Plato and Pythagoreanism is a fascinating, intelligent, and effective book. Its aim is to explain the methodology and content of the philosophical speculations of the so-called μαθηματικοί Pythagoreans, and accordingly to detect some instances of its presence in and influence on Plato’s philosophy.
As a first step (chapter 1, 3–35), Horky convincingly identifies the μαθηματικοί with οἱ καλούμενοι Πυθαγόρειοι of Aristotle’s Metaphysics and determines their πραγματεία: they inquired into the διότι of things (i.e. mathematical objects) and referred the phenomena to them by means of demonstrations. However, it is difficult to elaborate this description if one considers only the traditional sources, as Horky points out by reference to Hippasus, who is usually regarded as the first μαθηματικός. In chapter 2 (37–85), in fact, thanks to a careful analysis of the most important doxographical sources, Horky shows that ancient testimonies concerning Hippasus depend on the historiographical tradition that originally stems from the Old Academy, and which was widely made use of in the following centuries (as was the counter tradition of Aristotle and Theophrastus). This testifies to the necessity of supplementing the doxographical inquiry with a new perspective. Accordingly, in chapter 3 (85–124) Horky develops an account of democratic rebellions in southern Italy in the period of ca. 473–53 BCE by focusing mainly on the political historiography of Timaeus of Tauromenium: some Pythagoreans, led by Hippasus, upheld democratic positions against oligarchic governments that other Pythagoreans persisted in defending, and at the same [End Page 837] time promoted a diffusion of philosophical knowledge. This opposition reflects what subsists between μαθηματικοί and ἀκουσματικοί and mirrors the contrast between an exoteric conception of science and an esoteric one. Thus, Horky posits a new philosophical, political and “ideological” description of the mathematical Pythagoreans: they searched for the διότι of things and its relation to the phenomena by means of demonstrations, and at the same time engaged in a “democratization” of knowledge, both in the field of science and of politics.
This is the basis for the second part of the book, which is devoted to the influence and presence of mathematical Pythagoreanism in Plato’s works. Horky again applies an original approach and starts by detecting a first instance of mathematical Pythagoreanism in the Cratylus (chapter 4, 125–66). At 401b–d a Pythagorean approach (that of Philolaus) is set against another (that of Epicharmus, whose Pythagorean affiliation and doctrines are deeply analysed by Horky): accordingly, Plato ascribes to the former the idea that the essences of (ontologically stable) things can be grasped, and to the latter an association between the essence and the flux of things. A similar exegetical perspective is then applied to some key passages of the Phaedo (chapter 5, 167–99). In particular, Horky identifies in the account of causality at 96e–97c an implicit reference to a “growing argument” ascribable to Empedocles (who, according to Timaeus of Tauromenium, is considered a mathematical Pythagorean; this claim should probably have been discussed more thoroughly). This perspective is extended to 101b–c (and then at 103e–104c), where Plato posits a model of formal causation. Such a model, too, has (as Horky argues) as one starting point a mathematical Pythagorean theory: by introducing ideas, Plato develops the perspective of Philolaus, who felt the need for a stable ground of being. But mathematical Pythagoreanism also plays an important role in Plato’s dialectic and cosmological theories, as Horky emphasizes by means of a noteworthy analysis of Plato’s heurematological myths (chapter 6, 201–64). In fact, in his later dialogues Plato refers to “first discoverers,” which must often be identified with Pythagoreans, as making positive contributions to philosophy: in the Philebus the “certain Prometheus” is Hippasus and the “forefathers” are Archytas and Philolaus, while in the Timaeus Plato relies on Pythagorean principles (both mathematical and empirical, above all with respect to music) and makes use of them within his cosmology.
The impressionistic synthesis of a review is not able to cover the quantity of sources and references that Horky carefully considers, and may give only a general idea of the multifaceted method Horky...