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Pythagoras RevivedMathematics and Philosophy in Late Antiquity$

Dominic J. O'Meara

Print publication date: 1990

Print ISBN-13: 9780198239130

Published to Oxford Scholarship Online: April 2004

DOI: 10.1093/0198239130.001.0001

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(p.217) Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

(p.217) Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

Source:
Pythagoras Revived
Author(s):

Dominic J. O'Meara

Publisher:
Oxford University Press

The text of Psellus' works On Physical Number and On Ethical and Theological Arithmetic which I published in 1981 is reprinted here.1 Information concerning manuscripts, principles of the edition, and other textual matters may be found in O'Meara (1981) and in the discussion of the manuscript tradition of Nos. 4–6 in Psellus, Philosophica minora II. I have inserted, very tentatively, vertical lines where I would suggest the joints between Psellus' excerpts might occur (for grounds in favour of this I refer the reader to Chapter 3 above and to the note on On Physical Number, line 27, below). Given the nature of Psellus' texts, the English translation makes no pretence at elegance. For translation of Greek mathematical terms I have followed the ‘Glossary’ in D'Ooge et al. (1926), 291 ff., where references to explanations of these terms may be found. Finally I have appended references linking Psellus' excerpts to similar passages in Neopythagorean and Neoplatonic literature (similarities in vocabulary and phrasing in Iamblichus' extant works are also noted). This is not intended, however, to replace the analysis proposed above in Chapter 3. (p.218)

Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

(p.219) On Physical Number* *

  • You were surprised when, at our meeting yesterday, I said
  • that there was another, physical number besides mathematical
  • number. But if you only knew of the variety of number, you would
  • have asked me about intelligible, essential, and ideal number. For     5
  • number of this 〈latter〉 kind is truly the highest and first.
  • Mathematical number is seen in common concepts. Physical number
  • is found in the lowest things, things generated and divided in
  • bodies. For the principles mixed in bodies, both in animals and
  • plants, are physical numbers, for each of these is born, grows,     10
  • and dies at determinate times. | And the philosopher should fit
  • the appropriate numbers to the causes in nature.|
  • And since form is, in nature, the first and most important
  • cause (for the being of all depends on it), thus such numbers as
  • provide being to nature and are essential, these are connatural     15
  • with forms. Physical numbers of the formal type are: all odd
  • numbers, numbers properly called ‘perfect’, symmetric numbers
  • such as multiples and superparticulars, ordered numbers such as
  • square and cubic numbers. The beauty in numbers, which shows in
  • their symmetry; the self‐sufficiency that is apparent in perfect     20
  • numbers; the generativeness seen in 〈the numbers〉 seven and nine;
  • the power that is observed especially in the tetractys; the
  • primacy that is found in the one; and the identity, purity, and
  • paradigmatic character appearing in the first numbers; and the
  • equality that may be seen in square number; all of these     25
  • 〈properties〉 fit physical cause as form.|
  • Since matter is an important cause in nature, we will find
  • it in physical numbers by taking all the opposites of the numbers
  • we have mentioned as regards formal causes. The numbers then that
  • are appropriate to matter are those that are even, imperfect,     30
  • differentiating, dissimilar, and all others such as are in
  • opposition to formal numbers.|
  • There is an efficient cause in physical numbers: one may see
  • this in the generative numbers shown in animal generation. | And
  • the principle of movement according to difference and inequality     35
  • in numbers shows an efficient cause. | But this is especially
(p.220)

Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

(p.221)

