PHILOSOPHY 289 whole that has organismic unity. Thus Gill’s tical pattern (14 and throughout). This is put in project is something I approach sceptically. Even terms of two opposed positions, a middle path, more so because it turns out that reuniting the and the destruction of the rapprochement. All the disiecta membra that are supposed to constitute pairs of elements that served to characterize the exercise about Being is not enough. In sections of the exercise in Plato’s own descrip- practice, Gill imports huge amounts of machinery tions of it (and his summaries of the results in the from elsewhere: she has (in chapter 7) to interrupt instance he composes) are dropped from Gill’s her discussion of the crucial bit of the Sophist in description of her pattern. In fact, it is necessary order to develop and then apply a controversial for Gill to transition away from the architectonic interpretation of a passage in the Philebus. In structure suggested by Plato if her texts about many cases she relies – sometimes tacitly, Being are to fit her pattern. Yet she transitions so sometimes explicitly – on doctrines of Aristotle’s far from Plato’s descriptions to her own that I (not just his reports of doctrines of Plato or the query her claim that the texts she will reassemble Academy, but his own views on the metaphysical really do constitute a new round of the structure of sensible individuals, on actuality and Parmenides exercise. potentiality, and on the agent and patient of Even for readers for whom Gill is not credible change). Gill remarks correctly, ‘Plato does not as a hedgehog, she will still be interesting as a fox. leave his audience to their own devices … The There is much of interest in this book for those of audience must pay attention to signals of various us who do not agree with her architectonic claim. kinds in the text, which urge them to make a She treats very important passages, and her discus- connection with something said before’ (12). So sions of many are intricate and interesting. I the question for each reader is whether, as we do believe that each of them should be judged on its that, the interpretation offered in this book is own merits. The process of doing this is one that confirmed or disconfirmed. The intellectual readers may profitably undertake for themselves. activity involved in responding to Gill’s sugges- CONSTANCE MEINWALD tions thus amounts to the valuable and difficult University of Illinois at Chicago activity of doing philosophy with Plato. [email protected] Gill represents her project as grounded in the adjuration in the Parmenides to repeat the exercise demonstrated there with variations in the subject: HORKY (P.S.) Plato and Pythagoreanism. she proclaims repeatedly that the structure of the Oxford: Oxford University Press, 2013. Pp. Parmenides exercise provides the backbone of her xxi + 305. £47.99. 9780199898220. book (at 3 and throughout). Because of this, I find doi:10.1017/S007542691500107X it very awkward that she does not respect Plato’s own lengthy and granular description of the In spite of the title, the author is aware of the fact exercise at Parmenides 135d7–36c8. Given her that his project does not provide a comprehensive interpretation of the terms appearing in this account of all the ways Pythagoreanism might passage (chapter 2), Plato’s description must be have influenced Plato’s philosophy. His book is an seriously miscomposed. For Plato’s description so important contribution to the history of the mathe- interpreted (a) mentions only half the sections of matic Pythagoreans, in the light of a great number argument that are produced in the demonstration of testimonia. that is given explicitly to illustrate the method, (b) In the first half of his work, Horky presents describes less than the full contents of each section sound evidence that shows that Pythagoras and his it does mention and (c) emphasizes through followers had a rival group of ‘pretenders’, who, tedious repetition a distinction that does not point according to Isocrates and Plato, practised their to anything important about the demonstration’s way of life in order to achieve fame. However, results. In being committed to a reading of this key Timaeus of Tauromenium believes that the text in which these methodological remarks do not ‘exoterics’ who published the Pythagorean secrets adequately describe the demonstration that is did so in order to denunciate the oligarchical given to illustrate them, Gill seems to me to Pythagoreans and to defend the democratization of violate a basic interpretative constraint. arcane Pythagorean knowldege. Horky suggests Instead of finding an adequate interpretation that ‘there might be some overlap’ between of the description of the exercise in Plato’s text, Aristotle’s mathematic Pythagoreans and Timaeus’ Gill manufactures her own description of a dialec- ‘exoteric’ Pythagoreans (123). He also thinks that

