Joel Kalvesmaki, The Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity
2. Generating the World of Numbers: Pythagorean and Platonist Number Symbolism in the First Century
3. The Rise of the Early Christian Theology of Arithmetic: The Valentinians
4. The Apogee of Valentinian Number Symbolism: Marcus “Magus”
5. Alternate Paths in the Early Christian Theology of Arithmetic: Monoïmus and the Paraphrase of the “Apophasis Megale”
6. The Orthodox Limits of the Theology of Arithmetic: Irenaeus of Lyons
7. The Orthodox Possibilities of the Theology of Arithmetic: Clement of Alexandria
8. How the Early Christian Theology of Arithmetic Shaped Neo-Platonism and Late Antique Christianity
Excursus A. One versus One: The Differentiation between Hen and Monad in Hellenistic and Late Antique Philosophy
Excursus B. The Pythagorean Symbol of the Τετρακτύς
Excursus C. The Dyadic Character of A Valentinian Exposition
Appendix. Greek Texts
7. The Orthodox Possibilities of theTheology of Arithmetic: Clement of Alexandria
Clement, a Christian intellectual who flourished in late second-century Alexandria, offers a perspective on the orthodox theology of arithmetic that departs from, yet complements, that of Irenaeus. Unlike Irenaeus and his head-on refutation, Clement criticizes the Valentinians subtly, preferring to co-opt heretical number symbolism for orthodox ends. And Clement’s interest only begins with gnosticizing Christians. Just as important to him are Platonists and Stoics, whom he engages with number symbolism to show that Christ and Christian theology surpass their teachers and doctrines.
In this chapter I explore three significant arithmological motifs found in Clement’s writings. In each case, Clement engages an area previously discussed by Irenaeus, a Valentinian, or a school of philosophy. First is his doctrine of God, and his use of the epithet ‘One’ for the godhead, a point of concern to Irenaeus and Platonists. Second is Clement’s use of number symbolism to build a novel anthropology that he intended to be a viable alternative to Valentinian and Stoic schemes. And third is Clement’s interpretation of the number symbolism built into the story of the Transfiguration, an allegory that departs from both Marcus’ version and Irenaeus’ dissent. In each of these, Clement threads the theoretical needle between or around the two alternatives, showing how an orthodox theology of arithmetic can remain both faithful to the tradition and compelling to the cultural elite.
Numbers in Clement’s Doctrine of God
Very little is known of Clement. The wealth and social status of his family al-lowed him to travel to pursue his education. Clement credits with his training in Christianity teachers from across the Roman world—Greece, Italy, Lebanon, Syria, and Egypt—particularly a certain Pantaenus, whose missionary travels to India are mentioned by Eusebius.  Once he settled in Alexandria, Clement conducted what was probably an informal Christian school, not to be confused with the famous academy that started under the auspices of Origen.  After the persecution of Christians in 202 Clement left Alexandria, and died presumably a short time later. 
Several of Clement’s numerous writings survive, in whole or in part, and in various states of editorial polish.  Evident in all his writings is an unflagging commitment to Christian orthodoxy. His style and spirituality differ from those of his contemporaries Irenaeus and Tertullian, but he nevertheless identifies himself with their opinions and the traditions preserved by the Church. Like them, he holds to a single God, the Father, and a single Son, the express image of the Father. As a self-proclaimed “ecclesiastic,” he uses the various titles for God and his Word—e.g. ‘Son of God,’ ‘Christ,’ ‘Savior,’ ‘Instructor,’ and ‘Jesus’—to describe one and the same person, unlike the Valentinians.  He holds to no theology of emanations from God, so he has no system of aeons organized into numerically symbolic groups. 
But Clement is more adventurous than other orthodox writers in using arithmetic to describe the movement from the godhead to the structures of creation. In his view, below the Father and the Son are numerous beings that form an elaborate hierarchy extending from heaven to earth, all with their source of being in unity, and unity as their goal. Clement says that these lower beings save each other “from One and through One.”  “From One” refers to the Father; “through One” to the Son. Abraham, according to Clement, embraced this unity of God in the alteration of his name from Abram, since the alpha that was inserted into his name represents his knowledge of the one and only God.  Clement’s sense of the unity of God is so strong that he calls him “the One” and applies the attributes of the number one to the godhead: just like the number one, God “the One” is indivisible, and therefore infinite, realized in his lack of extension. 
Clement even says that God “calls himself one,” on the basis of John 17.21–23: “In order that all might be one, just as you, Father, are in me and I in you,” and so forth.  But lest it be thought that his God is the Platonist One, Clement interprets John so as to affirm that God transcends all number: “God is one, and beyond the One, and above the Monad itself.”  Adopting here the now familiar idea that the Monad transcends the Hen, Clement says that God stands not only above the One (the Platonists’ highest principle) but above the Monad itself (the Pythagoreans’), and is therefore beholden to no number. Clement cautions readers that the epithet ‘One’ for God is an approximation, and not a true predicate of He Who Cannot Be Named.  Such negative theology was standard in the Platonism of his day. But Clement presents this idea of the indescribability of God, an idea that becomes quite important in Plotinus’ writings, not to press Christianity into a Platonic mold but to reinforce belief in the transcendence of God. For Clement there is no category, including number, that comprehends and stands over his nature. Thus Clement’s metaphors and pedagogical tools may be philosophical in origin, but in the substance of his theology he stands with Irenaeus as a Christian monotheist, not a Platonist. 
Although God stands above arithmetic, Clement finds arithmetical unity a helpful metaphor of the divine, and he states that man’s goal is a similar kind of unity. As a person becomes divinized and moves into a state of dispassion, he becomes purely “Monadic.”  This unity is epitomized for Clement in the Church: “For just as God is one and the Lord is one … that which is most highly treasured is praised for its solitude since it is an imitation of one principle. Thus, the one Church also has a portion in the nature of the One, which nature the [heretics] strive to chop into many heresies.”  This joint share in God’s unity allows the Church to collect people “into the unity of the one faith of its proper testaments—rather of the one testament from different ages—by the will of the one God, through the one Lord.”  Thus the Church, which is the earthly image of the heavenly Church, reflects precisely the unity of God, and humanity’s return to that unity. 
The Anthropological Decalogue
Clement’s longest extant work is his Stromateis (Miscellanies), a lengthy patchwork of discussions on various theological topics, intended for study by Christians prepared to think about advanced topics. Book 6 of the Stromateis contains his richest meditation involving number symbolism (§§133–148). Following up a principle mentioned earlier in Book 6, that Christians can profitably use the four mathematical disciplines, Clement applies arithmetic to Scripture, particularly the Ten Commandments, and Scripture to arithmetic. In his excursus, a small treatise in its own right—I call it On the Decalogue here for convenience—Clement demonstrates how an advanced Christian might use his education, especially in arithmetic or geometry, to explain passages from the Bible.
On the Decalogue falls in two parts. The first half (133.1–137.1) relates Moses’ Decalogue and its number symbolism to creation and anthropology. Clement uses the number ten as a structural device around which to frame a Christian alternative to Stoic anthropology, and his system, difficult to understand on first reading, illustrates how a Christian might profitably use number symbolism. In the second half (137.2–148.4), Clement explains the theological significance of eight of the Ten Commandments. When he arrives at the commandment to keep the Sabbath holy, Clement pursues a lengthy tangent, to discuss the relationship between the numbers six, seven, and eight (138.5). He interrupts this tangent—which draws from Jewish, Christian, and Hellenistic arithmology—with yet another, an arithmological interpretation of the Transfiguration (140.3), the centerpiece of On the Decalogue, which I explore toward the end of this chapter.
The first half of On the Decalogue begins with a meditation on the well-ordered multiplicity of creation and humanity. Although not a unity, as God is, says Clement, creation has been imprinted with a unifying harmony that reflects its divine origin. To demonstrate this harmony, he carefully constructs three lists of ten elements each—types of decalogues, all of which, he says, the Decalogue encompasses (περιέχει: 133.3, 4). The first, the heavenly decalogue, is sun, moon, stars, clouds, light, wind, water, air, shadow, and fire. The second decalogue’s ten items relate to earth and the sea: humans, cattle, reptiles, beasts, fish, whales, carnivorous birds, birds of a delicate palate, fruit-bearing plants, and plants with no fruit. The first decalogue does not seem to follow a specific order, but the second list does. It follows in reverse the days of creation found in Genesis 1, which goes from plants (day three), to reptiles, birds, and fish (day five), to quadrupeds, land reptiles, beasts, and humans (day six).  The rough correspondence shows that Clement shaped the Genesis account to suit his number symbolism. In this he resembles the Valentinians, who drew from Genesis lists of ten and twelve items to support their doctrine of the Decad and Dodecad. 
The third decalogue Clement presents (134.2) is that of the human being, who he says consists of the five senses, along with (6) the ability to speak, (7) the ability to generate, (8) the formed spirit, (9) the ruling faculty of the soul, and (10) the characteristic mark of the Holy Spirit (a mark applied through faith).  This anthropological decalogue features in Clement’s other writings as well, and provides an important contrast with similar structures in Valentinianism and Stoicism. Details in his use of this decalogue illustrate how he used numbers to articulate highly nuanced points about the creation and salvation of the world. Clement may have imitated Valentinians and Stoics, but that was to entice them to embrace orthodox Christianity.
For example, in Book 2 of Stromateis, in his interpretation of Exodus 16.36 (“The omer was the tenth of the three measures”), repeating Philo nearly verbatim, Clement identifies the three measures as sense perception, reason, and intelligence, as well as the intended objects of these three faculties.  He then adds his own thoughts to Philo’s explanation: the true and just measure is the gospel teaching that “it is not what enters into the mouth that defiles a person, rather, that which exits a person’s mouth is that which defiles a person.”  Clement now draws from his anthropological decalogue.  That same measure is the “decad that encompasses the human being.” The three measures of Exodus 16.36 allude in summary form to that decad.  He then explains the decad in terms similar to those found in On the Decalogue: “That might be both the body and the soul: the five senses, the vocal faculty, the generative faculty, and the faculty of understanding or of the spirit, or whatever you want to call it.” 