  • manifest in the rotations and the revolutions of the heavens. And
  • the stars' configurations in relation to each other, their
  • periodic revolutions, all of their shapes, their powers, are
  • contained in the principles of numbers. And the moon's phases,     40
  • the order of the spheres, the distances between them, the centres
  • of the circles which carry them, numbers contain them all. Indeed
  • the measures of numbers determine health; crises in sickness are
  • completed according to determinate numbers; deaths come thus also,
  • nature having fulfilled the appropriate measures of change. |     45
  • Hence number is generative of animal life. For since animals are
  • made up of soul and body, the Pythagoreans say soul and body are
  • not produced from the same number, but soul from cubic number,
  • body from the bomiskos. For, they say, 〈soul's〉 being is from
  • equal times the equal equal times, coming to be in equality,     50
  • whereas body is a bomiskos, produced from unequal times the
  • unequal unequal times. For our body has unequal dimensions: its
  • length is greatest, its depth least, its breadth intermediate.
  • Thus soul, as they say, being a cube from the number 6 (which is
  • perfect), comes to be equal an equal times the equal as in the     55
  • cube 216, for this is 6 by 6 by 6. But body, being from unequal
  • sides an unequal times the unequal an unequal times, is neither
  • dokis nor plinthis but a bomiskos, having for sides 5, 6, 7: for 5
  • by 6 is 30, and 7 by 30 is 210. Thus seven‐month births occur in
  • 210 days, having a complete body. If then the soul alone were     60
  • generated, it would be born in 216 days, a perfect cube being
  • completed with its coming. But since the animal is made of soul
  • and body, 210 days are appropriate to the completion of the body:
  • the generation of the body dominates in the animal. | Thus soul
  • desires equality, the body relates to anomaly and inequality. |     65
  • The ancients thought altars should have all dimensions unequal. |
  • Since nature seems to form especially by change, one must
  • show how physical number has change. The causes of change then
  • relate to the dyad, the even, the heteromecic and suchlike
  • (generally whenever indeterminateness is found in numbers, there     70
  • change appears), difference and inequality (one is like a
  • relation and property, which is rest, the other a differentiating
  • and unequalizing, such that it is not the different and unequal
  • that are in change, but those made different and unequal). |
(p.222)

Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

(p.223)

  • And the power of the unlimited and of the limiting is both     75
  • in nature and in physical number. The limiting in nature is the
  • good, beautiful, equality, and suchlike, the unlimited 〈is〉 the
  • indeterminate, unordered, irrational, evil, ugly, and suchlike. |
  • In physical number the unlimited is the cause as regards plurality, the limited
  • the first cause as regards the one. |           80
  • Physical number has place. For if number contains bodies
  • and all extension, in the very same way it contains in itself the
  • place that accompanies bodies, not as if by touch but by
  • incorporeal power. | And the places of each number are ordered
  • according to the serial 〈order〉. For some numbers are by nature     85
  • and order odd and even, whereas some are by nature odd and by
  • order even. | And then again places are most influential in the
  • generation of things in the assimilation of the generated to them. |
  • Neither in nature nor in physical number is there void. Its     90
  • paradigm would be nothing other than lack of harmony and lack of
  • symmetry. But lack of symmetry is banished from numbers, unless
  • one wishes to speak of even number as a discontinuous gap. |
  • Now I know these are forceful demonstrations of physical
  • number. We agree with what the ancients say and pass them on to     95
  • you as for the most part right. For we do not accept completely
  • what concerns animal generation: there are other principles of soul's being
  • and body's making, demiurgic but not arithmetic.

On Ethical and Theological Arithmetic* *

  • As there are numbers fitting nature, so there are fitting
  • 〈ethical〉 habits. And as there is a physical, so there is an
  • ethical arithmetic. | The principle of all ethical philosophy is
  • measure itself and the measured in the being of numbers, which is     5
  • a pre‐eminent principle in all ethical ordering. After the one
  • principle there are other principles of all ethical philosophy,
  • such as limit, the perfect (for perfection unitarily completes
  • the best measure of life), then the order in numbers which fits
  • ethical good ordering, then the uniform and similar to the one,     10
  • such as is seen either in the tetrad, hebdomad, or decad. | There
(p.224)

Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

(p.225)

