It is somewhat paradoxical that the Presocratics, so often lauded as the forefathers of philosophy, would not have described themselves using any of the Greek cognates of that word, nor do their surviving fragments bear much formal resemblance to philosophical texts from Plato onwards. Nowhere is this paradox more salient than in the case of Parmenides, a figure widely recognised as authoring the earliest attested deductive arguments, but who chose to present them in the form of a mystical poem presented largely in the persona of an anonymous goddess. Much post-war anglophone scholarship on the Presocratics has been devoted to treating them seriously as philosophers, reconstructing and evaluating their arguments with great ingenuity and insight (note, especially, J. Barnes, The Presocratic Philosophers [1979]). The scholarly pendulum, however, has begun to swing in another direction, and more recent work has tended to foreground the importance of the cultural – and, in particular, literary – contexts of these shadowy figures, opening historically cogent perspectives that may be overlooked by a more narrowly philosophical focus. Although there have long been commentators who have paid due attention to these aspects – and with regards to Parmenides, A. Mourelatos's The Route of Parmenides (1970) must be given pride of place –, this sort of approach has gained momentum in recent years, with contributions such as S. Tor's Mortal and Divine in Early Greek Epistemology (2017) and M.M. Sassi's The Beginnings of Philosophy in Greece (2018). F.-W. joins this trend with this well-researched and elaborately argued monograph on Parmenides.

Accepting the traditional view of Parmenides’ momentous role in the development of deductive argumentation – the philosophical ‘Demonstration’ of the title –, F.-W. argues that Parmenides’ chief inspiration for this achievement came from Circe's instructions to Odysseus in Odyssey 12, especially with her deployment of the word and concept of hodos. This, as F.-W. is well-aware, is not an original claim: it was advanced by E. Havelock as long ago as 1958 (HSCPh 63) and refined by Mourelatos. But F.-W.'s contribution lies in the level of detail in which he draws the comparison, in the framework he applies (derived from M. Foucault's Archaeology of Knowledge [1972]) and in the application of another body of evidence that has seldom (if ever) been put to use in the study of ancient philosophy, the archaeology of ancient Greek roads. Rather than offering new interpretations of Parmenides’ philosophy or appreciation of his literary qualities (though he is full of praise for this often-maligned aspect), F.-W. hopes to have shed new light on why Parmenides used the term hodos, what ‘resources’ it offered him and how it might have ‘influenced him in turn’ (p. 275). So, this study is not so much a history of philosophy or literary criticism (though F.-W. is a very literary reader) as a history of ideas.

There is much to admire. F.-W. has taken on board a wide range of scholarship from across the fields of philosophy, literature, archaeology, history and critical theory in English, French, German, Italian and modern Greek, dating from the nineteenth century onwards. I found the sections on the archaeology and social context of ancient Greek roads (pp. 32–48) particularly instructive: unlike modern roads, according to F.-W., these had a rut on either side into which the wheels of vehicles fitted, thus facilitating a straight and steady course but hindering turning, something that may underly Parmenides’ use of the road-metaphor for the strictly linear sequence of arguments in the Way of Truth. The bulk of the book is devoted to Parmenides’ relationship to the Odyssey, and here, too, there are strengths. F.-W.'s attempt to describe this relationship with greater precision than the occasionally vague language of ‘influence’, ‘intertextuality’ or ‘reception’ is laudable, although I was not convinced that the application of the Foucauldian ‘rhetorical schema’ as a unit of comparison (pp. 119–45, 161–3) generated any more precise conclusions than more familiar narratological or intertextual terminology. Whilst the echoes of Circe's instructions are well-known (at least to those who are interested in that sort of thing), F.-W. presents an original and convincing point when arguing that Parmenides, in the Way of Truth, reverses the ‘discourse modes’ of the Homeric model (pp. 208–9): Circe describes a state of affairs using generalising present tense verbs in the third person to justify second-person statements and imperatives that outline possible courses of action (i.e. ‘Charybdis is that way and she is terrible, so do not go there’); by contrast, Parmenides’ goddess uses second-person utterances (fr. 2, ‘you could not know or indicate what is not’) to support the third-person description of a state of affairs (fr. 8, ‘so the only account left is what is and it has the following qualities …’). This contention does, I believe, provide some elucidation as to precisely how Parmenides adapted the sorts of practical arguments found in Homer to form his a priori deductions.

There are, however, criticisms to be made. For all its disavowal of the notion of a ‘Greek Miracle’ (pp. 3–4), the book maintains a traditional muthos to logos narrative, according to which genealogical forms of explanation give way to ones based on more abstract argumentation (p. 241). That is not a flaw per se, but the diachronic, progressive narrative proposed is vulnerable to the charge of treating absence of evidence as evidence for absence, especially when we are dealing with such fragmentary authors in a period with such a small number of surviving texts: Parmenides may present the earliest attested deductive arguments, but his achievement might seem less striking had the complete works of Xenophanes or the Milesians survived. F.-W. argues that the combination of ‘discursive systematicity’ and ‘argumentation’ that we find in Parmenides is absent from those earlier Presocratics (pp. 226–30), but there the evidence is lacking, and certain testimonia seem to indicate that Xenophanes offered arguments of some sophistication (e.g. DK 21A31). F.-W. makes this contention as he wants to argue that the catalyst for Parmenides’ development of these features was, rather than anything else, Homer's use of hodos-imagery. Thus, we are told that Parmenides’ method is ‘made possible by … the figure of the hodos’ (p. 281). But since one can deploy philosophical demonstration without the use of such a figure, I cannot help but feel that this argument would have been more convincing had it been expressed in a weaker form (e.g. ‘Parmenides presents what look like deductive arguments, and, among other possible sources of inspiration, he used Homer to do it’) or had a wider range of comparanda been enlisted to support it, encompassing, in greater detail than we find here, the various arguments made in Homer, Hesiod and Greek lyric poetry. At times it seems that F.-W. is suggesting that it is only the hodos that ‘allows for the expression of even quite abstract, ostensibly permanent relations, and not merely the depiction of actions’ (p. 248); but one finds these features in the gnomic statements that abound in early Greek literature.

The final chapter concerns possible connections between Parmenides and the sēmata and Odyssey 23, but rather than tease out the potential significance of such points of contact, the last few pages (pp. 298–300) reflect on how such questions do not admit of the kind of certainty afforded by Penelope's test of Odysseus or assumed by the goddess for the Way of Truth. I would have appreciated a more explicit statement of the book's aims and achievements than this kind of critical aporia.

The style is lively, with typographical and verbal flourishes that, depending on the reader, will delight or irritate (e.g. ‘K/Crisis’, p. 298; ‘How imag(in)e it?’, p. 291; ‘The Fixity of the Sign Signs Fixity (Fixedly)’, p. 289). Overall, this is an urbane and thought-provoking discussion that will be read fruitfully by scholars from a variety of disciplines, even if its boldest statements do not always stand up to scrutiny.