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 resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality. (shrink)

Forthcoming in S. Artemov and R. Parikh, Proceedings of the ESSLLI 2006 Workshop on Rationality and Knowledge.

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. (shrink)

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".

The standard relation of logical consequence allows for non-standard interpretations of logical constants, as was shown early on by Carnap. But then how can we learn the interpretations of logical constants, if not from the rules which govern their use? Answers in the literature have mostly consisted in devising clever rule formats going beyond the familiar what follows from what. A more conservative answer is possible. We may be able to learn the correct interpretations from the standard rules, because the (...) space of possible interpretations is a priori restricted by universal semantic principles. We show that this is indeed the case. The principles are familiar from modern formal semantics: compositionality, supplemented, for quantifiers, with topic-neutrality. (shrink)

Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent’s priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on (...) the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging and Jeffrey conditioning is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed. (shrink)

The dual character of invariance under transformations and definability by some operations has been used in classical works 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 article, we generalize a correspondence due to Krasner between invariance under groups of permutations and definability in L∞∞ so as to cover the cases that are of interest in the logicality debates, getting McGee’s theorem about quantifiers (...) invariant under all permutations and definability in pure L∞∞ as a particular case. We also prove some optimality results along the way, regarding the kinds of relations which are needed so that every subgroup of the full permutation group is characterizable as a group of automorphisms. (shrink)

Hintikka makes a distinction between two kinds of games: truthconstituting games and truth-seeking games. His well-known game-theoretical semantics for first-order classical logic and its independence-friendly extension belongs to the first class of games. In order to ground Hintikka’s claim that truth-constituting games are genuine verification and falsification games that make explicit the language games underlying the use of logical constants, it would be desirable to establish a substantial link between these two kinds of games. Adapting a result from Thierry Coquand, (...) we propose such a link, based on a slight modification of Hintikka’s games, in which we allow backward playing for ∃loïse. In this new setting, it can be proven that sequent rules for first-order logic, including the cut rule, are admissible, in the sense that for each rule, there exists an algorithm which turns winning strategies for the premisses into a winning strategy for the conclusion. Thus, proofs, as results of truth-seeking games, can be seen. (shrink)

What is a logical constant? In which terms should we characterize the meaning of logical words like “and”, “or”, “implies”? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. More precisely, we favor 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 answer to Belnap’s requirement of conservatity in terms of a local requirement on double line rules. (shrink)

What is a logical constant? The question is addressed 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.

The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation ⇒x. We investigate a function going in the other direction, thus extracting the constants of a given consequence relation, and we show that this function (a) retrieves the usual logical constants from the usual logical consequence relations, and (b) is an inverse (...) to—more precisely, forms a Galois connection with—the Bolzano-Tarski function. (shrink)

We take Carnap’s problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap’s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in (...) relational Kripke semantics. Except when restricted to finite domains, no modal logic characterizes all the Kripkean interpretation of P. Moreover, we show that, in contrast with the case of first-order logic, the obvious requirement of permutation invariance is not adequate in the modal case. After pointing out some known facts about modal logics that nevertheless force the Kripkean interpretation, we focus on another feature often taken to embody the gist of modal logic: locality. We show that invariance under point-generated subframes (properly defined) does single out the Kripkean interpretations, but only among topological interpretations, not in general. Finally, we define a notion of bisimulation invariance — another aspect of locality — that, together with a reasonable closure condition, gives the desired general result. Along the way, we propose a new perspective on normal neighborhood frames as filter frames, consisting of a set of worlds equipped with an accessibility relation, and a free filter at every world. (shrink)

Computer vision is one of AI’s most successful fields. In the last twenty years, machines have become increasingly good at extracting information from images and at identifying objects. But does this mean that machines really can see, or is computer vision just a fancy metaphor for object detection? This paper aims to provide a reasoned answer to the question. First, three criteria for vision attribution are reviewed and it is argued that a functionalist criterion, in terms of exploitable internal representations (...) based on visual stimuli, fares better than behaviourist or phenomenological ones. The functionalist criterion is then applied to vision algorithms based on neural networks and it is argued that such machines can indeed see, insofar as neural networks are precisely trained to generate representations of the visual data they are fed with. Those representations present the specific traits associated with successful training: They are hierarchical, robust, and versatile. We argue that these properties may be used as further constraints on representational devices in general, helping to solve some of the classical issues faced by teleosemantic theories of representation such as that expounded by Dretske. (shrink)