  • *is further as a model of good character the mean which binds
  • together the difference in numbers, making all harmonious,
  • producing all proportions, and making the soul into something
  • well‐adjusted. |                15
  • Soul's powers are related to number forms. For the intellect
  • is the one as unitary, science is 2 because it knows with cause,
  • opinion is plane number, sensation solid number because it
  • perceives solid bodies. | The decad contains the ethical
  • principles in us. | Life according to intellect contains limit,     20
  • and, suitable also, the hebdomad, for it is unitary. And the
  • hebdomad, like intellectual activity, neither generates another
  • equal to the decad by multiplication nor is born of another. |
  • If the form of virtue is defined by a measured and perfect
  • life, mean and perfect numbers fit natural virtue, superabundant     25
  • and deficient 〈numbers〉 〈fit〉 excesses and deficiencies in
  • relation to virtue. | And one must assign the opposites of what we
  • give to virtue to vice: lack of measure and of harmony, the
  • differentiating, the unequal, unlimited, and such‐like. For all
  • these fill the column of all vice. |           30
  • And each single virtue fits a number. For wisdom about
  • variable matters, or practical wisdom, fits the triad which uses
  • reasoning as if in 〈one dimension,〉 breadth. Wisdom which knows
  • 〈real〉 beings is related to the monad which sees what is known in
  • a unitary way. And according to the opposite, lack of wisdom     35
  • relates to the dyad, the unlimited and irrational to the
  • unlimited and irrational. And courage as manliness relates to odd
  • number, but as constancy it relates to square 〈number〉. What is
  • female such as cowardice is to be fitted to even 〈number〉,
  • inconstancy to oblong 〈number〉. Fitting temperance, cause of     40
  • symmetry, is 9 which is multiplied from the triad, for if all
  • square numbers produce equality, those produced from odd numbers
  • are the best for producing equality, and of these the first is
  • the square from the triad, 9, which comes from two perfect
  • numbers, the 3 and 6, according to the first perfect number, the     45
  • 3, perfected completely and as a whole. Justice as the faculty of reciprocity of
  • the equal and appropriate is contained by the mean
(p.226)

Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes

(p.227)

  • *of a square odd number. For 4 fits. justice, lying in between
  • the monad and the number 9, and the number by which it is less
  • than 9, by this number it is more than the monad. And 5 is the     50
  • ninth part of summation of the numbers going from the monad to
  • the ennead. Such then is arithmetic in ethics.|
  • The philosopher Iamblichus wrote an arithmetic of higher
  • natures, not treating of the numbers in them mathematically, nor
  • imaging the higher kinds through analogies, nor positing them as     55
  • hypostatic, self‐moved, intellectual, or essential numbers, but
  • he says 〈that〉 as the genus of higher 〈natures〉 transcends all
  • being, so is their number absolute and of itself.|
  • Speaking of the difference between the good and the one, he
  • says that as the nature of the good is generative, being prior as     60
  • cause to all goods, progresses in itself, and multiplies, thus the
  • complete cause of the one fills all from itself, holds beings in
  • itself, and multiplies in itself.|
  • Suitable and appropriate to the higher kinds is the higher
  • kind of mathematical number, such as the one, limit, the     65
  • determinate, equal, and such‐like. | As there is a physical cause
  • of physical numbers, an ethical for ethicals, thus of divine
  • number there is a uniform divine principle, prior as cause to the
  • causes in all numbers, a uniform unity pre‐existing even all
  • divine unified number itself. | The first then, the one properly     70
  • speaking, God as we would say, is henad and triad (for the triad
  • unrolls the beginning, middle, and end around the one); and the
  • intelligible and brightest monad ascends to the highest cause;
  • and the supercelestial of the 〈monad?〉 leader of 〈cosmic〉 order;
  • and the earthly, indivisible in the divided, full in the       75
  • lacking. | There is a divine dyad, unlimited power, never failing
  • progression of life, receiving the measure of the first one. For
  • the dyad is intelligible, intellectual, mathematical, in matter. |
  • So also the triad: one is intelligible, one intellectual, one
  • supercelestial, one celestial, one penetrating the universe.|        80
  • In this manner then of the account of this wondrous
  • arithmetic you might relate each in the natural flow of numbers
  • to the supernatural unities. But rather this is inferior and
  • appropriate to analogy. If one wished to see divine number
  • better, one would define this from the higher kinds themselves.       85
  • For there is a divine one and divine monad and divine dyad, and
(p.228)

Appendix I The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes *

(p.229)

  • odd and even, transcendent and thought in higher insights. And I
  • know that one might accept these things with difficulty. This
  • happens in our neglect of higher 〈beings〉. For we do not easily
  • accept the contemplation of the unaccustomed and unfamiliar.       90

Notes:

