75 Cf. Also 81-4, where the 'supernatural' beings are described as unities, ν σ ις.

presupposes a cause of its unity which, as such, must be prior and superior to it (κατ′ α τ αν π οηγουμ νη).

end p.81

This is a fundamental addition to the structure of reality sketched above: prior to and above the level of the gods (themselves 'above' being) is an ultimate principle of the unity of the gods.

Something very similar can be found in Iamblichus' On Mysteries. Here, in one passage, Iamblichus speaks of ascending degrees of unity ( νωσις) and being, culminating with the gods:

As for the gods, their order consists in the unity ( ν σ ι) of all; their primary and secondary classes and their many products all came to be in unity. The all in them is the One; the 'beginning, middle, and end' come to be according to the One. ⁷⁶ 

⁷⁶ 59, 15-60, 2. The Pythagorean motto is cited also in Psellus, On Eth. Theol. Arith. 72.

If it is not clear from this passage that the gods are above being and depend themselves on a higher principle for their unity, this can be shown from a later passage of On Mysteries:

Before true beings and the universal causes there is one god, the very first, even before the first god and king, remaining unchanging in the singleness of his unity. There is nothing intelligible or otherwise added to him. He is the model of . . . the one father god, the true good, for he is something greater and the first and the source of all. . . . From this One the self-sufficient god shone himself forth . . . , for he is cause and god of gods, monad from the One, prior to being and caüse of being. ⁷⁷ 

⁷⁷ 261, 9-262, 5 (Festugière [1950-4], IV 23 ff., has noted the Pythagorean character of this text). The same structure, in its basic features, is attributed to Iamblichus by Damascius (using Iamblichus' Commentary on the 'Chaldaean Oracles'), De princ. I 86, 3 ff. P. Hadot's argument (1968), I 97 n. 1, against the rapprochement of the texts in De myst. and in Damascius does not note that the monad named in Damascius is intelligible, which makes the principle above it equivalent to the supra-intelligible monad (or 'god of gods') of De myst., and the principle yet above it the same as the ultimate One, cause of the 'god of gods' in De myst.

Certain aspects of this text are clarified in a comparison with Psellus' excerpts, notably the expression 'god of gods': this indicates that the first god arising from the ultimate One is the source of the other gods, or, in arithmetical terms, the monad of divine number. On the other hand the text of On Mysteries suggests a possible reason why Psellus, in his excerpts, appears to have compared the first of the gods (rather than its source, the ultimate One) with the Christian god. ⁷⁸ 

⁷⁸ Cf. lines 70-2, discussed immediately below.

Had Iamblichus used expressions such as those used in On Mysteries of the first of the gods, e.g. 'first god and king', a superficial reader could

end p.82

have easily taken this to be equivalent to the highest Christian principle.

We have already moved in Psellus' excerpts from the ultimate One, cause of the unity of divine number, to the first of the series of divine numbers, the 'first god'. It is referred to as 'the first', the 'one', a 'henad', and 'triad' (70-1). The latter description shows, unless Psellus' excerpting is seriously misleading here, that Iamblichus is referring to the first of the gods and not to the ultimate One. Describing it as a triad is to indicate, by means of a Pythagorean motto (72, cf. above, n. 76), its dependence on a principle of unity. Is the term 'henad' equivalent to the term 'monad' used in On Mysteries of the first god? The structural correspondence between the systems of On Mysteries and of Psellus' excerpts suggests that it is, but the excerpts themselves do not yield specific evidence confirming this. ⁷⁹ 

⁷⁹ In a reference slightly later (86) to the gods as the 'divine one and (κα ) divine monad and divine dyad . . . ,' the first 'and' might possibly indicate a distinction. On the concepts of ν ς and μον ς cf. Burkert (1972), 231, Staehle (1931), 19.

If however Iamblichus organized his discourse about the gods on the analogy with the decadic series, one would expect that he would begin by reference to the first of the gods as monad. And Iamblichus, it appears, did refer to a divine monad, for Psellus' excerpts list monads at lower levels—an intelligible monad, a demiurgic monad, an earthly (physical) monad (73-5). Since the treatment of the 'divine' dyad is followed by a similar list of lower levels of dyads (75-8), the list of monads must also have been headed by reference to a divine monad in Iamblichus. But Psellus omits this, which makes his excerpting here particularly obscure and disjointed.

