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Two concepts of applied mathematics: reflective and performative

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I offer a novel distinction between two concepts of applied mathematics. The first, reflective applied mathematics, requires the target for representation or explanation be prior and unchanged by applying mathematics. The second, performative applied mathematics, produces or modifies its target of application via mathematical realization. I argue that the contemporary philosophical accounts of applied mathematics are primarily successful in formulating the reflective concept. By presenting two examples of performative applied mathematics, from computer science and economics, I show the limits of reflective applied mathematics to capture these instances. I then characterise two necessary conditions for performative applied mathematics and sketch how this distinction carries significant normative implications concerning central debates in philosophy of science as well as ethics of artificial intelligence.

This talk is part of the Departmental Seminars in History and Philosophy of Science series.

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