Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive (...) logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis. (shrink)

Hume is rightly credited with giving a brilliant, and perhaps the best, account of justice as convention. Hume's importance as a forerunner of modern economics has also long been recognized. However, most of Hume's readers have not fully appreciated how closely Hume's analysis of convention foreshadows a particular branch of economic theory, namely, game theory. Starting with the work of Barry, Runciman and Sen and Lewis, there has been a flowering of literature on the informal game-theoretic insights to be found (...) in classics of political philosophy such as Hobbes, Locke, Hume and Rousseau. A number of authors in this tradition, including Lewis, Gauthier, Mackie, and Postema, have identified passages in Hume which they interpret as giving informal examples of specific games. Yet, unlike his predecessors, Hobbes and Locke, Hume does much more than present examples which have a game-theoretic structure. In his account of convention, Hume gives general conditions which characterize the resolution of social interaction problems, and in the examples he uses to illustrate this account, Hume outlines several different methods by which agents can arrive at such a resolution. Hume's general account of convention and his explanations of the origins of particular conventions together constitute a theory of strategic interaction, which is precisely what game theory aspires to be. (shrink)

Vanderschraaf develops a new theory of game theory equilibrium selection in this book. The new theory defends general correlated equilibrium concepts and suggests a new analysis of convention.