deviation from that standard are specified.

Preface: The Review of Philosophy and Psychology Content Type Journal Article Pages 1-3 DOI 10.1007/s13164-010-0024-1 Authors Dario Taraborelli, University of Surrey Centre for Research in Social Simulation Guilford GU2 7XH United Kingdom Roberto Casati, Institut Jean Nicod, Ecole Normale Supérieure 29 rue d’Ulm 75005 Paris France Paul Egré, Institut Jean Nicod, Ecole Normale Supérieure 29 rue d’Ulm 75005 Paris France Christophe Heintz, Central European University Budapest Hungary Journal Review of Philosophy and Psychology Online ISSN 1878-5166 Print ISSN 1878-5158 Journal Volume Volume 1 Journal Issue Volume 1, Number 1

This paper explores the idea that vague predicates like “tall”, “loud” or “expensive” are applied based on a process of analog magnitude representation, whereby magnitudes are represented with noise. I present a probabilistic account of vague judgment, inspired by early remarks from E. Borel on vagueness, and use it to model judgments about borderline cases. The model involves two main components: probabilistic magnitude representation on the one hand, and a notion of subjective criterion. The framework is used to represent judgments of the form “x is clearly tall” versus “x is tall”, as involving a shift of one’s criterion, and then to derive observed patterns of acceptance for borderline contradictions, namely sentences of the form “x is tall and not tall”, relative to the acceptance of their conjuncts

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity.

This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower Paradox, both in the framework of first-order arithmetic and in that of modal logic with fixed point operators. It is shown that the notion of a syntactical treatment of modalities is ambiguous between a self-referential treatment and a metalinguistic treatment of modalities, and that these two notions are independent. I survey and compare the provability interpretations of modality respectively given by Skyrms, B. (1978, The Journal of Philosophy 75: 368–387) Anderson, C.A. (1983, The Journal of Philosophy 80: 338–355) and Solovay, R. (1976, Israel Journal of Mathematics 25: 287–304). I examine how these interpretations enable us to bypass the limitations imposed by the Knower Paradox while preserving the laws of classical logic, each time by appeal to a distinct form of hierarchy.

I discuss the problem of whether true contradictions of the form “x is P and not P” might be the expression of an implicit relativization to distinct respects of application of one and the same predicate P. Priest rightly claims that one should not mistake true contradictions for an expression of lexical ambiguity. However, he primarily targets cases of homophony for which lexical meanings do not overlap. There exist more subtle forms of equivocation, such as the relation of privative opposition singled out by Zwicky and Sadock in their study of ambiguity. I argue that this relation, which is basically a relation of general to more specific, underlies the logical form of true contradictions. The generalization appears to be that all true contradictions really mean “x is P in some respects/to some extent, but not in all respects/not to all extent”. I relate this to the strict-tolerant account of vague predicates and outline a variant of the account to cover one-dimensional and multidimensional predicates.

Attitude verbs fall in different categories depending on the kind of sentential complements which they can embed. In English, a verb like know takes both declarative and interrogative complements. By contrast, believe takes only declarative complements and wonder takes only interrogative complements. The present paper examines the hypothesis, originally put forward by Hintikka (1975), that the only verbs that can take both that -complements and whether -complements are the factive verbs. I argue that at least one half of the hypothesis is empirically correct, namely that all veridical attitude verbs taking that -complements take whether -complements. I distinguish veridical verbs from factive verbs, and present one way of deriving the generalization. Counterexamples to both directions of the factivity hypothesis are discussed, in particular the case of emotive factive verbs like regret , and the case of non-veridical verbs that licence whether complements, in particular tell, guess, decide and agree . Alternative accounts are discussed along the way, in particular Zuber (1982), Ginzburg (1995) and Saebø (2007).

Practices of concept-revision among scientists seem to indicate that concepts can be improved. In 2006, the International Astronomical Union revised the concept "Planet" so that it excluded Pluto, and insisting that the result was an improvement. But what could it mean for one concept or conceptual scheme to be better than another? Here we draw on the theory of epistemic utility to address this question. We show how the plausibility and informativeness of beliefs, two features that contribute to their utility, have direct correlates in our concepts. These are how inclusive a concept is, or how many objects in an environment it applies to, and how homogeneous it is, or how similar the objects that fall under the concept are. We provide ways to measure these values, and argue that in combination they can provide us with a single principle of concept utility. The resulting principle can be used to decide how best to categorize an environment, and can rationalize practices of concept revision.

This paper revisits Buridan’s Bridge paradox (Sophismata, chapter 8, Sophism 17), itself close kin to the Liar paradox, a version of which also appears in Bradwardine’s Insolubilia. Prompted by the occurrence of the paradox in Cervantes’s Don Quixote, I discuss and compare four distinct solutions to the problem, namely Bradwardine’s “just false” conception, Buridan’s “contingently true/false” theory, Cervantes’s “both true and false” view, and then the “neither true simpliciter nor false simpliciter” account proposed more recently by Jacquette. All have in common to accept that the Bridge expresses a truth-apt proposition, but only the latter three endorse the transparency of truth. Against some previous commentaries I first show that Buridan’s solution is fully compliant with an account of the paradox within classical logic. I then argue that Cervantes’s insights, as well as Jacquette’s treatment, are both supportive of a dialetheist account, and Jacquette’s in particular of the strict-tolerant account of truth. I defend dialetheist intuitions (whether in LP or ST guise) against two objections: one concerning the future, the other concerning the alleged simplicity of the Bridge compared to the Liar.

Résumé — Toute vérité est-elle connaissable en principe ? Une réponse négative à cette question suit d’un argument logique dû à F. Fitch, voisin du paradoxe de Moore, et connu sous le nom de paradoxe de la connaissabilité. Le paradoxe de Fitch constitue un obstacle à la conception antiréaliste de la vérité et, plus généralement, semble-t-il, à l’idéal positiviste d’après lequel toute vérité devrait nous être accessible en principe. Dans cet article, j’examine différentes tentatives pour préserver le principe selon lequel toute vérité est connaissable, chacune inspirée d’une forme propre d’antiréalisme . Ces différentes approches sont comparées à une conception réaliste du positivisme, évoquée récemment par Burgess, qui postulerait seulement que toute vérité nécessaire est connaissable. Selon cette conception, certaines vérités contingentes sont effectivement inconnaissables, mais l’accessibilité de principe des vérités nécessaires demeure suffisante pour garantir la confiance positiviste dans la science.— Are all truths knowable ? A negative answer to this question follows from a logical argument related to the Moore Paradox and due to F. Fitch, also known as Fitch’s Knowability Paradox. Fitch’s paradox is widely considered to be an obstacle to the antirealist conception of truth, but even for a realist, it appears to threaten the positivist faith in the accessibility of all truths to our minds. In this paper, I first review different strategies to circumvent the paradox, each of them inspired by a different form of antirealism . I then compare these approaches to a realist version of positivism, discussed recently by Burgess, which would only postulate that all necessary truths are knowable. On that view, some contingent truths are indeed unknowable, but the idea that all necessary truths are within our reach remains sufficient to maintain the positivist faith in scientific knowledge

Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis- Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis- Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.

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)

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.