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The Vindication of Computer Simulations

In Martin Carrier & Johannes Lenhard (eds.), Mathematics as a Tool: Tracing New Roles of Mathematics in the Sciences. Springer Verlag (2017)

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  1. 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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  • Reproducibility and the Concept of Numerical Solution.Johannes Lenhard & Uwe Küster - 2019 - Minds and Machines 29 (1):19-36.
    In this paper, we show that reproducibility is a severe problem that concerns simulation models. The reproducibility problem challenges the concept of numerical solution and hence the conception of what a simulation actually does. We provide an expanded picture of simulation that makes visible those steps of simulation modeling that are numerically relevant, but often escape notice in accounts of simulation. Examining these steps and analyzing a number of pertinent examples, we argue that numerical solutions are importantly different from usual (...)
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  • Verification and Validation of Simulations Against Holism.Julie Jebeile & Vincent Ardourel - 2019 - Minds and Machines 29 (1):149-168.
    It has been argued that the Duhem problem is renewed with computational models since model assumptions having a representational aim and computational assumptions cannot be tested in isolation. In particular, while the Verification and Validation methodology is supposed to prevent such holism, Winsberg argues that verification and validation cannot be separated in practice. Morrison replies that Winsberg overstates the entanglement between the steps. The paper aims at arbitrating these two positions, by stressing their respective validity in relation to domains of (...)
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  • 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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