Invariance and Definability, with and without Equality, with F. Engström
The dual character of invariance under transformations and definability by some operations has been used in classical work by for example Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves could be characterized in terms of invariance. In this paper, we generalize a correspondence due to Krasner between invariance under groups of permutations and definability in $\L_{\infty\infty}$ so as to cover the cases (quantifiers, logics without equality) that are of interest in the logicality debates, getting McGee's theorem about quantifiers invariant under all permutations and definability in pure $\L_{\infty\infty}$ as a particular case. We also prove some optimality results along the way, regarding the kind of relations which are needed so that every subgroup of the full permutation group is characterizable as a group of automorphisms.

Groundedness, Truth and Dependence, with F. van Vugt.
Leitgeb has proposed a new approach to semantic paradoxes, based upon a direct definition of the set of grounded sentences in terms of dependence upon non-semantic state of affairs.. In the present paper, we account for the extensional disagreement between this dependence approach and more familiar alethic approaches. In order to do so, we study the behavior of dependence jumps and alethic jumps, and provide an equivalence result for the two approaches.

Logical Constants, or How to use Invariance in Order to Complete the Explication of Logical Consequence, Philosophy Compass, vol. 9 (1), 2014, p. 54-65.
The problem of logical constants consists in finding a principled way to draw the line between those expressions of a language that are logical and those that are not. The criterion of invariance under permutation, attributed to Tarski, is probably the most common answer to this problem, at least within the semantic tradition. However, as the received view on the matter, it has recently come under heavy attack. Does this mean that the criterion should be amended, or maybe even that it should be abandoned? I shall review the different types of objections that have been made against invariance as a logicality criterion and distinguish between three kinds of objections, skeptical worries against the very relevance of such a demarcation, intensional warnings against the level at which the criterion operates, and extensional quarrels against the results that are obtained. I shall argue that the first two kinds of objections are at least partly misguided and that the third kind of objection calls for amendment rather than abandonment.

Consequence Mining, with Dag Westerståhl, Journal of Philosophical Logic, vol. 41 (4), 2012.
In the present paper, we shall approach the notion of a logical constant from an unexplored direction. In a nutshell, the idea is to combine Bolzano's insight that any choice of constants determines a semantic consequence relation with a method for going in the opposite direction: to extract, from any given consequence relation, its constants. The method might thus be called consequence mining. We see this as a complement rather than an alternative to the invariance approach. The two approaches focus as it were on different aspects of logical constants. Very roughly, invariance targets logicality: the generality and formality of logic. Our approach here targets constanthood, in the sense of what must be held constant for an inference to be valid.

Metacognitive perspectives on unawareness and uncertainty(with P. Egré), in Foundations of Metacognition, M. Beran, J. Brandl, J. Perner and J. Proust (eds),   Oxford University Press, 2012, p. 321-342.
A state of ignorance about a proposition can result from two distinct sources: uncertainty about what the correct answer actually is, and unawareness of what the answer might possibly be. Uncertainty concerns the strength of one's evidence, whereas unawareness concerns the conceptual components needed to articulate a proposition. This chapter discusses the implications of the distinction between uncertainty and unawareness for metacognition, and more specifically for the problem of what it takes to know that one knows and to know that one does not know. In particular, we relate the distinction between uncertainty-based unknowns and unawareness-based unknowns to the two-stage model proposed by Glucksberg and McCloskey for decisions about ignorance.

Which Logic for the Radical Anti-Realist?, with M. Cozic, in The Realism-Antirealisme Debate in the Age of Alternative Logics, S. Rahman, G. Primiero, M. Marion (eds), 2012, p. 47-67.
Radical anti-realism is a radicalization of anti-realism which insists on feasiblity in practice, as opposed to feasibility in principle. We focus on the revisionist consequences of this view and in particular on the idea that a strengthening of the moderate anti-realist’s basic insights leads to linear logic rather than to intuitionistic logic. And we ask whether the price to pay is too high.

L'objet propre de la logique, Les études philosophiques 2011/2 (97), p. 259-280.
La logique est une théorie normative du raisonnement, qui vise à caractériser la classe des arguments déductifs valides en déterminant si la conclusion est conséquence logique des prémisses. Mais, selon la définition sémantique devenue classique, la caractérisation de la relation de conséquence logique dépend elle-même de la caractérisation de la classe des mots logiques, ces mots qui, comme « non », « et », « tous » ou « certains » servent à articuler nos raisonnements. J’examine dans cet article à quelles conditions une analyse conceptuelle des propriétés sémantiques des mots logiques permet d’éclairer et de compléter une analyse conceptuelle des propriétés distinctives de la relation de conséquence logique.

Précis de Philosophie des Sciences, ouvrage collectif codirigé avec A. Barberousse et M. Cozic, Vuibert, 2011.
Cet ouvrage aborde de manière pédagogique les grands domaines de la philosophie des sciences. Pour en présenter les développements récents, il couvre aussi bien les questions relevant de la philosophie générale de l’activité scientifique (qu’est-ce qu’une explication scientifique ? l’unité des sciences est-elle un mythe ou un idéal ?...) que celles portant sur l’épistémologie des sciences particulières (de quoi les mathématiques sont-elles l’étude ? l’économie est-elle une science empirique comme les autres ?...). Ce précis constitue, pour les étudiants de Licence 3 et de Master en philosophie et en sciences, un support d’approfondissement de leurs cours mais aussi de préparation aux épreuves d’épistémologie des CAPES scientifiques. Il sera également utile aux doctorants et aux chercheurs confirmés qui souhaitent élargir ou actualiser leur savoir dans ce domaine.

L'explication scientifique, in Précis de Philosophie des Sciences, A. Barberousse, D. Bonnay et M. Cozic (eds), Vuibert, 2011, p. 13-61.
Une introduction aux théories de l'explication

La philosophie des mathématiques, avec J. Dubucs in Précis de Philosophie des Sciences, A. Barberousse, D. Bonnay et M. Cozic (eds), Vuibert, 2011, p. 293-349.
Une introduction historique et conceptuelle à la philosophie des mathématiques.

Knowing one's limits, joint work with Paul Egré, forthcoming in Dynamic Formal Epistemology,  O. Roy, P. Girard and M. Marion (eds)., Springer, 2011, p. 103-126.
Following earlier work on Centered Semantics for epistemic logic, we introduce a variation on the standard semantics for epistemic updates. The resulting logic, Centered Dynamic Epistemic Logic, is then applied to analyze the Margin for Error paradox due to T. Williamson. We argue that the paradox stems from an incorrect assumption about the properties of consecutive estimates of margins for error. We provide a precise characterization of the demarcation between paradoxical and non-paradoxical scenarios in terms of the properties of sequences of estimates.

Principe de charité et sciences de l'homme, joint work with Mikaël Cozic, in Th. Martin (ed.) Les sciences humaines sont-elles des sciences ? Vuibert, 2011, p. 119-157.
According to the principle of charity, we always have to make the assumption that other people are rational when we try to interpret their behavior. This paper is a critical discussion of the principle and its methodological consequences in the light of recent advances in cognitive science concerning mentalization. We argue that the validity of the charity principle is limited by the likely existence of interpretative non-theoretical mechanisms (simulation theory). As a consequence, we claim that theories of rationality, scientific theories of cognition and behavior and products of mentalization can neither in fact nor in principle be identified with one another.

Logical Consequence Inside Out, with Dag Westerståhl, in Logical, Language and Meaning, M. Aloni et alii (eds), Lecture Notes in Computer Science, vol. 6042, Springer, 2010, p. 193-202.
Tarski’s definition of logical consequence for an interpreted language rests on the distinction between extra-logical symbols, whose interpretation is allowed to vary across models, and logical symbols, aka logical constants, whose interpretation remains fixed. In this perspective, logicality come first, and consequence is a by-product of the division between logical and extra-logical symbols. The problem of finding a conceptually motivated account for this division is a long-standing issue in the philosophy of logic. Our aim here is to short-circuit this issue and lay the basis for a shift in perspective: let consequence come first, so that the demarcation of a set of constants can be viewed as the by-product of the analysis of a relation of logical consequence. The idea for extracting logical constants from a consequence relation is the following: they are the symbols which are essential to the validity of at least one inference, in the sense that replacing them or varying their interpretation would destroy the validity of that inference. Conversely, definitions of logical consequence can be construed as providing us with mappings from sets of symbols to consequence relations. Extraction of constants is then expected to be an ‘inverse’ to generation of consequence relations.

