28 Cf. The references given in Appendix I, ad loc.
not so is the identification of numbers as efficient causes. Certain numbers, the 'generative numbers' (34) seem to do double-duty, since they have already been put in the class of formal causes (21-2). Psellus' excerpts suggest here too at most a superficial match between Pythagorean arithmetic and Aristotle's Physics. Again, however, the later Neoplatonic commentators on the Physics show that this need not be the case. Having dealt with formal and material causation in Physics I, Aristotle adds in Physics II two further causes: efficient and final causes. Already in I 6 he had intimated that the Platonists identified formal with efficient causation (189 b 14-16), as we have seen above in the case of 'generative numbers'. Indeed in Physics II 7 Aristotle himself finds that formal, efficient, and final causes in nature are often identical, in form at least, if not in number. The later Neoplatonic commentators went even further in identifying formal with efficient causes in nature. For them Aristotle's description of the efficient cause as 'the first cause of change' (Phys. 194 b 29-30) implied that only the first source of all change in the universe is properly speaking an efficient cause; all other immanent causes, or 'natures', are formal causes. 29
29 Simplicius, In phys. 315, 10-15 (quoting Alexander of Aphrodisias). Cf. Syrianus, In met. 82, 4-5.
Thus Iamblichus' use of the same numbers for different causal functions need not imply a superficial treatment of Aristotle's Physics, if indeed he is using the Physics in On Pythagoreanism V.
(V) Change
The first clear evidence that Iamblichus attempted in On Pythagoreanism V a critical, 'Pythagorean', reading of Aristotle's Physics is found in Psellus' excerpts on the subject of change (67-74). In the corresponding section of the Physics (III 1-2) Aristotle formulates a definition of change presented as superior to those of his predecessors, in particular the Platonic-Pythagorean identification of change with
end p.64
difference, inequality, non-being, i.e. the dyad. Such an identification, he allows, is plausible in view of the relation change seems to have with the indefinite. Yet he rejects it:
Difference, inequality, non-being are not necessarily changed, whether they are different, unequal, or non-existent. 30
30 Phys. 201 b 16-27: . . . Τ τητα κα νισ τητα κα τ μ ν σκοντ ς ε ναι τ ν κ νησιν ν ο δ ν ναγκαι ον κινει σθαι, ο τ ν τ α ο τ′ ν νισα ο τ′ ν ο κ ντα.
Not only do Psellus' extracts retain, however, the association of change with the dyad—referring indeed to the relation noted by Aristotle between change and the indefinite (70-1)—but they add a qualification:
The causes of
change . . . difference and inequality (one is like a
relation and property, which is rest (
μ
α),
the other a 'differentiating' (
τ
ο
ωσις)
and 'unequalizing' (
ν
σωσις),
such that it
is not the different and unequal that are in change, but those made
different and unequal).
(69-74)
The relevance of this qualification would not be clear if one did not have in mind the Aristotelian passage quoted just before. By comparing the two texts we can see that Iamblichus is defending the Pythagorean association of change with the dyad by making a distinction between difference as a relation and as a 'differentiating' intended to respond to Aristotle's criticism. We have thus discovered evidence in Psellus' excerpts showing that Iamblichus, in On Pythagoreanism V, attempted to come to terms with Aristotle's criticisms of Platonism-Pythagoreanism in the Physics.
But what exactly was Iamblichus' response to Aristotle? It is hard to reconstruct a complete answer from the meagre fragments in Psellus. The distinctions made and the language used are found again, however, in Simplicius' commentary on the passage of the Physics, and this suggests that Simplicius might give some idea of what might have been Iamblichus' position. Simplicius distinguishes between (a) difference as a Form; (b) what is different by sharing in the Form; and (c) 'differentiating' ( τ ο ωσις). Plato and the Pythagoreans identified change with (c), whereas Aristotle took them, so Simplicius claims, to be referring to (a). Aristotle's criticism is misdirected (In Phys. 432, 35 ff.). 'Differentiating' expresses the fact that when something changes it becomes different from what it was before. 31
31 Simplicius, In phys. 433, 35-434, 1 (almost identical to On Phys. Numb. 72-4).
Thus
end p.65
some essential features of Aristotle's account of change are silently adopted in Simplicius' 'Pythagorean' theory of change: change, as a 'differentiating', involves a subject and two end-points, what the subject was and the something else it becomes. 32
32 The term τ ο ωσις recalls Aristotle's term λλο ωσις referred to by Simplicius (In phys. 432, 35-433, 1), and is found in Aristotle, Phys. 217 b 26.
