1. On Pythagoreanism: a Brief Review

Despite the quantity and variety of materials used in On Pythagoreanism—Platonic, Pythagorean, Aristotelian texts—a unity of conception and of purpose has been found to organize the whole. The work is a protreptic to 'Pythagorean philosophy', leading the reader from more familiar, 'common' truths up towards the higher 'mysteries' of Pythagoreanism. This movement from the familiar to the transcendent has been observed not only within Book II (the Protreptic) but also in the other books. Book I (On the Pythagorean Life) already begins the initiation of the reader in providing evidences of the divine origin of Pythagoreanism and in using the actions and speeches of Pythagoras to

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Introduce the reader, at an elementary level, to Pythagorean philosophy.

The education of the reader continues upwards in Book II. In Book III (On General Mathematical Science) the reader at last finds himself in the realm of Pythagorean philosophy properly speaking, which consists of the mathematical sciences and, above them, 'contemplation', the knowledge of true being and of the divine. The initiation to mathematics proceeds step-by-step. The general introduction in Book III leads to specific, more technical introductions to each of the four mathematical sciences (Books IV, VIII-X). From the system of Pythagorean philosophy just alluded to, it will be seen that On Pythagoreanism covers only the first, lower half of what Iamblichus considers to be Pythagorean philosophy, namely mathematics. Were it to cover the whole, it would have to deal, after Book X, with true being and (especially) with the divine. However, these higher regions of Pythagoreanism are foreshadowed in Book VII where an analogy is developed between arithmetic and the gods who transcend being.

Within the work a conception of Pythagorean philosophy emerges which is consistent on the whole, although some details, especially those having to do with the structure of reality, are expressed at first somewhat vaguely and appear to receive precise formulation, if at all, only in the later books. ² 

2 Cf. For example the distinction between being and the divine in Books I, III, VII (above, pp. 45, 81). Some vague areas remain unclarified, as far as can be determined (above, p. 45).

But this is a consequence of the order of exposition, i.e. that of a gradual ascent, chosen by Iamblichus for his work.

The figure of Pythagoras is presented at the beginning of the work with the purpose, I have suggested, of recommending Pythagorean philosophy to the reader by providing evidence of its divine origin. Iamblichus collects the legends associated with Pythagoras. But he also indicates his opinion of them: he is concerned with the origin and mission of Pythagoras' soul. Pythagoras' soul is in fact one of the souls of the divine company of Plato's Phaedrus which parades above the rim of the heavens and contemplates the immaterial Forms, or true being. Pythagoras' soul does not fall from this vision, but is sent down to the material world to impart knowledge to the fallen souls of those who have lost it, thus saving them. This interpretation represents, I have argued, an integration of the Pythagorean legend into Iamblichus' Neoplatonic view of the origin and purpose of soul in the world.

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Pythagoras seems to have communicated many different sorts of knowledge to mankind, but for Iamblichus the specifically Pythagorean revelation consists in the 'most scientific', unerring forms of knowledge, those having to do with pure, immaterial unchanging realities, namely mathematics and the study of true being and of the divine. The mathematical sciences are inferior to the study of being and the divine, because they deal with inferior objects. Mathematical objects may, through their immateriality and unchangingness, transcend the material world, but they are products, images, of true being. This means, however, that mathematics can train and prepare the soul, as indicated in Plato's Republic, for higher wisdom.

Although subordinate, mathematics has a pivotal role. In view of the organization of the material world according to number, mathematics includes in paradigmatic form a theory of physics and of ethics as well as foreshadowing the highest Pythagorean science. These extra-mathematical implications of mathematics are introduced in Book III of On Pythagoreanism and became the objects of separate and detailed treatment in Books V-VII. In Book V Iamblichus developed a Pythagorean arithmetical physics, that is, a 'Pythagorean' reformulation of Aristotelian physics, in which Aristotelian criticisms of Pythagorean ideas were met and 'Pythagorean' improvements of Aristotle's theories were introduced. Given the paradigmatic relation between numbers and the forms immanent in, and organizing the material world, the latter were described as 'physical numbers' and were shown, in their instantiation of physical theory, to exhibit the various characteristics of mathematical number. The same 'Pythagoreanizing' of Aristotelian theory, in this case ethics, was attempted in Book VI, the same sorts of associations sought between aspects of ethical behaviour and the mathematical properties of number. When the reader came to Book VII, he moved from these extrapolations of Pythagorean mathematics to lower sciences, upwards to mathematics as anticipating the highest objects of Pythagorean philosophy, the gods. Here Aristotle could scarcely be adapted (Pythagoreanized) for the purpose. A response had to be made to criticisms in the Metaphysics, and advantage was taken of the mathematical properties of number in order to foreshadow, by a method of analogy, the series of the gods.

This system of sciences ³ 

³ The place of psychology in the system remains obscure. It is parallel in some way to mathematics. But the relation between the two sciences (and their respective objects) is not clearly determined in the available evidence.

corresponds to a structure of reality which

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is most fully and precisely presented at the highest stage in the 'ascent' of the reader, namely in Book VII. The major aspects of the structure appear to be the following. There is an absolute first principle, an ultimate 'One' above, as presupposed by, the unity of a series of gods. This series possesses unity in itself and in each of its members. On the analogy with a numerical series the divine series originates from its first members, a 'first one' (perhaps also described as a 'monad') and a divine dyad. Acting together as principles of limit and of the power limited, these two generate the following members of the divine order. The order of the gods (or 'divine number', in mathematical analogy) transcends the level of pure being, the intelligible, 'ideal' number, in which monad, dyad, and triad are also found, presumably again in virtue of mathematical analogy. Distinct and inferior to the intelligible is an 'intellectual' level, concerning which little is said in what survives of On Pythagoreanism, apart from the idea that here too analogues of monad, dyad, triad are to be found. Below this level comes 'mathematical reality' whose characteristics have served to describe by analogy the higher orders. Proximate in some way to mathematical reality is soul, but the relations between these two orders remain obscure. Below soul and mathematical number is the multiplicity of enmattered forms ('physical numbers') which organize the material world and where again analogues of monad, dyad, etc. occur.

