Branching space-time

Belnap, Nuel D.

doi:10.1007/bf00414289

Cited by 178 publications

(157 citation statements)

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“…The paper is based on an existing theory of causationNuel Belnap's theory of causae causantes (Belnap, 2003b), the background for which is branching space-times (Belnap, 1992). In this paper, we presuppose the notation of Belnap (2003b), which should be consulted.…”

Section: Causal Dependencies and Probabilitiesmentioning

confidence: 99%

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Probability Theory and Causation: A Branching Space-Times Analysis

Müller¹

2005

The British Journal for the Philosophy of Science

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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. Causal dependencies and probabilitiesProbability theory describes the likelihood of outcomes of chance set-ups. In this paper, we will assume that the framework of probability theory applies to single, concrete chance set-ups such as a single coin toss at a specific place and time. This assumption appears to be uncontroversial in view of the fact that probability theory is actually successfully applied. Since we are after a metaphysical picture combining causation and probabilities, we will assume that both causal relations and single case probabilities are objective. The aim of this paper may be described as trying to make sense of that assumption by showing how it might be true.Probability theory by itself has nothing to say about causation. However, questions of probabilities and questions of causation are obviously related. E.g., one may ask whether probabilities can be a guide to discovering causal relations. The literature on this question is large. When moved from an epistemic to a metaphysical level, the question gets a different reading: What are the objective influences of objectively existing causal relations on objectively existing probabilities? If a concrete situation involves more than one chance set-up, the causal interrelation of the set-ups may impose constraints on the probabilistic structure of the situation. E.g., if depending on the outcome of one chance set-up, another one is enabled or not, that causal structure should be mirrored in the probabilistic structure.

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Section: Causal Dependencies and Probabilitiesmentioning

confidence: 99%

“…This is a kind of chance set-up that Belnap (1992) has called "indeterminism without choice": the transition from I to its suprema is generally indeterministic, but no choice in I determines the outcome. With respect to this set-up, two questions arise:…”

Section: Application: Probability Of Suprema Of a Chainmentioning

confidence: 99%

Probability Theory and Causation: A Branching Space-Times Analysis

Müller¹

2005

The British Journal for the Philosophy of Science

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“…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 (2008) based on a model-theoretic characterization of indeterminism. It delineates BST branching against the background provided by Earman's (2008) distinction between individual vs. ensemble branching.…”

Section: Introductionmentioning

confidence: 99%

“…The theory appeared in Belnap (1992) (henceforth BST92 for the publication, and BST for the theory), and has since been developed by several philosophers in a variety of directions. For relevant publications, see items in the list of references by Belnap et al, by Müller et al, and by Placek et al BST92 built on earlier work on the "branching times" (henceforth BT) representation of indeterminism that goes back to a passing suggestion in an unpublished letter from S. Kripke to A. N. Prior dated September 3, 1958, 2 to the short discussion in Prior (1967), and to its working out in Thomason (1970).…”

Section: Introductionmentioning

confidence: 99%

On Belnap’s Branching Space-Times

Placek

2003

Philosophy and Logic in Search of the Polish Tradition

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Abstract 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.

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confidence: 99%

Indeterminism is a modal notion: branching spacetimes and Earman’s pruning

Placek

Belnap

2010

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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

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Branching space-time

Cited by 178 publications

References 20 publications

Probability Theory and Causation: A Branching Space-Times Analysis

Probability Theory and Causation: A Branching Space-Times Analysis

On Belnap’s Branching Space-Times

Indeterminism is a modal notion: branching spacetimes and Earman’s pruning

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