In the previous chapter, I identified a serious problem with Badiou's ontology in its failure to properly account for the difference between ontological and non-ontological (empirical) situations. I attempted to correct this deficiency through a foray into the philosophy and cognitive science of mathematics, with the intent of naturalising Badiou's understanding and employment of mathematics. In order to flesh out in more detail what this naturalisation entails it is time to shift gears and turn, in this chapter and the next, to a problem that I have left, so far, under-examined: realism.