The Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity

  Kalvesmaki, Joel. 2013. The Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity. Hellenic Studies Series 59. Washington, DC: Center for Hellenic Studies.

2. Generating the World of Numbers: Pythagorean and Platonist Number Symbolism in the First Century

Two intellectual traditions from classical antiquity laid the foundation for the early Christian theology of arithmetic. The first, and most easily identified, was the rich tradition of number symbolism in the ancient Mediterranean. Numbers had been used symbolically from very early times and in many cultures, as attested by cuneiform tablets and Egyptian hieroglyphs. In the Greco-Roman world of the first century, strands of number symbolism drawn from different periods and cultures had coalesced into a single amorphous tradition. For inhabitants of the Roman Empire it provided a rich storehouse of ideas with which they could interpret omens, religious texts, the natural world, and the mathematical sciences.

The second great tradition was metaphysical speculation. The earliest Greek philosophers were noted for asking how many sources or roots—ἀρχαί—there were to the universe. Was it monadic, dyadic, polyarchic, or a synthesis? How many levels of reality, if any, existed above the material world? If the universe started out as a monadic unity, how did the second element or level originate? What kind of metaphysical entity were numbers? These questions were discussed by the earliest Greek philosophers, including Plato, but they were addressed with renewed vigor in the first century BCE, when so-called Middle Platonist philosophers, inspired by Pythagorean speculation, put forward new metaphysical theories inextricably linked to the definition and symbolism of numbers.

In this chapter I discuss these two traditions, which early Christian theology brought together. To explain the culture of number symbolism in the first century—the ways numbers were used in antiquity to interpret literature and the natural world—I turn to the writings of Philo of Alexandria and Plutarch of Chaeronaea. Both men incorporate number symbolism into their arguments, and so show us its importance in persuading ancient readers to adopt a certain perspective or interpretation. In the second half of the chapter I turn to the Greek philosophical tradition. After setting out in very broad strokes the metaphysical issues that concerned classical philosophers, I focus on the innovations of early Middle Platonism, namely the Pythagorean and Platonist philosophies described by Alexander Polyhistor, Eudorus of Alexandria, and Moderatus of Gades. I offer new interpretations of texts written by the last two, and in so doing I explain how Greek metaphysics took a turn toward monism and numerically patterned metaphysics.

Numbers to Interpret the World: Philo of Alexandria and Plutarch of Chaeronea

In the first century, the rich mélange of number symbolism that circulated in the Mediterranean was associated with Pythagoras, but that association was ana-chronistic. Pythagoras, who had flourished seven centuries earlier, left behind no writings, and his followers had disappeared by the time of Aristotle. Whatever lore they had in arithmetic, geometry, and music had been assimilated into general intellectual culture and dissociated from these extinct Pythagoreans: the pseudo-Pythagorean texts composed between the time of Aristotle and the founding of the Roman Empire contain very little mathematical symbolism. [1]

This ambivalence is seen in The E at Delphi, which is styled as a Socratic or Aristotelian dialogue. Plutarch includes himself and Ammonius, his former teacher, as two of the six named participants. The subject at hand is the meaning behind an “Ε” inscribed at Delphi. The various participants note that the inscription could be read as a number or a letter, and either reading could be interpreted in different ways. One by one the participants offer seven possible explanations for why the letter was inscribed on the temple.

The first answer, proposed by Plutarch’s brother Lamprias, takes the Ε as a numeral, which he says represents the five wise men of Greece: Khilon, Thales, Solon, Bias, and Pittakos, all of whom are reported to have met at Delphi, where they agreed to consecrate the letter in honor of their number (Plutarch of Chaeronea The E at Delphi 3 [385d–386a]). Ammonius dismisses the suggestion, as does the participant who offers the next explanation, that the Ε, being the second of seven vowels, represents the second of the seven planets—the sun, which followed the moon in ancient cosmology—and therefore Apollo (4 [386a–b]). This suggestion too is dismissed.

