- •Preface
- •Introduction
- •Dominic j. O'Meara
- •19 See below, Ch. 2 n. 22.
- •Dominic j. O'Meara
- •13 In Nic. 125, 14-25 (expanding on 118, 11-19); cf. 3, 13 ff. I shall return to this passage in the next chapter. The book on music is also referred to at 121, 13; 122, 12.
- •Introduction to Pythagorean Mathematics:
- •Dominic j. O'Meara
- •3 I 135; for a sceptical view of these claims, cf. Lemerle (1977), 200-1, 245.
- •21 Of the issues raised by Psellus' excerpts I shall discuss only those relating to the reconstruction of Iamblichus' books in what follows.
- •23 Cf. The division of the text proposed below, Appendix I.
- •28 Cf. The references given in Appendix I, ad loc.
- •29 Simplicius, In phys. 315, 10-15 (quoting Alexander of Aphrodisias). Cf. Syrianus, In met. 82, 4-5.
- •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.
- •4. On Pythagoreanism VI
- •45 At least one omission in the excerpts is a treatment of friendship promised in In Nic. 35, 5-10.
- •51 Iamblichus, De an., in Stobaeus, Anth. I 369, 9-15; cf. Festugière (1950-4), III 194.
- •64 In met. 181, 34-185, 27, especially 183, 26-9.
- •71 In met. 140, 10-15 (cf. Psellus' excerpts, 73-4). For the intelligible/intellectual distinction in Porphyry as compared to Iamblichus cf. P. Hadot (1968), I 98-101.
- •72 Κατ κ ττους ννο ας (87). Cf. Above, p. 47.
- •75 Cf. Also 81-4, where the 'supernatural' beings are described as unities, ν σ ις.
- •Dominic j. O'Meara
- •1. On Pythagoreanism: a Brief Review
- •Introduce the reader, at an elementary level, to Pythagorean philosophy.
- •2 Cf. For example the distinction between being and the divine in Books I, III, VII (above, pp. 45, 81). Some vague areas remain unclarified, as far as can be determined (above, p. 45).
- •9 The point is made by Elter (1910), 180-3, 198.
- •3. Pythagoreanism in Hierocles' Commentary on the Golden Verses
- •21 If 40, 15-17 ('divine men') alludes to the Phaedo and/or Phaedrus. On 'demonic' men in Hierocles cf. Also Aujoulat (1986), 181-8.
- •27 Cf. Kobusch (1976), 188-91; Aujoulat (1986), 122-38; and especially I. Hadot (1979), who provides extensive references.
- •6 Syrianus
- •Dominic j. O'Meara
- •37 For this division in Iamblichus, cf. Above, p. 44 (Iamblichus' text is very probably the source of inspiration of Syrianus' tripartite division of reality).
- •48 Cf. 103, 15 ff.; 186, 30-5; 45, 33-46, 5; for the difference between Forms and universals in the soul cf. 105, 37-106, 5.
- •56 Cf. Also 137, 6-10; 138, 27-139, 1; 142, 10-12; Proclus, In Tim. I 310, 3-311, 4 (on Syrianus).
- •Dominic j. O'Meara
- •17 Cf. Tannery (1906), 262-3.
- •23 Cf. Saffrey and Westerink's note ad loc.
- •35 In Alc. § 235, 15-18; cf. O'Neill (1965), ad loc.
- •Dominic j. O'Meara
- •8 Cf. Or. Chald. 198 (with des Places's references); Syrianus, In met. 182, 24; Proclus, In Crat. 32, 22 and 28; Saffrey and Westernik's notes in Proclus, Theol. Plat. III 145; IV 120-1.
- •18 Cf. In Parm. 926, 16-29.
- •Intelligible. Finally, on the subject of the practical arts, Proclus makes explicitly (25, 6-7) the use implicitly made in Iamblichus (57, 26-7) of Plato's Philebus.
- •2. Arithmetic and (Or?) Geometry
- •Dominic j. O'Meara
- •15 In the strong Greek sense of science of course. To the extent that modern physics regards its claims as probable, it seems to be no more ambitious than Timaeus' discourse.
- •16 Cf. I 337, 29-338, 5, with 346, 29-347, 2; 348, 23-7.
- •27 Cf. Nicomachus, Intro. Arith. 126, 12-128, 19.
- •28 II 23, 30-2; this is Aristotle's caveat, An. Post. I 7, 75 a 38.
- •29 On these mathematical terms cf. Festugière ad loc. (III 52 n. 2); cf. In Tim. I 17, 4-6.
- •33 Cf. Annas (1976), 151.
- •Dominic j. O'Meara
- •7 Cf. Theol. Plat. I 40, 5-13 (with Saffrey and Westerink's notes); In Tim. I 276, 10-14.
- •2. The Science of Dialectic
- •12 Cf. In Parm. 645, 9-27; 727, 8-10; 1132, 20-6; 1140, 19-22; 1195, 26-30; 1206, 1-3.
