Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

There is no EPR-like funny business if (contrary to apparent fact)our world is as indeterministic as you wish, but is free from theEPR-like quantum mechanical phenomena such as is sometimes described interms of superluminal causation or correlation between distant events.The theory of branching space-times can be used to sharpen thetheoretical dichotomy between EPR-like funny business and noEPR-like funny business. Belnap (2002) offered two analyses of thedichotomy, and proved them equivalent. This essay adds two more, bothconnected with Reichenbachs principle of the (...) common cause, theprinciple that sends us hunting for a common-causal explanation ofdistant correlations. The two previous ideas of funny business and thetwo ideas introduced in this essay are proved to be all equivalent,which increases ones confidence in the stability of (and helpfulnessof) the BST analysis of the dichotomy between EPR-like funny businessand its absence. (shrink)

permits a sound and rigorously definable notion of ‘originating cause’ or causa causans—a type of transition event—of an outcome event. Mackie has famously suggested that causes form a family of ‘inus’ conditions, where an inus condition is ‘an insufficient but non-redundant part of an unnecessary but sufficient condition’. In this essay the needed concepts of BST theory are developed in detail, and it is then proved that the causae causantes of a given outcome event have exactly the structure of a (...) set of Mackie inus conditions. The proof requires the assumption that there is no EPR-like ‘funny business’. This seems enough to constitute a theory of ‘causation’ in at least one of its many senses. Introduction The cement of the universe Preliminaries 3.1 First definitions and postulates 3.2 Ontology: propositions 3.3 Ontology: initial events 3.4 Ontology: outcome events 3.5 Ontology: transition events 3.6 Propositional language applied to events Causae causantes 4.1 Causae causantes are basic primary transition events 4.2 Causae causantes of an outcome chain 4.3 No funny business Causae causantes and inns and inus conditions 5.1 Inns conditions of outcome chains: not quite 5.2 Inns conditions of outcome chains 5.3 Inns conditions of scattered outcome events 5.4 Inus conditions for disjunctive outcome events 5.5 Inns and inus conditions of transition events Counterfactual conditionals Appendix: Tense and modal connectives in BST. (shrink)

We suggest a rigorous theory of how objective single-case transition probabilities fit into our world. The theory combines indeterminism and relativity in the “branching space–times” pattern, and relies on the existing theory of causae causantes (originating causes). Its fundamental suggestion is that (at least in simple cases) the probabilities of all transitions can be computed from the basic probabilities attributed individually to their originating causes. The theory explains when and how one can reasonably infer from the probabilities of one “chance (...) set-up” to the probabilities of another such set-up that is located far away. (shrink)

We provide a formally rigorous framework for integrating singular causation, as understood by Nuel Belnap's theory of causae causantes, and objective single case probabilities. The central notion is that of a causal probability space whose sample space consists of causal alternatives. Such a probability space is generally not isomorphic to a product space. We give a causally motivated statement of the Markov condition and an analysis of the concept of screening-off. 1. Causal dependencies and probabilities1.1Background: causation in branching space-times1.2What are (...) probabilities defined for?2. Basic transitions2.1Basics of basic transitions2.2Sets of basic transitions3. Causal probability theory3.1Some simple cases3.2General causal probabilities3.3Application: probability of suprema of a chain. (shrink)