The third and the fourth hypotheses explain the Ε (in Plutarch’s time it was called ee, not epsilon), according to the way it was spoken, ει. So one participant says that the Ε represents either the word ‘if’ (εἰ), the keyword used to discover from the god the outcome of a future endeavor; or the ‘if’ governing the optative mood, to indicate wishes or prayers (4–5 [386b–d]). Another claims that the ‘if’ indicates the force of syllogistic logic (6 [386d–387d]).

As if entangled in his own obscurity, Plutarch leaves this line of thought unresolved, and reverts to his original explanation, that the number five is native to divinity because it generates either itself, like fire, or perfection, like the universe. So, he goes on, five also appears frequently in music, in the interval of the fifth (literally διὰ πέντε), one of the five basic intervals (10 [389c–f]). Furthermore, Plato affirmed there to be five worlds, Aristotle taught five elements, and there are five fundamental geometrical shapes in the Timaeus. [10] Plutarch associates the five senses with the five elements, and he refers to Homer, who divided the cosmos into five parts (12–13 [390b–c]). He appeals to the sequence point, line, plane, and solid, and argues for its continuation to a fifth level, the soul, which in turn naturally separates into five parts. There are five classes of living things in the world: gods, daemons, heroes, people, and beasts (13 [390c–f]). [11] Five is the sum of the first two squares, provided that one is willing to take the monad as a square (14 [390f–391a]). Plato posits five chief principles, causes, and categories. Therefore, Plutarch argues, the Delphic inscription was set up to anticipate Plato’s doctrine (15 [391a–d]). The crowning point in this rambling encomium—now longer than all the previous five explanations combined—is a riddle about why, when the priestess is led to the Prytaneum, five sortitions are first performed. One of the participants, Nikandros, warns that the reason should not be uttered. “Until such time as we become holy men,” Plutarch answers, smiling, “and God grants us to know the truth, this also shall be added to what may be said on behalf of the Five.” [12]

Ammonius, offering the seventh and final explanation, responds skeptically to Plutarch’s praise. He notes that just about any number’s praises could be sung, especially Apollo’s native number seven (17 [391e–392a]). For him, the more plausible explanation for the Ε is “you are” (εἶ). For the rest of the treatise, this seventh and final explanation deals with what it means to ascribe eternal, unchanging being to Apollo, given our own fleeting, fluctuating condition (18–21 [392a–394c]).

The length of the sixth explanation shows that Plutarch was fascinated with numbers and their symbolism. But the philosophical heft of the seventh makes it difficult to determine how seriously he regarded them. The mathematical interpretation of the Ε is the longest, but it is trumped by Ammonius’ ontological explanation. Of all the participants, Ammonius, the mathematician and Pythagorean, would be the one expected to emphasize the number symbolism of the Ε. At the end of The E at Delphi, the reader is left with no definite indication as to which explanation is most to be trusted.

Number symbolism was part of that single reason and providence for both Philo and Plutarch. In the first century, to engage piously with symbols was to grapple with the truth. Number symbols could explicate religious mythology and thereby persuade readers to embrace a particular religious world view. They could provide a gossamer portal to the harmonies of the world or to the divinity that pervades it. But number symbols could also be abused or misinterpreted. They could be tools of superstition, such as in Plutarch’s numbers concerning cats. Or they could be contested, just as the six days of creation could be a sign of either the inferiority or the superiority of the God of the Bible. Numbers were important for interpreting the world, and for persuading others to embrace that interpretation.

Monism, Dualism, and Pluralism

This trend is central to the early Christian theology of arithmetic, so here we must slow down. Although the later effects are quite evident, the original sources are scarce, and tersely reported. We have far fewer texts of Hellenistic philosophy (treatises written after Aristotle but before Plotinus) than we do for other periods, and it is easy to allow the voluminous writings of Plutarch and Philo—who did not participate in this trend—to drown out other writers from the period who were equally prolific but not lucky enough to have their works preserved. To linger on these fragmentary sources is important, because entire metaphysical systems are condensed and summarized in only a few sentences, often in obscure Greek where every word counts.