The difference or inequality that causes change is the difference between cause and effect, the gap in perfection that moves what changes (the effect) from imperfection to the perfection represented by the cause (433, 20-34).
(VI) Place
Another, fainter trace of Iamblichus' attitude to Aristotle's Physics can be detected in the excerpts of Psellus concerning number and place (On Phys. Numb. 81-9). These excerpts follow some sentences on the finite and infinite (75-80). In his Physics Aristotle had listed form, matter, extension, and the boundary of the containing body as possible definitions of place (IV 4, 211 b 7-9). He prefers the last of these (212 a 2-6). In Psellus' excerpts, however, place is described as 'accompanying bodies', συνακολουθου ντα τοι ς σ μασι (83). If this matches neither Aristotle's position nor the other possibilities he mentions, it is, we can now assume, for a good reason. Fortunately this is confirmed and the few words in Psellus clarified by Simplicius who quotes extensively from Iamblichus' Commentary on the Timaeus à propos the same subject:
Iamblichus writes: Every body inasmuch as it is body subsists in place. Place therefore comes into being connaturally with bodies (συμ υ ς α τοι ς σ μασιν τ πος συνυ στηκ ). 33
33 Iamblichus, In Tim. fr. 90, 8-10 (Dillon's transl., modified).
In what follows in Simplicius, Iamblichus contrasts this view of place with other views, including that of Aristotle and another mentioned by Aristotle (place as extension). 34
34 The third view mentioned by Iamblichus (In Tim. fr. 90, 13-15), place as χω ματα δι κ να, recalls the Pythagorean concept of void discussed below.
Iamblichus is concerned here with the interpretation of Plato's Timaeus, not with Aristotle's Physics. Yet what he says implies criticism of Aristotle. He distinguishes a central from a purely extraneous role given to place. Aristotle's view of place assumes it is something peripheral to bodies. But if place is an essential part of
end p.66
what it is to be a body, 35
35 The ontological importance of place is already stressed by Plotinus; corporeal existence (as opposed to incorporeal being) depends on place (cf. e.g. V 9, 5, 44-9).
then it must be intimately involved in the existence of bodies. It is not a mere boundary, but rather a bond of bodies. If it encloses them, it does so, not as a circumambient limit, but as a power supporting, gathering, delimiting bodies. 36
36 Cf. also Iamblichus, In Tim. fr. 20.
Simplicius does not inform us much more about Iamblichus' views on place. He does, however, consider them to be related to those of Aristotle's pupil Theophrastus and of Simplicius' own master Damascius. Theophrastus, as quoted by Simplicius (In Phys. 639, 15-22), saw place as the relative position of parts in a whole, position being closely tied to the nature of the whole. Damascius' theory of place is extremely complicated, 37
37 Cf. Hoffmann (1979) and (1980).
and I can only note some aspects of it here. He distinguished between a 'proper ordering' ( θ τισμ ς) of parts, which is connatural (σ μ υτος), and an extraneous ( π σακτος) local situation. 38
38 Simplicius, In phys. 625, 15 ff.; 626, 3 ff.
The connatural 'proper ordering' has an organizing, preserving function recalling that given to place by Iamblichus as reported by Simplicius. 39
39 Simplicius, In phys. 639, 24 ff.
In Psellus' excerpts numbers are said to have place as 'containing' bodies in their power, a causal rather than a local 'enclosing'. If numbers 'contain' bodies in this sense, then they also 'contain' a connatural part of bodies, namely place (81-4). The excerpts also ascribe to numbers place in a different sense, that rather of Theophrastus: numbers, as constituting an ordered series, have 'places' in the order of succession of the series (84-7). This latter sense of place is applied elsewhere by Iamblichus, not only to numbers, but also to other immaterial realities. 40
40 Iamblichus, In Parm. fr. 313 (Larsen); cf. Galperine (1980), 334-5; Simplicius, In phys. 641, 10-15; 642, 1-4 and 25-7; 644, 15-17.
(VII) The Void
The excerpts in On Physical Number deal finally with a related topic, the void (90-3). Here Iamblichus seems as firm as Aristotle (Phys. IV 6-9) in denying the existence of a void. This is surprising, since Aristotle includes the void in Pythagorean doctrine, 41
41 Phys. 213 b 22-7; cf. DK I 420, 8 (Eurytus).
and Iamblichus
end p.67
could hardly have ignored the divergence between Aristotle and Pythagoreanism on this point. In fact a qualification preserved in the excerpts (92-3) turns out to be an element of a resolution which can be found, again fully explained, in the later Neoplatonic commentaries on the Physics. Psellus' excerpts concede the existence of a void, 'if one wishes to speak of even number as a discontinuous gap (διεχη . . . δι κ νον)' (92-3). The meaning of this phrase emerges if it is compared to Simplicius' and Philoponus' comments on the corresponding section of Aristotle's Physics. Both commentators understand the Pythagorean concept of void reported by Aristotle as referring to the difference between Forms, the separation between bodies. Thus the Pythagoreans, in introducing the void, were speaking in fact of a principle of differentiation. 42