The structure as a whole represents not only ontological distinctions between types of reality, but also an ontological subordination of these types and a causal derivation going from the higher to the lower, from the ultimate One down eventually to the material world. The details of the derivation of reality are not clear, although the 'flow' of numbers from the first two members of the decad was, it seems, an important model for explaining derivation.

If a brief comparison is made between Iamblichus' 'Pythagorean' structure of reality and the system of hypostases in Plotinus, it will be noted that Iamblichus has introduced new ontological distinctions and levels, namely an order of gods interposed between the ultimate principle and pure being, and an 'intellectual' order distinguished from and inferior to pure being or the intelligible. ⁴ 

⁴ For Iamblichus as anticipating Proclus' theory of 'henads', cf. below, Ch. 10 n. 25; for the difference between Porphyry and Iamblichus on the intelligible/intellectual distinction cf. above, Ch. 3 n. 71.

The evidence does not reveal the reasons for such introductions into the Neoplatonic system of reality. It will also be noted that, in contrast to Plotinus,

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Iamblichus makes systematic use of mathematics in the analysis of reality. This gives his more complicated system a strong sense of continuity, a continuity on each level of reality in its articulation in analogy with the numerical progression (or flow) from monad to decad, and between all levels in the pervasiveness of relations imaged in or imaging numerical relations. This mathematization of the structure of reality, which seeks at the same time to preserve the distinctions between physics, ethics, mathematics, and metaphysics, represents a systematic application of the Pythagorean principle that 'all is likened unto number'. It is thus an important consequence of Iamblichus' programme to Pythagoreanize Neoplatonic philosophy.

2. The Relation of on Pythagoreanism to Iamblichus' Other Works and Interests

In order to assess the significance of On Pythagoreanism it is necessary first to determine, as far as possible, its place vis-à-vis Iamblichus' other philosophical works and the ideas expressed in these works. The problem might be stated in an extreme form by means of the following questions. Is On Pythagoreanism without any importance or relevance with respect to Iamblichus' other work? Did he compose it without any regard to what he himself considered philosophically significant? Was it perhaps the work of a beginner (who nevertheless knew a great deal of philosophy and could wrestle with Aristotle), to be put aside when, with maturity, different projects were undertaken? ⁵ 

⁵ Cf. Dillon (1973), 20. Against Dillon's dismissive attitude to On Pythagoreanism a more direct approach is required than the occasional rapprochements made by Larsen (1972) in the course of his review of Iamblichus' other works.

If these options are implausible, it is none the less not easy to identify the place of On Pythagoreanism within Iamblichus' philosophical corpus for the simple reason that much of the corpus is lost. Only quotations from, and reports on, Iamblichus' commentaries on Plato and Aristotle survive. The same is true of other major works, such as the Commentary on the 'Chaldaean oracles'. On Mysteries is Iamblichus' only work (not counting individual volumes of On Pythagoreanism) to be available to us in its entirety. Thus the most that can be attempted is a survey of indications pointing toward the place of On Pythagoreanism in Iamblichus' philosophy. However, it turns out that there are a good number of such indications and that they are very

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strong. They fall into two groups: (i) Iamblichus' own suggestions in On Pythagoreanism as to the relation between it and certain of his other works; and (ii) references to Pythagoreanism in Iamblichus' other work.

(i) It has been noted above that On Pythagoreanism does not cover the whole range of what Iamblichus represents as Pythagorean philosophy. It deals with the lower Pythagorean sciences, the four mathematical sciences, preparing the way for, and anticipating, the study of true being and of the divine. But it does not deal with these higher regions of Pythagoreanism in their own right. The work as a whole thus indicates what should follow it: a treatise (or treatises) on being and, especially, on the divine. Indeed Iamblichus himself refers the reader, in On Pythagoreanism (Pr. 120, 15-18), to his work On God (Πε θεου ), for a more specific and technical account of the eternal, immaterial, intelligible, unchanging class of the gods. This reference, with its characteristic distinctions between the common (familiar) and the specific, between the elementary and the technical, shows that Iamblichus envisages his work On God as a sequel to the mathematical volumes of On Pythagoreanism, dealing at a higher level of exposition with a higher subject-matter.

Not much is known about the work On God. The subject-matter included the class of intelligible gods: the singular reference of the title should not therefore be taken in a monotheistic sense. The work may perhaps be the same as the treatise On the Gods (Πε θεω ν) cited by Iamblichus in On Mysteries, in which he says the reader will find a more accurate treatment of the cosmic and supra-cosmic gods, 'which gods lead up and according to which of their powers, how they set free from fate and through which hieratic ascents, what sort of order the cosmos has and how the most perfect intellectual activity rules over it' (VIII 8, 271, 10-17). Proclus refers to a work On the Gods by Iamblichus where he says Iamblichus discussed the gods of the intellectual order, arguing that the major kinds of being of Plato's Sophist should be placed at this level and not at that of the intelligible order. ⁶ 

⁶ Theol. Plat. I 52, 2-13; there is a reference also in Damascius, De princ. I 132, 12-13.

On the Gods thus seems to have dealt with the divine at a variety of levels, cosmic and supra-cosmic, intellectual, and intelligible. This multi-level approach has been noticed already in the treatment of monad, dyad, and triad in On Pythagoreanism VII.

Whether or not On the Gods is the work referred to as On God in On

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Pythagoreanism II, one can conjecture that the latter was inspired at least to some degree by a writing going under the title Sacred discourse or On the Gods attributed to Pythagoras, since Iamblichus uses it in On Pythagoreanism. ⁷ 

⁷ Vit. Pyth. 81, 20 ff. For this Sacred Discourse cf. Thesleff (1965), 164-6.

This work appears to have dealt with numbers, from the monad to the decad, and to have related gods and demons to them, namely as produced by them. Such, roughly, was the structure of Nicomachus' Theologoumena, and Nicomachus may have in fact used the Pseudo-Pythagoras. ⁸ 

⁸ Cf. Thesleff (1965), 166 (with notes).

But of the relation (if any) of Iamblichus' On God (= On the Gods?) to this work, nothing is known. If Iamblichus' On God was indeed a 'Pythagorean' theology, i.e. a treatise on the divine based on Pythagorean literature, then it would have completed, on the basis of Pythagorean sources, the coverage of Pythagorean philosophy begun in On Pythagoreanism.

Iamblichus also wrote 'theologies' based on Platonic, Egyptian, and Chaldaean sources. His Commentary on Plato's Parmenides interpreted the first 'hypothesis' of the Parmenides as concerning god and the gods. ⁹ 

⁹ In Parm. fr. 2; cf. Saffrey and Westerink in Proclus, Theol. Plat. I lxxxii-lxxxiii; III xvii ff. For a critique of evidence for a Platonic Theology by Iamblichus cf. Saffrey (1987a), 40-1.

On Mysteries is yet another theology, derived this time from supposedly Egyptian (but also Chaldaean) sources. ¹⁰ 

¹⁰ Cf. De myst. 1, 8-2, 9; 4, 1-4; 5, 8-13; 14, 7-8; 286, 10-11.

Finally Iamblichus produced an enormous Chaldaean Theology in which the 'Chaldaean Oracles' were interpreted with help of the Pythagoreans and of Plato's Philebus. ¹¹ 

¹¹ Damascius, De princ. I 86, 3-87, 4 (discussed above, Ch. 3 n. 77). On Chaldaean Theology as a title for Iamblichus' Commentary on the 'Chaldaean Oracles', cf. Larsen (1972) I 58.

It thus turns out that if one starts from the system of philosophy presented in On Pythagoreanism, one requires as a sequel a work treating of being and especially of the divine. Iamblichus himself refers to such a sequel in On Pythagoreanism, namely his (lost) work On God. It is possible that this work was a 'Pythagorean' theology. Iamblichus also produced other theologies, based on Platonic, Egyptian, and Chaldaean sources. These too could complete the coverage of Pythagorean philosophy begun in On Pythagoreanism, if one assumption is made, namely that Iamblichus saw, and continued to see, a unity between the theologies of the Pythagoreans, of Plato, of the Egyptians, and of the Chaldaeans. In what follows I would like to indicate briefly the extent to which this assumption can be made.

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In On Pythagoreanism Iamblichus uses the Platonic dialogues in such a way as to indicate that he regarded Plato as a Pythagorean. The legend of Pythagoras' apprenticeship under Egyptian priests is repeated:

He spent two and twenty years in Egypt in the temples, doing geometry, astronomy, and being initiated, but not in a superficial or haphazard way, into all the rites of the gods. ¹² 

¹² Vit. Pyth. 13, 8-11; cf. 89, 7-22.

Pythagoras is reported as having been educated in mathematics and in theology not only by the Egyptians, but also by the Chaldaeans:

Further they say that his divine philosophy and cult was composite, some things being learnt from the Orphics, some from the Egyptian priests, some from the Chaldaean mages, some from Eleusinian rites. . . . ¹³ 

¹³ Vit. Pyth. 85, 14-18; cf. Comm. 66, 21-67, 2. Iamblichus had Pythagoras' own testimony, so he thought, to the debt to Orphism: cf. Thesleff (1965), 164 = Iamblichus, Vit. Pyth. 82, 12-83, 5.

Iamblichus does not make clear how Pythagoras' 'learning' of the main parts of Pythagorean philosophy (mathematics and theology) from the Egyptians and the Chaldaeans can be reconciled with Pythagoras' role as divine revealer of all sciences to man. Nor can reports he reproduces be regarded as reflecting precisely his own views. However, to judge from On Pythagoreanism, it is unlikely that he would have considered Pythagorean theology to be at odds with Egyptian and Chaldaean theology. It is clear at any rate that he identified Platonism with Pythagoreanism.

On Mysteries stresses the dependence of Pythagoras, Plato, and other Greek philosophers on the Egyptian priests. ¹⁴ 

¹⁴ De myst. 2, 9-3, 5 (reading ογ αμματ ων with Parthey; cf. 260, 11). Cf. Proclus, In Tim. I 386, 8-12 = Dillon (1973), 140, 312-13.

But here Pythagoras appears as a lesser figure than that found in On Pythagoreanism. His role as a divine guide to the knowledge which can only be mediated to men through divine help is now assumed by Hermes and by Iamblichus' Egyptian priest Abammon: as the ancient Egyptian priests guided and initiated Pythagoras, so will Abammon enlighten the addressee of the work, Porphyry. ¹⁵ 

¹⁵ Cf. De myst. 1, 5-3, 5.

Pythagoras and other Greek philosophers are thus disciples vis-à-vis the Egyptians, not masters. On the other hand, Chaldaean theology is treated as equal to Egyptian

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theology and indeed as in agreement with it, despite some differences. ¹⁶ 

¹⁶ De myst. 5, 8-11 (agreement implied); 249, 3 ff. (differences).

Even within ancient Egyptian sacred literature there are divergencies (260, 10-261, 8), but Iamblichus does not consider this a threat to the integrity of Egyptian theology. An all-too-brief indication is given of how diversity and unity, not only within Egyptian theology, but also between Egyptian and Chaldaean theology could be reconciled:

This is true of all of the sciences conveyed to men by the gods. As they advance in time, they are often mixed in with much that is mortal, losing the divine character ( θος) of the knowledge. (277, 13-18)

This idea, intended to explain the contradictions Porphyry found in astrology, suggests that the divinely revealed knowledge mediated by Egyptians, Chaldaeans, their pupils Pythagoras, Plato . . . , acquires diversity and even impurity in the course of its historical tradition.

It is not certain that this view of the relations between Egyptian, Chaldaean, Pythagorean, and Platonic philosophy is precisely that presupposed either by On Pythagoreanism or by the Chaldaean Theology. Concerning the latter work, all that can be said on the subject is that Iamblichus thought it suitable to introduce Pythagorean and Platonic ideas in his interpretation of the 'Chaldaean Oracles'.

In conclusion, it is safe to say that for the Iamblichus of On Mysteries, a Platonic, Egyptian, or Chaldaean Theology could very suitably be read as a sequel to On Pythagoreanism. It is likely that such would have been his view also in his Chaldaean Theology and in On Pythagoreanism. In On Pythagoreanism itself he refers to a sequel, his work On God, which may indeed have been a 'Pythagorean Theology', but not for all that very different from what he there understood to be the theology of Plato, of the Egyptians, and of the Chaldaeans.

(ii) In the preceding pages I have argued that On Pythagoreanism is related to certain of Iamblichus' other works, taking my cue from indications given in On Pythagoreanism itself: a specific reference to a sequel, the work On God; and the system of philosophy presented in On Pythagoreanism as susceptible of fulfilment also by Iamblichus' other theological works. In what follows I shall approach the matter from another angle. The presence of a Pythagoreanizing programme in what remains of Iamblichus' other works will be brought out, so as to show that his interest in it extended well beyond the composition of a work specifically devoted to it. I shall discuss what can be learnt in

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particular about Iamblichus' lost commentaries on Plato and Aristotle. It will soon emerge that a tendency to Pythagoreanize is a very significant feature of these commentaries. I shall confine myself to presenting here some major aspects, rather than all elements, of this large subject. ¹⁷ 

¹⁷ Cf. Larsen (1972), chs. V-VI, for a review of the evidence relating to the commentaries of Iamblichus.

It must also be noted that most of the available evidence has to do with Iamblichus' commentaries on Aristotle's Categories and on Plato's Timaeus. His other commentaries are, in comparison with these, poorly represented in the reports on Iamblichus to be found in later Neoplatonic authors.

Simplicius makes extensive use of Iamblichus' Commentary on the Categories in his own commentary on the Aristotelian text. He also provides a general description of Iamblichus' work: Iamblichus added in various ways to Porphyry's commentary, often including texts taken from a logical work attributed to the Pythagorean Archytas. Not only did Iamblichus believe—incorrectly—the Archytas text to be authentic, but he thought that Aristotle was inspired by the Pythagorean. The harmony of Archytas and Aristotle was to be shown, reflecting the complete indebtedness of Aristotelian to 'Archytas" logic. Where—and it was seldom—Archytas and Aristotle differed, such differences had to be explained. ¹⁸ 

¹⁸ Iamblichus, In cat. fr. 2 (= Simplicius, In cat. 2, 9-25). Iamblichus quotes Archytas in In cat. frs. 21, 22, 26, 36, 78, 89, 90, 96, 106, 107, 108, 110, 112. Cf. Larsen (1972), I 233-301. For the date of the (Pseudo-) Archytas and its use of Aristotle's Categories, cf. Szlezák (1972), 14-19, who edits the text and indicates that its authenticity was not accepted by all in the fourth century.

Simplicius gives an example of this:

It seems, Iamblichus says, that the Aristotelian position has been turned away (perverted, πα ατ τ θαι) from Pythagorean teaching. The reason is that the moderns do not have the same view of number and of change as do the ancients, but the former think these are accidents, supervening from outside ( ξωθ ν π σακτα) whereas the latter see them as essential (ο σι δη). ¹⁹ 

¹⁹ Iamblichus, In cat. fr. 109.

This conception of a perverting among the moderns (Aristotle) of the ancient tradition (Pythagoras) from which they derive their knowledge is similar to the idea found above in On Mysteries of a divine revelation of knowledge to man which is gradually corrupted with the progress of time. What it entails here is using 'Pythagorean' logic, the (Pseudo-) Archytas, as a standard or guide for the assessment of Aristotle's

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Categories. ²⁰ 

²⁰ In Iamblichus' In cat. Archytas is set up as a 'guide' (fr. 106, 2 γ μ να π ο σταται), just as Pythagoras is in On Pythagoreanism (Vit. Pyth. 6, 2-3 γ μ να . . . π οστησ μ θα) and Hermes in On Mysteries (1, 6-8 τω ν λ γων γ μ ν . . . . . . π ο στηκ ς).

Where both texts agree, Aristotle is Pythagorean and right; where Aristotle diverges, he is perverting the ancient tradition. In the case, for example, of the problem of time, this curious retreat to the supposed sources of Aristotle becomes in fact a means of advancing beyond Aristotle in the direction of a theory a good deal more complicated than that found either in Aristotle or in Pseudo-Pythagorean texts. ²¹ 

²¹ Cf. above, p. 68. Much could also be said about Iamblichus' use of specific Pythagorean principles in the interpretation of Aristotle's Categories; cf. Iamblichus, In cat. frs. 33, 37, 53, 56, 58.

The reconstruction of Books V and VI of On Pythagoreanism suggests that Iamblichus' attitude there to Aristotelian physics and ethics was similar to his view of Aristotelian logic in his Commentary on the Categories. He could follow Aristotle's physical and ethical treatises, and yet correct them and substitute Pythagorean materials where appropriate, on the assumption that those treatises were fundamentally Pythagorean in inspiration, if sometimes corrupted or perverted in relation to their source. ²² 

²² Cf. Syrianus, In met. 192, 15-27.

Turning to the evidence concerning Iamblichus' commentaries on Plato, we find Pythagoreanism important both in Iamblichus' theories about the Platonic corpus and its exegesis, and in his interpretation of individual dialogues. It is a well-established fact that Iamblichus fixed the canon of Platonic dialogues which became 'for more than two centuries the standard curriculum in the Platonic schools'. ²³ 

²³ Westerink, in Anon. Prol. Plat. xxxvii.

This canon consisted of two cycles, the first including ten dialogues dealing successively with ethical, logical, physical, and theological subjects, the second comprising two dialogues, the Timaeus and Parmenides, which sum up the first ten dialogues and cover respectively physics and theology. ²⁴ 

²⁴ Cf. Anon. Prol. Plat. xxxvii-xl; Festugière (1969).

This arrangement is hardly arbitrary. Its closest analogue is mathematical: the decad that comprises all numbers, and the first two numbers, the monad and dyad, that pre-contain and produce all other numbers. Porphyry, it might be recalled, had also organized Plotinus' treatises in his edition along numerical lines, dividing them into six sets of nine ('Enneads').

