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  1. Past, Present and Future Modally Introduced.Tomasz Placek - forthcoming - Synthese:1-22.
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  • Generalised Manifolds as Basic Objects of General Relativity.Joanna Luc - forthcoming - Foundations of Physics:1-23.
    In this paper non-Hausdorff manifolds as potential basic objects of General Relativity are investigated. One can distinguish four stages of identifying an appropriate mathematical structure to describe physical systems: kinematic, dynamical, physical reasonability, and empirical. The thesis of this paper is that in the context of General Relativity, non-Hausdorff manifolds pass the first two stages, as they enable one to define the basic notions of differential geometry needed to pose the problem of the evolution-distribution of matter and are not in (...)
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  • The Truth About the Future.Jacek Wawer - 2014 - Erkenntnis 79 (S3):365-401.
    There is a long-standing disagreement among Branching-Time theorists. Even though they all believe that the branching representation accurately grasps the idea that the future, contrary to the past, is open, they argue whether this representation is compatible with the claim that one among many possible futures is distinguished—the single future that will come to be. This disagreement is paralleled in an argument about the bivalence of future contingents. The single, privileged future is often called the Thin Red Line. I reconstruct (...)
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  • Defining Determinism.Thomas Müller & Tomasz Placek - 2018 - British Journal for the Philosophy of Science 69:215-252.
    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 equations, one based on mappings (...)
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  • A Generalized Manifold Topology for Branching Space-Times.Thomas Müller - 2013 - Philosophy of Science 80 (5):1089-1100.
    The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we (...)
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  • On Topological Issues of Indeterminism.Tomasz Placek, Nuel Belnap & Kohei Kishida - 2014 - Erkenntnis 79 (S3):1-34.
    Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to study (...)
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  • On A- and B-Theoretic Elements of Branching Spacetimes.Matt Farr - 2012 - Synthese 188 (1):85-116.
    This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with (...)
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  • A Locus for “Now”.Tomasz Placek - 2010 - In Dennis Dieks, Wenceslao Gonzalo, Thomas Uebel, Stephan Hartmann & Marcel Weber (eds.), Explanation, Prediction, and Confirmation. Springer. pp. 395--410.
    We investigate the concepts of past, present, and future that build upon a modal distinction between the settled past and the open future. The concepts are defined in terms of a pre-causal ordering and of qualitative differences between alternative histories. Finally, we look what an event's past, present, and future look like in the so-called Minkowskian Branching Structures, in which histories are isomorphic to Minkowski spacetime.
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  • Branching Space-Times, General Relativity, the Hausdorff Property, and Modal Consistency.Thomas Muller - unknown
    The logical theory of branching space-times, which is intended to provide a framework for studying objective indeterminism, remains at a certain distance from the discussion of space-time theories in the philosophy of physics. In a welcome attempt to clarify the connection, Earman has recently found fault with the branching approach and suggested ``pruning some branches from branching space-time''. The present note identifies the different---order theoretic vs. topological---points of view of both discussion as a reason for certain misunderstandings, and tries to (...)
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  • Branching for General Relativists.Tomasz Placek - unknown
    The paper develops a theory of branching spatiotemporal histories that accommodates indeterminism and the insights of general relativity. A model of this theory can be viewed as a collection of overlapping histories, where histories are defined as maximal consistent subsets of the model's base set. Subsequently, generalized manifolds are constructed on the theory's models, and the manifold topology is introduced. The set of histories in a model turns out to be identical with the set of maximal subsets of the model's (...)
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  • Relativity, the Open Future, and the Passage of Time.Oliver Pooley - 2013 - Proceedings of the Aristotelian Society 113 (3pt3):321-363.
    Is the objective passage of time compatible with relativistic physics? There are two easy routes to an affirmative answer: (1) provide a deflationary analysis of passage compatible with the block universe, or (2) argue that a privileged global present is compatible with relativity. (1) does not take passage seriously. (2) does not take relativity seriously. This paper is concerned with the viability of views that seek to take both passage and relativity seriously. The investigation proceeds by considering how traditional A-theoretic (...)
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  • Newtonian Determinism to Branching Space-Times Indeterminism in Two Moves.Nuel Belnap - 2012 - Synthese 188 (1):5-21.
    “Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “global”) indeterminism. This essay indicates how BST might be seen (...)
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  • Branching of Possible Worlds.Philip Percival - 2013 - Synthese 190 (18):4261-4291.
    The question as to whether some objects are possible worlds that have an initial segment in common, i.e. so that their fusion is a temporal tree whose branches are possible worlds, arises both for those who hold that our universe has the structure of a temporal tree and for those who hold that what there is includes concrete universes of every possible variety. The notion of “possible world” employed in the question is seen to be the notion of an object (...)
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  • Time and Determinism.Thomas Müller - 2015 - Journal of Philosophical Logic 44 (6):729-740.
    This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.
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  • A Future for the Thin Red Line.Alex Malpass & Jacek Wawer - 2012 - Synthese 188 (1):117-142.
    The thin red line ( TRL ) is a theory about the semantics of future-contingents. The central idea is that there is such a thing as the ‘actual future’, even in the presence of indeterminism. It is inspired by a famous solution to the problem of divine foreknowledge associated with William of Ockham, in which the freedom of agents is argued to be compatible with God’s omniscience. In the modern branching time setting, the theory of the TRL is widely regarded (...)
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  • On Individuals in Branching Histories.Tomasz Placek - 2012 - Synthese 188 (1):23-39.
    Against the background of the theory of branching space-times (BST), the paper sketches a concept of individuals. It discusses Kripkean modal intuitions concerning individuation, and, finally it addresses Lewis’s objections to branching individuals.
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