We do not have enough of Alexander’s original text—indeed, we know hardly anything about Alexander himself—to know what he made of this system. But the quotation above shows that in the first century BCE there was circulating a Pythagorean cosmology with three innovative features. First, it emphasized the monadic origin of the world: only the monad is preexistent; the dyad exists because of the monad. Second, it multiplied the number of immaterial levels—seven realms unfold, one from the other, before corporeality is achieved. And third, these seven regions are primarily mathematical—arithmetic precedes geometry, and within arithmetic monad precedes dyad, both of which precede numbers. The world is described numerically, with the monad advancing step by step to fill up the material universe. Thus, although the author of the Pythagorean Memoirs draws from motifs found in the cosmogony of the Timaeus, he develops a position that differs from classic Platonism and early Pythagoreanism—indeed from any form of ancient Greek philosophy.

Arithmetic also plays a key role in the systems Eudorus reports. The terms ‘one,’ ‘monad,’ and ‘dyad’ recur throughout, and Eudorus highlights how the one functions numerically in the metaphysical scheme. His critique is built upon the notion that, on its own, the one is capable of generating all beings; but when treated as a peer of the indefinite dyad its function is incomplete, responsible for only half of a limited set of objects. Both Eudorus and his loftier Pythagorean system prefer an account of the universe where the one is responsible for the generation of all things.

The Pythagorean themes advanced by Eudorus and the Pythagorean Memoirs are confirmed by Moderatus, who flourished in the first century CE and who, like the other two, collected and commented on Pythagorean lore. [39] In two key passages, Moderatus outlines two metaphysical systems, the first belonging to the Pythagoreans, the second to Platonists. Moderatus’ text, like Eudorus’, is preserved by Simplicius, but this time via Porphyry’s treatise On Matter. Moderatus’ account falls in two sections. This first is somewhat paraphrastic, with explanatory comments from either Simplicius or, more likely, Porphyry. Simplicius states:

This highly compressed fragment is worth reading again. Although it is a sludge of jargon, it tells a complex metaphysical story. The first half outlines the relationships of a hierarchy of three ones. The second half explains the material world, in terms both of nature and of matter, which derive from the third one. The physical world is both a decorative impression of the upper ones, and the first existential instantiation of nonexistence, the result of unity’s entering the dimension of quantity. The phrase ‘eclipse-shadow’ (σκίασμα) implies a technical term familiar to Moderatus’ audience. The term alludes to Plato’s allegory of the shadows cast by a fire on a cave wall, but more directly likens the material world to the shadow cast by the earth on the moon, implying that nonexistence (μὴ ὄν), the act of first existing (πρότως ὄν), and quantity (ποσότης) were likened, in the original metaphor, to the sun, sunlight, and earth. Like the two Pythagorean systems described earlier, Moderatus’ Pythagorean system is dominated by monism, with the superexistential one presiding over lower monistic levels and bestowing on them its unitary constitution. The metaphysical edifice is built from the blocks of arithmetic, with the four levels of the universe emerging from unity through quantity into material reality.

At the beginning of the quote above, Simplicius promises Moderatus’ account of what the Pythagoreans and Plato thought about matter. The first passage presents the Pythagorean account. Simplicius’ second passage from Moderatus follows on the heels of the first, reporting the Platonist account. This time it is a direct quotation, again via Porphyry. Note the arithmetical terms ‘unitary’ and ‘quantity’:

And these things Porphyry has written about in the second book of On Matter, quoting the [comments] of Moderatus: “ ‘When the unitary logos wanted, as Plato says somewhere [Timaeus 29d7–30a6], to have the generation of beings constituted from itself, it made room for quantity by its own privation, by depriving [quantity] of all its logoi and forms. He called this a quantity shapeless, undifferentiated, and without outline, but receptive of shape, form, differentiation, quality, and everything of this sort.’ He says, ‘Plato was likely to have predicated of this quantity a great number of names, calling it all-receptive and formless and invisible and least capable of participating in the object of intellection and scarcely grasped by spurious reasoning and everything related to these [terms].


[ back ] 1. Thesleff 1961, 1965.

[ back ] 2. Kahn 2001:88–93.

[ back ] 3. Runia 1995.

[ back ] 4. Philo’s lost treatise On Numbers is reconstructed by Stähle 1931; a fragment preserved in Armenian is found in Terian 1984. The tradition of handbooks of number symbolism began possibly with Posidonius (ca. 135–ca. 51 BCE). See Robbins 1921.

