Applying unrigorous mathematics: Heaviside's operational calculus

Abstract

Applications of unrigorous mathematics are relatively common in the history and current practice of physics but underexplored in existing philosophical work on applications of mathematics. I argue that perspicuously representing some of the most philosophically interesting aspects of these cases requires us to go beyond the most prominent accounts of the role of mathematics in scientific representations, namely versions of the mapping account. I defend an alternative, the robustly inferential conception (RIC) of mathematical scientific representations, which allows us to represent the relevant practices more naturally. I illustrate the advantages of RIC by considering one such case, Heaviside's use of his unrigorous operational calculus to produce and apply an early generalization of Ohm's law in terms of “resistance operators.”