21 Of the issues raised by Psellus' excerpts I shall discuss only those relating to the reconstruction of Iamblichus' books in what follows.

Psellus first distinguishes in On Physical Number (3-8) between different sorts of number, ideal or intelligible, mathematical and physical. He then relates numbers to formal (13-26), material (27-32), and efficient causation (33-6), to change (67-74), to the finite and infinite (75-80), to place (81-9), and to the void (90-3). One will recognize here roughly the agenda of topics of Aristotle's Physics I-IV, as listed for example by the later Greek Neoplatonists Proclus (In Tim. I 6, 24-6) and John Philoponus (In Phys. 2, 13-16). One major topic is missing in Psellus, time; no doubt it could be found in the Iamblichean original. That the topics of Physics I-IV only are represented can hardly be accidental. For Porphyry had argued for, and imposed on Aristotle's treatise, a division into two parts, I-IV concerning physics, V-VIII concerning change. ²² 

²² Simplicius, In phys. 802, 7-13; cf. Moraux (1985), 229.

It seems then that in On Pythagoreanism V Iamblichus followed in general the agenda of Aristotle's Physics (I-IV) in dealing with the implications of number in physics.

One might wonder, however, if Psellus' excerpts in On Physical Number might have been taken from some introductory pages of On Pythagoreanism V, and thus that the sequence of subjects discussed might not after all reflect the overall plan of the work, which may, for example, have adopted the traditional plan of Pythagorean decadic literature—that also of Nicomachus' Theologoumena—dealing in succession with each number of the decad and with its various associations. The evidence, however, such as it is, does not support this supposition. Iamblichus' reference in On Pythagoreanism IV to an ordering of the implications of number 'according to the physical . . . account' (In Nic. 125, 19-22) supports, and is clarified by, a plan for On Pythagoreanism V in which number would have been discussed according to an order inspired by Aristotle's Physics. The manner of Psellus' excerpting points in the same direction: some excerpts consist merely of lines cited out of context, others are fuller and more intelligible. ²³ 

23 Cf. The division of the text proposed below, Appendix I.

This suggests uneven dipping in a wide span of text rather than excerpting from a small number of pages. This impression will be

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strengthened later when the degree to which On Pythagoreanism V came to terms with Aristotle's Physics becomes clearer. It will be useful in the meantime to keep Aristotle's Physics in mind, so that traces of the use of Aristotle's work may be recognized when they are encountered.

(II) Physical Number

The sorts of number which Psellus presents at first to his puzzled companion—intelligible or ideal ( δητικ ς) number, mathematical, and physical number (On Phys. Numb. 4-8)—recall distinctions between different sorts of number appearing already in On Pythagoreanism III: ideal number, self-moved number, ²⁴ 

²⁴ Apparently relating to soul, which has some close but obscure relationship with mathematicals.

and the principles and forms in bodies (Comm. 64, 2-19). These last are described in Psellus' excerpts as 'physical number'. They correspond to (Aristotelian) immanent forms and (Stoic) 'seeds' which organize matter and which had been introduced into the Platonic universe by Plotinus and by Platonists before him. ²⁵ 

²⁵ For these in Iamblichus, cf. Comm. 55, 26-56, 2 ( δη υσικ ); De myst. 169, 7 ff.; In Tim. frs. 47-8; In Parm. fr. 2, 13-14. Cf. Proclus, In Tim. II 25, 1-3.

To call them 'physical numbers', however, is unusual. ²⁶ 

²⁶ The expression υσικ ς ιθμ ς is found in Nicomachus, Intro. 52, 1; 88, 17. Cf. Plato, Rep. 525 d 7-8; Plotinus, VI 6, 16, 45-6.

On Pythagoreanism IV points to the reasoning behind this: the demiurgic god organized the world by means of numerical forms and principles, ε δεσι κα λ γοις τοι ς κατ' ιθμ ν (In Nic. 79, 5-8). The numerical organization of the world allows one to describe the immanent, organizing principles of physical bodies as numbers, physical numbers to distinguish them from mathematical numbers, which are the paradigms of such numbers. According to Psellus' excerpts the philosopher should 'fit' these 'physical numbers' to the causes in nature (On Phys. Numb. 11-12), which is indeed what is done in the following excerpts.

(III) Formal and Material Causation

Psellus' excerpts next speak of two sorts of cause and assign various numbers and groups of numbers to each (On Phys. Numb. 13-32). In particular, numbers related to the monad (odd numbers) are said to be

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formal causes, and even numbers, associated with the dyad, are identified as material causes. This rapprochement between monad and form, dyad and matter, had already been made in On Pythagoreanism IV: the properties of number are said there to derive from monad and dyad, just as all in the physical universe is based on form and matter; matter has the indefiniteness and inequality of the dyad, just as the monad has a formal function in constituting numbers (In Nic. 77, 22-79, 8). Indeed Aristotle himself had suggested in Physics I (189 b 8-16, 191 b 35-6) that the Platonic theory of 'the one' and the dyad (the 'great and small') anticipated his distinction between formal and material causes. Yet Aristotle also felt that he had superseded the Platonic theory, the inadequacy of which he seeks to show in Physics I 9.

There is no trace in Psellus' excerpts of a response to Aristotle's critique of the Platonic theory of causes (presumably assumed by Iamblichus to be Pythagorean). One wonders consequently, on the supposition that Iamblichus used Aristotle's Physics in On Pythagoreanism V, if that use might have been very superficial, perhaps merely a naïve adaptation of the Aristotelian theory of causes to Pythagorean numerical lore, involving little effort to meet Aristotle's criticism of Platonic-Pythagorean speculations. Yet the later Neoplatonic commentators on the Physics Simplicius and Philoponus (both end of the fifth/early sixth century) show that Aristotle's critique in Physics I 9 was not thought by Neoplatonists to be justified. Aristotle's main point was that the Platonists failed to distinguish between matter and privation; their theory postulated only two of the three causes (form, matter, privation) required if difficulties in accounting for physical changes were to be avoided (cf. 192 a 3-12). Simplicius argues, however, that Plato did know of 'privation', defined as 'absence ( πονσ α) of the forms to be produced in matter'; it is found namely in his concept of an all-receptive matrix. Such a cause, however, is only logically distinguishable from matter. Being a cause only as absence, it is not an element constitutive per se of physical bodies and thus is not included in the list of such elements. ²⁷ 

²⁷ In phys. 245, 19-29; 246, 2-16 ( πουσ α> is Aristotle's own term, 191 a 6-7). Cf. Philoponus, In phys. 182, 20-5; 183, 11-184, 8.

This need not have been Iamblichus' assessment of Aristotle's critique in Physics I 9, but it shows at least that the critique need not have been felt to support Aristotle's claim to have gone beyond the Platonic-Pythagorean account of causation in the physical world.

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(IV) Efficient Causation

Psellus' excerpts next concern efficient causation (On Phys. Numb. 33-64). It is argued, for example, that the numerically defined rhythms of the heavens, of health, disease, birth, and death, show numbers to act as efficient causes. The instances of numbered rhythms given are banal enough in the Pythagorean tradition; ²⁸