Following Burkert’s magisterial Lore and Science in Ancient Pythagoreanism (Harvard University Press, 1972), a consensus emerged that Pythagoras was not a mathematician or scientist but rather an expert on religious ritual and the fate of the soul, who founded a way of life. A set of taboos governed almost all aspects of life and Pythagoreans were divided into those who followed them without asking for any explanations and those who learned the reasons for them and who, unlike Pythagoras, did produce the first rational Pythagorean cosmology (Philolaus) and became the first Pythagorean mathematicians (Hippasus and Archytas). Leonid Zhmud’s new book (a revision and expansion of his 1997 book, published in German) provides a barrage of important challenges to this view. Since Zhmud has an enviable mastery of the sources for and scholarship on Pythagoreanism, any serious scholar of ancient Greek philosophy will have to confront these challenges and either yield to Zhmud’s position or be ready to show where he has gone astray.
Despite its title, the book is not really an overview of the philosophy of Pythagoras and the early Pythagoreans but rather an argument for a series of theses about the nature of those philosophies. If the book were an overview of early Pythagoreanism, there would surely need to be, e.g., a section devoted to the astronomical system of Philolaus, the best attested early Pythagorean astronomical system. But, while Zhmud refers to that system frequently, he never attempts to present a coherent account of it. The book is full of bold new theses. One repeated claim is that there is no development from myth to reason in Pythagorean philosophy. Most of the mythical elements are added in the later tradition. The exception is Pythagoras himself. He was a complex figure who had both a religious and a scientific/mathematical side. The surprise is that, while Pythagoras himself believed in metempsychosis, taught a way of life that involved some religious notions and claimed to be able to perform miraculous deeds, there is no trace of such ideas in any other early Pythagorean. Nor were the Pythagoreans divided into acusmatici, who followed the superstitious maxims known as acusmata, and mathematici, who emphasized scientific study. This division was invented in the second century AD. We have no evidence that any Pythagorean lived in accordance with the maxims. They were instead a literary phenomenon, which grew by accretion in much the same way as something like the Hippocratic corpus grew around the name of Hippocrates. Both the famous tetraktys and the idea that ten is the perfect number arose not among the early Pythagoreans but rather in Plato’s Academy.
Many of the features of Zhmud’s account of Pythagoreanism flow from the way in which he determines who counts as a Pythagorean. He includes a number of figures that have not typically been considered Pythagoreans. Zhmud argues against inclusion on doctrinal grounds because this begs the question of what doctrines should be counted as Pythagorean. Instead he starts with individual Pythagoreans and sees what their views and interests were. We can identify individual Pythagoreans from the list of Pythagoreans at the end of Iamblichus’ On the Pythagorean Way of Life, which was taken from a well-informed early source, Aristoxenus. Zhmud comes to the surprising conclusion that the Pythagoreans were so varied in their interests that it makes little sense to talk about a shared Pythagorean philosophy (e.g. p. 394). When Zhmud talks about Pythagoreans he is talking about Menestor, Iccus, Hippon, Milon and Alcmaeon as much as more usual Pythagoreans such as Hippasus, Philolaus and Archytas. For Zhmud there is no common element that unites all Pythagoreans; he invokes Wittgenstein’s notion of a family resemblance. This produces the paradox that the Pythagoreans have no common characteristic except that they are Pythagoreans. I confess that this makes no sense to me. Aristoxenus surely had some criterion according to which he included Pythagoreans on his list. Presumably he knew that they belonged to a Pythagorean brotherhood and lived a recognizably Pythagorean way of life. Zhmud might agree to the first part of this statement. He stresses that the Pythagorean groups were hetairiai, i.e. they were political associations. One had to share common political ideals to be a member. After the demise of the political power of the Pythagoreans in the middle of the fifth century, the groups lose even this common characteristic. Zhmud denies that there was any way of life that all Pythagoreans followed. He suggests that the code of behavior of the Pythagoreans was similar to the typical aristocratic ideals of the day. But this is contradicted by assertions in Plato ( R. 600b) and Isocrates ( Busiris 29) that over a hundred years after the death of Pythagoras his followers still stood out among others.
Another surprising result of Zhmud’s emphasis on figures like Menestor and Alcmaeon is his conclusion that “the philosophical views of the early Pythagoreans lay not so much in mathematics as in natural sciences and medicine” (p. 23). This claim is in tension with his attempt elsewhere in the book to show that the Pythagoreans were at the forefront of the mathematical sciences too. Indeed, one of Zhmud’s central goals is to rehabilitate Pythagoras himself as a mathematician, although he is careful not to make extravagant claims for Pythagoras’ mathematical work.
Does Zhmud make convincing arguments for his new theses? As Zhmud himself emphasizes, this is an issue of source criticism. In my own case I find that the questions that he raises about the evidence are more fruitful than his own interpretations of it. In a short review I can only give a few examples. Zhmud concludes that already by the beginning of the fourth century there was a clear tradition associating Pythagoras with mathematics and natural philosophy. He uses two main arguments. He suggests that the reference to Pythagoras’ wisdom and enquiry in authors such as Herodotus and Heraclitus indicate that he was involved in rational cognitive activity and was not just a religious figure. However, the evidence of Herodotus shows that enquiry ( historia) could just as easily be applied to the collection of myths and religious lore as to natural science,1 so that these texts do not show us that his wisdom was scientific rather than religious.2 Zhmud also argues that “the testimony of Isocrates refutes the argument that pre-Platonic tradition did not know Pythagoras as a philosopher and a mathematician” (p. 50). The key passage reads: “After Pythagoras of Samos went to Egypt and became their student, he was the first to bring the rest of philosophy to the Greeks and was more clearly interested than others in the sacrificial rites and the temple rituals” ( Busiris 28). Zhmud emphasizes the assertion that Pythagoras brought “the rest of philosophy to the Greeks” and that, in his description of the philosophy of the Egyptian priests six sections earlier (23), Isocrates included astronomy, arithmetic and geometry. However, in the sections that specifically deal with Pythagoras (28-9) Isocrates makes no mention of mathematics and instead draws our attention to Pythagoras’ interest in sacrificial rites and temple rituals.
