Thales, Pythagoras, Socrates - what can we know about such figures over and above the mere fact that they were turned into legends? If any of them wrote anything themselves, their writings certainly have not come down to us. What we have, of course, is other people's interpretations of them and their work. It is generally assumed that it is Plato's account of Socrates that we should trust, rather than Xenophon's, let alone the portrait of him as an irresponsible, cheating sophist in Aristophanes. But the wide differences between those representations should give us pause.
Most of the detailed information about Pythagoras comes from much later authors. Two of the most important, the neo-Pythagoreans Porphyry and Iamblichus, lived more than 700 years after his death. They are our chief sources for the story that he had a golden thigh, for his predicting the exact number of fish that certain fishermen had caught in their nets, and for many of his moral injunctions and dietary rules - where, however, there are not just variations but outright inconsistencies in what we are told.
For some, Pythagoras and his followers were strict vegetarians, while for others they prohibited only certain kinds of meat. While it is clear that - unlike Orpheus and Heracles - Pythagoras was a historical figure, many of the stories of his miracle-working assimilate his reputation to theirs.
Faced with the indeterminacies, the incompatibilities and the general unreliability in most of our sources, how are we to proceed to recover "his life, teaching and influence", the target of Christoph Riedweg's study (first published in German and translated into English by Steven Rendall in collaboration with the author)? There have been three major breakthroughs in tackling the problems in recent times. Walter Burkert's Lore and Science in Ancient Pythagoreanism (1972) introduced a new critical approach to the sources. Burkert's evaluation led him to draw a sharp contrast between the "lore", much of which he thought went back to Pythagoras himself in the 6th century BC, and the "science", particularly the mathematical interests that belonged, Burkert argued, mainly to the late 5th or even 4th centuries, the work of Philolaus and of Plato's contemporary Archytas.
A second important development came with Catherine Osborne's book Rethinking Early Greek Philosophy (1987). Dealing especially with one particular late source, namely Hippolytus (3rd century AD), Osborne argued that an essential preliminary to using him as testimony for early Greek philosophers was to analyse his interests and agenda. His account of Aristotle can be used as a check because we have plenty of material in Aristotle's treatises by which to test the way Hippolytus worked. The outcome was to confirm that Hippolytus did not engage in wholesale fabrication of Aristotle's teaching, though he did wrench it from its original context in his bid to use him in his "refutation of all the heresies".
Then a third breakthrough in the interpretation of late 5th and early 4th century Pythagoreanism, at least, came with the close analysis of the reasons that may have weighed with Aristotle when he represented them as holding that numbers are the material components of which things are made.
The key point is that in his own philosophy of mathematics, Aristotle insisted that mathematics studies the mathematical properties of physical objects, not (as Plato had held) separate mathematical entities with an ontological status intermediate between the intelligible Forms and perceptible particulars. That opens up the possibility that the Pythagoreans whom Aristotle had in mind were not themselves concerned with material causes: it is just that Aristotle believed that, without any notion of matter themselves, they were somehow committed to numbers being such causes.
How does Riedweg proceed? He dedicates this book to Burkert, though he distances himself often enough from his views, especially where Burkert takes a sceptical line on how far back certain doctrines and practices go.
But Riedweg ignores not just most of the recent work on the Aristotelian interpretation of Pythagorean mathematics, but also Osborne.
I would argue that the best way ahead is via a detailed analysis concentrating on how the later sources, Porphyry and Iamblichus, especially, constructed their interpretations of Pythagoras, but that possibility is not explored here. The organisation of the book seems indeed rather to put the cart before the horse. Instead of focusing on each one of our principal sources and asking what their assumptions and agenda were, Riedweg's first chapter bundles all the evidence together to give what is, it has to be said, a bewildering picture of the man and his teaching. It is only in chapter two, "In search of the historical Pythagoras", that he begins to separate the earlier from the later testimonies. That starts promisingly enough, asking what we can learn about Pythagoras from his near contemporaries Xenophanes and Heraclitus.
But Riedweg soon gives in to the temptation to bring in material from later sources that he decides preserves the core teaching of Pythagoras. But how precisely we can distinguish that core teaching from later accretions is exactly where the problems lie, and they do not receive as much critical attention as they need. Pythagoras is cast in the role of a Weberian charismatic teacher, which he may well have been. That then opens the door to all sorts of items matching that description. But that, too, is a dangerous tactic when there are obvious inflationary tendencies in our late sources with regard to the legend of Pythagoras's wonder-working.
The German title of the book calls it an introduction. The reader is indeed introduced to a considerable array of material, but is not given much help in the tasks of sifting through it and assessing it critically. The author is also not well served by his translator's lame renderings of his text, nor by the carelessness of his publisher. An egregious misprint that puts BCE for CE in relation to the dates of the main sources, on the very first page of the preface, will mislead many an innocent reader.
Sir Geoffrey Lloyd is emeritus professor of ancient philosophy and science, Cambridge University.
Pythagoras: His Life, Teaching, and Influence
Author - Christoph Riedweg
Publisher - Cornell University Press
Pages - 184
Price - £15.50
ISBN - 0 8014 4240 0