Ways of Worlds I–II Two Special Issues on Possible Worlds and Related Notions

Abstract

Ways of Worlds II is the second of two special issues of Studia Logica on possible worlds and related notions. Historical and philosophical tracking of possible worlds was partly, but not exclusively, the business of the first issue which was launched as volume 82, no. 3, 2006. This volume featured papers by M. Cresswell, S.O. Hansson, D. Jacquette, A.-V. Pietarinen, A. Varzi and A. Zanardo. Ways of Worlds II focuses more on applications and alternative frameworks. In ‘First Order Classical Modal Logic’ by H. Arlo-Costa and E. Pacuit, the stage is initially set for following D. Scott and R. Montague’s alternative framework for modalities known as neighborhood semantics. Completeness results are proved for a variety of classical systems of first order logic. Then the neighborhood frames with constant domains are used to study some recently proposed epistemic modalities together with models for monadic operators of high probability both of which are either very difficult or down-right impossible to model in standard relational Kripke-semantics. The paper is concluded with the presentation of a general first order neighborhood semantics which is strong enough to provide characterization results for the full family of classical first order modal systems. It is convincingly argued that the neighborhood semantics program is the first platform for the semantic unification of classical first order modal systems. In A. Brandenburger’s and H. Jerome Keisler’s ‘An Impossibility Result Theorem on Beliefs in Games’ a doxastic self-referential paradox in games is identified which in turn gives rise to a game-theoretic impossibility result similar to Russell’s paradox. The paradox is formalized using belief models and a first order language and the impossibility theorem then says that ‘No belief model can be complete for a language that contains first-order logic’ ! This interesting and surprising result may be interpreted as saying that if