After this book, a second volume devoted to the Ionians is expected to follow (and then possibly further ones); so, this one is meant to outline a standard for the series. For each Eleatic thinker the editors offer three sections: an introductory note, Greek (and Latin) texts with facing translation and an extended commentary. The general introduction and the sections on Parmenides and Zeno were contributed by Macé, while Brisson authored the section on Melissus. Since the third co-editor, Pradeau, plays no role in this volume, it is reasonable to expect that he will be involved in subsequent volumes in the series.

The texts offered seem rather reduced. On Parmenides’ life, work and doxai we find only a quotation from Plato and one from Diogenes Laertius (almost incredible given the increased attention now paid to the ‘naturalist wisdom’ of Parmenides); B8 DK is duly fractioned according to what our sources offer (a welcome but rare practice); the collection of texts by Parmenides includes some lines from Basilius of Caesarea that other editions usually ignore (they are meant to expand on the word hudatorizon, but have no chance to pass for a further fragment). The texts offered on Zeno are straightforward and well chosen, while the section on Melissus, more generous, differs considerably – and tacitly – not only from the canonical Diels–Kranz but also from recent reference collections such as D.W. Graham (2010), A. Laks/G.W. Most (2016) and M. Brémond (2017). One wonders why nothing is said to account for these differences, all the more since further texts on Melissus have been included in the commentary but not integrated into the corpus of sources.

The commentary comprises the bulk of the volume. The solid commentary on Parmenides (pp. 91–148) is clearly rooted in the twentieth-century scholarly tradition. The much shorter section devoted to Zeno (pp. 149–71) is marked by a considerable level of originality: the word ‘paradox’ occurs just once, the idea that Zeno devised a number of paradoxical stories has been removed, and the mathematical expansions of some celebrated paradoxes (as well as their most outstanding examinations, e.g. N. Huggett's ‘Zeno's Paradoxes’ in the Stanford Encyclopedia of Philosophy) have been ignored without a word on the rationale of these choices. Nevertheless, the treatment of Zeno deserves special attention since Macé disregards paradoxes and focuses on the possibility that Zeno's book was long or very long, as Proclus states at least three times and Simplicius once. He suggests that Zeno wrote a lot on his double arguments (‘opposed arguments’, antilogiai) without a word on the surviving dialogue with Protagoras (it is ostensibly short). Besides, it would be difficult to imagine that to the Achilles Zeno devoted one or more pages, while it is a possible assumption that 29B1–B2–B3 DK were part of a much longer series of arguments. If so, Zeno's book would have possibly consisted of two differentiated parts: a larger one, covering several opposed arguments, and a shorter one, devoted to voicing and making plausible the most celebrated paradoxical stories. Such a possibility surfaces thanks to the inspiring one-sidedness of the commentary on Zeno in this book, and it seems to have no precedent. It will certainly deserve closer scrutiny.

A sort of reticence is recurrent: there is no footnote to account for the most controversial choices made in the treatment of Zeno, nothing is said in order to go back from the interpretation of the remains of each author to the authors themselves nor in order to outline who, according to the editors, were Parmenides, Zeno and Melissus. Not to say anything suggests that, according to Macé and Brisson, there is nothing to say, i.e. that only some details, not the basic ideas of each of them, deserve refinement: this seems surprising, if only because of the unique – and impressive – competence deployed by Melissus as a connoisseur of the ‘ontological’ section of Parmenides’ poem. Indeed, that Melissus, and only Melissus, reached incomparable levels of understanding of just a section of the poem (that Parmenides’ poem included much more, in addition to the ‘doctrine’ of non-being and being, is largely attested by fragments 10–18 [or at least 10–14 and 16–18] DK as well as by dozens of testimonies) is a bare fact, although the scholarly community was and continues to be often not prepared to acknowledge it.

As a consequence, a polarisation of the attention to the ‘ontological’ section of Parmenides’ poem, much as if the poem finished with fragment 8 or 9 DK, affected not only ancient thinkers such as Gorgias, Plato and Aristotle, but also the scholarly community of the twentieth century and subsequent decades. The present commentators have nothing to say on this point either. The overall impression is that the general readership should take this book with confidence, sure to find in it nothing controversial or surprising.