The first dialogue in the first cycle, the Alcibiades, was regarded by

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Iamblichus as containing implicitly all that would emerge in the following dialogues, i.e. logic, ethics, physics, and theology. At least, this is Proclus' understanding of why Iamblichus gave the Alcibiades first place in the cycle. Proclus says:

And indeed it seems to me that it is for this reason that the divine Iamblichus allotted it the first place among the ten dialogues in which he believes the whole philosophy of Plato to be contained, their entire subsequent development being pre-contained as it were in seminal form in this dialogue. ²⁵ 

²⁵ Iamblichus, In Alc. fr. 1 (transl. Dillon, slightly modified).

The metaphor of a seed as 'pre-containing' what will evolve from it is common enough in Neoplatonic philosophy. It should be noted, however, that the subject here is the first member of a series of ten, i.e. a monad, and that the metaphor of the seed appears in Nicomachus and Iamblichus as a way of describing how the monad pre-contains the other numbers of the decad that flow out from it. ²⁶ 

²⁶ Cf. Nicomachus, Intro. arith. 113, 2-6; Iamblichus, In Nic. 11, 11-17; 81, 23-4, and especially 10, 12-13; Hermias, In Phaedr. 141, 16-17; Syrianus, In met. 3, 22-3.

This provides further evidence of the mathematical conception underlying Iamblichus' canon of Platonic dialogues. For in the first cycle of this canon Iamblichus compared the relation between the first and the following dialogues to the relation between monad and the rest of the decad.

One might also note that in terms of the system of philosophy of On Pythagoreanism there is one important gap in the ascending sequence of sciences covered by both cycles of Platonic dialogues, a gap coming between physics and theology. Mathematics, namely, is missing, i.e. the pivotal stage covered in On Pythagoreanism.

Some of the exegetical principles Iamblichus applied in interpreting Plato are regarded by him as Pythagorean. One of these consists in explaining the absence of certain matters in a text in terms of the need to introduce various subjects in appropriate contexts, so that, for example, more profound ideas should be presented in higher, more technical treatments. This principle is applied in On Pythagoreanism, as we have seen, and is used by Iamblichus in interpreting Plato's Timaeus:

. . . he has allotted deeper investigation of these matters to more suitable occasions; for this was the custom not only of Plato but before Plato of the Pythagoreans, which indeed was something that Aristotle particularly sought, to deal with the problems of philosophy in essays devoted each to a special subject. ²⁷ 

²⁷ Iamblichus, In Tim. fr. 66 (transl. Dillon). Cf. Dillon's argument for this passage as Iamblichean, (1973), 350-1.

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A related Pythagorean principle is applied by Iamblichus as a method of exegesis in interpreting the opening part of Plato's Timaeus:

Others consider that it Republic> has been placed before the whole physics as an image of the organization of the universe. For it was the custom of the Pythagoreans to place before scientific teaching the revealing of the subjects under enquiry through similitudes and images, and after this to introduce the secret revelation of the same subjects through symbols . . . ²⁸ 

²⁸ Iamblichus, In Tim. fr. 5 (transl. Dillon, slightly modified).

The Pythagorean method of teaching through images and symbols is described in On Pythagoreanism. ²⁹ 

²⁹ Dillon ad loc. refers to Vit. Pyth. 37, 4-7; 59, 17-60, 1; cf. also Pr. 104, 26 ff.

The recourse to Pythagorean practices as providing exegetical principles was particularly suitable in relation to Plato's Timaeus, since it seems that in his Commentary on the Timaeus Iamblichus regarded Timaeus' discourse as Pythagorean:

One should put it this way, then, that Timaeus, being a Pythagorean, follows Pythagorean principles ( χαι ς). And these in turn are Orphic principles . . . this Pythagoras himself states. ³⁰ 

³⁰ Iamblichus, In Tim. fr. 74 (transl. Dillon); cf. above, n. 13, and Dillon's commentary, (1973), 363-4.

A rapprochement between Pythagoras and Orpheus has already been found above in On Pythagoreanism. Iamblichus' approach to Timaeus' discourse also suggests that in his commentary he made use of Pythagorean mathematical principles in the interpretation of Timaeus' physics, much as he had emphasized mathematical principles in his Pythagoreanizing of Aristotle's physics in On Pythagoreanism V. The evidence indeed shows that Iamblichus referred to the relations between the monad and the numbers flowing from it in explaining the relations in the Timaeus between the 'Model Living Being (τ α τοζ ον)' and other living beings (fr. 43), between transcendent soul and other souls (frs. 50, 54), and between the gods (fr. 77). Nor is it unexpected that when he came to Timaeus' account of the constitution of soul through various numbers, Iamblichus drew attention to the special properties ( δι ματα) of the numbers concerned, those properties paradigmatic and symbolic of the structure and dynamic of physical and of transcendent reality. ³¹ 

³¹ Iamblichus, In Tim. fr. 53; cf. also fr. 48. In some brilliant pages Harder (1926), xvi-xvii, argues that Iamblichus used a text (falsely) attributed to the Pythagorean Timaeus of Locri in his Commentary on the Timaeus, in the way that he used the Pseudo-Archytas in his Commentary on the Categories.

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The Pythagoreanizing tendencies of Iamblichus' commentaries on Aristotle and Plato deserve a larger treatment than that provided here. ³² 

³² Cf. also Iamblichus, In Philebum (a 'theological' dialogue) fr. 3, where Iamblichus follows 'Pythagoras' in his exegesis of a passage. Cf. Praechter (1910), 191-3 with 200 n. 2.

