51 Iamblichus, De an., in Stobaeus, Anth. I 369, 9-15; cf. Festugière (1950-4), III 194.

This last list contains three of the cognitive powers mentioned in Psellus' excerpts, and the passage illustrates how these powers might have been brought into a discussion of psychology with reference to ethics in On Pythagoreanism VI. It is at any rate clear that Iamblichus substituted for Aristotle's account of the soul a 'Pythagorean' psychology based, in part at least, on reports found in Aristotle himself.

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(IV) Virtue

Aristotle's ethics next lead to a definition of moral virtue as the excellence of that rational aspect of soul which obeys reason. On the analogy of natural excellence or virtue ⁵² 

⁵² Cf. Eth. Nic. 1106 a 16 ff.; 1144 b 1 ff., with 1106 b 16.

and with much recourse to mathematics, Aristotle defines moral virtue as a 'mean' between two extremes, excess and deficiency (Eth. Nic. II 6). Psellus' excerpts recall this definition, ⁵³ 

⁵³ Lines 24-7; also Iamblichus, Ep. ad Sop., in Stobaeus, Anth. III 9, 5-10.

comparing virtue to 'mean' and 'perfect' numbers, and vices to 'superabundant' and 'deficient' numbers. Such a comparison had already been made by Nicomachus. Psellus' excerpts, however, concern natural, rather than moral virtue (26). They appear to derive from a section on natural functioning and excellence which may have introduced, as it does in Aristotle, an account of ethical functioning and virtue. ⁵⁴ 

⁵⁴ For the theory of natural virtue in post-Iamblichean Neoplatonism cf. Blumenthal (1984), 480, 482.

Psellus' excerpts continue with a passage (27-30) putting the unmeasured, the unlimited, etc., in 'the column' of vice. A preceding passage might be missing, in which measure, limit, etc., may have been put in a 'column' of virtue such as that alluded to in Aristotle. ⁵⁵ 

⁵⁵ Cf. Eth. Nic. 1096 b 5-7, 1106 b 29-30; cf. Psellus, On Phys. Numb. 76-9, 28-31.

Having defined moral virtue, Aristotle next gives examples of virtues as means and vices as extremes (Eth. Nic. II 7-8). Although there is nothing corresponding to this in Psellus' excerpts, there is an interesting related passage to be found already in On Pythagoreanism IV:

This agrees . . . with thinking correctly that the virtues are measured states and means between excess and deficiency, and are not extremes . . . , evil opposing evil, and both opposing one good, yet good not at all opposing good, but opposite at the same time to two evils, as cowardice is opposed to audacity . . . and both are opposed to courage. . . . (In Nic. 32, 25-33, 7)

Examples follow, taken both from Eth. Nic. II 7 and Eth. Eud. II 3, illustrating Aristotle's point about the oppositions between vices and between them and virtues (Eth. Nic. II 8, 1108 b 11-15) as well as his remark in Eth. Nic. II 6, 1106 b 28 ff. on the unity of virtue and the diversity of vice, or, as Iamblichus phrases it, 'the rarity of the perfect, as belonging to something good and not to some manifold evil' (In Nic. 33, 15-17).

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(V) Particular Virtues

Psellus' excerpts next concern analogies between certain numbers and specific virtues, namely practical deliberation or wisdom, theoretical wisdom, courage, temperance, and justice (31-52). It is not clear from Psellus' excerpts here whether they derive from a variety of chapters (each devoted perhaps to a particular virtue) or represent a fairly continuous extract from one chapter. It is, however, likely that Iamblichus discussed other virtues besides those retained by Psellus (above, n. 45). The group of virtues mentioned in Psellus is symptomatic of the curious mix of Platonic and Aristotelian ethics that will reappear later. The order in which the virtues are treated corresponds roughly to that used in Plato's Republic (428 a ff.), not that in Aristotle, who deals first with moral, and then with intellectual virtues. However, the distinction between practical and theoretical wisdom is Aristotelian, as are the descriptions of practical wisdom as concerned with 'variable matters' (Psellus, 32) and of theoretical wisdom as concerned with 'beings'. ⁵⁶ 

⁵⁶ τ ντα (34); compare Aristotle's τιμι τατα (Eth. Nic. 1139 a 5-11, 1141 a 20, 1141 b 3).

