 The nineteenth-century physicists Kirchhoff and Mach objected that causal notions are “infected by vagueness” (Kirchhoff 1876: v, my translation) and “lack the precision” (Mach 1905: 278, my translation) of the mathematical functional dependencies associated with physical theories. This criticism is echoed in the twenty-first century by John Norton (2003) and John Earman (2011), among others.