Impossible States at Work: Logical Omniscience and Rational Choice

Mikaël Cozic (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

Logical omniscience is a never-ending problem in epistemic logic, the main model of full beliefs. It is seldom noticed that probabilistic models of partial beliefs face the same problem. As far as choice models are built on such doxastic models, they necessarily inherit the problem as well. Following some philosophical (Hacking, 1967) and decision-theoretic (Lipman, 1999) contributions, we advocate the use of nonstandard or impossible states to tackle this issue. First, we extend the nonstandard structures to the probabilistic case; an axiom system is devised, i.e. proved to be complete with respect to nonstandard probabilistic structures. Second, we show how to substitute weakened doxastic models for the idealized ones in choice models, and discuss the questions raised by this ''unidealization''.

Mots clés: Bounded rationality; epistemic logic; logical omniscience; probabilistic logic

Domaines: Histoire, Philosophie et Sociologie des sciences

Mikaël Cozic. Impossible States at Work: Logical Omniscience and Rational Choice. Topol, R. Cognitive Economics: New Trends, Elsevier, pp.1-2, 2007. ⟨halshs-00791818⟩