[ back ] 5. Philo On the Creation of the World 13–14: τῶν τε γὰρ ἀπὸ μονάδος πρῶτος τέλειός ἐστιν ἰσούμενος τοῖς ἑαυτοῦ μέρεσι καὶ συμπληρούμενος ἐξ αὐτῶν, ἡμίσους μὲν τριάδος, τρίτου δὲ δυάδος, ἕκτου δὲ μονάδος, καὶ ὡς ἔπος εἰπεῖν ἄρρην τε καὶ θῆλυς εἶναι πέφυκε κἀκ τῆς ἑκατέρου δυνάμεως ἥρμοσται· ἄρρεν μὲν γὰρ ἐν τοῖς οὖσι τὸ περιττόν, τὸ δ’ ἄρτιον θῆλυ· περιττῶν μὲν οὖν ἀριθμῶν ἀρχὴ τριάς, δυὰς δ’ ἀρτίων, ἡ δ’ ἀμφοῖν δύναμις ἑξάς. ἔδει γὰρ τὸν κόσμον τελειότατον μὲν ὄντα τῶν γεγονότων κατ’ ἀριθμὸν τέλειον παγῆναι τὸν ἕξ, ἐν ἑαυτῷ δ’ ἔχειν μέλλοντα τὰς ἐκ συνδυασμοῦ γενέσεις πρὸς μικτὸν ἀριθμὸν τὸν πρῶτον ἀρτιοπέριττον τυπωθῆναι, περιέξοντα καὶ τὴν τοῦ σπείροντος ἄρρενος καὶ τὴν τοῦ ὑποδεχομένου τὰς γονὰς θήλεος ἰδέαν. In this book all translations not otherwise credited are my own.

[ back ] 6. Sources and analysis in Burkert 1972:33–34.

[ back ] 7. For other examples, see refs. in nn. 1–2 above.

[ back ] 8. Lamprias’s catalogue, nos. 74, 163.

[ back ] 9. The thought is repeated in Plutarch The Obsolescence of Oracles 36 (429d). See also Plutarch Isis and Osiris 56 (374a).

[ back ] 10. Plutarch The E at Delphi 11 (389f–390a), a meditation expanded in his Obsolescence of Oracles 32–33 (427a–428b).

[ back ] 11. The soul was normally trisected in the Platonic tradition, and, indeed, in Plutarch’s other writings. Dillon 1996:194.

[ back ] 12. The E at Delphi 16 (391d–e): “οὐκοῦν” ἔφην ἐγὼ μειδιάσας “ἄχρι οὗ τἀληθὲς ἡμῖν ὁ θεὸς ἱεροῖς γενομένοις γνῶναι παράσχῃ, προσκείσεται καὶ τοῦτο τοῖς ὑπὲρ τῆς μεμπάδος λεγομένοις.”

[ back ] 13. Lamberton 2001:5.

[ back ] 14. Lamberton 2001:26, 149, 156–158.

[ back ] 15. Dillon 1973:190.

[ back ] 16. Isis and Osiris 18 (358a), 42 (368a).

[ back ] 17. Isis and Osiris 63 (376e).

[ back ] 18. Compare Galen, who more forcefully argues against the Pythagoreans, who theorized that odd-numbered days, because they are male, induce a major change (κρῖσις) in a sick patient (De diebus decretoriis 922–924). Galen attributes this power to the moon and its rhythms.

[ back ] 19. Plutarch Isis and Osiris 10 (354–355).

[ back ] 20. Plato Republic 546b; Plutarch Isis and Osiris 56 (373f–374a).

[ back ] 21. Cf. Philo On the Contemplative Life 65–66, which claims that the number five is “the most natural” (φυσικότατος) number because it is drawn from the orthogonal triangle that is the “source of generation of the universe” (ἀρχὴ τῆς τῶν ὅλων γενέσεως). For another extended application of the orthogonal triangle to generation and copulation (but without direct reference to five as ‘marriage’), see the scholia on Homer, set D, 19:119. There, the triangle is used to explain why infants are viable in the seventh and ninth months, but not in the eighth, a common belief in the ancient world.

