The chapter asks if the first part of the Parmenides (including the “Third Man”) shows that Plato abandoned Platonic forms, and argues instead that Plato’s “Third Man” passage is not an indirect proof of anything: it simply shows the youthful Socrates not able to defend his views on forms. The exercise Parmenides then prescribes and demonstrates is the way forward Plato provided. It leads us to distinguish two kinds of predication, corresponding to two kinds of facts about forms. Better-organized thinking about forms lets us reject the notion that to perform their work in Plato’s theory, they must be perfect exemplars along the lines of “the Platonic ideal of the banana split.” This dispels the underlying problem which led to confusion over the “Third Man.” We can face down analogues of that argument for any form, from the Fox and Triangularity to Likeness and the Beautiful. This interpretation emerges from detailed construal of the text, taking account of both its literary and overtly philosophical aspects; the chapter brings together background for Plato’s agenda in his previous works, in the works of Anaxagoras and the historical Parmenides, and in Greek usage.

In Plato’s dialogues, Socrates calls things like justice, piety, and largeness “forms.” In several of these dialogues, he makes clear that forms are very different from familiar objects like tables and trees. Why, exactly, does he think that they differ and how are they supposed to do so? This chapter argues that in the Phaedo Socrates does not assume that they are different, but rather, over five stages of the dialogue, provides an account of how and why they do so. To fully understand the claims made in the first stage, one must look to the next stage, and so on until the final stage. Socrates' ultimate reason for distinguishing forms from ordinary objects does not depend on our intuitions about things like justice and largeness, nor on the distinction between universals and particulars. Ultimately, forms cannot be ordinary objects because the form of f-ness must cause every f-thing to be f, but no ordinary object could serve as such a cause. They cannot do so because they have multiple parts and are receptive of opposites; by contrast, the form of f-ness must be simple and unchanging, since it causes every f-thing to be f.

This introduction has three goals: to locate this book’s arguments in contemporary scholarship on Parmenides, to outline its methodology and structure, and to establish the stakes of the project as a whole. The first considers Parmenides’ invention of extended deductive argumentation and the practice of demonstration – the central topic of this book – as a relic of the ‘Greek Miracle’ paradigm; it also addresses discussions of Parmenides’ use of poetry and his relationship to Homer. The second addresses distinctions between actors’ and observers’ categories and between reasoning and discourse, and explores the Foucauldian discourse analysis that anchors the book’s treatment of the relationship between Parmenides and Homer. The third requires setting out what this book does not intend to do in order to specify its main contribution: providing an account of how Parmenides’ use of the image of the hodos helps him invent extended deductive argumentation and the practice of demonstration. The Introduction sketches out the three axes of the book’s argument: an exploration of the physical reality of archaic and classical Greek roads, a discussion of the semantics of the word hodos, and an articulation of the relationship between Parmenides’ and Homer’s poems.

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.