Abstract: Outlines a physicalistic version of set theoretic realism (a sort of monism), and compares and contrasts it with Field's nominalism, with structuralism, and with modalism. I conclude that, despite metaphysical differences, versions of all these views share the new challenge raised in Ch. 4: how are new axiom candidates to be rationally evaluated?

Keywords: Field, modalism, monism, nominalism, physicalism, set theoretic realism, structuralism,