[ back ] 22. On Superstition and Isis and Osiris 11 (355c–d), 67 (378a). Cf. Gwyn Griffiths 1970:100–101, 291.

[ back ] 23. Plutarch Isis and Osiris 67 (377e–f).

[ back ] 24. Kirk et al. 1983:22–33.

[ back ] 25. Kirk et al. 1983:34–41, 24–26, 56–57. See also Burkert 1972:38–39.

[ back ] 26. Kirk et al. 1983:414–415.

[ back ] 27. For more on Pythagorean pluralism and its relationship to Parmenides see Burkert 1972:32–35, 48–49, and Huffman 1993:23.

[ back ] 28. Patricia Curd has challenged the long-standing consensus that Parmenides was a material monist (2005:xvii–xxix).The only known pre-Platonic monist after Parmenides was Diogenes of Apollonia (Curd 2005:131). For a more complete account of the turn from monism to pluralism via Parmenides, see Rist 1965.

[ back ] 29. Burkert 1972:17, and Ross 1924:169–171.

[ back ] 30. Outlined at Metaphysics 987b14–29, with further refs. and discussion in Burkert 1972:21–22.

[ back ] 31. Ross 1924:166–168 for references and discussion. See also Annas 1976:13–21, on the possibility that the intermediate mathematicals were introduced after Plato.

[ back ] 32. Burkert 1972:31–34. Although Aristotle misrepresents the Pythagorean tradition in key places, he seems to be accurate here. For according to testimony independent of Aristotle, the Pytha-gorean Philolaus championed not numbers but limiters and unlimiteds as his highest principles. And even these principles are corporeal, not immaterial; see Huffman 1993:37–53.

[ back ] 33. On the shift from older, dualist Pythagoreanism to the innovative monist strain see Dillon 1996:344, 373, 379; Armstrong 1992:34–41; Kahn 2001:97–99; and Thomassen 2000:3–4.

[ back ] 34. ἀρχὴν μὲν τῶν ἁπάντων μονάδα· ἐκ δὲ τῆς μονάδος ἀόριστον δυάδα ὡς ἂν ὕλην τῇ μονάδι αἰτίῳ ὄντι ὑποστῆναι· ἐκ δὲ τῆς μονάδος καὶ τῆς ἀορίστου δυάδος τοὺς ἀριθμούς· ἐκ δὲ τῶν ἀριθμῶν τὰ σημεῖα· ἐκ δὲ τούτων τὰς γραμμάς, ἐξ ὧν τὰ ἐπίπεδα σχήματα· ἐκ δὲ τῶν ἐπιπέδων τὰ στερεὰ σχήματα· ἐκ δὲ τούτων τὰ αἰσθητὰ σώματα, ὧν καὶ τὰ στοιχεῖα εἶναι τέτταρα, πῦρ, ὕδωρ, γῆν, ἀέρα· (quoted in Diogenes Laertius [fl. third c. CE] Lives of the Philosophers 8.25).

[ back ] 35. “κατὰ τὸν ἀνωτάτω λόγον φατέον τοὺς Πυθαγορικοὺς τὸ ἓν ἀρχὴν τῶν πάντων λέγειν, κατὰ δὲ τὸν δεύτερον λόγον δύο ἀρχὰς τῶν ἀποτελουμένων εἶναι, τό τε ἓν καὶ τὴν ἐναντίαν τούτῳ φύσιν. ὑποτάσσεσθαι δὲ πάντων τῶν κατὰ ἐναντίωσιν ἐπινοουμένων τὸ μὲν ἀστεῖον τῷ ἑνί, τὸ δὲ φαῦλον τῇ πρὸς τοῦτο ἐναντιουμένῃ φύσει. διὸ μηδὲ εἶναι τὸ σύνολον ταύτας ἀρχὰς κατὰ τοὺς ἄνδρας. εἰ γὰρ ἡ μὲν τῶνδε ἡ δὲ τῶνδέ ἐστιν ἀρχή, οὐκ εἰσὶ κοιναὶ πάντων ἀρχαὶ ὥσπερ τὸ ἕν.” καὶ πάλιν “διό, φησί, καὶ κατ’ ἄλλον τρόπον ἀρχὴν ἔφασαν εἶναι τῶν πάντων τὸ ἕν, ὡς ἂν καὶ τῆς ὕλης καὶ τῶν ὄντων πάντων ἐξ αὐτοῦ γεγενημένων. τοῦτο δὲ εἶναι καὶ τὸν ὑπεράνω θεόν” (Simplicius Commentary on Aristotle’s “Physics” 9.181.10–19).