Clement then says one must overleap all these faculties so as to stand at the mind, as if overleaping the nine portions of the universe. These, he says, are the four elements (that is, earth and the sublunary region; portion 1), the seven planets (portions 2–8), and the ‘unmoved ninth’ (the fixed sphere of stars: portion 9). What he has just termed the mind—the tenth portion, the complete number—resides above these nine, and is one’s attainment of the knowledge of God.  Thus, the nine faculties of the human being, capped by the tenth, the mind, resemble the structure of the universe, in which nine celestial levels are subordinate to God as the tenth.  Clement’s cosmological decalogue depends directly upon Philo, but his anthropological one is original. 
Back to Book 6 and On the Decalogue. Clement twice identifies the mark of the Holy Spirit explicitly as the tenth number or element in the human being (134.2: δέκατον; 135.1: τὸν δέκατον ἀριθμόν), thus emphasizing afresh his tenfold anthropology. This point is easily missed when reading 135.1. This terse passage describes the ninth and tenth human elements (ruling faculty and the characteristic mark of the Holy Spirit) as agents that perfect other activities. The text is difficult to translate without some expansion:
The soul is added [to the senses and limbs]. And the ruling faculty, by which we reason and which is begotten without the casting of seed [cf. Hebrews 11.11], is added before this, so that the tenth number [i.e. the characteristic mark of the Holy Spirit] is brought in without it [i.e. seed]. By these things [i.e. the ruling faculty and the characteristic mark of the Holy Spirit] every activity of a person is perfected. 
In this terse passage (made difficult by the vagueness of the relative pronoun ὧν) Clement notes that the ninth and tenth anthropological elements—the ruling faculty and the characteristic mark of the Holy Spirit—are not dependent upon physical generation but are bestowed from above. They are, together, agents of perfection. These two highest faculties stand above and apart from the lower eight.
This is not Clement’s only anthropological decalogue. He presents another one, independent from but compatible with his main decalogue, at 134.3, where he states that the law was laid down for the ten parts of the human, and he restricts the list to the five pairs of sense organs—sight, hearing, smell, touch, and taste. The doubled sense organs resemble the two tablets upon which the Decalogue was inscribed. And the feet and hands also resonate with the Decalogue. Clement says, in a rather confusing formulation, “Again, the laying of the law seems to be assigned to these certain ten human parts: to sight and hearing, to smell, and to touch and taste and to their assisting organs, being double, both to hands and feet.” 
His major and his minor anthropological decalogues show that Clement saw the human being, both specifically (body only) and generally (from lowest faculty to highest), as being imprinted with the decad. These patterned decads are not unusual. The symbolism of the number ten runs throughout Clement’s works. Later in this excursus (145.7) he notes that the Decalogue—thanks to the iōta, the Greek numeral for ten—invokes the blessed name ‘Jesus.’  Clement earlier (84.5) calls the number ten “all perfect.”  In Book 2, he likens the number ten to attaining the knowledge of God. For Clement, this level of perfection explains why a tithe (and no other denominator) was to be given to God, and why the Paschal feast starts on the tenth of the month. 
The broader parallels between Clement and Monoïmus are noteworthy. Both authors plumb the books of Moses to locate patterns and groups of ten. Both play on the role of iōta as a Greek numeral. Yet they approach the matter very differently. Monoïmus begins with the glyph ι as a symbol of the relationship that holds between the two supreme beings and their emanating powers. Clement is interested in ten qua number or qua numeral, but not qua glyph. Further, he does not share Monoïmus’ metaphysics, so he uses ten as a symbol mainly of the structures of creation and their interrelated connection to Scripture, not of the godhead. And unlike Monoïmus, who never uses the name ‘Jesus,’ Clement sees the iōta in the Decalogue and the Psalms as prefiguring only Jesus. 
A closer parallel, one pertaining to anthropology, is found in Heracleon, his contemporary and rival. Heracleon was said to be a Valentinian, and he flourished, at least for a time, in Alexandria.  He shared with Clement an interest in number symbolism. Relevant here are Heracleon’s comments on John 2.20 (“The Jews said, ‘This temple was built in forty-six years …’ ”), which outline an anthropological decalogue comparable to Clement’s.  Claiming that the temple is an image of the Savior, Heracleon analyzes the constituent parts of the number forty-six. He says that six refers to matter or substance (ὕλη), that is, the formation of man (πλάσμα). Forty, “which is the Tetrad … which does not admit union,” refers “to the infusion, and the seed in the infusion.”  That is, Heracleon relates the number forty-six to anthropology, treating six as the lower, material number, and forty (a number he tacitly converts to the Valen-tinian term ‘Tetrad’) as the higher, spiritual number.
Heracleon shares with Ptolemy, his fellow Valentinian, a common vocabulary and an express interest in the number ten. Heracleon’s term for “does not admit union,” ἀπρόσπλοκος, is reminiscent of the Ptolemy’s three uses of ἀσύμπλοκος ‘not woven’ in his Letter to Flora as a quasi-technical epithet for the Decalogue, the most perfect of the three parts of the law.  To Ptolemy, the Decalogue is “not interwoven” with evil, and is therefore at the highest of the three levels of the Law, which suggests that Heracleon regarded the “unionless Tetrad” as the highest principle, corresponding to the place Ptolemy assigns the Decalogue. 
Heracleon identifies the Tetrad with the infusion and its seed, “infusion” (ἐμφύσημα) here being another technical term commonly used by Christian authors to refer to God’s breathing life into Adam.  Heracleon has already invoked the language of Genesis by relating the number six to the material creation of man. By mentioning the infusion and the seed in the infusion (a differentiation made but not explained), Heracleon alludes to the story of God’s breathing into Adam, and interprets the account as the implanting of the Tetrad in the human race. The forty-six years of the temple are an image of the Savior, who is himself the perfect synthesis of the Tetrad and the number six, the two parts of human nature, his higher infusion and his lowly matter. So Heracleon, like Clement, seems to have embraced an anthropological decalogue. Heracleon numbers the higher and lower faculties at four and six, whereas Clement divides the human being into two higher faculties and eight lower.
Whether Clement knows of, and now answers in his own orthodox fashion, the anthropological decalogue Heracleon based on John 2.20, cannot be determined. The opposite is just as plausible, that Heracleon dissents from Clement. But clearly, both were responding to Stoic anthropology. Stoicism would have been the basis for any Christian anthropology—whether orthodox or Valentinian—that carefully enumerated the parts of the human being. The earliest Stoics, to show the essential material unity of the human soul, rejected the tripartite soul taught by the Platonists, and instead divided the soul into a hierarchy of parts.  A number of these lists are extant, and a few of them differ, both in terminology and in the order and number of the parts. But the sources generally agree that to the Stoics the human being had eight parts. The seven lower faculties—that is, the five senses, the voice, and the reproductive capacity—were said to be governed by the higher one, the ruling faculty (ἡγεμονικόν). 
Clement expands the eight Stoic parts of the soul into a decalogue through two modifications. He moves the ruling faculty from the eighth to the ninth place and then inserts two new faculties: the formed spirit, in the eighth position, and the mark of the Holy Spirit, in the tenth. To understand the significance of these modifications, we must understand Clement’s ideas behind his two new faculties, the formed spirit (eighth) and the mark of the Holy Spirit (tenth).
Both new faculties are mentioned in Stromateis Book 4, where Clement discusses the potential for a gnostic—his preferred term for the spiritually advanced orthodox Christian—to become a god. He contrasts the composition of the human being in general with that of specific individuals. “So the human being in general is formed (πλάσσεται) in accordance with the form (ἰδέαν) of the connate spirit.”  He associates this spirit with the shape of the human being, both in essence and in physical form, and he says it explains why man lacks neither form nor shape “in the factory of nature.” Thus, the “connate spirit” here corresponds to the eighth faculty in his anthropological decalogue, since it is higher than, but nevertheless affects, the physical shape of human beings. In contrast with the general human being, “the individual man is characterized (χαρακτηρίζεται) by the impression (τύπωσιν) of his choices entering into (ἐγγινομένην) the soul.”  The parallel terminology to 134.2 (quoted above: προσγινόμενον, χαρακτηριστικόν), where the tenth part, the mark of the Holy Spirit, is discussed, shows that the faculty that “impress[es one’s] choices” in the soul in Book 4 is the same as the tenth element in Clement’s anthropological decalogue. This is confirmed further on: “By this [impression] we say that Adam, as regards his formation, was perfect. For he lacked none of the things that characterize (χαρακτηριζόντων) the form and shape of a human being.”  At the root of both this description and that of the tenth and highest part of the anthropological decalogue is the idea of a person freely choosing the things that characterize or—to capture the overtones of χαρακτήρ—‘inscribe’ themselves into a person’s soul.
Further into his excursus on the Decalogue, Clement returns to this contrast between the lower eight and the upper ninth and tenth human faculties (136.4). The two tablets on which the Ten Commandments were written are said to indicate that “the commandments are given to the two spirits, both the one formed and the ruling faculty (ἡγεμονικῷ).”  The difference between the two spirits corresponds to the difference between sense perception and the mental process (137.1). This describes the eighth and the ninth faculties of the anthropological decalogue. The eighth element is conceived to be part of the realm of sense perception. The tenth element is referred to earlier in Book 6 (103.5), where Clement compares the perfected gnostic to Moses, whose face shone (Exodus 34.29). This glorified face is called the “characteristic mark (ἰδίωμα χαρακτηριστικόν) of the just soul”—once again, his preferred terminology for the tenth faculty. For Clement, a person incorporates this faculty into his life as his highest divine power. When the gnostic is perfected as far as his human nature allows, this radiance unites him to God (104.1).
To bring all these threads together: Clement’s eighth faculty is the breath or spirit that God breathed into man at his creation (Genesis 2.7). It is common to all people, and it provides for them their structure, both their physical makeup and their essence. This formed spirit is part of the faculties of sense perception, although it is the highest of these, placed above language (i.e. the voice) and the capacity for procreation. The Stoic ruling faculty, the ἡγεμονικόν, the governor of all sense perception, is Clement’s ninth faculty. His tenth faculty, the characteristic mark of the Holy Spirit, is the highest divine principle, applied by a person as he chooses the things he wishes to imprint upon his soul. The mark of the Holy Spirit transcends the ruling faculty, since it allows a person to be assimilated to God, as far as human nature allows.