Charité et pluralisme, in
Construction, Festschrifft for Gerhard Heinzmann, P.E. Bour, M. Rebuschi, L. Rollet (eds), College Publications, Tribute Series, 2010, pp. 312-323.
Le développement de nombreux systèmes logiques `non-classiques' pose la question du statut, privilégié ou non, de la logique classique et de la nature des rapports entre ces systèmes. D'un côté, les tenants du pluralisme logique ont cherché à soutenir que plusieurs systèmes logiques pouvaient coexister en quelque sorte pacifiquement. D'un autre côté, la possibilité même de logiques rivales de la logique classique a été contestée sur la base d'arguments d'inspiration quinienne liés au principe de charité. Dans quelle mesure l'acceptation du principe de charité est-elle compatible avec la reconnaissance de l'utilité et de la fécondité des logiques non-classiques ? Je me propose d'apporter quelques éléments de réponse à cette question, dans un cas bien particulier, celui de la modélisation de la compétence inférentielle. Il s'agira d'abord de distinguer deux manières différentes d'invoquer le principe de charité, l'une `linguistique' portant sur la possibilité de logiques rivales de la logique classique, l'autre `cognitive' portant sur la rationalité des agents. Je soutiendrai qu'il est possible d'accepter la première utilisation du principe de charité tout en refusant la seconde. Reste alors la question de savoir quels genres de systèmes logiques non-classiques sont susceptibles d'éclairer notre compréhension de la compétence inférentielle des agents sans pour autant constituer des rivaux à la logique classique. Cette dernière question sera discutée sur la base restreinte d'une comparaison entre plusieurs sémantiques paraconsistantes.

Vagueness, Uncertainy and Degress of Clarity, joint work with Paul Egré (first author), forthcoming in a special issue of Synthese edited by R. van Rooij
The focus of the paper is on the logic of clarity and the problem of higherorder vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare different theories of vagueness understood as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s twodimensional 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.

Logique, preuve et vérité, anthologie, Textes clés de philosophie de la logique, dirigée avec M. Cozic, Vrin, 2009.
La logique est un compagnon naturel de la philosophie. Qu'est-ce qu'un raisonnement correct ? Qu'est-ce qu'une preuve ? Peut-on définir le concept de vérité ? Que faire face aux paradoxes ? Ces questions sont débattues par les philosophes depuis l'Antiquité. La logique moderne, usant de langages formels, développe une analyse rigoureuse de ces concepts les plus fondamentaux. Les onze textes classiques réunis ici proposent un retour réflexif sur cette discipline et sur la signification philosophique de ses achèvements. Ils s'adressent à quiconque souhaite prendre la mesure des enjeux conceptuels de la logique, et à tous les étudiants désireux de compléter leur apprentissage de la discipline par une réflexion épistémologique sur ses fondements.

Inexact Knowledge with introspection, joint work with Paul Egré, Journal of Philosophical Logic, 38, pp. 179-227, 2009.
Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resourcesensitive logic with implications for the representation of common knowledge in situations of bounded rationality.

Carnap’s Criterion of Logicality, Carnap's Logical Syntax of Language, P. Wagner (ed.), Palgrave-McMillan, 2009, p. 147-166.
I thought Carnap's way of drawing the line between logical and descreptive expressions was well worth a second look. I address some technical issues that are raised by the formal definition Carnap gives in the context of the Logical Syntax and discuss whether the definition supports his philosophical claims about the nature of logic and mathematics.

Modal Logic and Invariance, joint work with Johan van Benthem, Journal of Applied and Non-Classical Logic, 18 (2-3), pp. 153-173, 2008.
Consider any logical system, what is its natural repertoire of logical operations? This question has been raised in particular for first-order logic and its extensions with generalized quantifiers, and various characterizations in terms of semantic invariance have been proposed. In this paper, our main concern is with modal and dynamic logics. Drawing on previous work on invariance for first-order operations, we find an abstract connection between the kind of logical operations a system uses and the kind of invariance conditions the system respects. This analysis yields (a) a characterization of invariance and safety under bisimulation as natural conditions for logical operations in modal and dynamic logics, and (b) some new transfer results between first-order logic and modal logic. mes sémantiques des opérations logiques.