However, the brief review of the subject that I have proposed is adequate, I believe, for the purpose here pursued, namely to show that Iamblichus' interest in Pythagoreanism was not limited merely to composing a work on the subject. In his Commentary on the Categories he considered Aristotle's text to be a somewhat corrupt version of Pythagorean theory. (On Pythagoreanism V and VI imply a similar attitude to Aristotle's physics and ethics.) Not enough is known of Iamblichus' commentaries on other works of Aristotle to determine if such an approach was adopted there too. In discussing Plato's dialogues Iamblichus resorted to Pythagorean ideas (as he understood them) to explain his canon of Platonic dialogues and to produce exegetical methods to be applied to it. He regarded the Timaeus as a physics based on Pythagorean principles. And when his reader moved up the scale of dialogues, reaching the highest level, the theological dialogues (Philebus in the first cycle, Parmenides in the second cycle)—equivalent to the highest level of Pythagorean philosophy according to On Pythagoreanism—there too he would read texts which were, if we follow Iamblichus' interpretation of Plato in On Pythagoreanism, Pythagorean in inspiration.

It has been noted above that Iamblichus explicitly connects On Pythagoreanism with his work On God (Gods?). In view of his understanding of the relations between Pythagoreanism, Plato, the Egyptians, and Chaldaeans, On Pythagoreanism is also implicitly connected with his works on Platonic, Egyptian, and Chaldaean theology in so far as they constitute appropriate sequels to it. The general position in On Pythagoreanism regarding the relations between Pythagoras, Plato, and Aristotle is also found in, and governs, his commentaries on (at least some of) the works of Plato and Aristotle. Both Plato and Aristotle owe their philosophy to Pythagoras. When Aristotle diverges, he corrupts the truth in its tradition among men. This latter idea appears in a larger context in On Mysteries, where knowledge is regarded as a divine revelation, mediated by priests, mages, etc., and gradually corrupted with time. From this point of view the Greek philosophical tradition derived from Pythagoras appears as a relatively recent (thus

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corrupted) stage. Could this also be the ultimate point of view presupposed in On Pythagoreanism? The same theory of a divine revelation of knowledge to man is found there, the same recourse to the ancients (in Greek philosophy). The connections with Egyptian and Chaldaean teachers are made. But the evidence goes no further. Certainly the historical thesis of On Mysteries was not confined to that work. It is found again in what survives of one of Iamblichus' more technical philosophical treatises, On the Soul, where the tradition of Greek philosophy and especially its best representatives, Plato and the Pythagoreans, are measured (to their disadvantage) against a more venerable authority, the 'ancients', meaning apparently the Egyptians and Chaldaeans. ³³ 

³³ Cf. Iamblichus, De an., in Stobaeus, Anth. I 366, 5-11; 384, 27-28 (with Festugière's note, [1950-4], III 236 n. 3); especially 454, 25-458, 21 (with Festugière's notes, 240-8, 263). More and less accurate (and pure) forms of Platonism/Pythagoreanism are distinguished at 364, 6; 382, 11; 454, 27, corresponding sometimes (not always) to earlier and more recent times: cf. 365, 5-366, 11. Cf. Larsen's discussion (1972), I 197 ff., of the De an.

3. Iamblichean Pythagoreanism and Its Predecessors

In the final section of this chapter I would like to compare Iamblichus' Pythagoreanizing tendencies with those of his predecessors, notably the philosophers of the second and third centuries ad discussed above in Chapter 1. If Iamblichus' Pythagoreanism is to be assessed correctly, it must be viewed not only within the context of his other work, but also in its relations—of debts and of difference—with its predecessors. Since the fragmentary nature of the evidence concerning most of Iamblichus' work does not permit of asserting without reserve that his understanding of the place of Pythagoras in the history of Greek philosophy and, more broadly, in the tradition of knowledge among men, remained the same in each of his works, ³⁴ 

³⁴ However, the frequent connections observed above, not only in sect. 2 of this chapter, but also in Ch. 3, suggest considerable continuity.

it will be prudent to consider separately various aspects of Pythagoreanism appearing in his different works.

The conception in On Mysteries (also assumed to some degree in On the Soul) of Greek philosophy as a relatively modern, somewhat degraded version of the teachings of ancient Egyptians and Chaldaeans (themselves divinely inspired) appears to have been central to

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many of Porphyry's writings. This was not of course a new idea. As has been pointed out, it was a popular notion since the time of Plato and Aristotle. However, by writing extensively about the Egyptians, Chaldaeans, Persians, as well as about ancient Greek sages, Porphyry gave to this non-philosophical literature an important place in the reading-lists of later Greek philosophy. Plato and Aristotle became subordinate figures, even if, in fact, they provided the system in terms of which the more ancient literature was understood.

If Iamblichus' immediate debt to Porphyry in this respect is evident, his position also seems in some aspects somewhat different. He appears more committed to Porphyry's view than Porphyry himself was. At least, this is the case in regard to Porphyry's Letter to Anebo which, although expecting to find the answers to Greek philosophical questions in Egyptian religion, nevertheless formulates philosophical criticisms of certain religious practices. In On Mysteries, however, Iamblichus is quite radical in his insistence that all aspects of Egyptian religion must be accepted, though through an interpretation of them, it must be said, that is highly philosophical.

A comparison of Porphyry and Iamblichus on this subject also suggests that Iamblichus was more systematic in the subordination of Greek philosophy to ancient revelation. This subordination expresses itself in the conception of a historical tradition of knowledge among men which is also a gradual corruption of this knowledge. In view of Porphyry's historical erudition one can certainly suppose that such a conception may have been inspired by him. But the emphasis in Iamblichus on a degradation of truth coming with its expression in time reminds one rather of the degradation that had been traced already by Numenius on a smaller scale in his history of Plato's Academy.

If one turns from the universal tradition of knowledge to its expression among the Greeks, one can also observe a more committed and systematic approach in Iamblichus' commentaries on the Categories and on the Timaeus, as well as in On Pythagoreanism, with regard to the relations between Pythagoras, Plato, and Aristotle. Certainly Porphyry tended to Pythagoreanize Platonism and Platonists (Plotinus), and also brought Aristotle into the Neoplatonic curriculum. But in the evidence concerning him there is no equivalent to Iamblichus' rigorous reduction of all in Plato and all that he thought good in Aristotle to Pythagoreanism. Such a reduction was greatly facilitated by the availability of supposedly Pythagorean works that Iamblichus took

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to prove the dependence of Plato and Aristotle on Pythagoreanism, although in fact they were cribbed from Plato and Aristotle. ³⁵ 

³⁵ On Iamblichus' unprecedented activity in resurrecting Pseudo-Pythagorica cf. Harder (1926), xv ff.