The distinction between the eighth and tenth faculties mirrors one of Clement’s better-known theological themes, the distinction between the image and the likeness in God’s creation of humanity, according to Genesis 1.26: “And God said, ‘Let us make man in our image and in [our] likeness.’ ” Clement takes ‘image’ in the biblical text to refer to the state of man at his creation, and ‘likeness’ to his eventual acquisition of perfection.  Such distinctions between image and likeness run throughout the patristic tradition.  It is no different here: the eighth faculty, the formed spirit, corresponds to the image of God; the tenth faculty to the likeness. All people have the eighth; only the redeemed can truly have the tenth.
Clement’s anthropological decalogue is intended to argue that the standard Stoic anthropology is incomplete, lacking two prominent aspects of man taught in the Scriptures and recognized by experience. By inserting into the Stoic scheme the faculty of the formed spirit (his new eighth element), Clement teaches that the divine image is common to all people. The Stoics had a notion of human nature’s being stamped by the divine, but nothing in their eightfold anthropology made this explicit. Clement’s inclusion of the mark of the Holy Spirit as the tenth and highest faculty shows that he regarded the ruling faculty (the ἡγεμονικόν) alone as unable to account for the way people could be assimilated to the likeness of God. There must be a faculty higher than the ἡγεμονικόν. After all, everyone has a ruling faculty, but not everyone who diligently exercises it becomes divine.
His subordination of the spiritual faculty to the ruling faculty, and not vice versa, shows that he held God’s spirit to be an essential part of every human being, and not just the elect or the clever. For Clement, the spiritual faculty is more central and basic to human existence than is even governance over the senses. It is possible to detect here a tacit criticism of Valentinianism, which sorted people into three categories—corporeal, soulish, and spiritual—and which taught that only the elect were spiritual. For Clement, the spirit, imparted in creation, is found universally. All people are inherently spiritual, in that they carry the breath of God. The only faculty that might be missing from, or at least minimized in, a person is the tenth. This principle is applied in Book 2, where he urges his readers that they need to take the initiative and overleap the nine faculties to the tenth, the mind.  The active presence of the tenth faculty is not guaranteed without effort.
Clement developed his intricate anthropological decalogue to provide a coherent and distinctively Christian account of the world, an account that did not merely repeat the philosophical tradition, but responded with an alternative that was just as, if not more, numerically harmonious. And he ensured that its essence was orthodox, not Valentinian.
Clement Transfigures Marcus’ Transfiguration
In the second half of On the Decalogue, Clement interprets the significance of eight of the Ten Commandments (Stromateis 6, 137.2–148.4). He had planned to treat his subject “in a cursory manner” (133.1: κατὰ παραδρομήν), that is, to discuss briefly only several of the Ten Commandments. But, absorbed by the topic, he wound up writing more than he anticipated, resulting in lengthy asides and confusion over the numbering of the Commandments.  When he reaches the Commandment pertaining to the observation of the Sabbath (137.4), Clement begins a lengthy excursus. He argues that God needs no rest, so the Sabbath rest, really intended for us, indicates cessation from sin, our enlightenment by wisdom and knowledge, and our establishment in dispassion (137.4–138.2). He then says that his discussion (138.5: λόγος) has slipped into the theme of the hebdomad and ogdoad, and here he begins a self-acknowledged tangent (ἐν παρέργῳ), a treatment of the number symbolism of six, seven, and eight. He says, “The ogdoad is likely to be chiefly a hebdomad, and the hebdomad, a hexad, at least apparently. The first is likely to be chiefly the Sabbath, but the hebdomad, a woman worker.”  This initiates an arithmological excursus in which Clement explains the paradox of how an eight can be considered Sabbath-like, and seven worker-like.
So Clement moves from Sabbath to seven to a larger discussion of the symbolism of six, seven, and eight. The second shift may seem unintuitive, but it fits his overall approach to numbers. Seven symbolizes for Clement a place of rest and completion, and eight a higher state wherein the divine presence resides. Many times, when Clement invokes a symbolic seven, he then notes the need to transcend it to reach the number eight. The hebdomad symbolizes rest, but it is surpassed by the ogdoad, wherein is the promise of gnostic perfection. For example, in Book 6 (108.1), Clement says that those who reach the highest levels of perfection have not remained in the hebdomad of rest, but have advanced into the inheritance of the benefit of the ogdoad (ὀγδοαδικῆς εὐεργεσιάς). Elsewhere Clement says the ark of the covenant symbolizes the ogdoad, and the cherubim symbolize the rest that remains with the glorifying spirits. “Rest,” of course, points to the number seven.  And in a third example, Clement applies this theme to Ezekiel 44.26–27, where Ezekiel’s requisite purification of seven days is said to represent the completion of creation and the ritual observance of rest. The propitiation (ἱλασμόν), which makes acquiring the promise possible, is brought on the eighth day (not specified in the Septuagint). According to Clement, Ezekiel’s references to seven and eight days point to the doctrine of the hebdomad and ogdoad. 
Clement does not think this is a private conceit. Quoting from Clement of Rome, he discusses his namesake’s treatment of Psalm 33.13 (34.12): “Who is the man desiring life / yearning to see good days?”  Breaking into the quotation, Clement comments, “He”—referring to either Clement of Rome or the psalmist—“then adds the gnostic mystery of the hebdomad and the ogdoad.” Then the citation of Clement of Rome and the next two verses of Psalm 33 resumes: “Stop (παῦσον) your tongue from evil / and your lips from uttering deceit. / Turn away from evil and do good, / seek peace and pursue it.”  So to Clement, either David or Clement of Rome knew of and invoked the symbolism of seven and eight. The mystery of the hebdomad is in the verb παῦσον, translatable as ‘rest!’ and thereby invoking the seventh day, the Sabbath. The number eight is referred to perhaps in the last verse, in commands to turn away (ἔκκλινον), seek (ζήτησον), and pursue (δίωξον), presumably the realm of the ogdoad.
For Clement, not only the Bible and his predecessors were attuned to the doctrine of the hebdomad and ogdoad. Even Plato knew it. Clement cites the Republic: “Now when seven days had reached the [spirits] that were in the meadow, on the eighth they were obliged to proceed on their journey and arrive on the fourth day.”  He claims that Plato prophesies the Lord’s Day. His phrase “seven days” refers to the motions of the seven planets, hastening to their goal of rest; the meadow constitutes the eighth, fixed sphere (τὴν ἀπλανῆ σφαῖραν), and the journey represents the passage beyond the planets to the eighth motion and day. This eighth level, the fixed sphere, Clement elsewhere calls Atlas, the dispassionate pole, and the unmoved aeon.  For Clement, the gnostic Christian should be sensitive enough to the doctrine to detect it in certain keywords that would elude the careless or less disciplined reader of Plato, the Scriptures, or the luminaries of the Church. 
Variations of Clement’s doctrine of the hebdomad and ogdoad were taught by a number of Valentinians. In Irenaeus’ extended group of Valentinians, seven is the symbol of the Demiurge, and eight of Akhamoth or Wisdom. Heracleon makes six, seven, and eight the symbols of material evil, the aeonic realm, and spiritual perfection respectively.  Theodotus, a second-century Valentinian whose doctrines fascinated Clement, held to a similar doctrine. 
So in his On the Decalogue, after introducing the Sabbath, Clement itemizes the various properties of each of the numbers six, seven, and eight (138.6–140.2).  Much of this discussion, and later parts of On the Decalogue (141.7–142.1), build upon a Jewish tradition of arithmology, a tradition evident in the writings of Philo and Aristobulus, who argued that Jewish law and custom harmonize with Hellenic philosophy.  Clement spends the most time on the number six, pointing out its role in the cosmogony, in the course of the sun, and in the cycles of plant life. He appeals to the importance of six in embryology and to the arithmetical properties that led the Pythagoreans to make it a symbol of mediation and marriage. Six is a function of generation and motion. Seven is depicted as motherless and childless, like its arithmetical properties, since seven neither is the product of, nor produces, any of the numbers in the Decad.  Seven was traditionally assigned to Athena, the virgin born without a mother. Clement, however, takes the Pythagorean epithet to refer allegorically to the Sabbath and the form of rest in which “there is neither marrying nor being married” (Matthew 22.30). The ogdoad is briefly described as the cube, the fixed sphere, and a participant in the Great Year. 
Up to this point, Clement has marked only the differences between six, seven, and eight. There is nothing yet to justify his claim at 138.5 that there is an identity between them, or a transformation from one to another. To make this connection Clement turns to the Transfiguration (140.3). He locates the event on the eighth day, and the Lord as the fourth person (after Peter, James, and John). The Lord ascends the mountain, and at the appearance of Moses and Elijah (i.e. two more persons) becomes the sixth. Clement reckons the voice of God as the seventh character, and Jesus is made manifest as the eighth, God.
This passage owes much to Marcus’ explanation of the Transfiguration (see chapter 4). As Niclas Förster has suggested, Clement’s knowledge of Marcus relied exclusively upon Irenaeus.  Clement does not employ Marcus’ doctrine anywhere else, and his departures from Irenaeus’ account are in line with his other adaptations of Against Heresies.  Sometimes he quotes Irenaeus verbatim; other times he adds to the account, so as to make Marcus’ interpretation his own (underlining indicates textual parallels):
ταύτῃ τοι ὁ κύριος τέταρτος ἀναβὰς εἰς τὸ ὄρος ἕκτος γίνεται καὶ φωτὶ περιλάμπεται πνευματικῷ, τὴν δύναμιν τὴν ἀπ ᾽ αὐτοῦ παραγυμνώσας εἰς ὅσον οἶόν τε ἦν ἰδεῖν τοῖς ὁρᾶν ἐκλεγεῖσι, δι᾽ ἑβδόμης ἀνακηρυσ-σόμενος (15) τῆς φωνῆς υἱὸς εἶναι θεοῦ, ἵνα δὴ οἳ μὲν ἀναπαύσωνται πεισθέντες περὶ αὐτοῦ, ὁ  δέ, διὰ γενέσεως, ἣν ἐδήλωσεν ἡ ἑξάς, ἐπίσημος  ὀγδοὰς ὑπάρχων φανῇ, θεὸς ἐν σαρκίῳ τὴν δύναμιν ἐνδεικ-νύμενος, ἀριθμούμενος μὲν ὡς ἄνθρωπος, κρυπτόμενος δὲ ὃς ἦν·
So on this [eighth day]  the Lord, as the fourth, after ascending the mountain becomes a sixth and is radiated by a spiritual light, laying bare his power—as far as it is possible for those chosen to see to perceive—and heralded by the seventh, the voice, to be the Son of God, so that those who are persuaded about him might rest, while he, being an episēmos ogdoad, might be manifest through his generation (which the hexad makes clear) as God, demonstrating his power in a bit of flesh: numbered as man, but keeping hidden who he was.
(Clement of Alexandria Stromateis 18.104.22.168)
Τούτου τοῦ λόγου καὶ τῆς οἰκονομίας ταύτης καρπόν φησιν ἐν ὁμοι-ώματι εἰκόνος πεφηνέναι ἐκεῖ(νον) τὸν μετὰ τὰς ἓξ ἡμέρας τέταρτον ἀναβάντα εἰς τὸ ὄρος καὶ γενόμενον ἕκτον, τὸν καταβάντα καὶ κρατη-θέντα ἐν τῇ Ἐβδομάδι, ἐπίσημον Ὀγδοάδα ὑπάρχοντα καὶ ἔχοντα ἐν ἑαυτῷ τὸν ἅπαντα τῶν στοιχείων ἀριθμόν.
[Marcus] says that the fruit of this account and this plan is that he was manifest in the likeness of an image [Romans 1.23], he who, after six days, ascended the mountain as the fourth and became a sixth, he who descended and was held in the Hebdomad, being an episēmos ogdoad and possessing within himself every number of the oral letters.
(Irenaeus Against Heresies 22.214.171.1242–277)
Armand Delatte claims that the two passages complement and explain each other. Clement’s description of Jesus as ἐπίσημος is intelligible only when we consider that Marcus calls Jesus this because his name consists of six letters.  Likewise, Marcus’ peculiar phrase, that Christ was held in the hebdomad, is rendered intelligible by Clement’s version, where the seventh is identified with the voice that possesses Jesus at his baptism and declares him to be the Son of God.  According to Delatte, both Clement and Marcus represent Christ as six, seven, and eight inclusively, numbers that symbolize the Incarnation. Thus Clement’s version of Marcus’ Transfiguration account synthesizes the previous sections discussing the properties of six, seven, and eight (138.5–140.2), and help demonstrate Clement’s claim, since Christ himself is six, seven, and eight.
The problem with Delatte’s overall interpretation is that strictly speaking, Marcus and Clement identify Christ not with seven but only with six and eight. Seven is reserved in Clement for the voice of God, not Jesus. Marcus regards the hebdomad as the seven vowels, which receive an eighth letter so as to equal the size of the other two levels of the aeonic alphabet. Thus six, seven, and eight are not indiscriminately all symbols of Jesus. And what started Clement on this tangent in the first place was the proposal that the ogdoad is a hebdomad, and the hebdomad a hexad (138.5). This requires a transitive relationship, of 6 → 7 → 8, or 8 → 7 → 6. But neither Clement’s nor Marcus’ account of the Transfiguration suggests that Jesus went from being the sixth to becoming the eighth, via the seventh. Clement may have originally (138.5) proposed to demonstrate a transformation of six into eight, but that does not occur here (at 140.3). The only numerical transformation in this passage is from four to six, when Jesus becomes the sixth after the appearance of Moses and Elisha. Clement states (as does Marcus) that Jesus is simultaneously six and eight—the ‘episēmos ogdoad’—without implying any transition between the two (at least, not in 140.3). Both passages emphasize the differences, not the transformations, among six, seven, and eight. Clement’s version constitutes a Christian counterpart to the “secular” arithmology of 138.6–140.2, which lists common ideas in the Greco-Roman world about six, seven, and eight. Clement uses a single event, the Transfiguration, to depict the Christian understanding of the symbolic significance of six (generation), seven (the voice), and eight (divinity), arraying the symbolism for all three numbers in a single, static image.
A closer look at the vocabulary of 140.3 bears this out. I have mentioned above the care Clement shows when he reads other authors and “discovers” in them the doctrine of the hebdomad and ogdoad. Sometimes this is made explicit by keywords, such as those in Plato’s Republic. Other times, the association emerges through ideas, not terms, as in Clement of Rome and Psalm 33 (34). Clement considers Scripture to have been written with extreme care. There are no superfluous words, and each word is chosen for its symbolic overtones, no matter how subtle. He composes his explanation of the Transfiguration with the same care. His words are tinged with overtones of number symbolism, and thereby present a complex Christian arithmology of six, seven, and eight.
Clement gives to Christ the epithet ‘episēmos ogdoad.’ This epithet, which features prominently in Marcus’ theology, conjoins six and eight, a mathematical and theological paradox. Six represents the created, material world; and eight, spiritual perfection, the divine realm. Notice how the paradox is reflected at the end of 140.3, where Jesus is “numbered as man,” but hidden as “he was.” Six corresponds to “man,” and eight, to his constant state of being, i.e. God. Between these two phrases, however, is θεὸς ἐν σαρκίῳ τὴν δύναμιν ἐνδεικνύμενος, a phrase that can also be interpreted as a cipher for ‘six-eight’: σαρκίῳ is six; θεός and δύναμις eight. The entire clause, from ὁ δέ to the end, reiterates in three compact phrases the mystery of the Incarnation as a combination of six and eight.
Likewise, the first instance of δύναμις (line 13), just as the second (line 18), should also suggest the number eight. This is consistent with Clement’s exposition, since this first instance describes how Christ revealed his divinity, as much as his companions could manage. Divinity is often represented as the number eight in Clement. The spiritual light in which Jesus is cloaked is the radiance of this “eightness.” This entire phrase alludes to the eightness of the Transfiguration, and complements the next phrase, which explicitly identifies seven with the voice that permits his disciples to find rest: ἑβδόμης, φωνῆς, and ἀναπαύσωνται all cross-resonate. By finding rest, the disciples, who are products of generation and therefore symbolized by six, move from the realm of six into seven.
Read this way, most of the text in 140.3 that is not emphasized (from καὶ φωτὶ to περὶ αὐτοῦ), which has no parallel in Marcus or Irenaeus, constitutes a miniature Christian arithmology on eight, then seven. It moves on to six—the generative aspect of Jesus—where Clement picks up again from Irenaeus’ text, and then ends in a terse meditation on the Incarnation as a combination of six and eight (from Θεὸς ἐν σαρκίῳ to ὃς ἦν). Thus the material not in Marcus/Irenaeus is Clement’s careful augmentation.
From here, Clement’s account of the Transfiguration moves not to the baptism of Jesus, as Marcus’ does, but to the order of the alphabet and numerical notation. This too is a theme for Marcus, but Clement pursues the matter further. He begins by explaining that six is included in the order of the numbers, but that the sequence of the alphabet shows that the ἐπίσημον is not written with a letter. That is, numerals, using the alphabetic system of numeration, follow the sequence α´, β´, γ´, δ´, ε´, Ϛ´, ζ´, η ´, and so on. The number six is represented by the ἐπίσημον. But when the alphabet is written out—α, β, γ, δ, ε, ζ, η, and so on—the ἐπίσημον is not written. He explains that the difference between the two sequences is created by the intrusion of the ἐπίσημον, which disrupts the alphabet, a disruption that he takes as a cipher for his doctrine of the six and seven, and subsequently of the seven and eight. Here is the relevant text:
τῇ μὲν γὰρ τάξει τῶν ἀριθμῶν συγκαταλέγεται καὶ ὁ ἕξ, ἡ δὲ τῶν στοιχείων ἀκολουθία ἐπίσημον γνωρίζει τὸ μὴ γραφόμενον. ἐνταῦθα κατὰ μὲν τοὺς ἀριθμοὺς αὐτοὺς σῴζεται τῇ τάξει ἑκάστη μονὰς εἰς ἑβδομάδα τε καὶ ὀγδοάδα, κατὰ δὲ τὸν τῶν στοιχείων ἀριθμὸν ἕκτον γίνεται τὸ ζῆτα, καὶ ἕβδομον τὸ ηˉ.  Ἐκκλαπέντος  δ ᾽ οὐκ οἶδ ᾽ ὅπως τοῦ ἐπισήμου εἰς τὴν γραφήν, ἐὰν οὕτως ἑπώμεθα, ἕκτη μὲν γίνεται ἡ ἑβδομάς, ἑβδόμη δὲ ἡ ὀγδοάς·.
For the [number] six is included in the order of the numbers, but the sequence of the oral letters makes known that the ἐπίσημον is unwritten. Thus, according to the numbers themselves, each monad is preserved in sequence, up to the hebdomad and the ogdoad. But according to the number of oral letters, the zeta becomes sixth, and the eta seventh. But when the ἐπίσημον—I don’t know how—slips into  writing (should we pursue it in this manner) the hebdomad becomes the sixth [letter], and the ogdoad the seventh. 
(Clement of Alexandria Stromateis 6.140.4–6.141.1)
To unravel this cryptic passage, preliminary comments on two aspects of Greek grammar are in order. First, as already discussed, the grammarians distinguished στοιχεῖον, the oral letter, from γράμμα, the written.  Clement also holds to this distinction. The phrases τὸ μὴ γραφόμενον and εἰς τὴν γραφήν show that he sees the ἐπίσημον as dwelling in the written sphere, not the oral. That is, the ἐπίσημον is seen, not heard.
