1.
INTRODUCTION
In this paper, I provide a logical framework for defining conventions,elaborating on the game-theoretic model proposed by David Lewis.The philosophical analysis of some of the key concepts in Lewis’smodel reveals that a modal logic formalization may be a naturalone. The paper will develop on the analysis and critique of suchconcepts as those of common knowledge, indication, and the dis-tinction between epistemic and practical rationality. In particular: (i)the analysis of Lewis’s definition of common knowledge reveals thata suitable formalization can be obtained by adopting an approachanalogous to that of awareness structures in modal logic; moreover(ii) the analysis of the notion of indication reveals that the agentsmay be required to make inductive inferences yielding probabilis-tic beliefs. I shall stress that such aspects, however, pertain to thesphere of epistemic rationality (i.e., they deal with the justificationof the agents’ beliefs) rather than to the sphere of practical rational-ity. Confounding the two spheres may lead to the wrong conclusionthat, in order to make sense of, say, salience as a coordination device,one should incorporate psychological assumptions into an undividednotion of rationality. On the contrary, practical rationality standsas the usual notion of game-theoretic rationality, whereas epistemicrationality incorporates those aspects pointed out in (i) and (ii) above.This attempt to provide a formal framework for Lewis’s theory of convention follows those of Vanderschraaf (1995, 1998) and Cubittand Sugden (2003). In his work on Lewis, Vanderschraaf provides acharacterization of convention as correlated equilibrium, adopting aformal framework close to the set-theoretical one proposed by Au-mann (1976). Cubitt and Sugden point out that such a frameworkdoes not take into account certain elements that are however pres-ent in Lewis’s original theory, and propose a different formal setupaltogether. In this paper, I show how a formalization based on modallogic can incorporate those distinctive aspects introduced by DavidLewis in
Convention.
1แนะนำIn this paper, I provide a logical framework for defining conventions,elaborating on the game-theoretic model proposed by David Lewis.The philosophical analysis of some of the key concepts in Lewis’smodel reveals that a modal logic formalization may be a naturalone. The paper will develop on the analysis and critique of suchconcepts as those of common knowledge, indication, and the dis-tinction between epistemic and practical rationality. In particular: (i)the analysis of Lewis’s definition of common knowledge reveals thata suitable formalization can be obtained by adopting an approachanalogous to that of awareness structures in modal logic; moreover(ii) the analysis of the notion of indication reveals that the agentsmay be required to make inductive inferences yielding probabilis-tic beliefs. I shall stress that such aspects, however, pertain to thesphere of epistemic rationality (i.e., they deal with the justificationof the agents’ beliefs) rather than to the sphere of practical rational-ity. Confounding the two spheres may lead to the wrong conclusionthat, in order to make sense of, say, salience as a coordination device,one should incorporate psychological assumptions into an undividednotion of rationality. On the contrary, practical rationality standsas the usual notion of game-theoretic rationality, whereas epistemicrationality incorporates those aspects pointed out in (i) and (ii) above.This attempt to provide a formal framework for Lewis’s theory of convention follows those of Vanderschraaf (1995, 1998) and Cubittand Sugden (2003). In his work on Lewis, Vanderschraaf provides acharacterization of convention as correlated equilibrium, adopting aformal framework close to the set-theoretical one proposed by Au-mann (1976). Cubitt and Sugden point out that such a frameworkdoes not take into account certain elements that are however pres-ent in Lewis’s original theory, and propose a different formal setupaltogether. In this paper, I show how a formalization based on modallogic can incorporate those distinctive aspects introduced by DavidLewis inประชุม
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