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.Logic is a normative theory of reasoning, which aims at characterizing the class of deductively valid arguments by determining whether a given conclusion logically follows from certain premisses. According to the standard semantic definition, the characterization of the relation of logical consequence depends itself on a characterization of the class of the so-called logical constants, those words, such as « not », « and », « all » or « some » which provide the logical structure of our arguments. In this paper, I shall make precise the conditions under which a conceptual analysis of the semantic properties of logical constants can complete, and shed light upon, a conceptual analysis of the distinctive properties of logical consequence. (shrink)

La logique est un compagnon naturel de la philosophie. Qu'est-ce qu'un raisonnement correct? Qu'est-ce qu'une preuve? Peut-on definir le concept de verite? Que faire face aux paradoxes? Ces questions sont debattues par les philosophes depuis l'Antiquite; et la logique moderne, usant de langages formels, developpe une analyse rigoureuse de ces concepts les plus fondamentaux. Les onze textes classiques reunis ici proposent un retour reflexif sur cette discipline et sur la signification philosophique de ses achevements. Ils s'adressent a quiconque souhaite prendre (...) la mesure des enjeux conceptuels de la logique, et a tous les etudiants desireux de completer leur apprentissage de la discipline par une reflexion epistemologique sur ses fondements. (shrink)

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. (shrink)

La logique IF prétend constituer une alternative à la logique classique du premier ordre : en libéralisant les schémas de dépendance entre quantificateurs, elle mènerait à leur terme les idées sous-jacentes à la logique classique. Mais les jeux de Hintikka ne constituent pas la seule manière possible de fournir une sémantique pour l’indépendance : on pourrait au contraire vouloir le faire dans le cadre d’une sémantique récursive avec des quantificateurs de Henkin. Nous présentons ici quelques arguments techniques et philosophiques en (...) faveur de IF, en montrant pourquoi son concept d’indépendance, élargi aux connecteurs, peut prétendre être pleinement général, et en montrant en quel sens la logique IF traite l’indépendance de manière analytique. Ce dernier point est réalisé à travers une explicitation du contenu épistémique de IF, sous la forme d’une traduction partielle dans la logique modale. (shrink)

Providing a principled characterization of the distinction between logical and non-logical expressions is a longstanding issue in the philosophy of logic. In the Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by "syntactic" means which sentences are valid and which are (...) not. Despite a renewed interest in the philosophical benefits of analyticity, both inside and outside of Carnap scholarship, Carnap's definition of logical expressions seems to have drawn too little attention. I shall argue that it is worth a second look. More precisely, my aim will be to defend this idea against some technical problems faced by Carnap's way of implementing it and against Quinean attacks on syntax-based conventionalism. Section 1 presents Carnap's definition in the context of Logical Syntax of Language, that is, how exactly the definition works, and why Carnap needs it. In section 2, I review three challenges that have been raised in the literature, and I propose to revise the definition accordingly. I argue that its modified version is immune to the previous challenges, and, to some extent, immune to new challenges as well. In the last section, I suggest that the definition has a philosophical interest of its own, because standard Quinean objections are not as conclusive as one might think when attention is paid to the fact that Carnap requires complete syntactic specification of validities. (shrink)

Since the ground-breaking contributions of M. Dummett (Dummett 1978), it is widely recognized that anti-realist principles have a critical impact on the choice of logic. Dummett argued that classical logic does not satisfy the requirements of such principles but that intuitionistic logic does. Some philosophers have adopted a more radical stance and argued for a more important departure from classical logic on the basis of similar intuitions. In particular, J. Dubucs and M. Marion (?) and (Dubucs 2002) have recently argued (...) that a proper understanding of anti-realism should lead us to the so-called substructural logics (see (Restall 2000)) and especially linear logic. The aim of this paper is to scrutinize this proposal. We will raise two kinds of issues for the radical anti-realist. First, we will stress the fact that it is hard to live without structural rules. Second, we will argue that, from an anti- realist perspective, there is currently no satisfactory justi cation to the shift to substructural logics. (shrink)

