Dominic j. O'Meara

The themes examined in this book, in their integration into Neoplatonic philosophy by Iamblichus and in their adoption and revision by Syrianus and Proclus, continued to have considerable influence on subsequent thinkers. Proclus' successor at Athens, Marinus, appears to have been a better mathematician than philosopher. At any rate he shared the high regard for mathematics that has been found already in Iamblichus, for we are told:

Some wonder why, if we learn (μανθ νομ ν) everything, the immaterial, the material, and what is between them, not all are called mathematics (μαθ ματα), but only the intermediate . . . and we say there are two reasons for this, one that mathematics possesses the solidity of demonstration, for we learn it accurately, but we conjecture rather than learn the others, for which reason the philosopher Marinus said 'Would that all were mathematics!' ¹ 

¹ Elias, In Porph. Is. 28, 24-9.

The place and function of Pythagoras in the history of philosophy and the role of mathematics in philosophy would thus merit investigation in their development in the thought of Marinus and in his successors. It seems, for example, that Damascius, later head of the school, claimed to make a return, in opposition to Proclus, to Iamblichean philosophy. ² 

² Cf. Westerink (1971).

The fortune of Iamblichus' Pythagoreanizing programme could also be examined in regard to the Alexandrian school. One might note here, for example, that Proclus' pupil Ammonius, in his more favourable attitude to Aristotle, took more seriously the Aristotelian idea of numbers as abstractions and attempted to combine this with the idea of numbers as projections of higher a priori concepts.

Worth considering also would be the impact Iamblichus' Pythagoreanizing programme would have, in the form given it in the Athenian and Alexandrian schools, on later periods. One might mention as an example Boethius' short theological work known as the De hebdomadibus which would provide, in its geometrical form, a

end p.210

model for scientific discourse to Western Medieval theologians. ³ 

³ Cf. Schrimpf (1966), Evans (1980), Lohr (1986).

Later the Latin translation of Proclus' Elements of Theology would become a paradigm of metaphysics for Bertold of Moosburg; the short altered Arabic version of the Elements in Latin, the De causis, had already served and would continue to serve as the basic textbook, along with Aristotle's Metaphysics, for Medieval metaphysics. When Proclus' Commentary on the Parmenides became available in Latin to Nicholas of Cusa, he would use it extensively in the development of his profound theories of the philosophical importance of mathematics with regard, in particular, to the divine. ⁴ 

⁴ Cf., for example, Imbach (1978), Schultze (1978), Beierwaltes (1975), 368-84.

One might mention furthermore the great interest taken by mathematicians in the Renaissance in Iamblichus' philosophy of mathematics as reformulated in Proclus' prologues to Euclid, an interest expressed in the idea of a mathesis universalis that can be traced up to Descartes and beyond. ⁵ 

⁵ Cf. Crapulli (1969), and Klein (1968), who discusses Proclus' work on Euclid in connection with Descartes.

It is not the purpose of this book, however, to examine the later history of Neoplatonic Pythagoreanism, as a thesis about the origins and history of wisdom and a theory about the relations between mathematics and the philosophical sciences. ⁶ 

⁶ Valuable materials concerning this are collected in Mahnke (1937).

I have been concerned rather with its beginnings in Iamblichus' philosophy and its reception by the first major philosophers of the Athenian school, with the aim of throwing some light on this obscure but important phase in the history of late Greek philosophy. The results might be summarized as follows.

A tendency to Pythagoreanize is common in the history of Platonism and is represented in different forms and to different degrees among Iamblichus' immediate philosophical predecessors, Numenius, Nicomachus of Gerasa, Anatolius, and Porphyry. However, Iamblichus' programme to Pythagoreanize Platonic philosophy was more systematic and far-reaching. This project is expressed in a number of Iamblichus' commentaries on Plato and Aristotle and is the subject of a ten-volume work by Iamblichus, On Pythagoreanism. In this work, in so far as it can be analysed on the basis of the extant (first four) books and of Psellus' excerpts from Books V-VII, various materials—texts from Plato, Aristotle, (pseudo-)Pythagorean literature—were assembled so as to initiate the reader, step-by-step, to 'Pythagorean' philosophy. At first the reader is presented with a

end p.211

portrait of Pythagoras that expresses Iamblichus' interpretation of him as an uncorrupted soul sent down to communicate wisdom to souls that have fallen away from insight. This interpretation of Pythagoras reflects Iamblichus' Neoplatonic theory of the various relations of soul to, and functions in, the material world. Pythagoras' revelation stands, in Iamblichus' view, for all that is true in the history of Greek philosophy: Plato and later true Platonists are Pythagoreans, as is Aristotle, to the extent that he remains faithful to Pythagoreanism/Platonism. Pythagorean philosophy, for Iamblichus, is distinguished especially by its concern with immaterial realities, objects which give it its scientific, i.e. demonstrative, character. One branch of this philosophy consists in mathematics, which has the special character of acting as a mediating knowledge, as Iamblichus shows in the case of arithmetic: arithmetic not only functions as a scientific paradigm for inquiries that are scarcely scientific, concerned as they are with material reality, physics, ethics, politics, poetics, but also prepares the mind and anticipates the intuitive truths of the highest level of Pythagorean philosophy, the science of the divine, theology. This highest level of Pythagoreanism was treated, not in On Pythagoreanism, but in a sequel no longer extant, On God. In developing the paradigmatic function of arithmetic in physics and ethics, Iamblichus adopted much of Aristotle's work on these subjects, modifying and elaborating it so that it would reflect better what Iamblichus regarded as its essentially Pythagorean inspiration. (In his Commentary on the Categories, Iamblichus also adopted and Pythagoreanized Aristotelian logic.) As for the relations between arithmetic and the science of the divine, Iamblichus distinguished between Pythagorean use of mathematics to image the divine and a higher approach to the divine. Little is known, however, of this higher approach in Iamblichus; mathematical imaging seems to have taken the form of matching the numbers of the decad and their properties to the divine at its highest levels and at lower levels in a hierarchy of reality of considerable complexity. The extent of Iamblichus' Pythagoreanizing programme can be seen in the fact that he established a canon of Platonic dialogues and an exegetical approach that are reflections of this programme. In Pythagoreanizing Neoplatonic philosophy Iamblichus in effect developed it further, one significant result being the mathematization of all areas of philosophy that is so striking a feature of later Greek philosophy.