Carl A. Huffman, Philolaus of Croton: Pythagorean and Presocratic. Cambridge: Cambridge University Press, 1993. Pp. xx + 444. $100. ISBN 0-521-41525-X.
Reviewed by Patricia K. Curd, Purdue University.
The Pythagoreans have never fit easily into the history of Presocratic thought. We know little of Pythagoras himself, and untangling the convoluted reports of Plato, Aristotle, and the later commentators is a daunting task. The split of what seems to have been the second generation of Pythagoreans into the acusmatici and the mathematici (and the ambiguous evidence concerning the nature of the split and who was responsible for it) only makes things worse. Light was shed on early Pythagoreanism by Walter Burkert in his Lore and Science in Ancient Pythagoreanism (translated by E. L. Minar, Jr., Harvard University Press, 1972), but his treatment of Philolaus raised almost as many questions as it answered. If Philolaus was, as Burkert suggested, more of a mythologist than an astronomer, whose interest in number was as a number-mystic as Burkert claimed, why should he count as a philosopher or one of the mathematici at all? Further, both Burkert's and Guthrie's treatments leave unanswered the larger question of the relation of the Pythagoreans to other Presocratic thinkers. Was Philolaus an anomalous figure, whose interests were radically different from those of, say, Anaxagoras, Empedocles, and Democritus (his closest philosophical contemporaries, according to Huffman, pp. 8-9)?
Some of these questions can now be answered. Carl Huffman's notable new book on Philolaus offers us a philosopher who is, as Huffman puts it in the subtitle, both a Pythagorean and a Presocratic. The first book devoted to Philolaus alone since A. Boeckh's Philolaus des Pythagoreers Lehren nebst den Bruchstücken seines Werkes of 1819, Philolaus of Croton is a clear and well-argued book in which Huffman provides an important reevaluation of the Philolaus fragments and testimonia and a significant rethinking of Philolaus' views.
Huffman's most important revisions concentrate on the role of number in Philolaus. From Aristotle on, the view has been that number (or the even and the odd) occupies first place in Philolaus' thought. But Huffman argues convincingly that Aristotle is presenting his own interpretation and not an historical account of Philolaus' views. On Huffman's account, primacy goes, not to number, but to limiters and unlimiteds. (Note the plurals: one of the fundamental indications of the misunderstanding of Philolaus in both Plato and Aristotle is their transformation of Philolaus' plurals into singular terms. Philolaus does not discuss the limited and the unlimited, but rather limiting things and unlimited things [Huffman, pp. 38-41].) Fragment 1 says clearly: "Nature (FU/SIS) in the world-order (KO/SMOS) was fitted together both out of things which are unlimited and out of things which are limiting (E)C A)PEI/RWN TE KAI\ PERAINO/NTWN), both the world-order as a whole and all the things in it." The source of the fragment, Diogenes Laertius (8.85ff.) asserts that this was the beginning of Philolaus' book; so if Aristotle is right that Philolaus claimed that "everything is number" we should expect to find that assertion here. But we do not. Indeed, as Huffman shows, none of the fragments that deal with the basic principles of the KO/SMOS includes a discussion of number; and in none of the extant fragments do we find limiters and unlimiteds discussed together with number, as we might expect if number were truly basic. (We might blame this silence on the vagaries of text transmission, but if there were a passage in Philolaus' book that directly supported Aristotle's claim it would most likely have survived through the work of the commentators.) On Huffman's account, Philolaus is arguing against those Presocratics who had thought that all that was needed for cosmology was some unlimited stuff(s); especially, perhaps, Anaxagoras with his unlimited extents of unlimited chrêmata. On the contrary, Philolaus responds, without limiters as well as unlimiteds nothing can be known (not even by Anaxagoras' Nous, fr. 3). But these two are not sufficient to account for the present world: in addition there must be harmonia, which connects unlikes and so can account for the "fitting together" of limiter and unlimited. (Huffman's treatment of harmonia might be clearer; at times he seems to say any construction out of the unlikes limiter and unlimited is a result of harmonia [p. 73], at other times he seems to restrict instances of harmonia to those that are pleasing or well-ordered [p. 48].)