In this way Pythagoras assumes a dominant role in Greek philosophy such as he does not appear to have in Porphyry. And as the Egyptians and Chaldaeans are original revelatory sources for all mankind, so Pythagoras is for Greek philosophy. Here again, I believe, we must refer to Numenius, to his rigorous reduction of 'true', 'pure' Platonism (as contrasted with its corrupted, i.e. materialized, forms) to Pythagoreanism. However Aristotle, in Numenius, was not, as far as we know, projected backwards on to Pythagoras (and thus integrated) in the way that he is in Iamblichus.

When it comes to the description of what actually constitutes 'Pythagorean philosophy', Iamblichus, in On Pythagoreanism, can be said to follow the lead of Nicomachus. He adopts Nicomachus' restriction of Pythagorean philosophy to the most 'scientific' form of knowledge, namely that corresponding to immaterial and unchanging reality. He exploits Nicomachus' notion that each number has specific properties ( δι ματα) in developing mathematical paradigms for physics and ethics. Such analogies to physics and ethics are also inspired by Nicomachus, as is the justification for the analogy to physics, namely the idea that the material world is structured according to the properties of numbers. The assimilations that Nicomachus proposed between numbers and deities were also taken up (but with some important changes that will be noted below) by Iamblichus. Indeed it can be said that Nicomachus' Introduction to Arithmetic and Theologoumena arithmeticae are the most important source of inspiration for On Pythagoreanism as a whole.

At the same time, however, there are fundamental differences between Nicomachus and Iamblichus. In general, Iamblichus' view of the system of philosophy and of the structure of reality is much more complicated, reflecting in fact the thought, not of a second century Platonist, but of Porphyry's most important and original pupil. The science of pure immaterial numbers is by no means the highest, as it appears to be in Nicomachus. Above the purely mathematical level are 'intellectual', 'intelligible', and 'divine' orders, all transcended by an ultimate principle, 'the One'. Mathematics thus is returned from the dominant position it seems to have in Nicomachus to an intermediary position such as is assigned to it

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in Plato's Republic. ³⁶ 

³⁶ Cf. Comm. 87, 17-88, 2, where Iamblichus insists, against the opinion of 'many of the more recent Pythagoreans', that mathematicals are neither the only nor the highest principles of reality and of science.

As a consequence Iamblichus is aware of the limits to an 'arithmetical theology': such a theology is based on analogy inferior to a higher, more commensurate grasp of the divine unities that transcend being.

If Iamblichus is closer to Nicomachus in his mathematical physics and ethics, he also shows considerable independence. He separates off into separate volumes the analogies to physics, ethics, and theology, which are treated together in Nicomachus' Theologoumena. He develops these analogies far beyond anything in Nicomachus by working them out in relation to Aristotle's physics and ethics. In theology, Iamblichus' approach in On Pythagoreanism VII may have come nearer to Nicomachus', yet the metaphysical system guiding this approach was considerably more complicated than that to be found in Nicomachus.

The impression of eclecticism that such comparisons between Iamblichus and his predecessors may convey must be corrected by emphasis on the fact that a comprehensiveness and systematic rigour are found in Iamblichus' conception of the nature of Greek philosophy that are not found in his predecessors. Not only is the reduction, in On Pythagoreanism and in some of the commentaries on Plato and Aristotle, of Greek philosophy to Pythagoreanism more comprehensive than it is in Numenius, more radical than it is in Porphyry, but its subordination, in On Mysteries and On The Soul, to an ancient revelation is more emphatic than in Porphyry. And if Iamblichus is indebted to Nicomachus in his account of what 'Pythagorean' philosophy actually consists of, he nevertheless transformed Nicomachus' Pythagoreanism so that it could express the much more developed system of philosophy and of reality of a successor to Plotinus and to Porphyry. That system was in turn transformed by the fact that it was now seen as 'Pythagorean'. For if mathematics was neither the only nor the dominant science, it nevertheless provided the concepts and theories in terms of which the objects of other sciences could be approached. Mathematical terms and concepts are of course by no means uncommon in the Platonic tradition. But the systematic mathematization which is so striking a feature of later Greek Neoplatonism, the pervasiveness of concepts of monad, dyad, triad, etc., is surely the consequence of Iamblichus' ambitious programme to

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Pythagoreanize Platonic philosophy. There had been, of course, earlier attempts by Platonists to revive Pythagoreanism—we have considered the examples of Numenius and Nicomachus—but Iamblichus' attempt was certainly the most elaborate and the most influential. ³⁷ 

³⁷ In the Conclusion I shall suggest some hypotheses concerning why Iamblichus sought to revive Pythagoreanism.

In the following chapters the extent of this influence will be examined in particular in the cases of two later Neoplatonic philosophers, Syrianus and Proclus.

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Part II Iamblichean Pythagoreanism in the Athenian School

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5 Hierocles

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Dominic J. O'Meara

Iamblichus died sometime between 320 and 326, having attracted a large following as master of a flourishing philosophical school in Syria. ¹ 

¹ Cf. Dillon (1973), 6, 11-14.

Of his pupils, only Dexippus and Theodorus of Asine are represented in a significant way in the surviving evidence. ² 

² Cf. P. Hadot (1974); Deuse (1973).

Of more importance is the influence Iamblichus would exert after his death on a philosophical school that emerged at Athens in the early 400s, the school of Plutarch of Athens, Syrianus, and Proclus. In Part II of this book I examine in particular the impact Iamblichus' Pythagoreanizing programme may have had on the Athenian school. I hope thus to reach an answer to the question as to the extent to which this programme, in reducing Plato and Aristotle to Pythagoras and in approaching in consequence the philosophical sciences along mathematical lines, gave new direction to the development of later Greek philosophy.

