 Infinitesimals, differentials, evanescent quantities and the like coursed through the veins of the calculus throughout the eighteenth century. Although nebulous—even logically suspect—these concepts provided, faute de mieux, the tools for deriving the great wealth of results the calculus had made possible. And while, with the notable exception of Euler, many eighteenth century mathematicians were ill-at-ease with the infinitesimal, they would not risk killing the goose laying such a wealth of golden mathematical eggs. Accordingly they refrained, in the main, from destructive criticism of the ideas underlying the calculus. Philosophers, however, were not fettered by such constraints.