One of the foundations of the current orthodoxy about Pythagoras is Burkert’s distinction between the Aristotelian presentation of Pythagoreanism, which he regards as more historically accurate, and the Academic presentation of Pythagoreanism, which inaugurates the Neopythagorean tradition according to which Pythagoras anticipated most of Plato’s philosophy.3 Zhmud makes a full frontal assault on this position. According to Zhmud, while the Academy presents Pythagoras in a favorable light, there is no evidence that it assigned Platonic and Academic doctrines back to him. It is rather Aristotle who tightly connects Platonism to Pythagoreanism and who invents a Pythagorean number-philosophy to serve as a background for the number-philosophy of the Academy including Plato’s unwritten doctrines. Zhmud is right that the evidence for the Academy’s view of Pythagoreanism is slender and much depends on few texts. Proclus’ commentary on Plato’s Parmenides in the Latin translation of William of Moerbeke reports that Speusippus assigned to the ancients, which in the context must be the Pythagoreans, the Platonic One and Indefinite Dyad as first principles. Some scholars accept this testimony at face value.4 Zhmud instead sides with others who regard the passage as Neoplatonic and not by Speusippus (p. 424). Zhmud here adopts a procedure that he also follows elsewhere: he does not present any new arguments on the issue or rehearse the arguments on each side but simply takes it as obvious that one side of the issue is correct (see e.g. p. 56, n. 108). On a text of this importance it would have been helpful to give a full examination of the arguments.
There are also problems with what Zhmud has to say about Aristotle. One of the signal achievements of recent scholarship according to Zhmud himself is Burkert’s widely accepted argument that a core of the fragments of Philolaus is authentic (pp. 2-4). However, Burkert’s argument for the authenticity of these fragments is precisely the reliability of Aristotle’s account of the early Pythagoreans. 5 His touchstone for the authenticity of individual fragments of Philolaus is whether they agree with Aristotle’s presentation. Therefore, if Zhmud is right that Aristotle is totally unreliable in his account of Pythagoreanism then Burkert’s argument for the authenticity of the fragments of Philolaus is undercut. Zhmud also overlooks one further feature of Aristotle’s presentation: it receives resounding support from Plato himself. Zhmud’s book oddly has very little to say about the dialogue in which Pythagoreanism most clearly appears, the Philebus. Plato refers to men before his time who had proposed limit and unlimited as basic principles (16c) and as both Aristotle’s reports and the fragments of Philolaus show this can only be a reference to fifth-century Pythagoreanism as represented by Philolaus. It is no accident that the Philebus is the dialogue where most scholars have found the clearest allusion to Plato’s unwritten doctrines.6 Hence, Plato himself presents his unwritten doctrines as a development of earlier Pythagorean principles and confirms Aristotle’s account of the relationship between Plato and the Pythagoreans. This does not mean that Aristotle’s report of fifth-century Pythagoreanism is entirely accurate. Zhmud is right that the system described by Aristotle according to which numbers are corporeal entities finds no support in the fragments of Philolaus. It represents Aristotle’s account of what he thinks Philolaus’ system amounts to rather than a literal presentation of it. The crucial point is that Aristotle’s reports are recognizably an interpretation of what is found in the fragments of Philolaus, and agree with what Plato says in the Philebus, so that we can confirm the authenticity of some of fragments of Philolaus as Burkert did while still recognizing that Aristotle is presenting the contents of those fragments under an interpretation.
So in the end I see no reason to abandon the present orthodoxy about early Pythagoreanism, which is based on Burkert. Nonetheless, I and anyone else who is not convinced by Zhmud’s thesis have to respond to his formidable arguments and may find that the standard view needs to be modified in some respects. This is a rich book from which readers will learn much.
1. See C. A. Huffman, “Heraclitus’ Critique of Pythagoras’ Enquiry in Fragment 129”, Oxford Studies in Ancient Philosophy 35 (2008): 19-47.
2. See G. E. R. Lloyd, “Pythagoras” in C. A. Huffman (ed.), A History of Pythagoreanism, Cambridge University Press, 2014: 24-45.
3. W. Burkert, Lore and Science in Ancient Pythagoreanism, Harvard University Press, 1972: 82-3.
4. Burkert, Lore and Science in Ancient Pythagoreanism, 63-4; J. Dillon, “Pythagoreanism in the Academic Tradition: the Early Academy to Numenius” in A History of Pythagoreanism (see n. 2), 250-73, esp. n. 1.
5. Burkert, Lore and Science in Ancient Pythagoreanism, 218-77.
6. See e.g. C. Meinwald, “Plato’s Pythagoreanism”, Ancient Philosophy 22 (2002): 87-101, and F. Sayre, Plato’s Late Ontology, Princeton University Press, 1983.