The authors address the following question: “Why is it that mathematics is so useful in empirical science?” They first consider a popular view that is commonly dubbed a “structural mapping” account: “One answer is simply that mathematics is a rich source of structures and therein lies its utility. Some mathematical structure is either designed to, or otherwise found to, accurately capture the important structural relations of an empirical set up, and we can thus read off important facts about the empirical set up from the mathematics” (Bueno and Colyvan 2011: 345).

Such doctrines are predicated upon a “warehouse” conception of mathematical activity; left to their own devices, mathematicians build up a large fund of “structures,” from which physical scientists can freely choose the particular appliances that suit their households. This presumption is central to the argument of Mark Steiner's The Applicability of Mathematics...

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