•  544
    If-Clauses and Probability Operators
    Topoi 30 (1): 17-29. 2011.
    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 assignme…Read more
  •  67
    Borel on the Heap
    Erkenntnis 79 (S5): 1043-1079. 2014.
    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 Bore…Read more
  •  179
    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 i…Read more
  •  108
    Tolerance and Mixed Consequence in the S'valuationist Setting
    with Pablo Cobreros, David Ripley, and Robert Rooij
    Studia Logica 100 (4): 855-877. 2012.
    In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can us…Read more
  •  164
    Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.
  •  54
    Inferences and Metainferences in ST
    Journal of Philosophical Logic 49 (6): 1057-1077. 2020.
    In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and…Read more
  •  62
    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 approa…Read more
  •  391
    Tolerant, Classical, Strict
    Journal of Philosophical Logic 41 (2): 347-385. 2012.
    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, which we call tolerant truth and…Read more
  •  184
    Reaching Transparent Truth
    Mind 122 (488): 841-866. 2013.
    This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases
  •  58
    Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.
  •  52
    Foreword: Three-valued logics and their applications
    Journal of Applied Non-Classical Logics 24 (1-2): 1-11. 2014.
  •  121
    Predicting moral judgments from causal judgments
    Philosophical Psychology 28 (1): 21-48. 2015.
    Several factors have been put forward to explain the variability of moral judgments for superficially analogous moral dilemmas, in particular in the paradigm of trolley cases. In this paper we elaborate on Mikhail's view that (i) causal analysis is at the core of moral judgments and that (ii) causal judgments can be quantified by linguistic methods. According to this model, our moral judgments depend both on utilitarian considerations (whether positive effects outweigh negative effects) and on a…Read more
  •  31
    From many-valued consequence to many-valued connectives
    Synthese 198 (S22): 5315-5352. 2018.
    Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, f…Read more
  •  89
    Editorial: Objects and Sound Perception (review)
    Review of Philosophy and Psychology 1 (1): 5-17. 2010.
    Editorial: Objects and Sound Perception Content Type Journal Article Pages 5-17 DOI 10.1007/s13164-009-0006-3 Authors Nicolas J. Bullot, École des Hautes Études en Sciences Sociales Centre de Recherches sur les Arts et le Langage (CRAL/CNRS) 96 Bd Raspail 75006 Paris France Paul Égré, Institut Jean-Nicod (ENS/EHESS/CNRS) Département d’Etudes Cognitives de l’ENS 29 rue d’Ulm 75005 Paris France Journal Review of Philosophy and Psychology Online ISSN 1878-5166 Print ISSN 1878-5158 Journal Volume Vo…Read more
  •  144
    Knowing whether A or B
    with Maria Aloni and Tikitu de Jager
    Synthese 190 (14): 2595-2621. 2013.
    The paper examines the logic and semantics of knowledge attributions of the form “s knows whether A or B”. We analyze these constructions in an epistemic logic with alternative questions, and propose an account of the context-sensitivity of the corresponding sentences and of their presuppositions.
  •  223
    Alternative questions and knowledge attributions
    Philosophical Quarterly 60 (238): 1-27. 2010.
    We discuss the 'problem of convergent knowledge', an argument presented by J. Schaffer in favour of contextualism about knowledge attributions, and against the idea that knowledge- wh can be simply reduced to knowledge of the proposition answering the question. Schaffer's argument centrally involves alternative questions of the form 'whether A or B'. We propose an analysis of these on which the problem of convergent knowledge does not arise. While alternative questions can contextually restrict …Read more
  •  46
    On the optimality of vagueness: “around”, “between” and the Gricean maxims
    with Benjamin Spector, Adèle Mortier, and Steven Verheyen
    Linguistics and Philosophy 46 (5): 1075-1130. 2023.
    Why is ordinary language vague? We argue that in contexts in which a cooperative speaker is not perfectly informed about the world, the use of vague expressions can offer an optimal tradeoff between truthfulness (Gricean Quality) and informativeness (Gricean Quantity). Focusing on expressions of approximation such as “around”, which are semantically vague, we show that they allow the speaker to convey indirect probabilistic information, in a way that can give the listener a more accurate represe…Read more
  •  223
    Vagueness: A Conceptual Spaces Approach
    Journal of Philosophical Logic 42 (1): 137-160. 2013.
    The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straightforward. The present paper aims to fill this lacuna.
  •  119
    Vagueness, Truth and Permissive Consequence
    In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth, Imprint: Springer. pp. 409-430. 2015.
    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 requi…Read more
  •  84
    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…Read more
  •  28
    Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2006 Prague Colloquium on "Reasoning about Vagueness and Uncertainty".
  •  109
    Vagueness: Why Do We Believe in Tolerance?
    Journal of Philosophical Logic 44 (6): 663-679. 2015.
    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…Read more
  •  480
    On Three-Valued Presentations of Classical Logic
    with Bruno da Ré, Damian Szmuc, and Emmanuel Chemla
    Review of Symbolic Logic 1-23. forthcoming.
    Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collaps…Read more
  •  23
    Editorial Introduction: Substructural Logics and Metainferences
    Journal of Philosophical Logic 51 (6): 1215-1231. 2022.
    The concept of _substructural logic_ was originally introduced in relation to limitations of Gentzen’s structural rules of Contraction, Weakening and Exchange. Recent years have witnessed the development of substructural logics also challenging the Tarskian properties of Reflexivity and Transitivity of logical consequence. In this introduction we explain this recent development and two aspects in which it leads to a reassessment of the bounds of classical logic. On the one hand, standard ways of…Read more
  •  17
    Knowledge, justification, and adequate reasons—erratum
    with Paul Marty and Bryan Renne
    Review of Symbolic Logic 1-1. forthcoming.
  •  61
    Knowledge, justification, and adequate reasons
    with Paul Marty and Bryan Renne
    Review of Symbolic Logic 14 (3): 687-727. 2021.
    Is knowledge definable as justified true belief? We argue that one can legitimately answer positively or negatively, depending on whether or not one’s true belief is justified by what we call adequate reasons. To facilitate our argument we introduce a simple propositional logic of reason-based belief, and give an axiomatic characterization of the notion of adequacy for reasons. We show that this logic is sufficiently flexible to accommodate various useful features, including quantification over …Read more
  •  41
    Suszko’s problem: Mixed consequence and compositionality
    Review of Symbolic Logic 12 (4): 736-767. 2019.
    Suszko’s problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two truth values. Malinowski showed that this number can equal three if some of Tarski’s structural constraints are relaxed. By so doing, Malinowski introduced a case of so-called mixed consequence, allowing the notion of a designated value to vary between the prem…Read more
  •  106
    Inexact Knowledge with Introspection
    Journal of Philosophical Logic 38 (2): 179-227. 2009.
    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.
  •  22
    Vagueness and Degrees of Truth by Nicholas J. J. Smith (review)
    Australasian Journal of Philosophy 89 (1): 177-80. 2011.