Mathematics and its Applications: Philosophical Issues

The problem of applicability is daunting and multifaceted, and much about it remains unclear. As such, it has become peripheral in recent philosophy of mathematics, making way for work on a variety of smaller, more tractable issues. Significant progress has been made on at least four of these issues in recent years, presenting the opportunity to forge links between them. These issues are: extra-mathematical explanation; intra-mathematical explanation; mathematics in scientific representation; and the cognitive benefits of mathematical thought, notation, and practice. It is time to capitalise on this progress.