Abstract
This paper argues that Plato’s gigantomachia is simultaneously concerned with first-order arguments about metaphysics and epistemology and with second-order arguments that reflect on the impact of ethical components, argumentative strategies and theoretical assumptions in the conversation. This complex argumentative structure reveals, I suggest, an organic and systematic conception of philosophy where all the elements are interdependent. This interpretation has four consequences, two at the second-order level, and two concerning the first-order arguments. First, it shows that there are methodological and ethical requirements without which philosophy is impossible. Second, it shows that the text does not refute materialism but tries to reflect the necessary conditions to consider possible the existence of incorporeal beings. Third, it argues that the text assumes a conception of knowledge where knowing something is a complex activity composed of two causal relations. Finally, it offers a new interpretation of the overall conclusion of the passage.
Second-order necessary conditions for optimality in nonsmooth nonlinear programming