The previous chapter locates Parmenides in his physical and linguistic contexts; this chapter locates him in his poetic, intellectual, and cultural milieux. It argues that we need to understand Parmenides’ poem in light of the late archaic revolution in the way that Homer was conceptualized. This chapter examines the epistemological framework Parmenides inherits from Hesiod and Xenophanes in considering the nature of human enquiry; the way that other poets in the late archaic period make use of the newly emergent figure of Homer and the corpus of Homeric poetry, especially with respect to their claims to knowledge and their relationship to the Muses; and the ways that scholars have characterized developments between Homeric poetry and the poetry of the late archaic period. I show how Parmenides uses the resources this Homeric tradition offers to launch a multipronged response to the challenges set down by Hesiod and Xenophanes. These include: reinitiating contact with a Muse-like figure in the proem; the use of crossroads imagery to articulate fundamental distinctions; ceding the voice of the poem to the unnamed goddess; the use of argument; and the return to the privileged poetic form of epic dactylic hexameter.

This chapter outlines the key methodological framework to be used to analyse Homer and Parmenides and detail the specifics of their relationship. I first set out the terms that Foucault develops in his Archaeology of Knowledge, and then detail the ways that these terms do and do not make contact with established topics of classical and Homeric scholarship, including text-types and discourse modes, A-B-C patterns, the oimē and theme, and catalogues and catalogic discourse. I use the hodos that Circe spells out in Odyssey 10 as a sample text to analyse according to this methodology; the result is a clearly defined textual architecture that the image of the hodos governs more generally.

This chapter pivots to Parmenides’ poem by examining at a more general level the close intertextual connections with Odyssey 12. I then examine in close detail how the krisis or exclusive, exhaustive disjunction in Parmenides’ Fragment 2 bears a close resemblance to the exclusive, exhaustive disjunction in the hodos that Circe spells out in Odyssey 12; I also detail important differences between Parmenides’ and Homer’s uses of this disjunction. Finally, I explore the importance of this disjunction for Parmenides’ groundbreaking extended deductive argument and, especially, its role in the practice of demonstration.

This appendix addresses Parmenides’ Fragment 5, which has sometimes been taken as a challenge to the linear, hodos-like structure of Parmenides’ argument. I establish the matrix of possible readings this fragment allows and show how this framework can organize different interpretations of it offered by previous scholars. Finally, I make clear that none of these readings of Fragment 5 undermines the argument made in the course of this book.