The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections (...) 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

This is a new release of the original 1949 edition.

This paper examines the strengths and weaknesses of one of science's most pervasive and flexible metaprinciples;optimalityis used to explain utility maximization in economics, least effort principles in physics, entropy in chemistry, and survival of the fittest in biology. Fermat's principle of least time involves both teleological and causal considerations, two distinct modes of explanation resting on poorly understood psychological primitives. The rationality heuristic in economics provides an example from social science of the potential biases arising from the extreme flexibility of (...) optimality considerations, including selective search for confirming vidence, ex post rationalization, and the confusion of prediction with explanation. Commentators are asked to reflect on the extent to which optimality is an organizing principle of nature, a set of relatively unconnected techniques of science, a normative principle for rational choice and social organization, a metaphysical way of looking at the world, or something else still. (shrink)

Contemporary philosophers interested in value theory appear to be largely concerned with questions of the following sort:What is value?What is the meaning of the word ‘good’?Does the attribution of value to an object have a cognitive, or merely an emotive, significance?The first question is metaphysical; to ask it is analogous to asking in physics:What is matter?What is electricity?The others are generally treated as semantical questions; to ask them is analogous to asking in statistics:What is the meaning of the word ‘probable’?Does (...) an attribution of probability express an objective fact, or merely a subjective attitude? (shrink)

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

This is a major contribution to the theory of rational choice which will be of particular interest to philosophers and economists. The author sets out the foundations of rational choice, and then sketches a dynamic choice framework in which principles of ordering and independence follow from a number of apparently plausible conditions. However, there is potential conflict among these conditions, and when they are weakened to avoid it the usual foundations of rational choice no longer prevail. The thrust of the (...) argument is to suggest that the theory of rational choice is less deterministic than many suppose. (shrink)

When John Harsanyi came to Stanford University as a candidate for the Ph.D., I asked him why he was bothering, since it was most un likely that he had anything to learn from us. He was already a known scho lar; in addition to some papers in economics, the first two papers in this vol ume had already been published and had dazzled me by their originality and their combination of philosophical insight and technical competence. However, I am very glad (...) I did not discourage him; whether he learned any thing worthwhile I don't know, but we all learned much from him on the foundations of the theory of games and specifically on the outcome of bar gaining. The central focus of Harsanyi's work has continued to be in the theory of games, but especially on the foundations and conceptual problems. The theory of games, properly understood, is a very broad approach to social interaction based on individually rational behavior, and it connects closely with fundamental methodological and substantive issues in social science and in ethics. An indication of the range of Harsanyi's interest in game the ory can be found in the first paper of Part B -though in fact his owncontri butions are much broader-and in the second paper the applications to the methodology of social science. The remaining papers in that section show more specifically the richness of game theory in specific applications. (shrink)