(*) 2 cf. Plato, Tim. 25 e 2–3 3–8 cf. Iambl. Comm. 64, 2–19; 92, 27–93, 2; In Nic. 3, 10–16; Syrian. In met. 122, 13–15; 135, 9–10 5 cf. Iambl. Comm. 64, 2; Bertier et al. (1980), 170–1 6 cf. Iambl. Comm. 15, 6–7 6–7 cf. Iambl. In Nic. 4, 4–8 7 cf. Iambl. Comm. 18, 15 7–11 cf. Syrian. In met. 25, 26–7; 190, 30–5 11–12 cf. Iambl. Vit. Pyth. 118, 16; Comm. 61, 19–20; Syrian. In met. 188, 2–3 14–15 cf. Nicom. in Phot. Bibl. III 41 (143 a 10); Iambl. In Nic. 77, 25–78, 1 15–16 cf. Iambl. Comm. 63, 29 19–20 cf. Iambl. In Nic. 34, 23–4 21 cf. anon. Theol. arith. 61, 5 ff.; 63, 1 ff. 21–2 cf. Iambl. Vit. Pyth. 119, 6–7 21–4 cf. Iambl. In Tim. fr. 53, 6–13 22–4 cf. anon. Theol. arith. 1, 4 ff. 27 δὲ καὶ in Psellus can sometimes mark the beginning of an excerpt; cf. below, lines 33, 81, and, for example, Philos. min. nos. 2, 32 34–5 cf. below, 45 ff. 35–6 cf. below, 67 ff. 36–42 cf. Iambl. Comm. 61, 16–22; 64, 8–13; 73, 20–7; Syrian. In met. 190, 26–30; Procl. In Eucl. 22, 26–8; In Tim. III 19, 30–2

(*) 38–9 cf. anon. Prol. in Nicom. 76, 12–14 42 cf. Iambl. Comm. 11, 26–7 43–4 cf. Aristoxenus, fr. 23, p. 14, 34–5 Wehrli; anon. Theol. arith. 71, 10–11 (= Nicom.); Anatolius, De dec. 35, 27; Theon Smyrn. Expos. 104, 9–12 48–64 cf. anon. Theol. arith. 63, 23–64, 17 (Nicom.); Nicom, in Phot. Bibl. III 45 (144 b 1–4); Syrian. In met. 130, 34; 143, 7; 188, 1–4; Lydus, De mens. 32, 15–16 54–5 cf. anon. Theol. arith. 42, 19–43, 2 (Anatolius); Theon, Expos. 45, 10–14; 101, 7–9; Iambl. In Nic. 34, 17–18 59 cf. anon. Theol. arith. 51, 16–19; 64, 5–11 65–6 cf. Nicom. Intro. arith. 107, 22–108, 1 69 cf. Anatolius, De dec. 31, 3; anon. Theol. arith. 8, 2 ff.; 32, 13–14 (Anatolius); Theon, Expos. 100, 9–11; Syrian. In met. 5, 20–4; 131, 28–31; Procl. In Remp. II 137, 23–5; Lydus, De mens. 24, 4–21 72 cf. Plato, Tim. 57 e 6–58 a 2 72–4 cf. Aristot. Phys. 201 b 16–27; Iambl. In Nic. 43, 22–5; Simplic. In Phys. 433, 35–434, 1

(*) 75–80 cf. Aristot. Phys. 207 a 35–b1, 207 b 35; Met. 986 a 15 ff. 79–80 cf. Syrian. In met. 10, 1–4; 166, 1–2 84–5 cf. Syrian. In met. 149, 31 85–7 Cf. Aristot. Phys. 226 b 34–227 a 4; Simplic. In Phys. 641, 9–15 and 35–642, 4; 875, 11–12 90–3 cf. Syrian. In met. 132, 23–9; 149, 28–31 92 cf. Iambl. In Nic. 91, 20 97–8 cf. Psell. Philos. min. nos. 22, 23, 27

(*) 1–2 cf. Iambl. In Nic. 35, 2–10; 125, 14–22; Comm. 88, 29–30 2 cf. Syrian. In met. 189, 13 4–10 cf. Iambl. Comm. 47, 1–6; Procl. In Eucl. 24, 4–17 4–5 cf. Plato, Phileb. 66 a 6–7 6 cf. Iambl. Comm. 91, 28