Quine est célèbre pour sa critique de la notion d’analyticité, mais il en a également proposé des substituts définissables en termes behavioristes. Cet article examine la question de savoir si de tels substituts peuvent ou non jouer un rôle épistémologique, en les comparant avec des tentatives récentes de réhabilitation de l’a priori. Il apparaît que la caractérisation de ce qu’est une définition acceptable en termes behavioristes est cruciale, et qu’un élargissement de la classe des comportements linguistiques pertinents peut ouvrir la (...) voie à une réhabilitation substantielle de l’analyticité.Quine is famous for his critics against the notion of analyticity used in epistemology and philosophy of science by philosophers of the Vienna circle. However, Quine has also proposed alternative definitions of the notion, which would be acceptable from a behaviorist perspective. In this paper, I address the question whether such alternative definitions can play any epistemologically significant role, by comparing them with recent attempts at a new defense of a priori knowledge. The upshot is that the answer cruccially depends on what is an acceptable definition in a behaviorist perspective. It might well be that an epistemologically significant notion of analyticity can be based upon a broad enough characterization of linguistic behavior. (shrink)

We discuss two interpretations of two-dimensional semantics (2DMS) due to D. Chalmers and R. Stalnaker. The main problem with both interpretations of the formal framework is the relinquishng of rigidity for terms. They are in a sense unfaithful to an agent's beliefs. We present alternative principles to capture what we take to be agents's beliefs, namely: the principles of hyper-rigidity and backward reference to actuality. We propose then to go back to a one-dimensional semantics which affords a satisfactory model of (...) beliefs reports. Our proposal, like 2DMS, addresses typical problems of representation for beliefs and epistemological difficulties related to modal knowledge. (shrink)

Philosophy of science studies the methods, theories, and concepts used by scientists. It mainly developed as a field in its own right during the twentieth century and is now a diversified and lively research area. This book surveys the current state of the discipline by focusing on central themes like confirmation of scientific hypotheses, scientific explanation, causality, the relationship between science and metaphysics, scientific change, the relationship between philosophy of science and science studies, the role of theories and models, unity (...) of science. These themes define general philosophy of science. The book also presents sub-disciplines in the philosophy of science dealing with the main sciences: logic, mathematics, physics, biology, medicine, cognitive science, linguistics, social sciences, and economics. While it is common to address the specific philosophical problems raised by physics and biology in such a book, the place assigned to the philosophy of special sciences is much more unusual. Most authors collaborate on a regular basis in their research or teaching and share a common vision of philosophy of science and its place within philosophy and academia in general. The chapters have been written in close accordance with the three editors, thus achieving strong unity of style and tone. (shrink)

Le Précis de philosophie des sciences vise à présenter, de manière pédagogique, l'état actuel des grandes questions et des grands domaines de la philosophie des sciences. C'est un ouvrage de niveau "intermédiaire", entre les ouvrages d'initiation et les ouvrages de recherche. Il peut être utilisé comme manuel pour des cours de philosophie des sciences au niveau Master, ainsi que dans le cadre de la préparation aux nouvelles épreuves d'épistémologie des CAPES scientifiques. Il a notamment pour vocation de servir de support (...) de cours pour des enseignements en épistémologie et philosophie des sciences de niveau L3, M1 et M2. (shrink)

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. (shrink)

This paper considers various objections to Carnap’s logical syntax definition of ’logical expression’, including those by Saunders Mac Lane and W. V. O. Quine. While the specific objections of these two authors can be answered, if necessary by a slight modification of Carnap’s definition, there are other objections that I do not see how to meet. I also consider the proposal by Denis Bonnay for avoiding the objections to Carnap’s definition. In light of the unresolved problems with Carnap’s (...) definition, I go on to consider what Carnap’s assumptions must have been in framing his definition and to assess how much damage is caused by this failure of Carnap’s definition. This damage is not as much as might be assumed. (shrink)

What are the processes, from conception to adulthood, that enable a single cell to grow into a sentient adult? Neuroconstructivism is a pioneering 2 volume work that sets out a whole new framework for considering the complex topic of development, integrating data from cognitive studies, computational work, and neuroimaging.

April 15, 2024: This article published in Early View in error. The article will republish shortly.

