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  1. On Dualities and Equivalences Between Physical Theories.Jeremy Butterfield - forthcoming - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett (eds.), Philosophy Beyond Spacetime. Oxford: Oxford University Press.
    The main aim of this paper is to make a remark about the relation between dualities between theories, as `duality' is understood in physics and equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall argue, worth (...)
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  • The Existence of Superluminal Particles is Consistent with Relativistic Dynamics.Judit X. Madarász & Gergely Székely - 2014 - Journal of Applied Logic 12 (4):477-500.
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  • The Machine as Data: A Computational View of Emergence and Definability.S. Cooper - 2015 - Synthese 192 (7):1955-1988.
    Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. (...)
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  • A Three-Pronged Simonesque Approach To Modeling And Simulation In Deviant “Bi-Pay” Auctions, And Beyond.Joe Johnson, Naveen Sundar Govindarajulu & Selmer Bringsjord - 2014 - Mind and Society 13 (1):59-82.
    In order to employ and exhibit our Simon-inspired approach to computational economics, and specifically defend our version of the view that even logically untrained humans are rational, albeit no more than “boundedly” so, we provide two models, both rooted in computational logic, of how it is that logically untrained humans perform in a seemingly irrational fashion in a particular “deviant” auction.
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  • Axiomatizing Relativistic Dynamics Using Formal Thought Experiments.Attila Molnár & Gergely Székely - 2015 - Synthese 192 (7):2183-2222.
    Thought experiments are widely used in the informal explanation of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to grasp thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based only on kinematical concepts and we can geometrically prove the Mass Increase Formula in a natural way, without postulates of conservation (...)
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  • Three Different Formalisations of Einstein’s Relativity Principle.Judit X. Madarász, Gergely Székely & Mike Stannett - 2017 - Review of Symbolic Logic 10 (3):530-548.
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  • Axiomatization and Models of Scientific Theories.Décio Krause, Jonas R. B. Arenhart & Fernando T. F. Moraes - 2011 - Foundations of Science 16 (4):363-382.
    In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate (...)
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  • Evidence, Explanation and Enhanced Indispensability.Daniele Molinini - 2016 - Synthese 193 (2):403-422.
    In this paper I shall adopt a possible reading of the notions of ‘explanatory indispensability’ and ‘genuine mathematical explanation in science’ on which the Enhanced Indispensability Argument proposed by Alan Baker is based. Furthermore, I shall propose two examples of mathematical explanation in science and I shall show that, whether the EIA-partisans accept the reading I suggest, they are easily caught in a dilemma. To escape this dilemma they need to adopt some account of explanation and offer a plausible answer (...)
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  • On the Epistemological Significance of the Hungarian Project.Michèle Friend - 2015 - Synthese 192 (7):2035-2051.
    There are three elements in this paper. One is what we shall call ‘the Hungarian project’. This is the collected work of Andréka, Madarász, Németi, Székely and others. The second is Molinini’s philosophical work on the nature of mathematical explanations in science. The third is my pluralist approach to mathematics. The theses of this paper are that the Hungarian project gives genuine mathematical explanations for physical phenomena. A pluralist account of mathematical explanation can help us with appreciating the significance of (...)
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  • Using Mathematics to Explain a Scientific Theory.Michèle Friend & Daniele Molinini - 2016 - Philosophia Mathematica 24 (2):185-213.
    We answer three questions: 1. Can we give a wholly mathematical explanation of a physical phenomenon? 2. Can we give a wholly mathematical explanation for a whole physical theory? 3. What is gained or lost in giving a wholly, or partially, mathematical explanation of a phenomenon or a scientific theory? To answer these questions we look at a project developed by Hajnal Andréka, Judit Madarász, István Németi and Gergely Székely. They, together with collaborators, present special relativity theory in a three-sorted (...)
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  • An Axiomatic Foundation of Relativistic Spacetime.Thomas Benda - 2015 - Synthese 192 (7):1-16.
    An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo’s set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. Entities known in differential geometry, up to a metric, are defined and have the usual properties. A set-realistic point of view is adopted. The intended ontology is a set-theoretical hierarchy with a broad base of the empty set and (...)
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  • Proof Verification and Proof Discovery for Relativity.Naveen Sundar Govindarajalulu, Selmer Bringsjord & Joshua Taylor - 2015 - Synthese 192 (7):2077-2094.
    The vision of machines autonomously carrying out substantive conjecture generation, theorem discovery, proof discovery, and proof verification in mathematics and the natural sciences has a long history that reaches back before the development of automatic systems designed for such processes. While there has been considerable progress in proof verification in the formal sciences, for instance the Mizar project’ and the four-color theorem, now machine verified, there has been scant such work carried out in the realm of the natural sciences—until recently. (...)
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  • The Temporal Logic of Two Dimensional Minkowski Spacetime is Decidable.Robin Hirsch & Mark Reynolds - 2018 - Journal of Symbolic Logic 83 (3):829-867.
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  • Motion and Observation in a Single-Particle Universe.Mike Stannett - 2015 - Synthese 192 (7):2261-2271.
    We outline an argument that a single-particle universe (a universe containing precisely one pointlike particle) can be described mathematically, in which observation can be considered meaningful despite the a priori impossibility of distinguishing between an observer and the observed. Moreover, we argue, such a universe can be observationally similar to the world we see around us. It is arguably impossible, therefore, to determine by experimental observation of the physical world whether the universe we inhabit contains one particle or many—modern scientific (...)
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