56 Cf. Also 137, 6-10; 138, 27-139, 1; 142, 10-12; Proclus, In Tim. I 310, 3-311, 4 (on Syrianus).

Of particular interest is the source of Syrianus' disagreement with Iamblichus. The latter had identified the Zeus of the Phaedrus, the first member of a series of twelve, with the demiurge of the Timaeus. But, for Syrianus, the demiurge is not the first of a series of twelve. He is rather a transcendent intellectual monad, principle (via a triad) of the series of twelve as a whole. In other words precisely because of the sort of mathematical principles that Iamblichus had used for theology—here in particular the distinction between the first (immanent) member of a series and the transcendent principle of the series as a whole—his interpretation of the theology of the Phaedrus must be amended. ⁵⁷ 

⁵⁷ The distinction between immanent and transcendent monad is also applied to theological relationships at 152, 15-19. One might mention here also Syrianus' insistence, against Iamblichus, that the ultimate One is not to be treated as if co-ordinate with the henads in the interpretation of the first hypothesis of the Parmenides (cf. Saffrey and Westerink in Proclus, Theol. Plat. III xl ff.).

Proclus reports another case of Syrianus being more rigorous in his application of mathematics than Iamblichus, ⁵⁸ 

⁵⁸ In Tim. I 20, 27 ff.

and the general spirit of this disagreement is well expressed by a later member of the Athenian school:

This is Simplicius' work, Iamblichus bestower of blessings, Forgive my defeating you, but it is through your words! ⁵⁹ 

⁵⁹ Scholium on Proclus, In Tim. I 175, 2 (468, 15-16); cf. Saffrey and Westerink in Proclus, Theol. Plat. I cliii; I. Hadot (1987b), 30-1.

It is likely enough that were more to be recovered of Iamblichus' lost works and were a truly comprehensive and detailed treatment by Syrianus of the structure of reality available, other differences could be noted. Useful comparisons could also be made between the hosts of lesser deities and demons in Iamblichus' On Mysteries and their counterparts, 'hypercosmic' and 'encosmic'—of which the 'jovial'

end p.139

plethora encountered above is but a dismaying sample!—in Syrianus and Hermias. Enough evidence has, however, been collected, I believe, to conclude that Syrianus' general approach to the structure of reality owes much to Iamblichus, and in particular to On Pythagoreanism. Number permeates this structure, not in virtue of the crude identifications of numbers with things that Aristotle finds in the Pythagoreans, but in virtue of the intermediate and pivotal status of mathematical objects: as exemplars of the physical world they express paradigmatically the formal principles immanent in the world; as lower images they foreshadow their origins, the realm of Forms and its own ultimate principles. In distinguishing between many levels or sorts of number—physical, mathematical or psychic, intellectual, intelligible, henadic or divine—Syrianus follows Iamblichus' example and also emphasizes Iamblichus' point that this expresses the transposability of mathematicals to other domains. The result, in Syrianus as in Iamblichus, is a 'physical arithmetic' and a 'theological arithmetic'. If the latter is much more fully represented in Syrianus' Commentary on the Metaphysics than in the few remains of Iamblichus' On Pythagoreanism VII, its function on the whole is somewhat negative: it acts as a standard against which Aristotle's anti-Pythagoreanism is corrected, rather than as a science presented in its own right. However, enough emerges to indicate that Syrianus, like Iamblichus, finds in mathematics distinctions and relationships that can be used to describe the characteristics of Forms, the structure of the realm of Forms, and its relation to a higher order, that of 'henads', which is also approached in mathematical terms. Syrianus is as aware as is Iamblichus that such a 'theological arithmetic' is based merely on analogy. Besides the evidence given above from Syrianus' Commentary, a good example of this methodological caution can be found in Hermias. The subject in question is again the series of twelve gods of the Phaedrus:

Some fit, in an arithmetical way, each of the ten gods (subtracting two monads from the twelve) . . . to the ten numbers of the decad . . . , giving the monad to Apollo, the dyad to Hera,. . . But is not to be understood in a simple arithmetical fashion, but each god organizes and is provident according to his characteristic ( δι της). . . . The characteristic of each is to be learnt from theology. . . . So there are certain characteristics in numbers which imitate the characteristics of the gods and are thus transposed to them. (139, 3-20).

Syrianus rejects the simple identifications of numbers with gods found in traditional Pythagorean decadic works such as that attributed to

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Anatolius. If he frequently compares the numbers with the gods ⁶⁰ 

⁶⁰ Cf. e.g. Hermias, 90, 21 ff.; 137, 4-6; 138, 11-13.

it is on the basis of transpositions whose basis and limitations he recognizes. Mathematics can help to lead us to higher things (191, 10-12). It can function as a 'bridge'—Nicomachus' image used by Syrianus in his Commentary (In Met. 96, 28-30). But its discursive methods and the images it uses are inferior in metaphysics to the direct 'insight' into the Forms and what transcends them such as is revealed by the inspired poets and the divine souls of Pythagorean philosophers.

end p.141

7 Proclus: Some Preliminary Issues

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