The latter is related to the monad and the former to the triad on grounds similar to those given earlier (17-18) for the assimilation of intellect to one and opinion to the triad.

Two forms of courage are distinguished in Psellus' excerpts, 'manly' courage and constancy (37-8). The former comes from Plato (Laws 802 e 9, Symp. 192 a 4-5). So does the latter, as can be seen from Iamblichus' Letter to Olympius, where it is related to courage as defined in the Republic. ⁵⁷ 

⁵⁷ Iamblichus in Stobaeus, Anth. III 319, 21 ff.; cf. Plato, Rep. 442 c 1-3.

In this Letter, however, Aristotelian courage is also present: as Aristotle's courageous man endures pain and danger 'for the sake of the fair', so does Iamblichus' paragon support such things 'for the sake of the good'. ⁵⁸ 

⁵⁸ Aristotle, Eth. Nic. 1117 a 17 ff., 33 ff., b 12-15; cf. Iamblichus in Stobaeus, Anth. III 320, 16-21.

The slight difference in formulation points to what one feels must separate the two models of courage: Iamblichus' man appears more indifferent to and unperturbed by the trials of this world than Aristotle's, based as his courage is on unchanging thought fixed on an otherworldly goal. For the two forms of courage, manliness and constancy, Psellus' excerpts give numerical analogues (37-8), the odd (always male in Pythagoreanism, as the even was female) and the foursquare—the latter is Aristotle's comparison (Eth. Nic. 1100 b 11-22).

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The relation between temperance treated as the cause of 'symmetry' in Psellus' excerpts (40) and temperance as described in Plato's Republic can again be illustrated from Iamblichus' Letters, in which 'symmetry' is regarded as the 'symphony' between the parts of the soul in Plato's definition of temperance. ⁵⁹ 

⁵⁹ Cf. Iamblichus in Stobaeus, Anth. III 257, 11-258, 4; Plato, Rep. 431 e 8, 442 c 10-d 1, but also Aristotle, Eth. Nic. 1119 b 15-16.

Once temperance is related to symmetry, Iamblichus can find the corresponding number, choosing namely nine, rather than the number three traditional in Pythagorean assimilations, on the mathematical grounds that nine is especially 'generative' of equality. ⁶⁰ 

⁶⁰ Cf. the references given below, Appendix I, ad loc.

Psellus' excerpts finally deal with justice. Given the strongly mathematical character of Aristotle's treatment of this virtue, it is hardly surprising to find Iamblichus following him more closely here. Aristotle first describes distributive and rectificatory justice and then introduces (Eth. Nic. V 5) Pythagorean 'reciprocal' justice. In his Letter to Anatolius Iamblichus presents an Aristotelian theory of distributive justice. ⁶¹ 

⁶¹ In Stobaeus, Anth. III 358, 5-17 (cf. Eth. Nic. 1129 b 29-30, 1130 b 30-2, 1131 a 25-7). Cf. Iamblichus, De myst. 187, 13-17.

Only reciprocal justice is represented however in Psellus' excerpts (46 ff.). Iamblichus replaces Aristotle's brief reference to this as a Pythagorean concept with a Pythagorean definition of reciprocal justice cited by Nicomachus. ⁶² 

⁶² Cf. the references given below, Appendix I, ad loc.

But Nicomachus' definition is slightly altered: the term π δοσικ at the beginning of the definition becomes νταπ δοσις in Psellus' excerpts (46), under the influence perhaps of Aristotle's references to τ ντιπ πονθ ς or νταπ δοσις in Pythagoreanism (Eth. Nic. 1133 a 3, 1132 b 21). In relating justice to the number four (or five), however, (48) Iamblichus does little more than follow a well-established Pythagorean tradition. ⁶³ 

⁶³ Psellus' text is corrupt here; should 4 at line 48 be corrected to 5? On justice see also Iamblichus, De an., in Stobaeus, Anth. I 455, 19-25 (Festugiere [1950-4], III 241, with notes) and the references below, ad loc., Appendix I. For later Neoplatonic treatments of the virtues in a more comprehensive context cf. Blumenthal (1984) and the references given there.

