Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. Here Penelope Maddy proposes a particularly austere form of naturalism called 'Second Philosophy'. Using the persona of an idealized inquirer - the 'Second Philosopher' - she constructs a properly second-philosophical line of thought which she then practises in reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized.