Estructuralismo, ficcionalismo, y la aplicabilidad de las matemáticas en ciencia

Abstract

This article has two objectives. The first one is a review of some of the most important questions in the contemporary philosophy of mathematics, including: 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 topic that guides these reflections is the debate between mathematical realism and anti-realism. The second objective of this article 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 objective. To this end, three aspects of the problem of the applicability of mathematics are distinguished: the (mere) utility of mathematics in science; the unexpected utility of some mathematical theories; and the apparent indispensability of mathematics in our best scientific theories, and in particular, in our best scientific explanations. Then I argue that none of these aspects constitutes a reason to adopt mathematical realism.