Second, Clement is not discussing the digamma, the archaic Greek letter derived from the Phoenician waw. His comments here are frequently misread because modern readers conflate the ἐπίσημον and the digamma. It is common knowledge today that the earliest Greek alphabets included in the sixth place the Phoenician letter waw, first written like a Y, but later as ϝ.  The digamma dropped out of use in the Greek language, but its written representation was preserved in the Milesian system of numeration. The ἐπίσημον is seen as the direct descendant of the obsolete waw. But late antique and medieval treatments of the digamma show no awareness that it was the ancestor of the numeral six. Greek grammarians in late antiquity did not even assign the digamma a place in the sequence of the alphabet. Further, no ancient discussions of the παράσημα—the nonalphabetic numerals—mention the letter digamma.  An ancient scholium on Dionysius Thrax precludes such an association. This scholiast entertains the theoretical objection that, because the digamma is a letter, Dionysius Thrax’s claim that there are twenty-four written letters must be faulty. The objection runs: both a character (χαρακτήρ) and a name (ὄνομα) are concomitant with every oral letter; the digamma has both, so it too should be reckoned with the oral letters. The scholiast lays out several responses to this argument, one of which runs: “Again, every character (χαρακτήρ) of the oral letters designates a number. For the α indicates the number one, and the β, two, and so forth. So therefore, if the character of ϝ doesn’t indicate a number, it is clear that it is not an oral letter.”  So this scholiast regarded the digamma as having no corresponding numeral and therefore no place in the order of the alphabet. The other parallel scholia discussing the digamma also do not associate it with the number six or any ordinal place in the alphabet. 
This explains why Ptolemy, in his Harmonics, uses both the digamma and the ἐπίσημον in the same sentence to refer to two different things: the digamma to a musical tone and the ἐπίσημον to a numeral.  In a sixth-century Greek text, The Mystery of the Letters, the godless Greeks are accused of moving the waw from its proper place and placing it after the nu. God is said to have providentially used the disruption to make the waw a symbol of Christ.  To this author, the Phoenician waw became not the digamma but the omicron!
All these late antique texts show that any original association there may have been between the numeral six and the digamma had been lost by the second century. This helps clear up a vexing textual problem at 140.4–141.2, one that is critical to understanding the entire passage. It is unclear whether Clement thought the letter slipped into writing, or fell out of it, since the prepositions in ἐκλαπέντος and εἰς τὴν γραφήν are contradictory. Some scholars have argued that the text should read εἰσκλαπέντος (which would have Clement regard the ἐπίσημον as entering the alphabet), others as ἐκ τῆς γραφῆς (to have him see the character fall into disuse).  The former are correct, but they are seemingly unaware of the grammatical background, just discussed.  Delatte’s proposal, which depends upon the latter group, has Clement, in agreement with modern scholarship, meditating on the development of the Greek alphabet from its Phoenician roots. But this is not Clement’s point. He was interested primarily in the difference between the alphabet and Greek numeration. Like others in his day, Clement saw no connection between the waw and the numeral six, since he considered the latter as a purely written symbol, not a spoken one. Thus the text should read Εἰσκλαπέντος δ ᾽ οὐκ οἶδ ᾽ ὅπως τοῦ ἐπισήμου εἰς τὴν γραφήν.  The numeral six, the ἐπίσημον, somehow entered into the writing system—Clement admits his ignorance on the historical specifics—and thus disrupted the order of the alphabet.
This makes Clement’s allegory clearer: the ἐπίσημον symbolizes Christ, who enters the writing of the world and alters the constitution of its oral letters/elements (στοιχεῖα). Clement plays on the ambiguity of στοιχεῖον, treating it primarily as a letter of the alphabet, but also alluding to its alternate meaning as an element of the universe. He regards the inconcinnity between the alphabet and the numbering system to be the key to interpreting the effect of the Incarnation on creation. This same inconcinnity explains the numbers latent in the Transfiguration. There on the mountain, Jesus is revealed as the ‘episēmos ogdoad,’ the number eight in the guise of the numeral Ϛ. The number eight is the unknowable God, the Ϛ is his entry into the writing system. Only here do we encounter the transition 6 → 7 → 8, and it pertains to the movement of believers who transcend their humanity. The intrusion of the Ϛ causes the sixth element (στοιχεῖον) to access the seventh, and the seventh element (στοιχεῖον) to access the eighth. Thus the apostles, by trusting in him on the mount of Transfiguration, entered into the rest of the seventh. We shall see below that Clement, by analogy, has the faithful move from the seventh to the eighth, but his interpretation of the Transfiguration (140.3) stops short of this. Instead, Clement now turns to Marcus’ teaching on the number six (141.3–7). He draws from parts of Scripture that speak to the doctrine of the ἐπίσημον, and then selects examples from geometry to establish the point he set out to make initially, that the ogdoad is likely to be a hebdomad, and the hebdomad a hexad. His argument runs:
διὸ καὶ ἐν τῇ ἕκτῃ ὁ ἄνθρωπος λέγεται πεποιῆσθαι ὁ τῷ ἐπισήμῳ πιστὸς γενόμενος ὡς εὐθέως κυριακῆς κληρονομίας ἀνάπαυσιν ἀπολαβεῖν. τοιοῦτόν τι καὶ ἡ ἕκτη ὥρα τῆς σωτηρίου οἰκονομίας ἐμφαίνει, καθ ᾽ ἣν ἐτελειώθη ὁ ἄνθρωπος. ναὶ μὴν τῶν μὲν ὀκτὼ αἱ μεσότητες γίνονται ἑπτά, τῶν δὲ ἑπτὰ φαίνονται εἶναι τὰ διαστήματα ἕξ. ἄλλος γὰρ ἐκεῖνος λόγος, ἐπὰν ἑβδομὰς δοξάζῃ τὴν ὀγδοάδα καὶ “οἱ οὐρανοὶ τοῖς οὐρανοῖς διηγοῦνται δόξαν θεοῦ.” οἱ τούτων αἰσθητοὶ τύποι τὰ παρ᾽ ἡμῖν φωνήεντα στοιχεῖα. οὕτως καὶ αὐτὸς εἴρηται ὁ κύριος “ἄλφα καὶ ὦ, ἀρχὴ καὶ τέλος,” “δι᾽ οὗ τὰ πάντα ἐγένετο καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν.”
So also, it is said that in the sixth [day] the human was made, becoming faithful to the ἐπίσημον, so as to receive straightaway the rest of the Lord’s inheritance. Even the sixth hour of the divine plan of salvation indicates this sort of thing; in it the human was perfected. Indeed, there are seven intermediates of eight things, and there seem to be six intervals of seven things. For there is that other saying, when the hebdomad glorifies the ogdoad and “the heavens declare to the heavens the glory of God.” [Psalms 18.2] The oral letters that are our vowels are perceptible types of these things. So also the Lord himself is said to be “alpha and o[mega], beginning and end” [Revelation 21.6], “through whom everything came into being, and without him not even one thing came into being” [John 1.3].
(Clement of Alexandria Stromateis 6.141.3–7)The parallel from Marcus runs:
Καὶ διὰ τοῦτο Μωϋσέα ἐν τῇ ἕκτῃ ἡμέρᾳ εἰρηκέναι τὸν ἄνθρωπον γεγονέναι· καὶ τὴν οἰκονομίαν δὲ ἐν τῇ ἕκτῃ τῶν ἡμερῶν, ἥτις ἐστὶν ἡ παρασκευή, <ἐν> ᾗ τὸν ἔσχατον ἄνθρωπον εἰς ἀναγέννησιν τοῦ πρώτου ἀνθρώπου πεφηνέναι, ἧς οἰκονομίας ἀρχὴν καὶ τέλος τὴν ἕκτην ὥραν εἶναι, ἐν ᾗ προσηλώθη τῷ ξύλῳ.
And because of this, Moses said that the human being came into existence on the sixth day, and the divine dispensation, on the sixth day [of the week], i.e. the Day of Preparation, in which the last human being is manifest for the rebirth of the first man. The beginning and end of this divine dispensation was the sixth hour, when he was nailed to the wood.
(Irenaeus Against Heresies 126.96.36.1990–285)
Καθὼς οὖν αἱ ἐπτά, φησίν, δυνάμεις δοξάζουσι τὸν Λόγον, οὕτως καὶ ἡ ψυχὴ ἐν τοῖς βρέφεσι κλαίουσα καὶ θρηνοῦσα Μάρκον δοξάζει αὐτόν. διὰ τοῦτο δέ καὶ τὸν Δαυὶδ εἰρηκέναι· “ Ἐκ στόματος νηπίων καὶ θηλαζόντων κατηρτίσω αἶνον,” καὶ πάλιν· “οἱ οὐρανοὶ διηγοῦνται δόξαν θεοῦ.”
He [Marcus] says: Therefore, just as the seven powers glorify the Logos, so also the soul in infants, crying and wailing, glorifies Marcus himself. Because of this, David also said, “From the mouth of infants and sucklings, you have perfected praise” [Psalms 8.3 (8.2)], and also, “The heavens declare the glory of God” [Psalms 18.2 (19.1)].
(Irenaeus Against Heresies 188.8.131.520–325)
Clement’s version is an orthodox, ecclesiastical revision of Marcus’ teaching. He notes, in Marcus’ words, that the human was created on the sixth day. He omits any mention of Moses, and thereby identifies the sixth day of creation with the day of Christ’s crucifixion. Clement parses the phrase “in the sixth [day] the human.” Using the same order of cases—dative, then nominative—Clement explains what ‘sixth day’ and ‘human’ mean. The sixth day of creation/redemption is the ἐπίσημον, and in that day man becomes faithful to Christ. Clement, again departing from Marcus, says that the purpose of the Creation and Redemption was to have humanity straightaway enjoy the rest of the Lord’s inheritance. His wording is precise. In a single phrase he uses ciphers of both seven (ἀνάπαυσιν) and eight (κυριακῆς κληρονομίας).  Thus Clement restates that the goal of humanity is to move from the sixth day of Creation, through the Sabbath rest, into the eighth day. He considers the connection between these days of creation as tight as the geometric relationship between points and the intervals between them (141.5).
As a further illustration, Clement appeals to Psalm 18 (19), which he emends so that the heavens declare the glory of God to the heavens (not in the Septua-gint), just as the hebdomad glorifies the ogdoad. The image evoked here is that of the seven planets glorifying the fixed sphere, the same image he uses to interpret Plato’s Republic, discussed above. In ancient number symbolism the seven planets were closely associated with the seven vowels. So the Lord, who is called alpha and ōmega, is symbolized in the Psalms by the heavens. The Lord, the creator of all things, is the beginning and the end of all seven vowels. The thrust of 141.6–7 is that Christ constitutes the harmony of the spheres, the one who communicates to all the glory of God.
