Structuralism and the applicability of mathematics
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| Abstract | In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended. | |||||||||
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Christopher Menzel (1990). Structuralism and Conceptual Change in Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:397 - 401.
Otávio Bueno (2011). An Inferential Conception of the Application of Mathematics. Noûs 45 (2):345-374.
Andrei Rodin (2011). Categories Without Structures. Philosophia Mathematica 19 (1):20-46.
Torsten Wilholt (2006). Lost on the Way From Frege to Carnap: How the Philosophy of Science Forgot the Applicability Problem. Grazer Philosophische Studien 73 (1):69-82.
Feng Ye (2010). The Applicability of Mathematics as a Scientific and a Logical Problem. Philosophia Mathematica 18 (2):144-165.
L. Luce (1991). Literalism and the Applicability of Arithmetic. British Journal for the Philosophy of Science 42 (4):469-489.
Mark Steiner (1995). The Applicabilities of Mathematics. Philosophia Mathematica 3 (2):129-156.
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