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  1. Karen François, Benedikt Löwe, Thomas Müller & Bart van Kerkhove (eds.) (forthcoming). Foundations of the Formal Sciences VII, Studies in Logic. College Publications.
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  2. Thomas Müller (forthcoming). A Generalized Manifold Topology for Branching Space-Times. Philosophical Explorations 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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  3. Nuel Belnap & Thomas Müller (2013). BH-CIFOL: Case-Intensional First Order Logic. Journal of Philosophical Logic (2-3):1-32.
    This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...)
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  4. Thomas Müller (2013). Alternatives to Histories? Employing a Local Notion of Modal Consistency in Branching Theories. Erkenntnis:1-22.
    Branching theories are popular frameworks for modeling objective indeterminism in the form of a future of open possibilities. In such theories, the notion of a history plays a crucial role: it is both a basic ingredient in the axiomatic definition of the framework, and it is used as a parameter of truth in semantics for languages with a future tense. Furthermore, histories—complete possible courses of events—ground the notion of modal consistency: a set of events is modally consistent iff there is (...)
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  5. Paul Ziche & Thomas Müller (2013). Paul Oppenheim on Order—The Career of a Logico-Philosophical Concept. In Nikolay Milkov & Volker Peckhaus (eds.), The Berlin Group and the Philosophy of Logical Empiricism. Springer. 265--291.
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  6. Nuel Belnap & Thomas Müller, CIFOL: Case-Intensional First Order Logic. (I) Toward a Theory of Sorts.
    This is Part I of a two-part essay introducing case-intensional first-order logic (CIFOL), an easy-to-use, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus (Yale University Press 1972). CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity is extensional. Definite descriptions (...)
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  7. Thomas Müller (2012). Branching in the Landscape of Possibilities. Synthese 188 (1):41-65.
    The metaphor of a branching tree of future possibilities has a number of important philosophical and logical uses. In this paper we trace this metaphor through some of its uses and argue that the metaphor works the same way in physics as in philosophy. We then give an overview of formal systems for branching possibilities, viz., branching time and (briefly) branching space-times. In a next step we describe a number of different notions of possibility, thereby sketching a landscape of possibilities. (...)
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  8. Thomas Muller (2012). Indeterminism and Persistence. Philosophia Naturalis 49 (1):113-136.
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  9. Thomas Müller & Niko Strobach (2012). A Letter on the Present State of Affairs. Synthese 188 (3):469-485.
    The paper re-evaluates Prior's tenets about indeterminism and relativity from the point of view of the current state of the debate. We first discuss Prior's claims about indeterministic tense logic and about relativity separately and confront them with new technical developments. Then we combine the two topics in a discussion of indeterministic approaches to space-time logics. Finally we show why Prior would not have to "dig his heels in" when it comes to relativity: We point out a way of combining (...)
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  10. Benedikt Löwe & Thomas Müller (2011). Data and Phenomena in Conceptual Modelling. Synthese 182 (1):131-148.
    The distinction between data and phenomena introduced by Bogen and Woodward (Philosophical Review 97(3):303–352, 1988) was meant to help accounting for scientific practice, especially in relation with scientific theory testing. Their article and the subsequent discussion is primarily viewed as internal to philosophy of science. We shall argue that the data/phenomena distinction can be used much more broadly in modelling processes in philosophy.
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  11. Thomas Müller (2011). Probabilities in Branching Structures. In Dennis Dieks, Wenceslao Gonzalo, Thomas Uebel, Stephan Hartmann & Marcel Weber (eds.), Explanation, Prediction, and Confirmation. Springer. 109--121.
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  12. Benedikt L.öwe & Thomas Müller (eds.) (2010). PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. College Publications.
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  13. Benedikt Löwe & Thomas Müller (eds.) (2010). Phimsamp: Philosophy of Mathematics: Sociological Aspsects and Mathematical Practice. College Publications.
     
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  14. Thomas Müller (2010). Formal Methods in the Philosophy of Natural Science. In F. Stadler, D. Dieks, W. Gonzales, S. Hartmann, T. Uebel & M. Weber (eds.), The Present Situation in the Philosophy of Science. Springer. 111--123.
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  15. Thomas Müller (2010). Towards a Theory of Limited Indeterminism in Branching Space-Times. Journal of Philosophical Logic 39 (4):395 - 423.
