Causes and (in)Determinism

Abstract

The five papers of the current issue originate from selected talks of a workshop Causes and Tenses: Formal Perspectives, held in Krakow (Poland) in September 2010. The aim of this event was to explore two relatively recent projects in formal philosophy: a rigorous analysis of a modal and tensed notion of (in)determinism and a study of common causation by means of probabilistic extendability. In contrast to the Laplacean (in)determinism framed in tenseless terms of laws of nature or models of a theory, the first project sets out the task of analyzing a notion of (in)determinism exhibited in claims like ‘‘It is not settled yet if there will be a sea battle tomorrow; however, by tomorrow evening it will have been settled whether or not there was the battle’’. The analysis draws on the insights of the PriorThomason tense logic as well as Kaplan’s logic of indexicals. Beginning with Belnap’s (1992) theory of branching space-times, another aim of the project is to relate tensed (in)determinism to spatiotemporal structures of current physics. The present issue begins with three papers on some aspects of this variety of (in)determinism. In the first paper Thomas Muller reflects on the notion of possible history, which is employed in all schools emerging from the Prior-Thomason theory of branching time. A history plays a distinctive role in assessing the truth values of the sentences to be evaluated in a given model. Possible histories also offer a theoretical grip on the concept of (in)determinism. They are usually defined as set-theoretically maximal objects of a certain kind. Although the formal details depend on the particular theory, the common idea is to read this maximality as maximality with respect to modal consistency. This calls in turn for spelling out a criterion of modal consistency (historicity) which would accord with insights of physics. The existing criteria, identifying possible histories with maximal chains or maximal upward directed subsets of a base set, are, however, in conflict with some relativistic