The received view of computation is methodologically bifurcated: it offers different accounts of computation in the mathematical and physical cases. But little in the way of argument has been given for this approach. This paper rectifies the situation by arguing that the alternative, a unified account, is untenable. Furthermore, once these issues are brought into sharper relief we can see that work remains to be done to illuminate the relationship between physical and mathematical computation.
I would like to thank Stewart Shapiro, Richard Samuels, and Chris Pincock for invaluable feed-back and support throughout the writing of this paper. Additional thanks go to Ethan Brauer, Steven Dalglish, Preston Lennon, and Damon Stanley for helpful comments and discussion. Early versions of this paper were presented to audiences at the 2019 Ohio State Fink Ceremony and the 2019 meeting of the Society for Exact Philosophy. I wish to thank the members of each audience for their questions. Finally, I wish to thank three anonymous referees whose insightful comments and suggestions significantly improved the final version.