42 Simplicius, In phys. 652, 7-19; Philoponus, In phys. 610, 7-21; cf. Aristotle, Phys. 213 b 24-6.
If we recall that in Pythagorean arithmetic the principle of differentiation is the first even number, the dyad, then the sense of Psellus' excerpt and its function in a reconciliation of the Aristotelian and Pythagorean positions emerges: Iamblichus was prepared to defend a Pythagorean concept of void, if by this is meant a principle of differentiation. This enabled him to take Aristotle's side on the question and yet to claim to be faithful to Pythagoreanism.
(VIII) Conclusion
Psellus' excerpts in On Physical Number reveal finally a good deal about Iamblichus' On Pythagoreanism V. Iamblichus developed here a 'Pythagorean' arithmetical physics following the plan of Aristotle's Physics I-IV. One major topic is missing in Psellus, time. Yet we know from another source something about Iamblichus' theory of time, as it was presented in his Commentary on the Categories in the form of an interpretation of a text supposedly by the Pythagorean Archytas. 43
43 Iamblichus, In cat. frs. 2 ff.; cf. Sorabji (1983), 37 ff.; Sambursky, Pines (1971); Hoffmann (1980). Archytas is cited in In Nic. 6, 20-2, and elsewhere in On Pythagoreanism (cf. above, p. 43).
It is a fair guess that the treatment of time in On Pythagoreanism V would not have been very different. In his Physics Aristotle occasionally criticized the Pythagoreans and Platonists and regarded his own physical theory as superior. Psellus' excerpts contain some indications showing that Iamblichus, far from ignoring Aristotle's criticisms, attempted to
end p.68
come to terms with them. This involved, in some cases at least, interpretation of Pythagorean doctrine so as to render it defensible. This may have led to some projection of Aristotelian physics backwards on to Pythagoreanism. At the same time, however, Iamblichus did not hesitate to go beyond Aristotle, in particular on the subject of place. This he did elsewhere, in the case of time, by appealing to a supposedly earlier, Pythagorean source, Archytas. Such advances were a source of inspiration for the sophisticated theories of place and time to be found in later Neoplatonists, Syrianus, Damascius, and Simplicius. More generally, the instances in which Psellus' excerpts have been found to anticipate specific arguments in Simplicius' and Philoponus' commentaries on the Physics suggest that Iamblichus' study of the Physics was of some importance for the development of these commentaries. 44
44 Simplicius and Philoponus are probably not specifically dependent on the reading of Aristotle's Physics given in On Pythagoreanism V. They would have had other sources, in particular Iamblichus' Commentary on the Timaeus. (We know of no commentary, properly speaking, on the Physics by Iamblichus.) Simplicius, however, would have known Iamblichus' On Pythagoreanism well, if we can trust Renaissance reports of a manuscript (no longer to be found) containing a commentary by him on Iamblichus' book; cf. I. Hadot (1987b), 28-9. Cf. above, n. 31, below, n. 50, for close verbal parallels between Simplicius and Iamblichus' On Pythagoreanism as excerpted by Psellus.
But what arithmetical physics emerges from the excerpts? In general it appears that the physical universe is structured by immanent forms, called 'physical numbers', which derive their character and behaviour from the properties of mathematical numbers. Mathematical numbers in fact exemplify, in paradigmatic fashion, the organization of the universe. This means that physical theory can be found pre-contained in mathematics and that the elements of such a theory are instantiated in the various physical expressions of different mathematical numbers. It is this last idea that is predominant in Psellus' excerpts: the components of an (Aristotelian) account of physical causality are shown to be embodied in different (physical) numbers or groups of numbers. The excerpts give the impression of a multiplicity and variety of immanent forms expressing the relative simplicity of physical theory. Although the latter appears in general to be Aristotelian, there are differences, at the very least in the case of place: place is an intimate part of the being of bodies and is produced by numbers (mathematical here, it seems, rather than physical), which possess their own immaterial 'places' in a serial organization.
end p.69
These results are no doubt incomplete. But to go much further in the attempt to reconstruct Iamblichus' On Pythagoreanism Book V on the basis of Psellus' excerpts would, I believe, involve speculations whose degree of reliability would be hard to measure.