Définir la logique, actes du colloque "Définitions", Travaux de logique du CdRS, Université de Neuchatel, 2008.
Qu'est-ce que la logique, et quels problèmes spécifiques rencontre-t-on lorsqu'on esssaie de la définir ? Cet article en français 'destiné à un large public' présente les définitions en termes de preuves et en termes sémantiques des opérations logiques. Mais comment de telles définitions sont-elles possibles si d'une part, on doit définir le plus compliqué à l'aide du plus simple, et si d'autre part la logique est ce qu'il y a de plus simple ? J'examine à la lumière de ce problème les concessions faites dans chacune des deux traditions, preuve-théorique et sémantique.

Logicality and Invariance, Bulletin of Symbolic Logic, 14, 1, pp. 29-68, 2008.
The paper presents the main results of my dissertation about logical constants, in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared  and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

Margin for Errors in Context, with P. Egré, forthcoming in Relative Truth, M. Garcia-Carpintero & M. Kölbel (eds.), Oxford University Press, 2008, p. 103-128.
This paper belongs to a series of joint paper with Paul Egre which are devoted to inexact knowledge and introspection. Our starting point was Williamson's argument in Knowledge and its limits showing that margin for error principles are not compatible with introspection. We have been working on a non-standard modal logic which is devised to make them compatible.

Règles et signification : le point de vue de la logique classique (Meaning and rules, from a classical point of view), 2007, in J.B. Joinet, ed., Logique, Dynamique et Cognition, Publications de la Sorbonne, p. 213-231, 2007.

Qu'est-ce qu'une constante logique? (What is a Logical Constant?), PhD Dissertation, University Paris I, 2006.
Here is an abstract.

A Non-standard Semantics for Inexact Knowledge with Introspection, with P. Egré, Proceedings of the ESSLLI 2006 Workshop Rationality and Knowledge, R. Parikh and S. Artemov (eds), 2006.

Are Two Dimensions Too Many? A One-dimensional Rival to Two-Dimensional Semantics, with S. Bourgeois-Gironde, Technical reports of the Institut Jean Nicod, 2005.
Two-Dimensional semantics brings a nice solution to a variety of epistemic puzzles, but introducing secondary intensions might be considered somewhat risky and counter-intuitive. We use (well-behaved) impossible worlds to offer a one-dimensional alternative.

Compositionality and Molecularismin M. Werning, E. Macherey, G. Schurz (eds), The Compositionality of Concepts and Meaning: Foundational Issues, Ontos, p. 41-62, 2005.
This is about the status of the principle of compositionality. Is it a constraint that any real language should abide by? I argue that compositionality is a reasonable requirement only if one accepts a molecularist view of meaning (as opposed to meaning holism). The second paper uses Hodges' abstract account of compositionality in order to capture what it means for a language to be both compositional and molecular.

Independence and Games, Philosophia Scientiae, vol. 9 (2); p. 295-304, 2005.


Tonk Strikes back, with B. Simmenauer, Australasian Journal of Logic, vol. 3, p. 33-44, 2005.
How should we characterize the meaning of logical expressions? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. In this paper, we develop on an approach, going back to Dosen and Sambin, in which the inferential role of a logical constant is captured by a double line rule which introduces it as reflecting structural links (for example, multiplicative conjunction reflects comma on the right of the turnstyle). Rule-based characterizations of logical constants are subject to the well known objection of Prior’s fake connective, tonk. We show that some double line rules also give rise to such pseudo logical constants. But then, we are able to find a property of a double line rules which guarantee that it defines a genuine logical constant. Thus we provide an alternative to Belnap’s requirement of conservatity in terms of a local requirement on double line rules.

Preuves et jeux sémantique, (Proofs and Semantic Games), Philosophia Scientiae, 8 (2), p. 105-123, 2004.

Defining Logical Constants: the Insight from Basic Logic, with B. Simmenauer, in L. Alonso et P. Egré (eds), Proceedings of the 9th ESSLLI Student Session, p. 27-35, 2004.

La logique sauvage de Quine à Levi-Strauss, (Logic and the Wild, from Quine to Levi-Strauss), with S. Laugier, Archives de Philosophie, 66, p. 49-72, 2003.