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Aconvention is a state in which agents coordinate their activity, not as the result of an explicit agreement, but because their expectations are aligned so that each individual believes that all will act so as to achieve coordination for mutual benefit. Since agents are said to follow a convention if they coordinate without explicit agreement, the notion raises fundamental questions: (1) Why do certain conventions remain stable over time?, and (2) How does a convention emerge in the first place? In a pioneering study, Lewis (1969) addresses these questions by applyingnoncooperative game theory. Lewis defines a convention as aNash coordination equilibrium of a noncooperative game that issalient, that is, it is somehow conspicuous to the agents so that all expect one another to conform with the equilibrium. This paper presents a new game theoretic definition of conventions, which formalizes the notion of salience and which also generalizes the class of conventions Lewis discusses in his work. I define a convention as acorrelated equilibrium (Aumann 1974, 1987) satisfying apublic intentions criterion: Every agent wants his intended action to becommon knowledge. I argue that many conventions correspond to correlated equilibria that are not Nash equilibria, and that this is consistent with Lewis' general viewpoint. Finally, I argue that game theoretic characterizations of convention, such as Lewis' and my own, help to explain a convention's stability, but that a fully satisfactory account of the emergence of convention requires a theory of equilibrium selection beyond the scope of Lewis' work.

At the start of Convention (1969) Lewis says that it is "a platitude that language is ruled by convention" and that he proposes to give us "an analysis of convention in its full generality, including tacit convention not created by agreement." Almost no clause, however, of Lewis's analysis has withstood the barrage of counter examples over the years,1 and a glance at the big dictionary suggests why, for there are a dozen different senses listed there. Left unfettered, convention wanders freely from conventional wisdom through conventional medicine, conventions of art and "conventions of morality" to conventions of bidding in bridge.2 Surely it is unwise to try to fell these all with a single stone. Lewis's original goal, however, pursued further in (Lewis 1975), was to describe the conventionality of language, and this may be a more reasonable target.

David Lewis has offered a reply to the standard argument for the claim that the truth of determinism is incompatible with anyone’s being able to do otherwise than she in fact does. Helen Beebee has argued that Lewis’s compatibilist strategy is untenable. In this paper I show that one recent attempt to defend Lewis’s view against this argument fails and then go on to offer my own defense of Lewis’s view.

Skyrms–Lewis signaling games illustrate how meaningful language may evolve from initially meaningless random signals (Lewis, Convention 1969 ; Skyrms 2008 ). Here we will consider how incommensurable languages might evolve in the context of signaling games. We will also consider the types of incommensurability exhibited between evolved languages in such games. We will find that sequentially evolved languages may be strongly incommensurable while still allowing for increasingly faithful descriptions of the world.

This article will compare and contrast two very different accounts of convention: the game-theoretical account of Lewis in Convention, and the account initially proposed by Margaret Gilbert (the present author) in chapter six of On Social Facts, and further elaborated here. Gilbert’s account is not a variant of Lewis’s. It was arrived at in part as the result of a detailed critique of Lewis’s account in relation to a central everyday concept of a social convention. An account of convention need not be judged by that standard. Perhaps it reveals the nature of an important phenomenon. Looked at in that light, these very different accounts are not incompatible. Indeed, neither should be ignored if one is seeking to understand the way in which human beings arrive at some degree of social order.

This is the first of a three-volume collection of David Lewis's most recent papers in all the areas to which he has made significant contributions. The purpose of this collection (and the two volumes to follow) is to disseminate even more widely the work of a preeminent and influential late twentieth-century philosopher. The papers are now offered in a readily accessible format. This first volume is devoted to Lewis's work on philosophical logic from the last twenty-five years. The topics covered include: deploying the methods of formal semantics from artificial formalised languages to natural languages, model-theoretic investigations of intensional logic, contradiction, relevance, the differences between analog and digital representation, and questions arising from the construction of ambitious formalised philosophical systems. The volume will serve as an important reference tool for all philosophers and their students.

In his new paper, “Eligibility and Inscrutability,” J. R. G. Williams presents a surprising new challenge to David Lewis’ theory of interpretation. Although Williams frames this challenge primarily as a response to Lewis’ criticisms of Putnam’s model-theoretic argument, the challenge itself goes to the heart of Lewis’ own account of interpretation. Further, and leaving Lewis’ project aside for a moment, Williams’ argument highlights some important—and some fairly general—points concerning the relationship between model theory and semantic determinacy.

In his new paper, “Eligibility and Inscrutability,” J. R. G. Williams presents a surprising new challenge to David Lewis’ theory of interpretation. Although Williams frames this challenge primarily as a response to Lewis’ criticisms of Putnam’s model-theoretic argument, the challenge itself goes to the heart of Lewis’ own account of interpretation. Further, and leaving Lewis’ project aside for a moment, Williams’ argument highlights some important—and some fairly general—points concerning the relationship between model theory and semantic determinacy.

The question whether and in what way languages and language use involve convention is addressed, With special reference to David Lewis's account of convention in general. Data are presented which show that Lewis has not captured the sense of 'convention' involved when we speak of adopting a linguistic convention. He has, In effect, attempted an account of social conventions. An alternative account of social convention and an account of linguistic convention are sketched.

A feature of David Lewis's account of conventions in his book "Convention" which has received admiring notices from philosophers is his use of the mathematical theory of games. In this paper I point out a number of serious flaws in Lewis's use of game theory. Lewis's basic claim is that conventions cover 'coordination problems'. I show that game-Theoretical analysis tends to establish that coordination problems in Lewis's sense need not underlie conventions.