On Minkowskian branching structures

Wroński, Leszek; Placek, Tomasz

doi:10.1016/j.shpsb.2009.06.003

Cited by 14 publications

(12 citation statements)

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“…Our construction of MBS's diverges from the constructions of Müller (2002) and Wroński and Placek (2009) because it aims to be more physics-oriented. The authors mentioned begin their work with specifying a set Σ of labels for scenarios and a collection {S σ,η } σ,η∈Σ of sets of splitting points, where each S σ η possesses properties listed in Fact 4(i)-(iv).…”

Section: Historical Remarksmentioning

confidence: 98%

“…Müller (2002); for a discussion of the chain condition, cf. Wroński and Placek (2009).] Finally, we define MBS's in the present sense.…”

Section: Condition 7 (The Chain Condition) Given M = σ F P For a mentioning

confidence: 99%

“…Splitting points are then a derived notion-see Definition 1 and, as Fact 4(i)-(iv) shows, they satisfy the conditions assumed by Müller and Wroński and Placek. Accordingly, given that M = Σ, F, P is an MBS in the sense of Definition 8, Σ, {S σ,η } σ,η∈Σ with {S σ,η } σ,η∈Σ defined by Definition 1 is an MBS in the sense of Wroński and Placek (2009). If finitistic assumptions concerning sets S σ η are assumed, Σ, {S σ,η } σ,η∈Σ is an MBS in the sense of Müller (2002).…”

Section: Historical Remarksmentioning

confidence: 99%

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

Placek

Belnap

2010

Synthese

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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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Section: Historical Remarksmentioning

confidence: 98%

“…Müller (2002); for a discussion of the chain condition, cf. Wroński and Placek (2009).] Finally, we define MBS's in the present sense.…”

Section: Condition 7 (The Chain Condition) Given M = σ F P For a mentioning

confidence: 99%

Section: Historical Remarksmentioning

confidence: 99%

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

Placek

Belnap

2010

Synthese

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“…In this way, one can work out branching history structures whose individual histories are all, e.g., Minkowski space-times (Müller 2002;Wroński and Placek 2009;Placek and Wroński 2009).…”

Section: Branching Space-times (Bst)mentioning

confidence: 99%

Introduction: The Many Branches of Belnap’s Logic

Müller

2014

Outstanding Contributions to Logic

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In this introduction to the Outstanding contributions to logic volume devoted to Nuel Belnap's work on indeterminism and free action, we provide a brief overview of some of the formal frameworks and methods involved in Belnap's work on these topics: theories of branching histories, specifically "branching time" and "branching space-times", the stit ("seeing to it that") logic of agency, and case-intensional first order logic. We also draw some connections to the contributions included in this volume. Abstracts of these contributions are included as an appendix.Nuel Belnap's work in logic and in philosophy spans a period of over half a century. During this time, he has followed a number of different research lines, most of them over a period of many years or decades, and often in close collaboration with other researchers: 1 relevance logic, a long term project starting from a collaboration with Alan Anderson dating back to the late 1950s and continued with Robert Meyer and Michael Dunn into the 1990s; the logic of questions, developed with Thomas Steel in the 1960s and 1970s; display logic in the 1980s and 1990s; the revision theory of truth, with Anil Gupta, in the 1990s; and a long-term, continuing interest in indeterminism and free action. This book is devoted to Belnap's work on the latter two topics. In this introduction, we provide a brief overview of some of the formal frameworks and methods involved in that work, and we draw some connections to the contributions included in this volume. Abstracts of these contributions are presented in Appendix A. 1 The biographical interview with Nuel Belnap provides some additional information on these research lines and on some of the collaborations. About this BookThis book contains essays devoted to Nuel Belnap's work on indeterminism and free action. Philosophically, these topics can seem far apart; they belong to different sub-disciplines, viz., metaphysics and action theory. This separation is visible in philosophical logic as well: The philosophical topic of indeterminism, or of the open future, has triggered research in modal, temporal and many-valued logic; the philosophical topic of agency, on the other hand, has led to research on logics of causation and action. In Belnap's logical work, however, indeterminism and free agency are intimately linked, testifying to their philosophical interconnectedness.Starting in the 1980s, Belnap developed theories of indeterminism in terms of branching histories, most notably "branching time" and his own "branching spacetimes". At the same time, he pursued the project of a logic of (multi-)agency, under the heading of stit, or "seeing to it that". These two developments are linked both formally and genetically. The stit logic of agency is built upon a theory of branching histories-initially, on the Prior-Thomason theory of so-called branching time. The spatio-temporal refinement of that theory, branching space-times, in turn incorporates insights from the formal modeling of agency. Both research lines arise in one...

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“…6 For a similar construction in the context of BST92, which however does not lead to generalized manifolds, see, e.g., Wroński and Placek (2009). An M n m -like construction is given in Visser (1996, 251-255); the book contains many pointers to relevant literature.…”

Section: Simple Branching: Generalized Minkowskian Manifoldsmentioning

confidence: 99%

A Generalized Manifold Topology for Branching Space-Times

Müller¹

2013

Philos. of Sci.

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The logical theory of branching space-times (Belnap, Synthese 1992), which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from the discussion of space-time theories in the philosophy of physics. Earman has criticized the branching approach and suggested "pruning some branches from branching space-time" (2008). This paper identifies the different-order-theoretic vs. topologicalpoints of view of both discussions as a reason for certain misunderstandings, and tries to remove them. Most importantly, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we introduce a differentialgeometrical version of branching space-times as a non-Hausdorff (generalized) manifold.

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On Minkowskian branching structures

Cited by 14 publications

References 10 publications

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

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

Introduction: The Many Branches of Belnap’s Logic

A Generalized Manifold Topology for Branching Space-Times

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