Syrianus had, as I shall show, an intimate knowledge of Iamblichus' work On Pythagoreanism: it inspired in particular the conception of true, i.e. 'Pythagorean' philosophy adopted in his Commentary on Aristotle's Metaphysics. It will be shown also that Proclus was familiar with On Pythagoreanism and used it as a source in his own work. Thus On Pythagoreanism constitutes a concrete link between Iamblichus and the first influential members of the Athenian school, a specific text in terms of which the degree of his influence on that school can be assessed in a detailed way.

The analysis will be guided by the two major questions discussed in Part I, namely (i) what is the place of Pythagoras in the history of Greek philosophy? (ii) What is the role of mathematics in philosophy? In looking at the positions taken by Syrianus and Proclus on these issues, I hope to indicate not only the ways in which they are inspired by Iamblichus, but also the ways in which they alter the programme formulated in On Pythagoreanism. Iamblichus' treatise will serve thus not only as an historical background for understanding certain ideas in Syrianus and Proclus, but also as a gauge against which the development of their own philosophical positions can be measured.

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1. The Introduction of Iamblichean Philosophy at Athens in the Fourth Century

Proclus, looking at his intellectual genealogy, saw himself as part of a succession going back from his teacher at Athens, Syrianus, to Syrianus' own master Plutarch of Athens (died 431/2) and from Plutarch back to Iamblichus. ³ 

³ Cf. Procl. In Parm. 1058, 21-2; Theol. Plat. IV 70, 12-13, with Saffrey and Westerink's note 3 (168).

If the succession leading from Plutarch to Proclus is clear enough (indeed as a young man Proclus had joined Plutarch's school a few years before Plutarch died and was succeeded by Syrianus), the link between Plutarch and Iamblichus is less evident. Separated from Iamblichus by more than one generation, Plutarch, we must suppose, was introduced to Iamblichean philosophy by followers of Iamblichus. There are indeed good indications that by the end of the fourth century Iamblichean philosophy had become part of the intellectual life of Athens. As the evidence for this has already been carefully presented and discussed, ⁴ 

⁴ By Saffrey and Westerink, in Proclus, Theol. Plat. I xxxv-xlviii.

I need do no more than summarize the more important points.

In the middle and late part of the fourth century a certain Priscus, philosopher and pupil of Aidesius (himself a disciple of Iamblichus), was resident in Athens. It was to him that the Emperor Julian turned in order to obtain a copy of Iamblichus' Commentary on the Chaldaean Oracles. This Iamblichean presence in Athens was strengthened towards the end of the century when another Iamblichus settled there. Named after the philosopher, he was grandson to Sopatros, Iamblichus' successor in the school in Syria. The relation between 'Iamblichus II' and Iamblichus was not merely one of name and family. Libanius places 'Iamblichus II' under the tutelage of Pythagoras, Plato, and Aristotle (as well as that of Iamblichus) and he is commemorated as having contributed with his wisdom, as well as with his generosity, to Athens in an inscription of c.400.

There was therefore ample opportunity at Athens for Proclus' philosophical 'grandfather' to come in contact with Iamblichus' ideas. So little, however, is known about Plutarch that not much more can be said about his contacts with Iamblichean philosophy than that he had pupils, namely Hierocles and Syrianus, who adopted this philosophy and attributed this to his direction. ⁵ 

⁵ Cf. Hierocles in Photius, Bibl. III 129-30, 173 a; for Syrianus, cf. below, Ch. 6.

The scarce evidence concerning

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Plutarch has even given some scholars the impression that Plutarch broke on certain issues with the Iamblichean tradition. This flies in the face, however, of the professed debts of Plutarch's Iamblichean pupils to their teacher and argues at best for the inadequacy of our information on Plutarch. ⁶ 

⁶ Cf. Saffrey and Westerink in Proclus, Theol. Plat. I, lxxxiv-lxxxviii; Blumenthal (1975); I. Hadot (1978), 74.

We are on safer ground, when it comes to the analysis of specific subjects, if we turn to those pupils of Plutarch whose work has in part at least survived.

Among Plutarch's pupils, Hierocles and Syrianus have already been mentioned as well as Proclus, who joined the Athenian school shortly before Plutarch's death. Proclus was certainly younger than Syrianus and probably also Hierocles' junior. But what little is known of Hierocles' life ⁷ 

⁷ Cf. I. Hadot (1978), 17-20; Aujoulat (1976).

—that he studied with Plutarch, to whom he claimed philosophical allegiance, and taught Platonic philosophy in Alexandria—is not enough to determine if he was Syrianus' senior, contemporary, or junior. For reasons of exposition I shall discuss Hierocles first, moving then to Syrianus, whose work is more immediately relevant to an examination of Proclus. If Hierocles' writings are contemporary with or later than Syrianus' Commentary on the Metaphysics, they do not constitute the earliest evidence of the influence of Iamblichean 'Pythagoreanism' on the Athenian school. If, however, they are earlier than Syrianus' Commentary they can indeed be claimed as providing the first signs of this influence. These signs may be found in the remarkable theory of the history of philosophy presented in Hierocles' work On Providence and in the use made of Pythagoreanism in Hierocles' Commentary on the (pseudo-Pythagorean) Golden Verses.

2. Hierocles on the History of Philosophy

The interest of Hierocles' views on the history of philosophy in On Providence has recently been emphasized and their Iamblichean origin demonstrated. ⁸ 

⁸ I. Hadot (1978), 67-76, and (1979), who has effectively disproved Praechter's theory that Hierocles represents a 'primitive' Alexandrian (i.e. pre-Plotinian) Christian-type philosophy, a theory recently adopted by Kobusch (1976), on whom cf. Baltes (1978a).

There are some aspects, however, which may be

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explored further in the light of what has emerged in Part I concerning Iamblichus' treatise On Pythagoreanism.

Hierocles' work On Providence survives in the form of a two-part précis given by the Patriarch Photius in his Bibliotheca (cod. 214, 251). Photius emphasizes in his account Hierocles' desire to show a harmony between the views of Plato and Aristotle on the subjects of providence, fate, and free will. That the impression conveyed by Photius here is unbalanced can be seen from his own indications about the contents of On Providence (cod. 214, 173 a), according to which the discussion of Aristotle was a subordinate part of a much larger scheme. ⁹