Tuesday, August 5, 2008


2008.08.01: Dirk Baltzly (ed.), Proclus. Commentary on Plato's Timaeus. Volume III, Book 3, Part 1: Proclus on the World's Body. Cambridge: Cambridge University Press, 2007. Pp. 205. ISBN 978-0-521-84595-3. $85.00. Reviewed by Marije Martijn, VU University Amsterdam

From 1816 until last year the English-but-not-Greek reading reader of Proclus' Commentary on Plato's Timaeus had to make do with Taylor's translation, which is not only rather esoteric but also based on a faulty text. But since last year a new translation in five volumes is appearing with CUP. This in itself is a reason for congratulations. Baltzly's translation of Proclus' Commentary on Plato's Timaeus book 3 part 1 is the third volume.

The new translation is the product of a project started some years ago in Australia, by Harold Tarrant, David Runia, Dirk Baltzly and Michael Share. The first volume, containing Tarrant's translation of the first book, also appeared in 2007. The second volume, containing the translation of the second book, is to appear later this year. The publication of the collection is timely, considering the impressive reappraisal of Neoplatonic philosophy in the English speaking world over the past decades.

As the editors themselves point out, there is a very good, and fairly recent, annotated French translation of the Commentary, by A.-J. Festugière.[[1]] Nonetheless, not only those who do not read French will benefit from this new translation. It is a valuable addition to Festugière's, because of the use that is made of the most recent publications on Proclus' work, because of the insightful introductions, which tackle some central -- and at times very complex -- issues in Proclus' philosophy, but most of all because of the extensive notes, which have a wider range of interest than those of Festugière. Moreover, as opposed to Festugière, the editors clearly aim at disclosing Proclus' text for the reader without Greek.

The third volume, which is the subject of this review, contains the translation of the first part of book 3 (In Tim. II 1-102 Diehl), in which Proclus comments on Tim. 31b-34b, concerning the body of the universe. The editors have split the translation of Proclus' book 3 over two volumes, one covering the body, and one covering the soul of the universe, because, as they put it in their introduction, of "the wealth of detail involved in Book 3 as a whole". The split works well for Baltzly's volume, which forms a coherent whole and ends very naturally at a point where Proclus employs an elegant ring structure to round off the discussion of the body of the world. The volume consists of a note on the translation (concerning the series as a whole, a text repeated in every volume), an introduction to Book 3 up to II 102, an analytical table of its contents, an annotated translation, references, an English-Greek glossary, a Greek word index, and a general index. ! Let me briefly go over each one of these sections.

In the introduction, Baltzly provides a summary of the main narrative and thematic themes of book 3 (pp. 1-6), as well as discussions of three central issues in Proclus' view of the body of the world: the elements (pp. 7-21), the cosmos being a visible god (pp. 21-27), and the arguments for the sphericity of the world (pp. 27-31). Baltzly announces that his main aim in the introduction is isolating Proclus' own contribution from the surrounding detail. And this is also one of its main qualities: Baltzly clearly (and, I would say, justly) starts from the assumption that Proclus should be taken seriously as a philosopher, not just as a collector of theories of his predecessors.

The analytical table of contents, a welcome tool to the eclectic reader, corresponds to the section headings inserted into the translation. The division made by Baltzly is largely the same as that of Festugière, and differences can mostly be explained from Baltzly's choice to make the translation accessible to an audience without Greek.

The translation is equipped with several aids to the reader. For example, key technical terms are given in transliterated Greek in parentheses, in-text quotations from the nearby lemmas of the Timaeus are in bold, just like the lemmas themselves, other quotes and cross-references are clearly indicated, and where needed the structure of Proclus' arguments is indicated with numerals in parentheses.

The quality of the translation is high. It reads well, although at times it is too liberal for my taste, no doubt for the sake of readability of Proclus' at times convoluted style. One aspect of the translation is especially noteworthy: Baltzly is very sensitive to Proclus' use of particles, which adds to the clarity and accessibility of the text (to give but one example: 'moving along then' for kai men kai, 101.14).

The amount of notes is good, and the occasions are well chosen. They consist primarily of clarifications of Proclus' philosophical system and obscure phrases, yet also offer interesting material for the more experienced reader, such as discussions of problematic arguments, textual remarks relevant to the reader with Greek, and plenty of references to relevant passages in ancient texts and secondary literature. The care and acuteness with which Baltzly offers different possible interpretations of complicated passages is admirable.

Both in the introduction and in the notes to the translation, Baltzly's work displays a deep understanding of Proclus' thinking in an analytic yet critical manner. Proclus' system is a true, but not trivial, application of the principle that 'everything is in everything, but appropriately to each' (see also below), and Baltzly shows a valuable sensitivity to the complexities thereof.

