Areté. Revista de Filosofía 31 (1):7-34 (2019)

Manuel Barrantes
University of Virginia (PhD)
“Structuralism, Fictionalism, and the Applicability of Mathematics in Science”. This article has two objectives. The first one is to review some of the most important questions in the contemporary philosophy of mathematics: What is the nature of mathematical objects? How do we acquire knowledge about these objects? Should mathematical statements be interpreted differently than ordinary ones? And, finally, how can we explain the applicability of mathematics in science? The debate that guides these reflections is the one between mathematical realism and anti-realism. On the other hand, the second objective is to discuss the arguments that use the applicability of mathematics in science to justify mathematical realism, and show that none of them reaches its aim. To this end, we will distinguish three aspects of the problem of the applicability of mathematics: the utility of mathematics in science, the unexpected utility of some mathematical theories, and the apparent indispensability of mathematics in our best scientific theories - in particular, in our best scientific explanations. Finally, I argue that none of these aspects constitutes a reason to adopt mathematical realism.
Keywords Mathematical realism  Realismo matemático  aplicabilidad  applicability  estructuralismo matemático  explicaciones matemáticas  factionalism  ficcionalismo  indispensabilidad  indispensability  mathematical explanations
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DOI 10.18800/arete.201901.001
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.

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