Perhaps the most impressive aspect of Huffman's story is the extent to which Philolaus turns out to be concerned with issues that exercised other Presocratic philosophers. Huffman rightly notes that many of those issues were epistemological and points out the relations of Philolaus' work to that of Xenophanes and Parmenides. Like them, Philolaus is concerned with what can be known securely. In fragment 6 he agrees with Xenophanes that knowledge of the details of "the being of things which is eternal, and inner nature in itself" is not available to human beings,1 but argues that nevertheless "it was impossible for any of the things that are and are known by us to come to be if the being of the things from which the ordered world came together, both the limiting things and the unlimited things, did not preexist" (fragment 6, continued). So, although the details of "the inner nature in itself" are closed to us, we can know what that nature must, at minimum, be like. But it is in response to the epistemological problems posed by Parmenides that Philolaus' ingenuity really shines. Parmenides had argued that any object of knowledge must be a complete and unified whole, something that is completely determinate. According to Huffman:Philolaus accepts Parmenides' claim that the object of knowledge must be a determinate state of affairs ... The bold step he takes is to argue that numerical relationships in particular and mathematical relationships in general solve the problem. They possess the requisite determinacy and at the same time they relate a plurality of entities and thus are capable of explaining a world that consists of a plurality of entities ... Philolaus might well argue that, although there are a plurality of entities, they each individually are completely determinate in the way required by Parmenides.2 (pp. 67-68)The role of number in Philolaus' thought then turns out to be neither mystical nor mysterious (except in some details): rather number has an epistemological role to play, guaranteeing that knowledge of the sensible world is possible. And this is just what we are told in fragment 4: "And indeed all the things that are known have number. For it is not possible that anything whatsoever be understood or known without this." But this statement does not explain the relation between things and numbers or how things are known through number, and the fragments do not provide these explanations. For Philolaus, "having number" apparently means having a structure which can be described mathematically (p. 70), but there is much here that remains obscure. There seems to be a connection between odd and even and limiters and unlimiteds, but just how they are connected remains unclear. It may be that no such explanations were forthcoming from Philolaus; as Huffman points out, such grand but unelucidated notions often appear in Presocratic thought; but "the impulse behind the correlation between numbers and things is presumably the belief that all phenomena will turn out to be numerically determined in the same way that the concordant musical intervals were discovered to be" (p. 191). A key issue is that of the interpretation of fragment 5, with its claim that "Number, indeed, has two proper kinds, odd and even, and a third from both mixed together, the even-odd. Of each of the two kinds there are many forms, of which each thing itself gives signs." Huffman's suggestion that the even-odd, that "from both [odd and even] mixed together" is parallel to things that are a result of the harmonizing of limiters and unlimiteds and is thus to be seen as "a derived class of numbers whose first member is, as the ancient tradition indicates, the one, but which also includes numbers that consist of even and odd numbers combined in ratios (e.g. 2:1, 4:3, and 3:2)" (p. 190) is attractive, for it connects the metaphysical and epistemological fragments in a satisfying way. The main problem here is how even and odd are to be connected with unlimiteds and limiters. Huffman's discussion of the crucial relation on p.182 is too brief to be truly satisfying. In the end we are left with tantalizing possibilities, but this is probably the fault of the paucity of our evidence, not with Huffman's attempts to deal with that evidence.
If Huffman's extremely plausible suggestions are correct, Philolaus is not a "number mystic" in the sense suggested by Burkert, but someone belonging to the mathematici (but not primarily a mathematician), using the Pythagorean interest in numbers to help solve the same problems that worried other Presocratic philosophers. He offers theories of cosmogony and astronomy, he has things to say about metaphysics and music theory, about Philolaus' methodology and epistemology, about the soul, and on medicine and embryology. All of these are carefully and intelligently treated by Huffman. His debt to Burkert is obvious, and he is generous in his acknowledgment of it. But he is not afraid to disagree, particularly in his account of Philolaus' use of number and his evaluation of the genuineness of fragments and testimonia (see pp. 17-18). Huffman's rejection of certain fragments and testimonia will no doubt be controversial, but he has been careful and consistent in applying his criteria, and he has made those criteria clear. As he points out on pp. 18-19, the great number of clearly forged, late "Pythagorean" writings makes the problem of authenticity, difficult enough for most Presocratic philosophers, doubly troublesome in the case of Philolaus. But he argues his case well and convincingly, and the "new" Philolaus who emerges from this book is an innovative and interesting philosopher who clearly understood the problems current in his own day and was an important influence on Plato. Among the many virtues of this book is Huffman's willingness to speculate intelligently and to make clear where the difficulties in interpretation lie. The commentary is both philological and philosophical: Huffman is always careful to give an analysis of Philolaus' arguments and to explain the philosophical significance of fragments and testimonia. Huffman begins with a series of interpretive essays and then goes on to commentaries on all the fragments and testimonia he accepts as genuine, and discussions of all those that he rejects as spurious or doubtful (and he is careful to draw distinctions between the two classes).
Cambridge University Press have produced a beautiful volume, in the old fashioned tradition of book making. Would that all academic volumes were as carefully produced. The printing and binding are beautiful, with changes in type-faces, particularly in the Greek, used to good effect. I found only four typographical errors (two on p. 149; read "derived" for "dervied" and "peculiarities" for "peculiarites") and two, ironically enough, in a bibliographical reference to one of Huffman's own papers (read "cosmogony" for "cosmogomy" and add quotation marks to the beginning of the citation for Huffman 1989, p. 424). This is an expensive book, and well worth the price.
I have touched on only a few of the significant and intriguing issues raised in this rich and rewarding volume. The book is clearly a labor of love, and Huffman does his best to give us a Philolaus who has important and intelligent things to say; but he is not blind to faults, honestly pointing out difficulties and obscurities where they occur in Philolaus' thought. "Important" is a term that is used far too often in book reviews; but this is an important book; it has been a long time since 1819, but Carl Huffman's Philolaus of Croton: Pythagorean and Presocratic has been worth waiting for.
 Here I think Huffman overestimates the scepticism of Xenophanes. As J. H. Lesher has recently shown, B34 does not commit Xenophanes to scepticism. Rather, Xenophanes claims that what is outside human experience cannot be known reliably. On this interpretation Philolaus is largely in agreement with Xenophanes, particularly on the issue of the limits of human knowledge (see Huffman, p. 65). See J. H. Lesher, Xenophanes of Colophon: Fragments (Toronto: 1992), reviewed in BMCR, February, 1993.  The last sentence seems to me to be particularly important; Parmenides need not object to a plurality of entities as long as each of those entities satisfies the criteria for unified being and knowability laid down in B8; Philolaus' connection of things and number seems designed to guarantee just this.