The last part of the book contains the English-Greek glossary, containing both Greek words and their transliterations, a Greek word index, and a General index, which -- as opposed to the analytic table of contents -- aims especially at allowing the reader to find topics and references, both ancient and modern, in introduction and notes. It is something of a pity that in the English-Greek glossary, when two English translations are used for one Greek word, there is only one entry. For example, onoma which is translated as either 'term' or 'name' is in the glossary under 't', but not under 'n'. Thus the reader "with little or no Greek" (p. xi) who wants to look up quickly what the Greek word is corresponding to 'name' at [In Tim.] II.14.9 will be disappointed by the glossary. I could end here, but for those readers who are interested in Baltzly's introduction, let us take a closer look at its contents.

The narrative and thematic structure of all of book 3 of Proclus' Commentary is determined by the enumeration of the ten gifts the Demiurge bestowed on the cosmos. The gifts pertaining to the body of the world are the perceptible elements, their being bound by proportion, the cosmos' being 'a whole of wholes', its spherical shape, its self-sufficiency and its axial motion. For Proclus the ten gifts are what make the cosmos a visible god (Tim.34ab). Baltzly's considerations (p. 1) concerning the manner in which the emphasis on the cosmos being a visible god contributes to Proclus' overall interpretation of the Timaeus as a theological physics are a welcome addition to Lernould's monograph, which concentrates on the first two books of the Commentary.[[2]]

The nicest example of Proclus' own contribution to philosophy is probably his theory of elements, to which Baltzly's introduction is a valuable guide.[[3]] Baltzly shows how Proclus refutes Aristotle's theory of the elements, especially concerning the number of elements and the element of the heavenly bodies. Proclus maintains that, in order for fire and earth to be truly opposite -- or at least more opposite than alike -- every element must of necessity possess three properties, rather than two. Moreover, in order for them to form a four-dimensional world, there must be four elements, bound by something analogous to geometrical proportion.

Plato's description in the Timaeus of the elements, of their properties, and of the proportions and means between them, is very complex. Proclus' explanation thereof is possibly even more complex, among others because he pays a lot of attention to the mathematical details. Fortunately, Baltzly's introduction equips the reader with the necessary background information to understand it. Note, however, that one of the subsections, 'Constructing the elements as cubes' (p. 16-18), in which Baltzly explains the notion of geometric means of cubes and similar solids by elaborating an example, contains a mistake.

Let me explain. Finding the geometrical mean is done, says Proclus, by taking two factors from one extreme term and multiplying them with one factor from the other extreme. For example, the cubes 8 (2x2x2) and 27(3x3x3) will have as geometrical middles 12 (2x2x3) and 18 (2x3x3), resulting in the continuous geometrical proportion 8, 12, 18, 27). In the case of cubes it does not matter which two factors are chosen, as all three are identical. Of similar solids, however, this does not hold. The example Baltzly uses to explain the similar solids is the following: 12 (2x2x3) and 96 (4x4x6) are similar solids because all three terms of the first 'solid' have a ratio 1:2 with the corresponding term of the second.

Finding the geometric proportion using the method Proclus describes could lead to 16 (2x2x4) and 72 (3x4x6), which, says Baltzly, does not give us a continuous geometrical proportion (the ratios between 12, 16, 72, 96 not being equal). Baltzly then mentions a second option, which could also result from Proclus' method, namely 24 and 48. Indeed, 12, 24, 48, 96 is a continuous proportion. But Baltzly constitutes them in the wrong manner, namely from 2x2x6 and 2x4x6 respectively. Although these series both add up to the required solids (namely 24 and 48), the factors used should be identical to the ones constituting the original sides of the cubes, but they are not (in other words, there is a 3 missing, a 4 too little, and a superfluous 2 and 6). What Baltzly could instead have given is either 24 (2x3x4) and 48 (2x4x6) or 24 (2x2x6) and 48 (4x4x3).

In itself the mistake is a minor one, but it does considerably diminish the explanatory power of Baltzly's example.[[4]]

Baltzly spends quite some time on the explanation of the relation between the physical and mathematical in Proclus' commentary. After his explanation of the mathematical details of Proclus' theory of the elements, he shows how Proclus identifies 'the life of the cosmos' as the physical analogue of proportion in mathematics, which fulfils the role of 'bond' between the elements. Baltzly rightly identifies that life with partial Nature. Note, however, that contrary to what Baltzly suggests in note 30, Proclus explicitly distances himself from Plotinus regarding the relation between Nature and Soul. Whereas Plotinus regards Nature as a lower kind of Soul, Proclus maintains that they are distinct, because, among other reasons, the latter is and the former is not separable from bodies.[[5]]

As may be clear from the above, in Proclus' theory of elements, as in the Timaeus, mathematics plays a crucial role. Unfortunately, Baltzly's explanation of the relation between mathematics and physics, which he refers to as a 'strong analogy', is incomplete (perhaps this problem will be solved, however, in the fourth volume, on the World Soul).[[6]] The explanation we get of this important notion of 'strong analogy', near the end of the section, refers to the relation between the mathematical proportions in the World Soul and the 'mechanics of procession', due to which we find images of those proportions on the physical level (p. 20). For a really informative explanation, however, especially for those readers new to Neoplatonism, Baltzly could have further emphasized and explained the mechanics of procession.

