64 In met. 181, 34-185, 27, especially 183, 26-9.

The passage at 59-63 in Psellus' excerpts, which, as noted above, appears to have nothing in common with the other excerpts, discusses the difference between the Good and the One and compares the

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multiplication of the One with the multiplication of the Good. In the case of the latter this multiplication relates to the nature of the Good, which is generative (γ νιμος ο σα, 60). The connection between these themes and Syrianus' commentary suggests a possible context for Psellus' excerpt: a reaction to a specific argument forming part of Aristotle's rejection of separately existing Forms or numbers in Metaphysics MN. ⁶⁵ 

⁶⁵ It is not clear which, if either, horn of Aristotle's dilemma Iamblichus accepted. The emphasis on multiplication points to Syrianus' position, yet the excerpt speaks of 'difference' (perhaps Psellus' word). Cf. Iamblichus, De myst. 261, 9-14 (quoted below, p. 82). Did Iamblichus produce a commentary on Aristotle's Metaphysics? Dillon (1973), 22, does not provide sufficient evidence of such a commentary. However Simplicius, In de an. 217, 23-8 (referred to by Steel [1978], 124) indicates that Iamblichus discussed at least the σκοπ ς (goal or intention) of Met. Λ (cf. also the scholium on Iamblichus, Pr. 22, 1 ff. printed at Pr. 127, 16-19).

This context would disclose in turn the relation between this excerpt and the other excerpts, which have to do with 'ideal' and 'divine' numbers.

If these conjectures about the original context of the excerpt at 59-63 are correct, they would show that at some point in On Pythagoreanism VII Iamblichus came to terms, to some extent, with Aristotle's criticisms of Platonic theories of Forms or 'ideal numbers'. If some compromise or adjustment was possible between Aristotle and Pythagoreanism—Platonism in the realms of physics and ethics, it was hardly so when Iamblichus came to the subjects of Aristotle's Metaphysics. ⁶⁶ 

⁶⁶ Cf. Syrianus' general assessment of Aristotle (In met. 80, 4-81, 6; discussed below, Ch. 6).

In order to present a science of separately existing ideal and divine numbers, Iamblichus would have to overcome the arguments in Metaphysics MN. However, there is no other trace of this response to Aristotle in Psellus' excerpts, ⁶⁷ 

⁶⁷ Syrianus cites On Pythagoreanism VII while discussing Met. M, 8 (In met. 140, 2-15), but not in such a way as to imply that Iamblichus was also dealing with the Aristotelian passage.

and it may not have been a major preoccupation in On Pythagoreanism VII. There is no trace, either, in Psellus' excerpts of a positive theory of 'ideal' or 'intelligible' numbers corresponding to the Forms, which Iamblichus could have presented in conjunction with his response to Aristotle, although earlier references may lead one to expect such a theory in On Pythagoreanism VII. ⁶⁸ 

⁶⁸ Cf. above, pp. 60, 62 (but the references are a little vague, and the title of Book VII includes no reference to an 'ideal' [ δητικ ς] arithmetic).

The excerpts concern almost entirely a sort of number which appears to be different, 'divine' number. The approach used by Iamblichus in treating of this sort of number will emerge as its nature is examined.

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(II) Divine Number

Psellus' theological excerpts begin with a summary and a quotation (53-8) emphasizing the transcendence of 'divine number' in relation to other sorts of number, 'hypostatic' (= mathematical?), 'self-moved' (= psychic), ⁶⁹ 

⁶⁹ Cf. Iamblichus, In Tim. fr. 55, 12-13, and above, p. 62.

intellectual (νο ς), essential (ο σι δης, i.e.: ideal or intelligible) ⁷⁰ 

⁷⁰ Cf. Psellus, On Phys. Numb. 4-5.

number. The sorts of numbers listed correspond to different and ascending degrees of reality. A roughly equivalent list, this time given in descending order, appears already in On Pythagoreanism III, where the Pythagoreans are said to 'fit' mathematicals (including numbers) to the gods, 'to their being and power, order and activities, according to an appropriate assimilation—what they thought especially worthwhile—finding which numbers are related and similar to which gods'; then to the intellectual (τ νο ον), pure being, i.e. ideal ( δητικ ν) number; then to self-moved existence, defined as self-moved number; then to the heavens and to enmattered forms, i.e. physical numbers (Comm. 63, 23-64, 19). The 'intellectual' and the 'intelligible' (pure being) are treated as one in this passage, although they are distinguished in Psellus. But a report in Syrianus confirms that Iamblichus wished to distinguish them in On Pythagoreanism VII:

Since, when they discuss the divine monads, they define differently the intelligible monad (νοητ ν . . . μον δα) from which comes forth the very first number . . . , from the intellectual and demiurgic monad (νο ν κα δημιου γικ ν) . . . concerning which many of the ancient and more recent have spoken, but most clearly of all the divine Iamblichus in the seventh book of his Pythagorean treatise. ⁷¹