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.

This chapter is in many ways the culmination of the book. It applies the analysis of chapters 3 and 4 to the structure of Parmenides’ Fragment 8, and shows how Parmenides uses the blueprint of Circe’s hodos in Odyssey 12 to craft what we would call an extended deductive argument; in this, it develops the discussion of Chapter 5. It cashes out the implications of Chapter 1 by showing how Parmenides takes advantage of rut road imagery to articulate what we would call a notion of logical necessity, and by showing how the durative and telic components of the word hodos define the teleological shape of his arguments. Building on Chapter 2, I set out the traditions Parmenides developed by creating a discursive structure that is both systematic and argumentatively rigorous. I also examine how the poem’s complex relationships between story, plot, and the time of narration plays a crucial role in bestowing on Parmenides’ arguments, and on demonstration more generally, an ostensibly timeless quality. Finally, I assess my conclusions about Parmenides’ invention of deductive argumentation in relation to other scholars’ discussions of his arguments, and clarify what my argument does not claim to offer – and what it insists on.

This chapter applies the analysis of the preceding chapter to the hodos that Circe spells out in Odyssey 12, which I argue serves as a discursive template or blueprint for Parmenides in his ‘Route to Truth’. In addition to building on the notions of the rhetorical schema and types of dependence developed in Chapter 3, I extend my analysis of the discursive architecture governed by the hodos to include the krisis or exclusive, exhaustive disjunction which is a central feature of Od. 12.55–126. I also show how the hodos in Odyssey 12 has distinctive features – including the use of modally charged negation and unusually lengthy description sections followed by argumentatively rich units of text – which link it to Parmenides’ poem but differentiate it in crucial ways from other texts and phenomena, including general patterns of Homeric deliberation, polar expressions, the crossroads in Hesiod’s Works and Days, and the so-called Orphic gold tablets.