Philosophy of Science 82 (5):941-955 (2015)

Authors
Sorin Bangu
University of Bergen
Abstract
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 persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one.
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DOI 10.1086/683343
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References found in this work BETA

Computing Machinery and Intelligence.Alan M. Turing - 1950 - Mind 59 (October):433-60.

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Citations of this work BETA

On the Presumed Superiority of Analytical Solutions Over Numerical Methods.Vincent Ardourel & Julie Jebeile - 2017 - European Journal for Philosophy of Science 7 (2):201-220.
Conceptual and Computational Mathematics†.Nicolas Fillion - 2019 - Philosophia Mathematica 27 (2):199-218.
Semantic layering and the success of mathematical sciences.Nicolas Fillion - 2021 - European Journal for Philosophy of Science 11 (3):1-25.
Numerical Instability and Dynamical Systems.Vincent Ardourel & Julie Jebeile - 2021 - European Journal for Philosophy of Science 11 (2):1-21.

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