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Nicolas Fillion
Simon Fraser University
  1. On the Epistemological Analysis of Modeling and Computational Error in the Mathematical Sciences.Nicolas Fillion & Robert M. Corless - 2014 - Synthese 191 (7):1451-1467.
    Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...)
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  2.  22
    Explanation and Abstraction From a Backward-Error Analytic Perspective.Nicolas Fillion & Robert H. C. Moir - 2018 - European Journal for Philosophy of Science 8 (3):735-759.
    We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding (...)
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  3.  50
    Conceptual and Computational Mathematics†.Nicolas Fillion - 2019 - Philosophia Mathematica 27 (2):199-218.
    ABSTRACT This paper examines consequences of the computer revolution in mathematics. By comparing its repercussions with those of conceptual developments that unfolded in the nineteenth century, I argue that the key epistemological lesson to draw from the two transformative periods is that effective and successful mathematical practices in science result from integrating the computational and conceptual styles of mathematics, and not that one of the two styles of mathematical reasoning is superior. Finally, I show that the methodology deployed by applied (...)
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  4. The Vindication of Computer Simulations.Nicolas Fillion - 2017 - In Martin Carrier & Johannes Lenhard (eds.), Mathematics as a Tool. Tracing New Roles of Mathematics in the Sciences. Springer Verlag.
    The relatively recent increase in prominence of computer simulations in scientific inquiry gives us more reasons than ever before for asserting that mathematics is a wonderful tool. In fact, a practical knowledge of scientific computation has become essential for scientists working in all disciplines involving mathematics. Despite their incontestable success, it must be emphasized that the numerical methods subtending simulations provide at best approximate solutions and that they can also return very misleading results. Accordingly, epistemological sobriety demands that we clarify (...)
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  5.  29
    Numerical Methods, Complexity, and Epistemic Hierarchies.Nicolas Fillion & Sorin Bangu - 2015 - Philosophy of Science 82 (5):941-955.
    Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a (...)
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  6.  7
    Concepts of Solution and the Finite Element Method: A Philosophical Take on Variational Crimes.Nicolas Fillion & Robert M. Corless - 2021 - Philosophy and Technology 34 (1):129-148.
    Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...)
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  7.  1
    Backward Error Analysis for Perturbation Methods.Robert M. Corless & Nicolas Fillion - 2019 - In James Robert Brown, Shaoshi Chen, Robert M. Corless, Ernest Davis, Nicolas Fillion, Max Gunzburger, Benjamin C. Jantzen, Daniel Lichtblau, Yuri Matiyasevich, Robert H. C. Moir, Mark Wilson & James Woodward (eds.), Algorithms and Complexity in Mathematics, Epistemology, and Science: Proceedings of 2015 and 2016 Acmes Conferences. Springer New York. pp. 35-79.
    We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps the most important is that backward error analysis can be used to demonstrate the validity of the solution, however obtained and by whichever method. This includes a nontrivial safeguard against slips, blunders, or bugs in the original computation. We also demonstrate its utility in deciding (...)
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  8.  21
    Clinical Equipoise and Adaptive Clinical Trials.Nicolas Fillion - 2019 - Topoi 38 (2):457-467.
    Ethically permissible clinical trials must not expose subjects to risks that are unreasonable in relation to anticipated benefits. In the research ethics literature, this moral requirement is typically understood in one of two different ways: as requiring the existence of a state of clinical equipoise, meaning a state of honest, professional disagreement among the community of experts about the preferred treatment; or as requiring an equilibrium between individual and collective ethics. It has been maintained that this second interpretation makes it (...)
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  9.  10
    The Reasonable Effectiveness of Mathematics in the Natural Sciences.Nicolas Fillion - unknown
    One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements (...)
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  10.  19
    The Content and Logic of Imperatives.Nicolas Fillion & Matthew Lynn - 2021 - Axiomathes 31 (3):419-436.
    This paper articulates an account of imperatives that sensibly supports the idea of a logic of imperative inferences. We rebuke common objections to the very possibility of such a logic, from a perspective based on recent linguistic work on the morphosyntax of imperatives. Specifically, we develop the notion that the content of an imperative sentence includes both a force operator alongside an imperational content to which the force applies. We further argue that this account of the content of imperatives constitutes (...)
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  11.  88
    J Ean -P Ierre M Arquis . From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory.Molly Kao, Nicolas Fillion & John Bell - 2010 - Philosophia Mathematica 18 (2):227-234.
    (No abstract is available for this citation).
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  12. La méthode axiomatique et la philosophie.Nicolas Fillion - 2007 - Revue Phares 7.
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  13.  5
    Algorithms and Complexity in Mathematics, Epistemology, and Science: Proceedings of 2015 and 2016 Acmes Conferences.Nicolas Fillion, Robert M. Corless & Ilias S. Kotsireas (eds.) - 2019 - Springer New York.
    ACMES is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including (...)
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  14. Critique Semi-Formelle de Théorie de la Justice de Rawls.Nicolas Fillion - 2006 - Revue Phares 6 (3).
     
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  15. Discours de la méthode du Discours de la méthode: Critique d'une conception naïve de la connaissance humaine.Nicolas Fillion - 2003 - Revue Phares 4 (2).
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  16. Épistémologie et sociologie de la connaissance.Nicolas Fillion - 2006 - Revue Phares 6 (3).
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  17.  31
    Natural Deduction: An Introduction to Logic with Real Arguments, a Little History, and Some Humour RICHARD T.W. ARTHUR Peterborough: Broadview Press, 2011; 452 Pp.; $44.95. [REVIEW]Nicolas Fillion & Bradley Zurcher - 2015 - Dialogue 54 (1):190-192.
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  18.  15
    Jean-Pierre Marquis. From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory: Critical Studies/Book Reviews.Molly Kao, Nicolas Fillion & John Bell - 2010 - Philosophia Mathematica 18 (2):227-234.
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  19.  1
    Semantic layering and the success of mathematical sciences.Nicolas Fillion - 2021 - European Journal for Philosophy of Science 11 (3):1-25.
    What are the pillars on which the success of modern science rest? Although philosophers have much discussed what is behind science’s success, this paper argues that much of the discussion is misdirected. The extant literature rightly regards the semantic and inferential tools of formal logic and probability theory as pillars of scientific rationality, in the sense that they reveal the justificatory structure of important aspects of scientific practice. As key elements of our rational reconstruction toolbox, they make a fundamental contribution (...)
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