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If my main criticism of Lewis is sound, we must conclude that there are at least two distinct types of convention: co-ordination conventions and conventions constituting autonomous practices. It is only possible in the case of the former, but not the latter, to specify the agents' structure of preferences, and the problem the convention is there to solve, antecedently and independently of the content of the conventions themselves. Conventions constituting an autonomous practice are constitutive of the point of, and the values inherent in the practice itself and hence they are not explicable in terms of solutions to co-ordination problems. Thus, from the vantage point of practical reasoning, Lewis' theory of conventions is partial and limited. It is superior, however, to the alternative offered by Gilbert, as it provides a good answer, albeit limited in scope, to the question of the normativity of conventions. Gilbert's analysis is more fundamentally flawed. She has failed to undermine Lewis' insight that conventions are arbitrary rules, due to her misconstrual of what arbitrariness consists in. Consequently, Gilbert's analysis of the normativity of social conventions in terms of ‘joint acceptance’ is doubly inadequate: it fails to distinguish conventions from many other types of rule people follow, and it fails to answer the question of the normativity of conventions in terms of reasons for action.

DOI: 10.1007/BF00413841

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