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.

6. The Orthodox Limits of theTheology of Arithmetic: Irenaeus of Lyons

Most scholarly reconstructions of Valentinianism attempt to excise Irenaeus’ interpretation, so as to achieve as uncontaminated an account of the movement as possible. The ultimate goal, a bias-free view of the Valentinians, is misguided. For the unintended consequence—or so I argue in this chapter—of excluding Irenaeus and his writings is to leave the picture of their number symbolism incomplete. Irenaeus’ critique of Valentinian theological arithmetic reveals the rules and restraints held in common by many Christians. And his vision for the appropriate use of number symbolism illuminates the general early Christian impulse to number symbolism that the Valentinians shared. Irenaeus’ ideals, and his success and failure in holding to them, provide a glimpse into tensions in early Christian thought, both orthodox and heretical. So to understand the Valentinians, we must study Irenaeus, too, on his own terms.

Setting aside the rhetorical flourishes expected in ancient theological polemic—Irenaeus’ often wry sarcasm and labeling (e.g. his accusation that Valentinianism derives from Pythagoreanism and paganism)—he advances four general theses against the Valentinian use of numbers. First, the aeons in their Pleroma are inconsistently numbered; second, their doctrine makes claims that depend upon the changing, culture-bound customs of language and numeration; third, their number symbolism does not correspond to the structures of the created, natural world; and fourth, their method of interpreting the rule of faith, Scripture in particular, is faulty. While pursuing these four lines of attack, Irenaeus promotes some basic principles about theology and exegesis, both to discredit his opponents and to articulate core principles of the faith held by the churches around the world.

Irenaeus’ sarcastic asides are of little substance. Yet his colorful insults provide context for his substantive points. He mocks the Valentinian Tetrad by inventing his own out of an emptiness, a gourd, a cucumber, and a melon (Against Heresies 1.11.4). This emanation of fruits, Irenaeus argues, is just as plausible as that of their aeons, and equally arbitrary. While reporting Marcus’ system, Irenaeus accuses him of trying to preach something more mystical than the other systems, of achieving new spiritual heights by breaking everything down into numbers. He also associates his opponents with pagan teachings and habits. A Pythagorean slur occurs in Book 2, where Irenaeus claims that the Valentinian tendency to translate everything into numbers comes from the Pythagoreans (2.14.6, upon which the rest of this paragraph is based). His logic: they were the first to make numbers the origin of everything, the first to make even and odd the foundation of numbers, and the first to make odd and even the basis of sensible and intelligible things. Even numbers are the basis for underlying substance (in Aristotelian terms, a ‘primary substance’), whereas odd numbers are the basis for intellection and essence. [4] The difference between even and odd resembles the parts of a statue, which has both substance (equivalent to even numbers) and form (odd numbers). This is the sort of model, he says, that the Valentinians apply to beings outside the Pleroma. They (the Pythagoreans or the Valentinians—the text is vague) claim that by knowing “what was first assumed” (quod primum adsumptum est), a person seeks out the beginnings of intellection and in exhaustion races to that which is one and indivisible. This One—the ἕν—is the principle of everything and the basis of all generation. From it come the Dyad, Tetrad, and Pentad—terms that the Valentinians use to describe the Pleroma and Depth. This Pythagorean number symbolism undergirds their doctrine of the syzygies. Marcus, boasting about the great novelty of his invention, speaks about the τετρακτύς of Pythagoras as if it were the origin and mother of everything.

Such ridicule and insults are mere flourishes to Irenaeus’ more substantive, theological arguments, which he presents directly and forcefully. Using counterexamples drawn from Scripture, history, and the natural world, he insists that the Valentinians—exemplified by the extended system of the Triacontad—have not correctly counted the number of aeons in the Pleroma (the first of his four main arguments). To make this point, he defends two claims. First, by their own reckoning, their Pleroma has fewer than thirty aeons. Second, the Pleroma ought to have more than thirty aeons. In each case, the Valentinian school is shown to be incapable of responsibly handling the numbers it so esteems in its theology.

And what about Silence (Thought), Depth’s consort (2.12.2)? Can any being be separated from its own silence and thought? Indeed, does not the very notion of conjugal unity forbid any idea of separation? If so, then Thought is in every way similar to Depth; they share a single existence. This applies as well to the other conjugal pairs. Mind and Truth, who always indwell one another, cannot be separated, just as water and moisture, fire and heat, and stone and hardness cannot be separated. Likewise, Word and Life, Human and Church, and all the other pairs of aeons cannot be disentangled. After all, the feminine aeon must necessarily be equal to the masculine, “since the former resembles the latter’s disposition.” [8] ‘Disposition,’ a Valentinian term, implies metaphysical unity. So we should count only syzygies, not aeons. Irenaeus anticipates their response, that the syzygies are in fact divided, so that individual aeons can be enumerated apart from their mates (2.12.4). But, Irenaeus charges, this renders absurd their other claim that the syzygies are unities and that the male and female are one. If the aeons of a given syzygy are separate, then the female gives birth to offspring apart from her mate. If so, then she is like a hen who hatches eggs without the help of a rooster. Irenaeus’ argument here boils down to whether the syzygies are real or only symbolic, and whether they are to be counted singly or doubly. The Valentinians’ inability to specify whether the syzygies are true unions or only token ones, he says, makes it impossible to tell whether they have counted accurately.