[ back ] 36. “φημὶ τοίνυν τοὺς περὶ τὸν Πυθαγόραν τὸ μὲν ἓν πάντων ἀρχὴν ἀπολιπεῖν, κατ’ ἄλλον δὲ τρόπον δύο τὰ ἀνωτάτω στοιχεῖα παρεισάγειν. καλεῖν δὲ τὰ δύο ταῦτα στοιχεῖα πολλαῖς προσηγορίαις· τὸ μὲν γὰρ αὐτῶν ὀνομάζεσθαι τεταγμένον ὡρισμένον γνωστὸν ἄρρεν περιττὸν δεξιὸν φῶς, τὸ δὲ ἐναντίον τούτῳ ἄτακτον ἀόριστον ἄγνωστον θῆλυ ἀριστερὸν ἄρτιον σκότος, ὥστε ὡς μὲν ἀρχὴ τὸ ἕν, ὡς δὲ στοιχεῖα τὸ ἓν καὶ ἡ ἀόριστος δυάς, ἀρχαὶ ἄμφω ἓν ὄντα πάλιν. καὶ δῆλον ὅτι ἄλλο μέν ἐστιν ἓν ἡ ἀρχὴ τῶν πάντων, ἄλλο δὲ ἓν τὸ τῇ δυάδι ἀντικείμενον, ὃ καὶ μονάδα καλοῦσιν” (Simplicius Commentary on Aristotle’s “Physics” 9.181.22–30).

[ back ] 37. My reading of Eudorus differs from that of Rist (1962:391–393), who sees Eudorus as having muddled up a single Pythagorean system, the same system Alexander Polyhistor reports. See also Dillon 1996:115–135; Kahn 2001:97–98; Trapp 2007:351–355; Bonazzi 2007; and Staab 2009.

[ back ] 38. Rist 1962:394.

[ back ] 39. For a fuller account of Moderatus, see Dillon 1996:344–351 and Kahn 2001:105–110.

[ back ] 40. (230.34) Ταύτην δὲ περὶ τῆς ὕλης τὴν ὑπόνοιαν ἐοίκασιν ἐσχηκέναι πρῶτοι (35) μὲν τῶν Ἑλλήνων οἱ Πυθαγόρειοι, μετὰ δ’ ἐκείνους ὁ Πλάτων, ὡς καὶ Μοδέρατος ἱστορεῖ. οὗτος γὰρ κατὰ τοὺς Πυθαγορείους τὸ μὲν πρῶτον ἓν ὑπὲρ τὸ εἶναι καὶ πᾶσαν οὐσίαν ἀποφαίνεται, τὸ δὲ δεύτερον ἕν, ὅπερ ἐστὶ (231.1) τὸ ὄντως ὂν καὶ νοητὸν, τὰ εἴδη φησὶν εἶναι, τὸ δὲ τρίτον, ὅπερ ἐστὶ τὸ ψυχικόν, μετέχειν τοῦ ἑνὸς καὶ τῶν εἰδῶν, τὴν δὲ ἀπὸ τούτου τελευταίαν φύσιν τὴν τῶν αἰσθητῶν οὖσαν μηδὲ μετέχειν, ἀλλὰ κατʹ ἔμφασιν ἐκείνων κεκοσμῆσθαι, τῆς ἐν αὐτοῖς ὕλης τοῦ μὴ ὄντος πρώτως ἐν τῷ ποσῷ ὄντος οὔσης σκίασμα καὶ ἔτι μᾶλλον ὑποβεβηκυίας καὶ ἀπὸ τούτου (Simplicius Commentary on Aristotle’s “Physics” 9.230.34–231.5). In my translation I have supplied in square brackets the text to be understood from the Greek text or the context. Parts of the translation enclosed by parentheses correspond to Greek text that I regard as the explanatory comments of Simplicius or Porphyry. For earlier literature see Dörrie and Baltes 1996:477, Tornau 2001, and Staab 2009:71–76.