As a consequence of the ontological dependence of physical reality on Soul the same structures that can be found on the higher, mathematical level of Soul are present also on the lower level, in a manner appropriate to that level -- this is an application of the above-mentioned principle that 'everything is in everything, but appropriately to each'. That physical elements are 'strongly analogous' to mathematical solids is thus a metaphysical statement. The relation of analogy between the physical and the mathematical is especially interesting because it figures in the debate on the mathematization of physics. The Timaeus has often been supposed to foreshadow the mathematization of nature of the scientific revolution, but Proclus would disagree. He does not consider a reduction of the physical to the mathematical a possible way of explaining the physical, and keeps emphasizing throughout the third book that mathematical explanations are valuable in a w! ork of physics, due to the above metaphysical relation of analogy, but not as such: they should always be translated, as it were, to the physical subject matter.[[7]]

In 'the cosmos as a visible god' Baltzly presents an interesting discussion of the paradox of Plato's pantheism and his rejection of the possibility of divine bodies, and Neoplatonic attempts at reconciling them. Baltzly explains how Proclus' 'world-affirming' attitude shows from his argument that the world body's actually contributes to its divinity: the corporeal nature of the universe establishes its 'internal friendship', completeness, singleness and perpetuity, a special cosmic kind of perception comparable to consciousness, self-sufficiency, maximally unified shape, and divine motion.

The last section of the introduction discusses some of Proclus' epistemological presuppositions, as emerging from his arguments for the sphericity of the world. This is an interesting section, although what its title promises (Proclus' engagement with mathematics and astronomy) is discussed only superficially. A more suitable title for this section would have been 'Proclus' hierarchy of kinds of arguments', because it shows that in arguing for the sphericity of the world, Proclus emphatically categorizes and orders his arguments. He offers what he calls Platonic demonstrations, followed by philosophical arguments, physical arguments, and mathematical arguments, but in fact the Platonic demonstrations do not obey Aristotelian requirements, the philosophical arguments are Iamblichean, the physical arguments are taken from Aristotle, and the mathematical arguments are actually arguments from the practice of astronomy. Moreover, Proclus takes the order of presentation of the ! arguments to reflect their value. The latter is a fascinating rhetorical principle related to his logic and linguistics, but it would take us too far to go into that here.

In conclusion, let me emphasize that despite its minor flaws this volume, as its companions, is a very important contribution to the library of anyone studying ancient philosophy, from the novice with an interest in Platonism to the veteran Proclus scholar. As a matter of fact, CUP would do well to consider publishing a paperback version of this beautiful book.[[8]]


1.   A.-J. Festugière (1966-8), Proclus. Commentaire sur le Timée, Vrin.
2.   A. Lernould (2001), Physique et Théologie, Septentrion. For a challenge of parts of his interpretation see my dissertation, "Proclus on Nature. Philosophy of Nature and its Methods in Proclus' Commentary on Plato's Timaeus", forthcoming (pdf available on request), chapter 1.
3.   Cf. on this issue D. Baltzly (2002), "What goes up: Proclus against Aristotle on the fifth element", Australasian Journal of Philosophy 80, 261-87.
4.   Note also that at the top of p. 16 'similar solids' should be 'similar planes'.
5.   See on this topic also chapter 2 of my dissertation and J. Phillips (2007) Order from Disorder. Proclus' Doctrine of Evil and its Roots in Ancient Platonism, Brill, chapter 4.
6.   The transformation of elements into one another is 'strongly parallel' (p.! 8) to finding middle terms in geometric proportion, the elements themselves are 'strongly analogous to similar solids and cubes' (p. 15, cf. 'a strong analogy', p. 16). Cf. also Baltzly's conclusion that 'a proper understanding of the elements shows how they are strongly analogous to similar solid numbers or magnitudes' (p. 18).
7.   On this topic see chapter 4 of my dissertation. Cf. D. J. O'Meara (1989) Pythagoras Revived, Oxford University Press.
8.   I did find some typos, e.g. p. x: "not philological matters" should be "no etc.", "parantheses", p. 29 n. 40 "dialectice", p. 33.23 "ones" seems to be superfluous, p. 33.27 "plane" should be plural, p. 73 n. 109 "Aprhodite".

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