In this passage Marcus’ numbers are more static than Clement’s. In the first paragraph, Marcus is concerned with the number six and with showing the relationships among the sixth day of Creation, the crucifixion on the sixth day of the week, and the nailing of Jesus at the sixth hour. He claims the sixth hour was the beginning and the end of redemption, a notion that harmonizes well with the Pythagorean idea of the perfection of the number six.  Six does not become anything. The second paragraph, which concerns itself with the number seven, is static. Clement adds the motif of numbers changing and turning into each other, in imitation of the divine dispensation and the Incarnation. He spins these two unrelated passages by Marcus into a new narrative, an orthodox vision of God’s becoming man so that man might attain divine unity.  The numbers in Clement’s new allegory symbolize the vertical transition of the faithful, as they ascend from the material world to the spiritual.
Having read Against Heresies, Clement would have known Irenaeus’ saucy rhetoric and his favored argument, the reductio ad absurdum. Yet Clement seems to take Marcus’ exegesis seriously. There is no express sarcasm or criticism, no attempt to show the arbitrariness of his opponent’s methods or conclusions. Throughout the Stromateis Clement uses the term γνῶσις ‘knowledge’, to reclaim it from the heretics, the self-declared spiritual, on behalf of his own “ecclesiastics.” In like manner he robs Marcus of the symbol ‘episēmos ogdoad,’ to make of it a sign of Jesus’ Incarnation, not of his emanation from and return to the Ogdoad. Both Marcus and Clement consider Jesus to be “noteworthy” because of his association with six. But for Marcus, the sixness is found most immediately in the number of letters in Jesus’ name, the number required to generate, with the Tetrad, the 24 letters of the alphabet needed to achieve the aeonic Triacontad. For Clement, the sixness lies not in letter counts but in its symbolism of the human nature of Christ, of the rupture in human discourse that brought about salvation. He ignores any sense of 30, 24, 801, or other numbers that appeal to Marcus. Marcus focuses on the connection between the aeons and the alphabet; Clement, on that between the Incarnation and redemption.
Clement shares with the Valentinians, Monoïmus, and deutero-Simon a fascination with arranging Scripture into arithmetically harmonious structures. Just as they do, he brings to the text a well developed sense of number symbolism. He massages the Scriptures, peers behind individual words, and chases down their overtones, to show how the Bible reveals those structures. The technique works outside the Bible, too. Clement reads ecclesiastical and philosophical literature with an eye to hidden number symbolism. The finest example is his investigation of Stoic anthropology, which he transforms into a Christian one by supplementing the missing parts and molding the structure into a pattern that better fits Scripture. The tactic resembles those of his theological opponents. For Clement, this is no inconsistency, since their error comes from their conclusions, not their tactics.
He does not adhere to all of Irenaeus’ four principles for the correct theological use of numbers. Like the Valentinians, Clement draws from human conventions in grammar and numeration to illustrate his theology (contra Irenaeus’ second principle). He also quite openly takes preconceived number symbols into the Scriptures and the ecclesiastical tradition, rearranging a bit of the furniture along the way (contra Irenaeus’ fourth principle). But other aspects of Clement’s number symbolism match Irenaeus’. He has no mathematical arrangement of the godhead, and the symbolism he draws from numbers found in the natural world is based safely on the science of his day (Irenaeus’ first and third principles). If Irenaeus were to have any problem with Clement’s number symbolism, it would probably revolve around exegesis. But we have already noted how Irenaeus bent his own second and third principles. So if Irenaeus held that Clement professed the apostolic rule of faith—and we have no reason to doubt this—then it is quite probable that Irenaeus would have shown him the same leniency he shows himself. For his part, Clement does not directly criticize Irenaeus. Whatever criticism can be detected is tacit. He faces the same opponents, but does not demand of them standards he fails to attain.
The two different models furnished by Clement and Irenaeus show that in practice, the orthodox theology of arithmetic consisted primarily of a few simple principles. God, in his simplicity, transcends the realm of numbers, which he created. Father, Son, and Spirit are three, not because three is perfect. Rather, three is perfect because Father, Son, and Spirit are the one God. In the rule of truth there reside many numerical symbols that reveal God’s ways. To indulge in these and to draw upon number symbolism from culture, science, and mathematics is quite permissible, provided it does not undermine the apostolic faith shared by the churches throughout the world. Such principles were less strictures than signposts, warning the faithful away from the precipices of private fantasy—in a word, heresy.
[ back ] 1. Clement of Alexandria Stromateis 1.1.11; Eusebius Church History 5.10–11.
[ back ] 2. Jakab 2001:93–106.
[ back ] 3. For more on Clement’s life, see DECL, s.v., and works cited there; on his corpus and his theological thought, see Quasten 1953:5–36, with updated bibliography in TRE, s.v., and DECL, s.v.
[ back ] 4. For a fresh perspective on Clement’s corpus, see Bucur 2009.
[ back ] 5. Clement prefers to distinguish himself and other orthodox churchmen as “of the Church,” a description he denies to Valentinians and other opponents who cultivate private revelation. See Kovacs 1997:415n5.
[ back ] 6. On the differences and similarities between Clement and the Valentinians, see Davison 1983 and Edwards 2000.
[ back ] 7. Stromateis 184.108.40.206.
[ back ] 8. Stromateis 220.127.116.11.
[ back ] 9. Stromateis 18.104.22.168. For discussions of the philosophical dimensions of Clement’s use of ‘one,’ see Choufrine 2002:165–166, 174–175, 186–188.
[ back ] 10. Clement of Alexandria Instructor 22.214.171.124.
[ back ] 11. ἓν δὲ ὁ θεὸς καὶ ἐπέκεινα τοῦ ἑνὸς καὶ ὑπὲρ αὐτὴν μονάδα. Instructor 126.96.36.199. See p. 181 below.
[ back ] 12. Stromateis 188.8.131.52.
[ back ] 13. This notion holds for all the Church Fathers, often wrongly characterized as Christianizing Platonists. See Edwards 2002 and Ramelli 2011.
[ back ] 14. Stromateis 184.108.40.206.
[ back ] 15. ἑνὸς γὰρ ὄντος τοῦ θεοῦ καὶ ἑνὸς τοῦ κυρίου, διὰ τοῦτο καὶ τὸ ἄκρως τίμιον κατὰ τὴν μόνωσιν ἐπαινεῖται, μίμημα ὂν ἀρχῆς τῆς μιᾶς. τῇ γοῦν τοῦ ἑνὸς φύσει συγκληροῦται ἐκκλησία ἡ μία, ἣν εἰς πολλὰς κατατέμνειν βιάζονται αἱρέσεις; Stromateis 220.127.116.11.
[ back ] 16. “εἰς ἑνότητα πίστεως” μιᾶς, τῆς κατὰ τὰς οἰκείας διαθήκης, μᾶλλον δὲ κατὰ τὴν διαθήκην τὴν μίαν διαφόροις τοῖς χρόνοις, ἑνὸς τοῦ θεοῦ τῷ βουλήματι δι’ ἑνὸς τοῦ κυρίου συνάγουσαν τοὺς ἤδη κατατεταγμένους; Stromateis 18.104.22.168.
[ back ] 17. Stromateis 22.214.171.124.
[ back ] 18. Possibly the first decalogue, too, follows the order opposite from Genesis. But there are noticeable differences: fire and clouds are not mentioned until Genesis 11.3 and 9.13, respectively, and ἀήρ does not feature in LXX Genesis at all. These three items excepted, the order in Genesis would be shadow, wind (= spirit), water, light, sun, moon, and stars. Possibly Clement considered fire and air to be implied in the first day of creation, and clouds in the second. If so, then his heavenly decalogue, like the earthly one, follows the days of creation in reverse order.
[ back ] 19. See p. 46 above.
[ back ] 20. τὸ διὰ τῆς πίστεως προσγινόμενον ἁγίου πνεύματος χαρακτηριστικὸν ἰδίωμα. The eighth, the formed spirit, is literally “that which is spiritual/breathing according to the formation” (τὸ κατὰ τὴν πλάσιν πνευματικόν), discussed below.
[ back ] 21. Philo On the Preliminary Studies 100.
[ back ] 22. οὐ τὰ εἰσερχόμενα εἰς τὸ στόμα κοινοῖ τὸν ἄνθρωπον, ἀλλὰ τὰ ἐξερχόμενα διὰ τοῦ στόματος ἐκεῖνα κοινοῖ τὸν ἄνθρωπον, Clement’s rendering of Matthew 15.17–18, at Stromateis 126.96.36.199–3.
[ back ] 23. Stromateis 188.8.131.52.
[ back ] 24. Stromateis 184.108.40.206: τοῦτ᾽, οἶμαι, τὸ κατὰ θεὸν ἀληθινὸν καὶ δίκαιον μέτρον, ᾧ μετρεῖται τὰ μετρούμενα, ἡ (Mondésert 1954; Stählin incorrectly writes ᾑ) τὸν ἄνθρωπον συνέχουσα δεκάς, ἣν ἐπὶ κεφαλαίων τὰ προειρημένα τρία ἐδήλωσεν μέτρα.
[ back ] 25. Stromateis 220.127.116.11: εἴη δ ᾽ ἂν σῶμά τε καὶ ψυχὴ αἵ τε πέντε αἰσθήσεις καὶ τὸ φωνητικὸν καὶ σπερματικὸν καὶ τὸ διανοητικὸν ἢ πνευματικὸν ἢ ὅπως καὶ βούλει καλεῖν.
[ back ] 26. Stromateis 18.104.22.168–22.214.171.124.
[ back ] 27. At 126.96.36.199 (see the Greek text above), there is some admitted confusion. The five senses plus what seems like three other faculties adds to eight. The wording seems to suggest that διανοητικόν and πνευματικόν are equivalent terms for the eighth faculty. At 188.8.131.52 the mind is called the tenth faculty, in analogy to Philo’s cosmological decalogue. Where is the ninth? At Stromateis 184.108.40.206 the faculties of understanding and of the spirit are the eighth and ninth levels. Clement’s offhand remark, at 220.127.116.11, “or whatever you want to call it,” suggests that there was either terminological fluidity or, as I argue below, a difference of opinion between those who wished to subordinate the spiritual faculty to the faculty of understanding and rank them eighth and ninth respectively, and those who preferred the opposite.