[ back ] 41. Dodds 1928.

[ back ] 42. (231.5) καὶ ταῦτα δὲ ὁ Πορφύριος ἐν τῷ δευτέρῳ Περὶ ὕλης τὰ τοῦ Μοδεράτου παρατιθέμενος γέγραφεν ὅτι “βουληθεὶς ὁ ἑνιαῖος λόγος, ὥς πού φησιν ὁ Πλάτων, τὴν γένεσιν ἀφ’ ἑαυτοῦ τῶν ὄντων συστήσασθαι, κατὰ στέρησιν αὑτοῦ ἐχώρησε τὴν ποσότητα πάντων αὐτὴν στερήσας τῶν αὑτοῦ λόγων καὶ εἰδ(10)ῶν. τοῦτο δὲ ποσότητα ἐκάλεσεν ἄμορφον καὶ ἀδιαίρετον καὶ ἀσχημάτιστον, ἐπιδεχομένην μέντοι μορφὴν σχῆμα διαίρεσιν ποιότητα πᾶν τὸ τοιοῦτον. ἐπὶ ταύτης ἔοικε, φησί, τῆς ποσότητος ὁ Πλάτων τὰ πλείω ὀνόματα κατηγορῆσαι “πανδεχῆ” καὶ ἀνείδεον λέγων καὶ “ἀόρατον” καὶ “ἀπορώτατα τοῦ νοητοῦ μετειληφέναι” αὐτὴν καὶ “λογισμῷ νόθῳ μόλις ληπτήν” (15) καὶ πᾶν τὸ τούτοις ἐμφερές. αὕτη δὲ ἡ ποσότης, φησί, καὶ τοῦτο τὸ εἶδος τὸ κατὰ στέρησιν τοῦ ἑνιαίου λόγου νοούμενον τοῦ πάντας τοὺς λόγους τῶν ὄντων ἐν ἑαυτῷ περιειληφότος παραδείγματά ἐστι τῆς τῶν σωμάτων ὕλης, ἣν καὶ αὐτὴν ποσὸν καὶ τοὺς Πυθαγορείους καὶ τὸν Πλάτωνα καλεῖν ἔλεγεν, οὐ τὸ ὡς εἶδος ποσόν, ἀλλὰ τὸ κατὰ στέρησιν καὶ παρά(20)λυσιν καὶ ἔκτασιν καὶ διασπασμὸν καὶ διὰ τὴν ἀπὸ τοῦ ὄντος παράλλαξιν, δι’ ἃ καὶ κακὸν δοκεῖ ἡ ὕλη ὡς τὸ ἀγαθὸν ἀποφεύγουσα. καὶ καταλαμβάνεται ὑπ’ αὐτοῦ εἰδητικοῦ μεγέθους λόγον ἐπιδεξομένης καὶ τούτῳ ὁριζομένης, τοῦ δὲ διασπασμοῦ τῇ ἀριθμητικῇ διακρίσει εἰδοποιουμένου. ἔστιν (25) οὖν ἡ ὕλη κατὰ τοῦτον τὸν λόγον οὐδὲν ἄλλο ἢ ἡ τῶν αἰσθητῶν εἰδῶν πρὸς τὰ νοητὰ παράλλαξις παρατραπέντων ἐκεῖθεν καὶ πρὸς τὸ μὴ ὂν ὑποφερομένων (Simplicius Commentary on Aristotle’s “Physics” 9.231.5–27).