(*) 14 cf. Plato, Rep. 546 b 7‐c 1; Iambl. in Stob. Anth. I 364, 22; De myst. 17, 17 15 cf. Plato, Rep. 400 d 3, 413 e 4; Theon, Expos. 11, 9–20; Iambl. Comm. 69, 10 16 cf. Iambl. Comm. 61, 15–16 17–19 cf. Aristot. De an. 404 b 22–4; Iambl. De an. in Stob. Anth. I 364, 15–18; Simplic. In de an. 29, 2–9 20–1 cf. Aristot. Eth. Nic. 1178 a 6–7 22–3 cf. Philolaus in DK I 416, 8–10; Theon, Expos. 103, 1–3 24–7 cf. Nicom. Intro. arith. 36, 6–37, 2; Anatolius, De dec. 31, 16–18; anon. Theol. arith. 19, 12–17; Iambl. In Nic. 17, 1–2; 32, 25 ff.; 53, 6–9 30 cf. Aristot. Eth. Nic. 1096 b 6 31 cf. Iambl. Comm. 56, 8–11; In Nic. 35, 2–3 32–3 cf. anon. Theol. arith. 16, 18–21; Nicom. in Phot. Bibl. III 43 (143 b 28) 32 cf. Aristot. Eth. Nic. 1139 a 8 33–4 cf. anon. Theol. arith. 4, 4–5 (Nicom.); Iambl. In Nic. 6, 6–7 37–9 cf. Plato, Rep. 442 c 1–3; Laws 802 d 9; Iambl. in Stob. Anth. III 320, 2; Syrian, In met. 131, 35–7 40 cf. Anatolius, De dec. 31, 16–18; anon. Theol. arith. 17, 10–12 (Anatolius); Iambl. in Stob. Anth. III 257, 14–258, 2; 271, 25–6 44–6 cf. Iambl. In Tim. fr. 53, 12–13 46–7 = anon. Theol. arith. 37, 2–4 (Nicom.) = Iambl. In Nic. 16, 16–18; cf. Anatolius, De dec. 31, 22–3; Iambl. Comm. 61, 1–3; Pr. 118, 1–3; Bertier et al. (1980), 158 47–8 cf. anon. Theol. arith. 29, 6–10

(*) 49–51 cf. anon. Theol. arith. 37, 4–10; Theon, Expos. 101, 14–23; Iambl. In Nic. 16, 18–17, 2 53–7 cf. Iambl. Comm. 63, 23–31 56 cf. Iambl. Comm. 64, 6 57–8 cf. Iambl. De myst. 23, 15–16; 160, 1–3 59–63 cf. Iambl. Pr. 23, 21–5; Comm. 16, 10–14; Syrian. In met. 182, 3–7 64–6 cf. Iambl. Comm. 63, 24–7; 92, 14–15; 61, 6 67–70 cf. Iambl. De myst. 261, 9–263, 7; 264, 13–265, 5; Procl. El. theol. prop. 113 (100, 5–9); Theol. Plat. III 12, 10–11; 36, 13–15 71–2 cf. Plato Laws 715 e; Ocellus in DK I 441, 7–8; Theon, Expos. 100, 13–14; 46, 15; anon. Theol. arith. 17, 4–5 (Anatolius); Iambl. De myst. 60, 1–2 72–4 cf. Syrian. In met. 140, 10–18 76–7 cf. anon. Theol. arith. 12, 10–11; Syrian. In met. 5, 22–3; 112, 16 and 35–113, 3; Procl. El. theol. prop. 152; Theol. Plat. I 122, 8–10; III 45, 3–5

(*) 88–9 cf. Psellus, Philos. min. no. 29, 106, 10–11

(1) By kind permission of Johns Hopkins University Press. I have made one minor change, at On Eth. Theol. Arith. 48, where, rather than indicating as before a lacuna after δικαιοσύνῃ, I would suggest correcting τέττα∂α to πέντɛ (as required by the context), but hesitate in view of the persistent indecision in Neopythagorean texts (cf. the references given ad loc.) as to whether justice is to be identified with the numbers four or five.