[ back ] 28. Philo On the Preliminary Studies 102–106.
[ back ] 29. ἐπεισκρίνεται δὲ ἡ ψυχὴ. Καὶ προεισκρίνεται [Stählin 1909: προσεισκρίνεται] τὸ ἡγεμονικόν, ᾧ διαλογιζόμεθα, οὐ κατὰ τὴν τοῦ σπέρματος καταβολὴν γεννώμενον, ὡς συνάγεσθαι καὶ ἄνευ τούτου τὸν δέκατον ἀριθμόν, δι᾽ ὧν ἡ πᾶσα ἐνέργεια τοῦ ἀνθρώπου ἐπιτελεῖται.
[ back ] 30. A difficult passage: ἔτι πρὸς τούτοις δέκα τισὶν ἀνθρωπείοις μέρεσι προστάσσειν ἡ νομοθεσία φαίνεται. τῇ τε ὁράσει καὶ ἀκοῇ καὶ τῇ ὀσφρήσει ἁφῇ τε καὶ γεύσει καὶ τοῖς τούτων ὑπουργοῖς ὀργάνοις δισσοῖς οὖσι, χερσί τε καὶ ποσίν. Does this mean the five senses plus the four limbs? Or does it mean each of the five sense-perceptive faculties understood “doubly,” with the hands and feet a later scribal gloss? Under the first option, the total comes to nine, not ten. The second alternative has problems too. Even though there are two eyes, two ears, and two nostrils, it is unclear what pairs of sense organs belong to touch and taste. Possibly Clement has garbled the Valentinian account, where the four senses of sight, hearing, smell, and taste (divided into bitter and sweet) have two organs each, an image of the upper Ogdoad. See Irenaeus Against Heresies 1.18.1 and discussion at p. 52n69 above. Compare the Theology of Arithmetic 68.3, where there are said to be seven orifices in the head, probably counting the tongue singly. Maybe it is the symmetry (and therefore doubleness) of the sense faculties that is key here. Note, too, that Clement’s order of the senses differs (as does Plutarch’s: The E at Delphi 12 [390b]) from that found in the Paraphrase of the “Apophasis Megale.” See p. 100n53 above. A third interpretation, which supplements the second, seems most likely: Clement is referring to the ten toes and ten fingers. Thus, he is stating here not one but three anthropological decalogues: the senses (doubled), the fingers, and the toes.
[ back ] 31. See pp. 46, 76, 118 above.
[ back ] 32. ἡ δεκὰς δὲ ὁμολογεῖται παντέλειος εἶναι. See p. 54n78 above.
[ back ] 33. 18.104.22.168–2. Tithe: Exodus 29.40, Leviticus 6.20; Pascha: Exodus 12.3 (see p. 90 above).
[ back ] 34. Clement of Alexandria Instructor 2.4.
[ back ] 35. Clement calls Heracleon the “most approved of the school of Valentinus” (ὁ τῆς Οὐαλεντίνου σχολῆς δοκιμώτατος; Stromateis 22.214.171.124). For a précis of the life and works of Ptolemy and Heracleon, see Thomassen 2006:494–496. There are two very different assessments of Heracleon: Castellano 1998 and Wucherpfennig 2002. Based on the fragments, Castellano argues for and explores Heracleon’s Valentinian connections. Wucherpfennig argues that Heracleon was not a proponent of gnosis, and not even a Valentinian. Much of this argument rests on the seeming lack of overt Valentinian doctrine in the extant fragments. But Castellano’s research, apparently unknown to Wucherpfennig, identifies convincing Valentinian themes. Michael Kaler’s observation (pers. comm.), however, that Origen never calls Heracleon a Valentinian suggests that research on Heracleon is yet in its early stages.
[ back ] 36. Heracleon, fragment 16 (= Origen Commentary on John 10.38.261). For other aspects of Heracleon’s number symbolism see p. 138 below.
[ back ] 37. Heracleon, fragment 16 (trans. Heine 1989–1993): “ὃ τετρὰς ἐστίν,” φησίν, “ἡ ἀπρόσπλοκος,” εἰς τὸ ἐμφύσημα καὶ τὸ ἐν τῷ ἐμφυσήματι σπέρμα.
[ back ] 38. Ptolemy Letter to Flora 33.5.1, 33.5.4, 33.6.6. See also Wucherpfennig 2002:85–86 and Sagnard 1947:654–655. Other aspects of Ptolemy’s number symbolism are discussed at p. 31 above.
[ back ] 39. In this, Heracleon resembles Marcus and the renowned Valentinian teacher discussed at Irenaeus Against Heresies 1.11.3. See pp. 31–33 and 75n25 above.
[ back ] 40. See e.g. Irenaeus Against Heresies 1.5.6, 1.30.9, 1.30.14; Justin Martyr Dialogue with Trypho 40.1; Clement of Alexandria Instructor 126.96.36.199, Epitomes 3.55.2.
[ back ] 41. On the rejection of the Platonic tripartite soul see Chrysippus Fragment 829 (SVF 2:226 = Origen Against Celsus 5.47). But in late antiquity some Stoics began to accept other ways of dividing the soul, such as the Platonic. On variations in the Stoic tradition see Schindler 1934:326–345, 53–70; van Straaten 1946:119–129; Spanneut 1957:96; and Pohlenz 1970–1972:2.100–112. The Stoic variations are dependent almost wholly upon Tertullian On the Soul 14, whose intention to make the Stoics contradict each other probably skews the picture. See also Dillon (1996:174–175), who lists the various divisions of the soul—sometimes contradictory systems—taught by Philo. This difficulty shows that Philo was not confused or capricious, but was aware that “each of these divisions expresses some aspect of the truth” (Dillon 1996:175).
[ back ] 42. Sometimes discrepancies in the sequence occur in the same source: Diogenes Laertius Lives of the Philosophers 7.110 (= Chrysippus, fragment 828 [SVF 2:226]) contrasts with 7.157. The primary sources that attest to the canonical eight parts are numerous: Zeno, fragment 143 (SVF 1:39 = Nemesius On the Nature of Man 96); Chrysippus, fragment 827 (SVF 2:226 = Aetius Placita 4.4.4); idem, fragment 830 (SVF 2:226 = Porphyry On the Soul in Stobaeus 1.49.25a); idem, fragment 831 (SVF 2:226 = Iamblichus On the Soul in Stobaeus 1.49.34); idem, fragment 832 (SVF 2:226–227 = Philo Questions and Answers on Genesis 1.75); idem, fragment 833 (SVF 2:227, assigned to various passages in Philo); idem, fragment 836 (SVF 2:227 = Aetius Placita 4.21); idem, fragment 879 (SVF 2:235–236 = Chalcidius On the “Timaeus” 220); Philo On the Creation of the World 117; Iamblichus On the Soul 12 (trans. Finamore and Dillon 2002:37). For discussions of the Stoic division of the soul, see Safty 2003:293–297, Dillon 1996:102, and Stein 1886–1888:1.119–125.
[ back ] 43. Stromateis 188.8.131.52: ὁ μὲν οὖν ἄνθρωπος ἁπλῶς οὕτως κατ’ ἰδέαν πλάσσεται τοῦ συμφυοῦς πνεύματος·
[ back ] 44. Stromateis 184.108.40.206: ὁ δέ τις ἄνθρωπος κατὰ τύπωσιν τὴν ἐγγινομένην τῇ ψυχῇ ὧν ἂν αἱρήσηται χαρακτηρίζεται.
[ back ] 45. Stromateis 220.127.116.11: ᾗ καὶ τὸν Ἀδὰμ τέλειον μὲν ὡς πρὸς τὴν πλάσιν γεγονέναι φαμέν· οὐδὲν γὰρ τῶν χαρακτηριζόντων τὴν ἀνθρώπου ἰδέαν τε καὶ μορφὴν ἐνεδέησεν αὐτῷ.
[ back ] 46. Stromateis 18.104.22.168: εἰκότως τούνυν αἱ δύο πλάκες τοῖς δισσοῖς πνεύμασι τὰς δεδομένας ἐντολὰς τῷ τε πλασθέντι τῷ τε ἡγεμονικῷ τὰς πρὸ τοῦ νόμου παραδεδομένας ἀλλαχῇ εἴρηνται μηνύειν.
[ back ] 47. Clement The Instructor 22.214.171.124, 126.96.36.199; idem Stromateis 188.8.131.52, 6.
[ back ] 48. See e.g. Crouzel 1956:67–70; Graef 1952; A. Hamman 1987; Ladner 1953; Merki 1952:44–59.
[ back ] 49. See p. 130 above. Compare also Irenaeus Against Heresies 5.6.1, who like Clement acknowledges that all have the image of God in their formation (in plasmate), but not all have the likeness established by the Spirit.
[ back ] 50. In my view, this confusion also results from a scribal intrusion. For the full argument see Kalvesmaki 2006:404–411.
[ back ] 51. κινδυνεύει γὰρ ἡ μὲν ὀγδοὰς ἐβδομὰς εἶναι κυρίως, ἑξὰς δὲ ἡ ἑβδομὰς κατά γε τὸ ἐμφανές, καὶ ἡ μὲν κυρίως εἶναι σάββατον, ἐργάτις δὲ ἡ ἑβδομάς· On ἐργάτις see Proverbs 6.8a LXX.
[ back ] 52. Stromateis 184.108.40.206.
[ back ] 53. Stromateis 4.25.158–159.
[ back ] 54. Stromateis 220.127.116.11–2, citing Clement of Rome Letter to the Corinthians 22.
[ back ] 55. Stromateis 18.104.22.168: εἶτα ἑβδομάδος καὶ ὀγδοάδος μυστήριον γνωστικὸν ἐπιφέρει· “παῦσον τὴν γλῶσσάν σου ἀπὸ κακοῦ καὶ χείλη σου τοῦ μὴ λαλῆσαι δόλον· ἔκκλινον ἀπὸ κακοῦ καὶ ποίησον ἀγαθόν, ζήτησον εἰρήνην καὶ δίωξον αὐτήν.”
