Conceptual and Computational Mathematics

Philosophia Mathematica:nkz005 (forthcoming)

Authors
Nicolas Fillion
Simon Fraser University
Abstract
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 mathematicians in modern scientific computing is a paradigmatic instance of this key lesson.
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DOI 10.1093/philmat/nkz005
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Progress and Its Problems.Larry Laudan - 1977 - Philosophy of Science 46 (4):623-644.
Holism, Entrenchment, and the Future of Climate Model Pluralism.Johannes Lenhard & Eric Winsberg - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (3):253-262.

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