Evolution of Inference
Evolution of Inference
Rousseau began his discussion of the origin of language with a paradox that echoes through modern philosophy of language. How can we explain the genesis of speech without presupposing speech, reference without presupposing reference, meaning without presupposing meaning? A version of this paradox forms the basis of Quine's attack on the logical empiricist doctrine that logic derives its warrant from conventions of meaning—that logical truths are true and logical inferences are valid by virtue of such conventions. Quine raised the general skeptical question of how conventions of language could be established without preexisting language, as well as calling attention to more specific skeptical circularities. If conventions of logic are to be set up by explicit definition, or by axioms, must we not presuppose logic to unpack those conventions? David Lewis (1969) sought to answer these skeptical doubts within a game theoretical framework in his book, Convention. This account contains fundamental new insights, and I regard it as a major advance in the theory of meaning. Lewis sees a convention as being a special kind of strict Nash equilibrium in a game that models the relevant social interaction. To say that a convention is a Nash equilibrium is to say that if an individual deviates from a convention which others observe, he is no better off for that. To say that it is a strict Nash equilibrium is to say that he is actually worse off. To this, Lewis adds the additional requirement that an individual unilateral deviation makes everyone involved in the social interaction worse off, so that it is in the common interest to avoid such deviations. A theory of convention must answer two fundamental questions: how do we arrive at conventions?, and by virtue of what considerations do conventions remain in force? Within Lewis' game-theoretic setting, these questions become, respectively, the problems of equilibrium selection and equilibrium maintenance. On the face of it, the second problem may seem to have a trivial solution— the equilibrium is maintained because it is an equilibrium! No one has an incentive to deviate.
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