    Branching space-times (BST; Belnap, Synthese 92:385–434, 1992 ) is the most advanced formal framework for representing indeterminism. BST is however based on continuous partial orderings, while our natural way of describing indeterministic scenarios may be called discrete. This paper establishes a theorem providing a discrete data format for BST: it is proved that a discrete representation of indeterministic scenarios leading to BST models is possible in an important subclass of cases. This result enables the representation of limited indeterminism in BST (...)
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  16. Thomas Müller (2009). Eliminating Modality From the Determinism Debate? Models Vs. Equations of Physical Theories. In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag.
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  17. Bernd Buldt, Benedikt Löwe & Thomas Müller (2008). Preface. Erkenntnis 68 (3):305 - 307.
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  18. Bernd Buldt, Benedikt Löwe & Thomas Müller (2008). Towards a New Epistemology of Mathematics. Erkenntnis 68 (3):309 - 329.
    In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.
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  19. Benedikt Löwe & Thomas Müller (2008). Mathematical Knowledge is Context Dependent. Grazer Philosophische Studien 76 (1):91-107.
    We argue that mathematical knowledge is context dependent. Our main argument is that on pain of distorting mathematical practice, one must analyse the notion of having available a proof, which supplies justification in mathematics, in a context dependent way.
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  20. Thomas Muller (2008). Mathematical Knowledge is Context Dependent Benedikt Lowe Universiteit Van Amsterdam, Universitat Hamburg & Rheinische Friedrich-Wilhelms-Universitat Bonn. Grazer Philosophische Studien 76:91-107.
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  21. Thomas Müller, Nuel Belnap & Kohei Kishida (2008). Funny Business in Branching Space-Times: Infinite Modal Correlations. Synthese 164 (1):141 - 159.
    The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for “funny business”, i.e., modal correlations such as occur through quantum-mechanical entanglement. This paper extends previous work by Belnap on notions of “funny business”. We provide two generalized definitions of “funny business”. Combinatorial funny business can be characterized as “absence of prima facie consistent scenarios”, while explanatory funny business characterizes situations in which no localized explanation (...)
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  22. Thomas Müller (2007). Branch Dependence in the “Consistent Histories” Approach to Quantum Mechanics. Foundations of Physics 37 (2):253-276.
    In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham’s history projector operator formalism. The former are too narrow for applications, and the latter’s generality comes at a certain cost, barring an intuitive reading of the “histories”. Branching (...)
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  23. Thomas Müller (ed.) (2007). Philosophie der Zeit: Neue Analytische Ansätze. Klostermann.
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  24. Thomas Müller (2007). Prior's Tense-Logical Universalism. Logique Et Analyse 199:223-252.
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  25. Thomas Muller (2007). A Branching Space-Times View on Quantum Error Correction. Studies in History and Philosophy of Science Part B 38 (3):635-652.
    In this paper we describe some first steps for bringing the framework of branching space-times to bear on quantum information theory. Our main application is quantum error correction. It is shown that branching space-times offers a new perspective on quantum error correction: as a supplement to the orthodox slogan, ``fight entanglement with entanglement'', we offer the new slogan, ``fight indeterminism with indeterminism''.
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  26. Tomasz Placek & Thomas Müller (2007). Branching Space-Times. Studies in History and Philosophy of Science Part B 38 (3):590-592.
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  27. Thomas Müller (2006). Book Review. [REVIEW] Erkenntnis 65 (3):441-447.
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  28. Thomas Müller (2005). Probability Theory and Causation: A Branching Space-Times Analysis. British Journal for the Philosophy of Science 56 (3):487 - 520.
    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 probabilities 1.1 Background: causation in branching space-times (...)
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  29. Thomas Müller (2005). Zur Ethik der Diagnosestellung am Beispiel der psychopathologischen Begriffe Genie und Wahnsinn im 19. und 20. Jahrhundert. [REVIEW] Schopenhauer Jahrbuch 86:73-91.
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  30. Thomas Müller (2002). Branching Space-Time, Modal Logic and the Counterfactual Conditional. In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer. 273--291.
  31. Thomas Müller & Tomasz Placek (2001). Against a Minimalist Reading of Bell's Theorem: Lessons From Fine. Synthese 128 (3):343 - 379.
    Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to (...)
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