- •21 Theol. Plat. II 66, 1-9.
- •Dominic j. O'Meara
- •In the second half of this book the impact of Iamblichus' Pythagoreanizing programme on his successors was examined in regard to
- •7 Cf. Saffrey (1975).
- •I. The Commentary on the Golden Verses Attributed to Iamblichus
- •Bibliography
- •I. Ancient Authors
- •Iamblichus, (?) Commentary on the Pythagorean Golden Verses, typescript of provisional incomplete English translation by n. Linley (communicated by l. G. Westerink).
- •2. Modern Authors
- •Imbach, r. (1978). 'Le (Néo-) Platonisme médiéval, Proclus latin et l'école dominicaine allemande', Revue de théologie et de philosophie 110, 427-48.
- •219. Lemerle, p. (1977). Cinq études sur le xIe siècle byzantin, Paris.
17 Cf. Tannery (1906), 262-3.
Domninus' manual provides a very clear and simple explanation of the main terms, concepts, and distinctions in the theory of numbers. The concision and orderliness of his exposition is not interrupted by extra-mathematical inferences or learned additions such as appear in Nicomachus' Introduction and in Iamblichus' version of Nicomachus (On Pyth. IV). Domninus' use of Euclidean ideas in his Manual has even provoked a modern admirer to see in his work a rejection of the Nicomachean tradition of arithmetic as perpetuated by Iamblichus and Proclus and a return to the 'mathematically sounder' Euclidean approach to arithmetic. 18
18 Tannery (1884), 107 ff.; (1906), 259 ff.
This seems exaggerated: Domninus makes extensive use of Nicomachus in his Manual and his chief contribution consists in the clarity and simplicity absolutely essential to a work as short as his. 19
19 Cf. Hultsch (1905), 1523-4, with his general estimate of the work, 1525; Domninus is also discussed in some detail by Klein (1968), 32-6; Ebbesen (1981), 251-2.
At the end of the Manual he promises an Elements of Arithmetic ( ιθμητικ στοιχ ωσις), probably a more ambitious project in which he intended to explain, among other things, mathematical theories in Plato. 20
20 Domninus, Manual 428-9; Ruelle's suggestion (1883), 83, that the other short surviving mathematical piece attributed to Domninus is a chapter from the Elements of Arithmetic seems unlikely: it is a self-contained technical solution to a specific mathematical problem (the attribution to Domninus is questioned by Tannery [1885b], 137).
2. Plato and Pythagoras
The dispute with Domninus had little effect on Proclus' professional career. Whatever difficulties it might suggest were soon overcome as
end p.145
Proclus quickly established his position at the head of the Platonic school at Athens. The effect of the conflict on Proclus' intellectual life is less easily gauged since so little is known of Domninus' ideas and of the details of Proclus' argument with him. The reports of Proclus' successors considered above, if they may be taken to reflect the master's view, suggest that Proclus felt it necessary to insist on the proper (Iamblichean) acceptance of religious customs in the face of Domninus' heterodox practice, and on the place and (especially) limits of mathematics in philosophy. The latter point will be discussed in more detail below. It will be appropriate, however, to begin our study of Proclus with some consideration of his views on the nature, function, and history of philosophy.
His views on these topics are in general the same, it would appear, as those of Iamblichus and of Syrianus. One does not have to read far into his major commentaries to find Pythagoreans and Orphics quoted as authorities supporting Plato. Aristotle is given a subordinate place: he is sometimes right, frequently mistaken. 21
21 Below, Ch. 9.
It is assumed that true Greek philosophy agrees with, and can be illustrated by, the inspired poetry of Homer and Hesiod and the barbarian revelations of the 'Chaldaean Oracles'. 22
22 On Proclus' treatment of inspired poetry and its relation to Syrianus' theory, cf. Sheppard (1980), 95 ff., 162-82.
A text from the opening of the Platonic Theology (I, ch. 5, 25, 24-26, 9) may serve to indicate in particular the relation between Pythagoras and Plato:
But we must show that each of these doctrines is in harmony with the first principles of Plato and with the secret revelations of the theologians. For all Greek theology derives from Orphic mystagogy, Pythagoras first (π του) learning from Aglaophemus the secrets concerning the gods, Plato after him (δ υτ ου) receiving the complete science of the gods from Pythagorean and Orphic writings. For in attributing in the Philebus the doctrine of the two kinds of principles to the Pythagoreans, he calls them 'dwellers with the gods' (16 c 8) and blessed. Indeed Philolaus the Pythagorean has written many wonderful things about these .
Plato's theology, or science of the divine, is then Pythagorean in inspiration. Proclus' authority for this, as the reference to Aglaophemus indicates, is the same as that used for the same purpose by Iamblichus and Syrianus, namely the (pseudo-) Pythagorean Sacred
end p.146
Discourse. 23