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 mathematic...

Este artículo tiene dos objetivos. El primero es una revisión de algunas de las preguntas más importantes de la filosofía de las matemáticas contemporánea, incluyendo: ¿Cuál es la naturaleza de los objetos matemáticos? ¿Cómo adquirimos conocimiento acerca de estos objetos? ¿Deben las afirmaciones matemáticas interpretarse de manera diferente a las afirmaciones ordinarias?, y finalmente, ¿cómo se explica la aplicabilidad de las matemáticas en la ciencia? El tema que guía estas reflexiones es el debate entre el realismo matemático y el antirrealismo. El segundo objetivo de este artículo es discutir cinco argumentos que usan la aplicabilidad de las matemáticas en ciencia para justificar el realismo matemático, y mostrar que ninguno de ellos consigue su objetivo. Con esta finalidad, distingo tres aspectos del problema de la aplicabilidad de las matemáticas: la (mera) ut...

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 mathematic...