(VI) Conclusion

To judge from Psellus' excerpts, it seems that Iamblichus again followed Aristotle's lead in On Pythagoreanism VI. Here it is Aristotle's ethics that provides the lines on which Iamblichus elaborated a

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'Pythagorean arithmetical ethics'. In view of the small amount of material excerpted by Psellus, it is likely that many topics of Aristotelian ethics were covered by Iamblichus, of which there is no trace in Psellus. Aristotle's influence on the ethics of On Pythagoreanism VI has been observed not only in the sequence of topics handled, but also in particular explanations and even in individual expressions. However Iamblichus attempted to change Aristotelian ethics into a 'Pythagorean' theory. This could be done by emphasizing the mathematical aspects of Aristotle's approach—in particular his discussions of moral virtue in general and of the virtue of justice—or by substituting Pythagorean definitions and theories where appropriate—e.g. on the parts or powers of the soul. Plato's ethics was also introduced as was, of course, Pythagorean numerical lore. The theory that emerges is structurally similar to the arithmetical physics of On Pythagoreanism V: the first principles, models, and concepts of ethics are found already in the various mathematical properties of numbers. Not only are the basic notions of ethics mathematical in inspiration, but specific virtues are paradigmatically contained in specific numbers. To judge correctly the overall impression given in Psellus' excerpts of a confusion between arithmetic and ethics, it is well to recall the care with which Iamblichus had stressed before in On Pythagoreanism (above, p. 48) the distinction between the sciences, as well as the applicability of mathematics outside its proper domain. The same methodological point will be made in Psellus' excerpts from the next book of On Pythagoreanism.

5. On Pythagoreanism VII

(I) General Plan

In coming to Psellus' excerpts from On Pythagoreanism VII, where he finally divulges his source (53 ff.), we reach matters which Iamblichus had presented earlier (above, p. 48) as the subject aimed at by, and transcending mathematics, namely pure beings and the divine. If this subject is not treated in its own right in On Pythagoreanism VII, it is at least adumbrated, to the extent that arithmetic foreshadows and leads to the study of being and of the divine. From this point-of-view On Pythagoreanism VII represents, in the scheme of the work as a whole, the highest stage in the ascent of the soul of the reader. In approaching

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the summit of Pythagorean philosophy, it also points to the goal of On Pythagoreanism itself, allowing us to view the work as a whole in relation to its finality. Unfortunately, but not surprisingly, it is also here that Psellus' excerpts are most deficient. They are fewer than before and sometimes extremely fragmentary. No general plan is evident. Psellus seems to have cared even less than before about what he was excerpting, and the relevance (and, presumably, danger) of the theological material to Christianity did not escape his notice (cf. 71). But what he does excerpt contains some important clues.

If no general plan is evident in the sequence of Psellus' excerpts, it appears at least that they are taken, as before, from various parts of On Pythagoreanism VII. A striking example is the passage at 59-63 which, as it stands, has little to do with the preceding and succeeding sections. A great deal of context must be supplied if some continuity is to be established between it and the other excerpts.

Since Iamblichus followed the general order of Aristotle's physics and ethics in organizing the previous two books of On Pythagoreanism, one wonders if something similar might be the case here too, particularly in view of the fact that an Aristotelian work concerning being and the divine was available, the Metaphysics.

A direct comparison of Psellus' excerpts with the Metaphysics does not at first glance reveal any relation. If, however, we apply a method used above in section 3, comparing Psellus' excerpts with a later Neoplatonic commentary on the Metaphysics, we come upon some interesting connections. The debt of Syrianus' Commentary on the Metaphysics to Iamblichus' On Pythagoreanism will be demonstrated below in Chapter 6. Here I would like to refer briefly to part of Syrianus' attempt to respond in his commentary to Aristotle's onslaught in Metaphysics MN on Platonic theories of separately existing Forms, numbers, or 'ideal numbers' ( δητικο ιθμο ). In N 4 Aristotle presents a dilemma: given their metaphysical theories, his opponents are in a position neither to subordinate 'the Good' to 'the One', nor to identify them, since this would produce an absurd plethora of goods. Syrianus, on the contrary, has no difficulty with a plethora of goods (the divine after all is without envy) and therefore maintains against Aristotle the identity of the One with the Good. ⁶⁴