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  1.  20
    Outline of a Dynamical Inferential Conception of the Application of Mathematics.Tim Räz & Tilman Sauer - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:57-72.
    We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan. We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness (...)
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  2.  60
    Modeling Causal Structures: Volterra’s Struggle and Darwin’s Success.Raphael Scholl & Tim Räz - 2013 - European Journal for Philosophy of Science 3 (1):115-132.
    The Lotka–Volterra predator-prey-model is a widely known example of model-based science. Here we reexamine Vito Volterra’s and Umberto D’Ancona’s original publications on the model, and in particular their methodological reflections. On this basis we develop several ideas pertaining to the philosophical debate on the scientific practice of modeling. First, we show that Volterra and D’Ancona chose modeling because the problem in hand could not be approached by more direct methods such as causal inference. This suggests a philosophically insightful motivation for (...)
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  3.  57
    Towards a Methodology for Integrated History and Philosophy of Science.Raphael Scholl & Tim Räz - 2016 - In Tim Räz & Raphael Scholl (eds.), The Philosophy of Historical Case Studies. Springer Verlag.
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  4.  74
    Say My Name. An Objection to Ante Rem Structuralism.Tim Räz - 2015 - Philosophia Mathematica 23 (1):116-125.
    I raise an objection to Stewart Shapiro's version of ante rem structuralism: I show that it is in conflict with mathematical practice. Shapiro introduced so-called ‘finite cardinal structures’ to illustrate features of ante rem structuralism. I establish that these structures have a well-known counterpart in mathematics, but this counterpart is incompatible with ante rem structuralism. Furthermore, there is a good reason why, according to mathematical practice, these structures do not behave as conceived by Shapiro's ante rem structuralism.
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  5.  64
    On the Application of the Honeycomb Conjecture to the Bee’s Honeycomb.Tim Räz - 2013 - Philosophia Mathematica 21 (3):351-360.
    In a recent paper, Aidan Lyon and Mark Colyvan have proposed an explanation of the structure of the bee's honeycomb based on the mathematical Honeycomb Conjecture. This explanation has instantly become one of the standard examples in the philosophical debate on mathematical explanations of physical phenomena. In this critical note, I argue that the explanation is not scientifically adequate. The reason for this is that the explanation fails to do justice to the essentially three-dimensional structure of the bee's honeycomb.
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  6.  36
    The Silent Hexagon: Explaining Comb Structures.Tim Räz - 2017 - Synthese 194 (5).
    The paper presents, and discusses, four candidate explanations of the structure, and construction, of the bees’ honeycomb. So far, philosophers have used one of these four explanations, based on the mathematical Honeycomb Conjecture, while the other three candidate explanations have been ignored. I use the four cases to resolve a dispute between Pincock and Baker about the Honeycomb Conjecture explanation. Finally, I find that the two explanations focusing on the construction mechanism are more promising than those focusing exclusively on the (...)
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  7.  26
    The Necessity of Learning for Agency.Tim Räz - unknown
    The present paper examines the notion of agency using a model from artificial intelligence. The main thesis of the paper is that learning is a necessary condition for agency: Agency presupposes control, and control is acquired in a learning process. This thesis is explored using the so-called PS model. After substantiation the thesis, the paper explores the relation between agency and different kinds of learning using the PS model.
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  8.  28
    Gone Till November: A Disagreement in Einstein Scholarship.Tim Räz - 2016 - In Raphael Scholl & Tilman Sauer (eds.), The Philosophy of Historical Case Studies. Springer Verlag.
  9.  21
    Review: Noson S. Yanofsky : The Outer Limits of Reason. What Science, Mathematics, and Logic Cannot Tell Us.Tim Räz - 2015 - Dialectica 69 (2):248-254.
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  10.  45
    Mathematical Explanations in Euler’s Königsberg.Tim Räz - unknown
    I examine Leonhard Euler’s original solution to the Königsberg bridges problem. Euler’s solution can be interpreted as both an explanation within mathematics and a scientific explanation using mathematics. At the level of pure mathematics, Euler proposes three different solutions to the Königsberg problem. The differences between these solutions can be fruitfully explicated in terms of explanatory power. In the scientific version of the explanation, mathematics aids by representing the explanatorily salient causal structure of Königsberg. Based on this analysis, I defend (...)
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  11.  14
    Euler’s Königsberg: The Explanatory Power of Mathematics.Tim Räz - 2018 - European Journal for Philosophy of Science 8 (3):331-346.
    The present paper provides an analysis of Euler’s solutions to the Königsberg bridges problem. Euler proposes three different solutions to the problem, addressing their strengths and weaknesses along the way. I put the analysis of Euler’s paper to work in the philosophical discussion on mathematical explanations. I propose that the key ingredient to a good explanation is the degree to which it provides relevant information. Providing relevant information is based on knowledge of the structure in question, graphs in the present (...)
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  12.  14
    Euler’s Königsberg: The Explanatory Power of Mathematics.Tim Räz - 2017 - European Journal for Philosophy of Science:1-16.
    The present paper provides an analysis of Euler’s solutions to the Königsberg bridges problem. Euler proposes three different solutions to the problem, addressing their strengths and weaknesses along the way. I put the analysis of Euler’s paper to work in the philosophical discussion on mathematical explanations. I propose that the key ingredient to a good explanation is the degree to which it provides relevant information. Providing relevant information is based on knowledge of the structure in question, graphs in the present (...)
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  13.  6
    The Volterra Principle Generalized.Tim Räz - 2017 - Philosophy of Science 84 (4):737-760.
    Michael Weisberg and Kenneth Reisman argue that the Volterra Principle can be derived from multiple predator-prey models and that, therefore, the Volterra Principle is a prime example for robustness analysis. In the current article, I give new results regarding the Volterra Principle, extending Weisberg’s and Reisman’s work, and I discuss the consequences of these results for robustness analysis. I argue that we do not end up with multiple, independent models but rather with one general model. I identify the kind of (...)
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