4. On Pythagoreanism VI

(I) General Plan

Psellus' excerpts in On Ethical and Theological Arithmetic fall into two sections, the first having to do with 'ethical arithmetic' (2-52), corresponding thus to On Pythagoreanism VI, the second containing 'theological arithmetic' (53-90), i.e. the subject-matter of On Pythagoreanism VII. I shall be concerned here with the first section and with the extent to which it reveals something of the content of On Pythagoreanism VI. The task of reconstruction is yet more difficult here than in the case of On Pythagoreanism V: there is only half as much available in terms of quantity of excerpts, and no related, i.e. ethical, Neoplatonic commentaries survive which could help in elucidating obscure passages.

Since it turns out that Iamblichus' ordering of the implications of number 'according to the physical . . . account' means in fact that the plan of On Pythagoreanism V follows that of Aristotle's Physics I-IV, one wonders if the same sort of situation might obtain with respect to the ordering 'according to the ethical . . . account' (above, p. 60) in On Pythagoreanism VI. And indeed it does. The sequence of topics in the first part of Psellus' On Ethical and Theological Arithmetic (2-52) corresponds roughly—with larger omissions, as one would expect with fewer excerpts—to that of Aristotle's ethical treatises: the first principles of ethics (2-15); the parts or powers of the soul (16-23); virtue defined (24-30); virtues intellectual and moral discussed individually (31-52). ⁴⁵ 

45 At least one omission in the excerpts is a treatment of friendship promised in In Nic. 35, 5-10.

For the same reasons as those given above a propos the plan of On Pythagoreanism V, Psellus' excerpts appear to be taken, not from a limited section, but from a range of chapters in On Pythagoreanism VI. They thus give some idea, however fragmentary, of the structure of the work. It is not clear, on the other hand, if Iamblichus follows one particular ethical treatise of Aristotle. He is familiar, as will be seen later, with both the Nicomachean and the Eudemian Ethics. His attitude

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to both may have been such that he did not feel bound to follow closely the one rather than the other. ⁴⁶ 

⁴⁶ Cf. Kenny (1978), 38-9 (similar situation in Simplicius and Philoponus). I shall refer to the Eudemian Ethics only when it is clear that it, and not the Nicomachean Ethics, is being used by Iamblichus.

At any rate it will be useful to keep Aristotle's ethics in mind as Psellus' excerpts are considered in more detail.

(II) The First Principles of Ethics

Aristotle begins his ethics starting from principles, χα . These principles are not 'absolute', i.e. those standing at the head of a science of ethics that is complete, but 'relative': they are what is at first best known to us, those facts that experience teaches and which only a mature student of ethics will possess. ⁴⁷ 

⁴⁷ Eth. Nic. I 4, 1095 a 31-b 8; I 7, 1098 b 1 ff.

Psellus' excerpts begin, however, with a list of first principles which are 'absolute' and on which ethics is grounded: measure, limit, perfection, order, unity. They are also mathematical. How they ground ethics can be illustrated from Aristotle's characterization of happiness as something perfect (τ δ′ ιστον τ λ ι ν τι α ν ται), as an activity of the soul according to the highest and most perfect virtue, in a perfect or complete life. ⁴⁸ 

⁴⁸ Eth. Nic. I 7, 1097 a 28, 1098 a 15-18.

Iamblichus seems to be thinking of this description of happiness when, on the subject of the perfect as first principle, he says: 'for perfection (τ λ ι της) unitarily completes the best ( ιστον) measure of life' (Psellus' excerpts, 8).

It is not, however, the perfect, but measure, or rather 'measure itself' and what is measured that are most important among the mathematical principles of ethics according to Psellus' excerpts (2-6). Measure and what is measured are in fact what come first in the list of 'possessions' whereby the human good, i.e. happiness, is constituted according to Plato's Philebus (66 a 6-7). On the assumption then that the Platonic dialogues are Pythagorean in inspiration, an assumption clearly made in On Pythagoreanism, the first elements of the human good in Plato's Philebus can be considered by Iamblichus as the absolute first principles of a Pythagorean 'arithmetical ethics'.

In the preceding chapter it was seen that mathematics not only furnishes ethics with its first principles. It also has a paradigmatic role in ethics. An example of this appears in Psellus' next lines: the 'mean'

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in numbers is like a model of the ethically good character which involves good harmonization of the soul (12-15), i.e. the virtue of temperance.

(III) The Powers of the Soul

Having defined happiness in outline, Aristotle develops his account by means of a brief discussion of the soul which yields a distinction between rational and non-rational psychic parts or powers. This produces in turn a differentiation between intellectual and moral virtue (Eth. Nic. I 13). Psellus' extracts contain a corresponding section (16-23), in which psychic powers are assimilated to numbers. For this purpose Iamblichus uses a text to be found in Aristotle's On the Soul (404 b 22-4), which he takes elsewhere to refer to Plato, ⁴⁹ 

⁴⁹ Iamblichus, De an., in Stobaeus, Anth. I 364, 15-18.

and here, presumably, to refer to the Pythagoreans. This text identifies intellect with the number one, science with two, opinion with three, and sense-perception with four. Iamblichus explains each identification and his explanations correspond exactly to those, given at slightly greater length, of Simplicius commenting on the same text of Aristotle. ⁵⁰ 

⁵⁰ Simplicius, In de an. 29, 2-9 (Simplicius refers in the plural to νδ ς, which must mean the Pythagoreans; cf. 28, 17 ff.). Such is the closeness of Simplicius to Psellus' excerpts (lines 17-19) that he can help clarify the condensed phrases of the excerpts.

The psychic powers mentioned in the excerpts relate only to the cognitive functions of the soul, and one must suppose that Iamblichus also treated of other psychic powers relevant to a 'Pythagorean' ethics, such as those he lists in his work On the Soul:

The Platonists, Archytas, and the other Pythagoreans declare the soul to be tripartite, dividing it into reason, spirit, and desire. For these are useful for the constitution of the virtues. But they reckoned the powers of the soul to include nature, imagination, sense-perception, opinion, the thought that moves bodies, the desire of the fair and good, and intellections. ⁵¹