Denis Bonnay

Vagueness, uncertainty and degrees of clarity

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.

Which Logic for the Radical Anti-realist?

Since the ground-breaking contributions of M. Dummett (Truth and Other Enigmas. Duchworth, London, 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, Dubucs (Synthese. 132:213–237, 2002) and Dubucs and Marion (Philosophical Dimensions of Logic and Science. Kluwer, Dordrecht, 2003) have recently argued that a proper understanding of anti-realism should lead us to the so-called substructural logics (see Restall (An Introduction to Substructural Logics. Routledge, London, 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 justification to the shift to substructural logics.

Dynamic Versus Classical Consequence

The shift of interest in logic from just reasoning to all forms of information flow has considerably widened the scope of the discipline, as amply illustrated in Johan van Benthem’s recent book Logical Dynamics of Information and Interaction. But how much does this change when it comes to the study of traditional logical notions such as logical consequence? We propose a systematic comparison between classical consequence, explicated in terms of truth preservation, and a dynamic notion of consequence, explicated in terms of information flow. After a brief overview of logical consequence relations and the distinctive features of classical consequence, we define classical and dynamic consequence over abstract information frames. We study the properties of information under which the two notions prove to be equivalent, both in the abstract setting of information frames and in the concrete setting of Public Announcement Logic. The main lesson is that dynamic consequence diverges from classical consequence when information is not persistent, which is in particular the case of epistemic information about what we do not yet know. We end by comparing our results with recent work by Rothschild and Yalcin on the conditions under which the dynamics of information updates can be classically represented. We show that classicality for consequence is strictly less demanding than classicality for updates.