The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching space-times (BST) of Belnap (1992), against criticism by Earman's (2008) based on a model-theoretic characterization of indeterminism. It delineates BST branching against the background provided by Earman's (2008) distinction between individual versus ensemble branching. Partly in order to motivate our responses to Earman, it describes a construction of physically motivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to Earman's criticisms leveled against BST by addressing a topological issue, the question of an actual future, the past/future asymmetry, and some semantical questions.Keywords Indeterminism/determinism · Spacetimes · Branching space-times · TensesIn current debates two different concepts of (in)determinism have been used, each having a different historical origin and each being applied in different fields. On the one hand, there is an everyday natural notion of (in)determinism, discussed first by Aristotle, and illustrated by alternative possible futures, one with a sea battle and the other without. On the other hand, there is a tradition started by Laplace, of characterizing

Abstract. We show that truth conditions for counterfactuals need not always be given in terms of a vague notion of similarity. To this end, we single out the important class of historical counterfactuals and give formally rigorous truth conditions for these counterfactuals, employing a partial ordering relation called "comparative closeness" that is defined in the framework of branching space-times. Among other applications, we provide a detailed analysis of counterfactuals uttered in the context of lost bets. In an appendix we compare our theory with the branching space-times based reading of counterfactuals recently proposed by Belnap.

The paper investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of General Relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative spacetimes, all of which are compatible with a given initial data set.

The article puts forward a branching-style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of (differential) equations, one based on mappings between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping-and the equations-based approaches. After giving a detailed formal explication of a branching-based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching-and the mapping-based approach. We conclude that the branching-based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories.

Contrary to its initial idea, Belnap's (1992) theory of Branching Space-Times (BST) has models in which histories do not resemble relativistic space-times or any other physical space-times. The aim of this paper is to define a certain class of BST models, called "Minkowskian Branching Structures" (MBS), in which histories are isomorphic to Minkowski space-time. By focusing on these models rather than on general BST models, we hope that one may be able to improve on earlier BST analyzes of physical phenomena. Also, introducing MBS' sets the stage for recent discussions about whether or not 'branching is a bad idea', physically speaking. * We read earlier versions of this paper at the seminar 'Chaos and Quantum Information' held at the Jagiellonian