Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King (review)

Diogenes Laertius described Archytas of Tarentum as "the one who rescued Plato by means of a letter, when he was about to be killed by Dionysius," adding that "he was also admired among the multitude for every virtue" (Lives of the Philosophers 8.79, trans. Huffman, 256). Archytas is known to historians of ancient philosophy for his connection to Plato, although the precise nature of the relationship is, as Huffman explains, not entirely clear. Archytas' work on mathematics and harmonics and his thought experiment regarding the limits of the universe have attracted the attention of scholars particularly interested in history and philosophy of science. But prior to this volume, there has been no book-length study of Archytas of Tarentum (as Huffman notes, O. F. Gruppe's Über die Fragmente des Archytas und der ältern Pythagoreer [Berlin, 1840] was not concerned with understanding Archytas' thought but with arguing that no authentic fragments survive). Huffman's work will serve as the definitive study of Archytas.

Overall, Huffman presents a very carefully considered account of Archytas' life, his work, and his influence. The study is meticulous in its detail, and Huffman writes engagingly and with humor. Furthermore, the merit of the volume is not confined to its usefulness for understanding Archytas and the history of Pythagorean thought. The subtitle of the volume—Pythagorean, Philosopher, and Mathematician King—only hints at the wealth of topics dealt with in the book. Through his detailed commentary, Huffman has produced a study that will be valuable for historians of philosophy, science, mathematics, and music who are more generally interested in problems such as the geometrical duplication of the cube and the division of the tetrachords in harmonics. Huffman's commentary engages closely and critically with the literature, providing an up-to-date review of relevant scholarship as well as fresh interpretations of some of the material. His thorough treatment of numerous issues and problems will be a valued resource for readers and encourage further discussion and study.

Huffman's study of Archytas is divided into three parts: the first consists of several introductory essays concerned with "Life, writings, and reception," "The philosophy of Archytas," and "The authenticity question." The second part is devoted to the genuine fragments, and the third to the genuine testimonia; both of these provide the texts, translations, and very detailed and enormously useful commentary. One appendix deals with spurious writings and testimonia; another focuses on Archytas' name.

As Huffman explains, the texts usually regarded as spurious far outnumber those that are thought to be genuine: only about one-hundred lines of text attributed to Archytas and printed in Diels-Kranz (Die Fragmente der Vorsokratiker (6th ed. [Dublin and Zürich, 1952], henceforth DK) are usually regarded as genuine, while over twelve-hundred lines of almost certainly spurious texts are collected in H. Thesleff, The Pythagorean Texts of the Hellenistic Period (Åbo, 1965). Huffman, who clearly describes his criteria of judgment (97–100, and in the relevant portions of the commentary), accepts basically the same canon of four fragments as DK, although, as he explains, for somewhat different reasons, and he supplements the testimonia with some overlooked by DK. Tackling the problems posed by the "hodgepodge" of Attic, Doric, Lesbian, and Epic forms preserved in the manuscripts, Huffman has adopted the general approach of DK, only printing the Doric forms when they are found in manuscripts or strongly suggested by manuscript readings (xiv).

Archytas was renowned in antiquity for a number of reasons. He was credited, controversially, with having intervened on Plato's behalf in order to rescue him from Dionysius II of Syracuse. He was also elected stratēgos numerous (arguably seven) times in Tarentum. And he was credited with having offered solutions to problems in geometry and harmonics, as...