- •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.
12 Cf. In Parm. 645, 9-27; 727, 8-10; 1132, 20-6; 1140, 19-22; 1195, 26-30; 1206, 1-3.
that is, as suggested above, as exemplifying scientific method.
Plato's figure Parmenides exhibits in the dialogue these attributes of the ideal 'guide' to dialectic: simplicity, purity, scientific rigour, presenting the subject by starting from 'on high', from 'the most unified principles', and demonstrating all else on the basis of such principles. These principles correspond to the hypotheses that Parmenides proposes to Socrates. They are hypothetical in two senses: as representing the beginnings of the ascent through hypotheses to an 'unhypothetical' first principle that is described as the first phase of dialectic in Plato's Republic; 13
13 Cf. In Parm. 622, 21-623, 28; 1033, 20-1034, 30 (where Proclus says he is following Syrianus); Beierwaltes (1979), 253-74.
and as corresponding to what functions as hypotheses, that is 'common notions' or axioms, in geometry. 14
14 Cf. In Parm. 930, 6-9; 1034, 1-2; 1092, 19-34; 1099, 39-1100, 10; Beierwaltes (1979), 261 ff.
We may say then that just as geometrical demonstrations proper have as starting-points certain evident truths, so, on a higher level, do dialectical demonstrations start from certain fundamental metaphysical truths such as are expressed in the hypotheses of the Parmenides. And indeed just as the first principles of geometry are a priori concepts given in psychic nature which the geometer 'projects'
end p.200
or 'unrolls' in his demonstrations, so the dialectician takes his beginning from certain primary a priori metaphysical concepts which he then articulates in his demonstrations. 15
15 Cf. 1151, 38-1152, 5; the first hypothesis of the Parmenides is described as a ν ημα in Theol. Plat. II 66, 1-8 (quoted below).
The idea that there are certain metaphysical concepts given in psychic nature and transcending mathematical concepts can be found already in Syrianus. 16
16 Cf. O'Meara (1986), 12.
In Proclus—if only because of the large amount of his work that survives—the meaning and importance of this idea are clearer. In particular Proclus associates (i) the (Stoic) notion that there are certain truths universally held by mankind, such as the existence and providence of the divine, with (ii) the (Aristotelian) notion that certain principles are known, not by demonstration, but by a sort of intellectual insight (νωυ ς), and with (iii) the geometrical concept of certain truths as evident, axioms. 17
17 Cf. the wealth of references collected by Saffrey and Westerink in their note in Theol. Plat. I 159-61; Trouillard (1972), 51-67.
Associating these notions, Proclus thus finds at the highest level of human reflection a number of concepts, of metaphysical content, intuitively known as given in the nature of soul, and functioning as the starting-points of the demonstrations of the dialectician. 18
18 Cf. In Parm. 980, 8-982, 30; 1125, 13-22.
In demonstrating fundamental metaphysical insights the dialectician does not attempt to prove them. Rather he 'unfolds' or explicates them, showing what they presuppose and what they entail. This procedure corresponds in fact to the structure of syllogistic argument, whereby the conclusion shows what is implied by the premises. In the treatment of his first hypothesis the dialectician begins with a truth that is not, according to what Plato suggests in the Republic, the very first metaphysical truth which all other metaphysical truths presuppose. 19
19 Cf. the references given in n. 13 above.
The dialectician must therefore work back from his starting-point to such an ultimate truth and then, again following the procedure prescribed by the Republic, work down from this truth, showing how all other truths derive from the first. In doing this the dialectician unfolds a series of concepts that corresponds to and speaks of the unfolding of the structure of reality from its ultimate source in the One. 20
20 Cf. Theol. Plat. III 82, 23-83, 2; the text quoted below, p. 202; In Parm. 1032, 15-29.
end p.201
The very first metaphysical truth from which the dialectician derives his science of the divine is, in Proclus' opinion, the first hypothesis of the Parmenides:
What then is the very first concept (ν ημα) of the science proceeding from intellect and revealing herself? What other shall we mention but the simplest and most knowable of all her concepts? For this concept is most akin to the contemplation of intellect. What is it then? Parmenides says (137 c): 'The One, if it is one, may not be many.' For the many must participate in the One. But the One does not participate in the One but is the One itself. 21