Between Weasels and Hybrids: What Does the Applicability of Mathematics Tell us about Ontology?

What are the implications of the significant and ubiquitous role of mathematics in physical explanations? I shall consider two answers to this question. The first takes this role to imply the existence of mathematical objects; the second takes it to imply that certain physical quantities have a ‘hybrid nature’. I shall close off one line of defence with regard to the first, by argu- ing that understood in its appropriate metaphysical context, this line loses its force. A similar focus on the relevant metaphysics allows us to block the second. The conclusion drawn is that at- tention needs to be paid to these metaphysical considerations if the debate over the role of mathematics is to move forward.