Downloaded from https://www.cambridge.org/core. University of Athens, on 25 Sep 2021 at 16:22:16, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S007542691500107X 290 REVIEWS OF BOOKS Aristotle’s division into acousmatic and mathe- brilliant fire’ who is credited with passing down matic Pythagoreans, ‘reflects actual division within dialectics to human beings, is likely to be the community’, against L. Zhmud’s arguments for Hippasus, while Pythagoras ‘must remain a a much later dating in the first century AD possible referent’ (259). As for ‘the forefathers’, (Pythagoras and the Early Pythagoreans, Oxford he understands that the term refers to Philolaus 2012, 174). Horky proposes that Iamblichus and Archytas. However, it seems difficult to excerpted a section from Aristotle’s lost works on understand how Pythagoras could be a referent of the Pythagoreans that accounts for the different Prometheus here if Horky agrees with W. Burkert pragmateiai of both groups which, he proves, were (Lore and Science in Ancient Pythagoreanism, available in Athens a generation before Aristole Cambridge MA 1972) and C.A. Huffman was writing, on the basis of the testimonia of (Philolaus of Croton: Pythagorean and Isocrates, Aeschines and Antisthenes (95), and Presocratic. A Commentary on the Fragments and concludes that the mathematicians are the same as Testimonia with Interpretive Essay, Cambridge the ‘so-called’ Pythagoreans of Metaphysics A, 1993) that he is not an early mathematician who used demonstration and established developing limiters and unlimited things (229). relationships of ‘similarity’ between numbers and On the other hand, in my view, the reference to the perceptibles. In his view, the methodological ‘brilliant fire’ does not need to be taken literally. fissure is due to the intellectual revolution of Be that as it may, the deep examination of Hippasus of Metapontum in the fifth century. Plato’s ‘heurematographical resources’ gives In the second half of his book Horky focuses sufficient support for Horky’s thesis that Plato on Plato’s testimonia. He argues that in the changed from a critical view of the mathematic Cratylus Philolaus is taken as ‘an antecedent to Pythagoreans in the Republic towards a much Plato’s argument that ontological stability is a more positive view of his antecessors, as he necessary condition for the possibility of happened to value their mathematic demonstra- knowledge’, while Epicharmus is rejected as a tions ‘by appeal to sensible objects’ in the representative of the fluxism employed by Philebus and Timaeus. Cratylus (167–68). In conclusion, this book turns out to be an One of the merits of the book is the convincing essential tool for anyone interested in the history argument that Philolaus anticipated Plato’s theory of mathematic Pythagoreanism. of participation in the Cratylus and that Plato BEATRIZ BOSSI obtained from him the vocabulary and rudimental Universidad Complutense de Madrid conceptualization of subsistent entities and the [email protected] concept of classification of essential properties. The author believes that Philolaus’ view that things in the cosmos could not have come to be if their LEROI (A.M.) The Lagoon: How Aristotle being did not pre-exist is essential to the Invented Science. London: Bloomsbury development of Plato’s theory of the Forms in the Circus, 2014. Pp. 501, illus. £25. 97814088- Phaedo (185) where ‘Plato sought to improve on, 36200. and not simply to reject, Philolaus’s unclear doi:10.1017/S0075426915001081 demonstrations’ (199). Though Horky is persuaded that Socrates seeks to prove the immortality of the This is an extraordinary book. Bringing to our soul through, in part, a metaphysical analysis of the awareness a fecund lagoon on the island of Philolaic ‘proper kinds’ (the Forms of the Even and Lesbos, Leroi attempts to uncover numerous the Odd) (186) the argument remains obscure. aspects of Aristotle’s biological investigations In the final chapter, the author examines the there. The volume tries to be many things at once way Plato camouflages his critical developmental – a smart coffee-table book, an accessible intro- responses to his competitors (Sophists such as duction to Aristotle’s biology for a general Protagoras and Hippias and the mathematic audience, a contribution to scholarship in the field Pythagoreans Philolaus and Archytas) by using of the history of zoology and a personal account of ‘heurematographical myths’ in the Protagoras, a deeply felt intellectual connection. This is what Republic, Phaedrus, Statesman, Philebus and makes the book so singular but what also leads to Timaeus. After a long and detailed examination of some of its difficulties. Like the elephant’s trunk the meaning of Philebus 16e5–d4, Horky (137–40), although fantastically versatile, there is concludes that the ‘Prometheus along with a most a limit to how many functions it can serve.

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