Denis Bonnay

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.

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.

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.

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.