Recent discussions of boundary theory, particularly in the field of ethnic relations, emphasize varying degrees of porousness of social boundaries and the importance of considering the effects of the intersections of multiple boundaries, most notably those of gender, ethnicity/race, and class. It is also increasingly acknowledged that within-group characteristics, including identities, of subordinate as well as of dominant groups may change, without their becoming less authentic distinctive collectivities. This article examines the changing identities of a specific collectivity—French-speaking Canadian women living (...) in Ontario—who, during the past century, have been either marginalized by, or excluded from, several larger collectivities for various reasons—religion, race/ethnicity, language, nationalism, region, and gender—related to boundary definitions of their multiple, intersecting identities. It explores the emergence of these various marginalities and the ability of these feminists to construct institutions and agendas on their own terms. (shrink)

The main aim of this paper is to propose the inclusion of the expertise of a prudent agent in the reflective equilibrium procedure, adding a disposition to identify reasonable beliefs that would be seen as the starting point of the method, which could avoid the criticism of conservatism and subjectivism. To do so, I will begin by analyzing the central characteristics of the method and its main faults. Afterwards, I will investigate the characteristics of prudence as a disposition to identify (...) the adequate means to achieve a good end. With this in mind, I will apply prudence to the procedure, so that it will be carried out by an agent who deliberates well, identifying reasonable moral beliefs and, then, we must justify them based on their consistency with ethical principles and with the factual beliefs of relevant scientific theories. Finally, I will argue that this deliberative process is consistent with ethical pluralism and democracy, and can be taken as a kind of moral knowledge. (shrink)

The concept of equilibrium has long been a focus for dissent between orthodox and heterodox schools of thought in economics. The paper explores the meanings of ‘equilibrium’ and attempts to tease apart salient appropriate and inappropriate modes of deployment of the concept. Under far-from-equilibrium conditions, equilibrium is not even an approximate description of the condition of the system, but an abstraction – a state of affairs which might obtain should a process under consideration run to its conclusion. The order of (...) the system is viewed from this standpoint, not as an equilibrium, but as a temporary and ephemeral balance of forces, destined to be disturbed by the passage of time. A specific instance of the deployment of the concept of equilibrium by a neoclassical writer – Robert Lucas – is examined and the conclusion drawn that the concept has been hypostatised: an aspect of a process has been one-sidedly emphasised and substituted for the whole. The temporary is made permanent, and process subordinated to stasis, with clear apologetic results. The paper concludes by suggesting that this hypostatisation exemplifies the contrast between formal and dialectical modes of thought, and that it is in the application of a dialectical notion of equilibrium that the heterodoxy can make its most telling contribution. (shrink)

Papers from a seminar held in Paris, Sept. 1995, organized by the International Union of Physiological Sciences and UNESCO.

Europeans seeking to understand tribal arts face obvious problems of comprehending the histories, values, and ideas of vastly remote cultures. In this respect the issues faced in understanding tribal art (or folk art, primitive art, traditional art, third or fourth-world art — none of these designations is ideal) are not much different from those encountered in trying to comprehend the distant art of “our own” culture, for instance, the art of medieval Europe. But in the case of tribal or so-called (...) primitive art, there are special complications. First, objects of tribal art are sometimes so strange to us that we cannot tell immediately whether they are intended to be works of art (or some local analogue of what we would call art) at all.1An African head-rest I once came across had an odd, extravagant extrusion which made the whole piece reminiscent of Arp. It seemed to my baffled, ignorant eyes to be much more than a mere head-rest, but I couldn’t tell what more it was supposed to be. Maybe that extension on the side of the object had some purely utilitarian function, acting as a handle, or perhaps it was a natural part of the original block of wood, left there merely because it looked nice to the eye of the carver. Though the head-rest seemed beautiful, I still don’t know if I was admiring as an essentially expressive object some simple item of practical use, or something that combined expression and utility. (shrink)

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 (...) a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new consequence-relation and discuss some of its properties. (shrink)

This study is about Brentano’s criticism of a version of phenomenalism that he calls “mental monism” and which he attributes to positivist philosophers such as Ernst Mach and John Stuart Mill. I am interested in Brentano’s criticism of Mill’s version of mental monism based on the idea of “permanent possibilities of sensation.” Brentano claims that this form of monism is characterized by the identification of the class of physical phenomena with that of mental phenomena, and it commits itself to a (...) form of idealism. Brentano argues instead for a form of indirect or hypothetical realism based on intentional correlations. (shrink)

Skilled action typically requires that individuals guide their activities toward some goal. In skilled action, individuals do so excellently. We do not understand well what this capacity to guide consists in. In this paper I provide a case study of how individuals shift visual attention. Their capacity to guide visual attention toward some goal (partly) consists in an empirically discovered sub-system – the executive system. I argue that we can explain how individuals guide by appealing to the operation of this (...) sub-system. Understanding skill and skilled action thus requires appreciating the role of the executive system. (shrink)