[ back ] 56. Stromateis 22.214.171.124–4, citing Plato Republic 10.616b: ἐπειδὴ δὲ τοῖς ἐν τῷ λειμῶνι ἑκάστοις ἑπτὰ ἡμέραι γένοιντο, ἀναστάντας ἐντεῦθεν δεῖ τῇ ὀγδόῃ πορεύεσθαι καὶ ἀφικνεῖσθαι τεταρταίους.
[ back ] 57. Stromateis 126.96.36.199.
[ back ] 58. For more examples (such as Stromateis 188.8.131.52–5) and analysis of the seven and eight in Clement of Alexandria, see Itter 2009:39–51.
[ back ] 59. Heracleon, frags. 15, 18, 40 (= Origen Commentary on John 10.248–250, 13.69–72, 13.416–426). Wucherpfennig denies that fragment 40 refers to the doctrine of the six, seven, and eight, and suggests rather that it refers to the seventh day of Creation and God’s restoring human nature to its original good standing (2002:320–321). But Heracleon (at Origen Commentary on John 13.424) discusses a nature that is “depicted” (χαρακτηρίζεται), not “restored.” In this passage natures are not transformed (as Wucherpfennig’s reading would require), they are revealed.
[ back ] 60. Clement of Alexandria Epitomes 3.63. On Theodotus, see DECL 571, Thomassen 2006:28, and Kalvesmaki 2008.
[ back ] 61. Clement’s excursus (§§138.5–145.7) has been studied most thoroughly and skillfully by Delatte (1915:229–245), who was also the first to recognize that Clement’s exegesis of the Transfiguration depends upon the teachings of Marcus. Delatte identifies Clement’s sources for his arithmology (1915:234–235). See also parallels in the Theology of Arithmetic at sections devoted to 6, 7, and 8.
[ back ] 62. See Delatte 1915:233, for the scope and evidence of Clement’s direct or (more likely) indirect use of Aristobulus. Although Clement uses Aristobulus, this is probably mediated through someone like Hermippus of Berytus, a grammarian (possibly Jewish or Christian) of the early second century, whose lost treatise On the Hebdomad is mentioned by Clement at §145.2. Compare also Stromateis 184.108.40.206–108.1, Clement’s catena of quotations from classical authors who praise the number seven.
[ back ] 63. There are many ancient parallels. See e.g. Aristotle, fragment 203 (= Alexander of Aphrodisias Commentary on Aristotle’s “Metaphysics” 38), Philo On the Creation of the World 100, Theology of Arithmetic 41.30, Theon of Smyrna Mathematics Useful for Reading Plato 103.14–16, Nicomachus of Gerasa in Photius Biblioteca 144b.
[ back ] 64. Fixed sphere: τὴν ἀπλανῆ … σφαῖραν: see Stromateis 5.106, cited above. Because of precession, the drifting of the earth’s axis across the stars, the zodiac appears over the centuries to rotate slowly around the earth. The time it takes for one house of the zodiac to return to its starting point, calculated by modern astronomers at 26,000 years, is called the Great Year, the length of which was a topic in classical antiquity. See e.g. Plato Republic 8.546.
[ back ] 65. Förster 1999:252n207.
[ back ] 66. See Behr 2000, le Boulluec 1982:707–713, and Patterson 1997. For a well-known parallel see Stromateis 220.127.116.11–110.1, adapting Irenaeus Against Heresies 18.104.22.168–84, and analysis in Hort and Mayor 1902 and Patterson 1997.
[ back ] 67. Substituting Delatte’s ὁ for the ὃ in SC and the οἱ (dittography from the previous line) in the manuscript.
[ back ] 68. I delete the comma here, following Sagnard 1947:378 and Dupont-Sommer 1946:47. On the coined phrase ‘episēmos ogdoad,’ see p. 72 above.
[ back ] 69. The precise referent of ταύτῃ is missing from the ANF and SC translations. It must refer to the ogdoad because that was the topic of the previous section and because ταύτῃ corresponds to Marcus’ μετὰ τὰς ἓξ ἡμέρας. It may possibly refer to the last word of §140.2, ἀνταποδόσεως, but even this term Clement gives the nuance of eightness. My reconstruction makes sense in light of Luke 9.28, which places the Transfiguration on the eighth day, unlike Matthew 17.1 and Mark 9.2, both of which place it “after six days.” Clement follows Luke; Marcus opts for Matthew and Mark.
[ back ] 70. Delatte 1915:238. Irenaeus Against Heresies 1.14.4.
[ back ] 71. Delatte 1915:238–239.
[ back ] 72. Ms reading. Stählin 1909: Εἰσκλαπέντος.
[ back ] 73. Or “slips out of.” See discussion below.
[ back ] 74. That is, the number seven comes to be represented by the sixth oral letter.
[ back ] 75. See p. 63 and n4 above.
[ back ] 76. The term digamma, attested in the postclassical period, comes from the character’s looking like one uncial gamma superimposed on another. See LSJ 752a s.v. “ϝ,” and Larfeld 1898:294.
[ back ] 77. All ancient references known to me concerning the ἐπίσημον are discussed above, pp. 66–88. Scholia on Dionysius Thrax 1.3:496.6–7 appears at first glance to identify the digamma with the Greek numeral for six. The scholiast entertains the question, Why are there twenty-four letters (γράμματα) when there are other characters and inscribed figures, and other nations have their own letters, and there are certain other figures: “the digamma, the koppa, the so-called παρακύϊσμα, the insignia, and things written alongside letters, and the crown?” (Διὰ τί δὲ κδ´ ἔφη εἶναι τὰ γράμματὰ εἰ γὰρ γράμματά εἰσιν οἱ χαρακτῆρες καὶ οἱ ξυσμοί, γράμματα δὲ καὶ τὰ παρὰ Χαλδαίοις καὶ Αἰγυπτίοις, καί τινα ἕτερα, τὸ δίγαμμα καὶ τὸ κόππα καὶ τὸ καλούμενον παρακύϊσμα, καὶ τὰ σημεῖα, καὶ τὰ παρεγγραφόμενα τοῖς στοιχείοις, καὶ ἡ κορωνίς, καὶ εἴ τι τοιοῦτον, ἀτόπως φησὶν ὅτι κδ´ ἐστίν.) This passage has guided scholars, including LSJ 1562a, s.v. “M,” and LSJ, Supplement 114, s.v. “xπαρακύϊσμα,” to define παρακύϊσμα—a hapax legomenon—as the term for the numeral ϡ. But this presumes that the author identified the digamma with the numeral Ϛ and intended to list all three nonalphabetic numerals. This should be shown, not assumed. In this passage παρακύϊσμα can be read with δίγαμμα and κόππα as a threesome, but it might be better grouped with τὰ σημεῖα to form a second pair of terms. Given the root meaning of παρακύϊσμα—a κύημα is a fetus—it is very difficult to see how the character ϡ could be inferred. Jannaris 1907:39, suggests that the ϡ “is a παρακλῖνον γέννημα,” “a slanting letter,” but offers no explanation of how it resembles “offspring.” In reality, we have no clue what παρακύϊσμα means. This scholium on Dionysius Thrax is the only ancient text that might possibly be interpreted to connect the digamma with the numeral six, a shaky foundation given other arguments below.
[ back ] 78. Scholia on Dionysius Thrax 1.3:187.22–25. Ἔτι πᾶς χαρακτὴρ στοιχείων σημαίνει ἀριθμόν· καὶ γὰρ τὸ α σημαίνει τὸν ἕνα ἀριθμόν, καὶ τὸ β τὸν δύο, καὶ ἑξῆς· εἰ ἄρα οὖν ὁ χαρακτὴρ τοῦ ϝ οὐ σημαίνει ἀριθμόν, δῆλον ὅτι οὐκ ἔστι στοιχεῖον.
[ back ] 79. Scholia on Dionysius Thrax 1.3:34.15–23; 2.1:76.32–77.12. At first glance, the Georgian alphabet seems to provide evidence that late antique grammarians knew about the connection between ϝ and Ϛ. The fifth, sixth, and seventh letters are ე [e], ვ [v], and ზ [z], and the alphabet was used for numerals in the fashion of Greek. But Mouraviev has demonstrated that the placement of extra Georgian letters, such as ვ in the alphabet had nothing to do with the Semitic alphabets, but was the careful, deliberate work of a phonologist (1984). The phonetic equivalent of waw is the 22nd letter, უ [ü/w], assigned the value of 400 in Georgian alphabetic numeration.
[ back ] 80. Ptolemy Harmonics 2.1.
[ back ] 81. The Mystery of the Letters 31–33 (Bandt 2007:170–174; cf. 227).
[ back ] 82. Delatte 1915:241.
[ back ] 83. Delatte (agreeing with Serruys) rejected Stählin’s argument (agreeing with Lowth) for the first option, since it rested on the view that the last sentence in Clement’s paragraph purports to say that the number seven then took the sixth place, and the number eight the seventh. Stählin argued for the first option by suggesting that the numbers themselves move. Of course, they do not. By affirming the second option, that the ἐπίσημον fell out of writing, Delatte influenced the SC edition (Descourtieux 1999:342–343), which departs from Stählin’s text—otherwise the preferred edition—in favor of the manuscript Laur. V 3.
[ back ] 84. There are other reasons for accepting the emendation. First, the alternate proposal, Ἐκκλαπέντος δ ᾽ οὐκ οἶδ ᾽ ὅπως τοῦ ἐπισήμου ἐκ τῆς γραφῆς, requires an alteration of three words, rather than just one. Second, the last sentence in Clement’s paragraph does not suggest what Stählin said and what Delatte discounted (see n. 83 above); my translation and explanation clarify Clement’s meaning. Third, the alternate proposal suggests that the ἐπίσημον was originally in the alphabet, then disappeared, contradicting Clement’s previous sentence, which states that before whatever happened to the ἐπίσημον, zeta was sixth and eta seventh in the order of the alphabet.
[ back ] 85. For parallels see Stromateis 22.214.171.124, 126.96.36.199, 188.8.131.52 and Epitomes 3.63.
[ back ] 86. See p. 54n78.
[ back ] 87. See p. 127 above.