A common metaphor compares mathematics to a building: The axioms are its foundation, the lemmas and theorems and corollaries are its stones and bricks, logical deduction is the mortar or cement that holds them together. Once it is agreed, as it came to be in the nineteenth century, that mathematics is to be organized as a deductive science, with new results logically deduced from old, and ultimately from axioms, certain questions, not themselves straightforwardly mathematical, about the choice and status of the axioms to be adopted then arise. These are metaphorically called “foundational” questions by philosophers.