Once the monad in the decadic series was applied by analogy to the gods, more especially (and quite probably) to the first of the gods, source of the other gods, and himself originating from the ultimate One, we would expect that the other numbers in the series, dyad, triad, etc., would have been brought by Iamblichus into relation with the series of the gods. Of this, however, Psellus preserves only a few lines concerning the dyad and triad. The 'divine' dyad is described as 'unlimited power, never failing progression of life, receiving the measure of the first one ( ποδοχ του π του ν ς μ τ ου)' (76-7). The 'first one' is perhaps the first god, or henad (cf. 70-1), a monad also, it seems. The two principles produce the subsequent gods, as monad and dyad, principles of limit and lack of limit, produce the following members of the numerical series. The description of the divine dyad

end p.83

as 'unlimited power' distinguishes it from the purely negative function of its analogue in the material world, undefined matter. The latter is alluded to in the list of lower dyadic principles next given in the excerpts: intelligible, intellectual, mathematical, and physical dyads (77-8). Psellus omits any reference to a 'divine' triad, as he did in the case of the divine monad, contenting himself with excerpting from the second part of Iamblichus' account, i.e. that concerning the lower triadic levels. Intelligible, intellectual, supra-celestial, celestial, and physical triads are listed (78-80).

(IV) Conclusion

I have summarized above what can reasonably be deduced from Psellus' excerpts concerning the general plan of On Pythagoreanism VII. It will suffice here to review the main features of the metaphysical theory suggested by the excerpts. The structure of reality in Iamblichus' On Pythagoreanism VII turns out to be quite complicated, as compared to the system expressed in earlier volumes of the work. Above the level of the physical world is a series of distinct and ascending orders, psychic/mathematical, intellectual, intelligible (true being), the divine above being, and above all orders an ultimate One, the absolute first principle. As numbers in the mathematical order can be projected downwards paradigmatically, producing physical numbers, so they can be projected upwards as fore-shadowing higher orders, producing, in particular, divine numbers. Our excerpts show no trace of a positive theory of intelligible being approached mathematically (i.e. ideal numbers), nor are the relations between psychic, mathematical, and intellectual orders clarified. But this may simply be due to wholesale omissions by Psellus. On the other hand a certain amount is disclosed about the analogy established between numbers and the order of the gods. This order, described mathematically as divine number, is characterized by unity, both of the order itself ( νωμ νου παντ ς ιθμου , 69-70) and of the gods in the order ( ν ;σ ις, 83). It thus presupposes a principle of unity transcending it, an ultimate One. The order of the gods is treated as a numerical series which flows out from its first member, the 'first one' (a monad), or rather from the interrelation of the two first members, monad and dyad, acting as principles of limit (or measure) and power limited (or measured). From monad and dyad emerge the first numbers, properly speaking, and so also by

end p.84

analogy do the following members of the order of the gods. Few details concerning this survive, however, in Psellus' excerpts. Psellus does retain traces of Iamblichus' illustrations, for each member of the divine decad, of lower instances corresponding to each of the levels of reality taken in descending sequence. The penetration of monad, dyad, triad through all levels of existence expresses not only the continuity of the structure, but also the extra-mathematical applicability of mathematical concepts. The limitations implicit in the latter idea are brought out in Psellus' last excerpts. Iamblichus is well aware, as we have seen, that his 'arithmetical theology', his numerical analysis of the order of the gods who transcend being, is an extrapolation, an analogy. It is inferior to a direct 'meta'-mathematical insight into the nature of the gods, whatever that may be.

How does Iamblichus' On Pythagoreanism VII, as reconstructed from Psellus' excerpts, compare with Nicomachus' Theologoumena arithmeticae? More generally, how does the Pythagoreanizing programme expressed in Iamblichus' work compare to that to be found in Nicomachus? Of what importance is this programme in Iamblichus' other philosophical writings? These and other related questions will be taken up in the next chapter.

end p.85

4 Iamblichus' Work on Pythagoreanism: General Conclusions

 show chapter abstract and keywords

 hide chapter abstract and keywords