[ back ] 43. Moderatus had an affinity for Pythagorean lore, whether he agreed with it or not (Porphyry Life of Pythagoras 48). This second passage falls into three parts: a quote from Moderatus, an interjected explanation from Porphyry, and then a paraphrase of yet more of Moderatus’ account. So although we can expect the first part to reflect Moderatus’ words, the second and third parts are Porphyry’s synthesis, drawn from who knows what other parts of Moderatus’ text. Distinguishing Simplicius’, Porphyry’s, and Moderatus’ voices is admittedly difficult. For those who know the text and have puzzled over it, here is my rationale: The clearest indicators for separating the three authors are verbs of speaking. The παρατιθέμενος of lines 5–6 (Diels 1882–1895:1.231) is one of Simplicius’ favored terms for introducing extended quotations, which he tends to reproduce conscientiously. (See e.g. his quote of Geminus paraphrasing Posidonius at 291.21–292.31, which also begins with παρατίθησιν, and in which he inserts no φησι of his own.) Thus I regard line 7 onward as having no words written by Simplicius (ending, presumably, at the close of line 24, where Simplicius assesses the role of ὕλη). In that section, verbs of speaking appear at lines 7 (φησιν ὁ Πλάτων), 10 ([Πλάτων] ἐκάλεσεν), 12 ([Μοδέρατος] φησι), 13 (ὁ Πλάτων … λέγων), 15 (φησι), and 18–19 (τοὺς Πυθαγορείους καὶ τὸν Πλάτωνα καλεῖν [ὁ Μοδέρατος] ἔλεγεν). The φησι at line 15 likely has Moderatus and not Plato as its subject, parallel to the φησι at line 12. (Thus the quotation marks in my translation, distinguishing Moderatus’ voice from Porphyry’s). The change from φησι (12, 15) to ἔλεγεν (18–19) is significant, for the latter not only changes the tense but introduces indirect discourse, a sign of Porphyry’s summarizing or paraphrasing Moderatus (also in evidence in our first passage). Further, the clause in which ἔλεγεν appears (starting at line 18 with ἣν) governs the rest of the quote down through line 24, a single sentence (despite Diels’s unnecessary terminal punctuation at line 21); and this long text comprises five explanatory clauses (18: ἣν, 19: οὐ … ἀλλὰ, 20: δι’ ἃ, 22: τῆς μὲν, 24: τοῦ δὲ). So lines 18–24 contain Porphyry’s summary of Moderatus’ system, drawn from texts not necessarily near the source of the quotation in lines 7–18. For other opinions on attribution, see Dodds 1928:138n3 and Tornau 2001:204–205n26.

[ back ] 44. On the background of the concept of privation, see Tornau 2001:207–208; for its later use, Thomassen 2006:271–279. Cf. Theology of Arithmetic 9.5–6, where the dyad divides itself from the monad: πρώτη γὰρ ἡ δυὰς διεχώρισεν ἑαυτὴν ἐκ τῆς μονάδος. For scholarly opinions on the nature and function of the internal forms and λόγοι of the unitary λόγος, see Tornau 2001:209n37.

[ back ] 45. There is an important lacuna in Porphyry’s account. Note that ποσότης (feminine) is linked not with ταύτην but with τοῦτο (neuter) at line 10, a τοῦτο with no obvious antecedent, but echoed at lines 15–16: τοῦτο τὸ εἶδος (itself asking us to remember an antecedent not readily obvious). If the two τοῦτοs are to be linked, then form is a peer or immediate subordinate of quantity.

[ back ] 46. Whereas μὴ ὂν is at the bottom of Moderatus’ Platonist system, posterior or equal to the material world, in the Pythagorean system μὴ ὂν precedes it, with existence and quality as intermediaries. No doubt Moderatus and his sources were grappling with the Parmenides and the Sophist—the Platonic dialogues that deal chiefly with nonexistence. But with the loss of context, it is hazardous (and for this study tangential) to infer the reason for the difference in the two systems.

[ back ] 47. Tornau 2001.

[ back ] 48. For other relevant primary sources and discussion, see Rist 1962, Rist 1965, and Thomassen 2006:270, 275–279, and references.

[ back ] 49. Compare On Flight and Finding 94–95 (the five powers of the one God) with On Abraham 121 (two powers). The two accounts are inspired by numbers Philo encounters in Scripture; hence the disparity. Because Philo molds each account to suit the number, one should not rely upon them as maps to his metaphysics.