Irenaeus also argues that the Valentinians’ system results in more than thirty aeons in their Pleroma (2.12.7, upon which this paragraph is based). They say that four other entities are projected—Limit, Christ, Holy Spirit, and Savior (see Figure 3, p. 38 above)—but they do not include them in the canonical thirty of the Pleroma. Why not? Irenaeus asks. Are they so weak as to be unworthy of the designation? Are they superior to the other aeons? It would be absurd to suggest that they are weaker, since they were projected to stabilize and correct the Pleroma. But it would be equally absurd to suggest that they are better than the primal Tetrad. So, if they are neither weaker than the weakest aeons in the Pleroma, nor better than the best, then either they should be numbered with the Pleroma, or the honor associated with such a name (πλήρωμα means “fullness”) should be removed from the other aeons since, obviously, the Pleroma does not include the fullness of the aeons.

Irenaeus’ second line of attack calls Marcus to account for his misuse of numeration conventions. He ridicules the notion that the Word the Father uttered consisted of thirty letters and four syllables (1.15.5). If this were so, then the Father, whose image the Word bears, should also consist of thirty letters and four syllables. Indeed, is this really the final arrangement? Marcus, says Irenaeus, bottles up the Creator in various numbers and patterns: at one time thirty, at another twenty-four, at another merely six. Even the technique he uses to calculate alphabetic numbers is inconsistent, since at one time he computes a name’s psephic value, at another time the number of letters in the word (2.24.1–2). ‘Jesus,’ Irenaeus points out, is not a Greek name, yet Marcus nevertheless makes its Greek transliteration the center of his theology. Sometimes he calls it the ἐπίσημον because it has six letters, and sometimes the fullness of the Ogdoad, since the psephic value of Ἰησοῦς is 888. But even if this were true, he does not do this with the Lord’s other names and titles, such as Σωτήρ. And no wonder, since neither its psephic value, 1,408, nor the number of letters in it, five, is related to the numbers or patterns in the Pleroma. The psephic value of ‘Christ,’ Χρειστός, is 1,485, but this has no arithmetical connection with the Pleroma that Christ allegedly stabilizes and corrects. The same applies to Πατήρ, Βύθος, Μονογενής, and other aeons. These inconsistencies—applying Greek linguistic conventions to Hebrew names and not applying the same method to the more important Greek names—proves that their system isfalse.

Later in Book 2, Irenaeus extends this argument (2.15.1). The Valentinians, he says, claim that the thirty aeons were not made for creation but vice versa. That is, the creation is the image of the thirty aeons, not the other way around. According to their reasoning, the month has thirty days because of the thirty aeons. So too the day has twelve hours, and the year twelve months, because of the Dodecad. The reasoning is arbitrary and incomplete, Irenaeus says, since it does not explain why Human and Church had to project twelve, no more and no less. It also does not explain why an Ogdoad, and not, say, a Pentad, Trinity, or Heptad, is the core of the Pleroma. If the year is an image of the Dodecad, and the month of the Pleroma, then of what important natural occurrence of the number eight is the Ogdoad an image?

Irenaeus accuses the Valentinians of using analogies that invert the order of nature (2.24.5). They appeal to the divisions of the year and the day as symbols of the Pleroma. The number of months and the number of hours of the day point to the Dodecad; the days in the month, to the Triacontad. The scheme is inconsistent. Each aeon is supposed to be one-thirtieth of the Pleroma, but a month is one-twelfth of a year. If the divisions of time really reflected those of the Pleroma, wouldn’t it have been more appropriate for the year to be divided into thirty months and each month divided into twelve days? The Savior must have been an idiot, Irenaeus chides them, to have made the month an image of the Pleroma and the year, the more important division of time, that of the Dodecad, a less important subset of the Pleroma. And their analogy does not account for the realities of the calendar. Not every month has precisely thirty days, just as not all days have twelve hours, depending upon the season of the year. Thus neither can the day be a true image of the Dodecad, nor can the month of the Pleroma. And why do they group the Pleroma into Ogdoad, Decad, and Dodecad and no other arrangement? (2.15.2) Why three divisions, and not four, five, six, or some other number more commonly found in creation? After all, the year is divided into four seasons (2.24.5). Were the year truly an image of the Pleroma, the aeons would fall into four major tiers, not three.

Whenever they are cross-examined about the Pleroma, Irenaeus says, they retreat to explanations about human dispositions and to discourses about creation (2.15.3). But this is to focus on secondary rather than primary matters, since the issue at hand is not harmony in creation or human dispositions, but the Pleroma, of which creation is an image. If the Pleroma is trisected into Ogdoad, Decad, and Dodecad, then they must admit that the Father arranged the Pleroma in vain and without providence, since its organization did not correctly anticipate the structures of the natural world. If so, then the Father acted irrationally and, like the Demiurge, made a deformity. Given their analogy between the Pleroma and creation, they must admit that the Forefather is just as inept as they say the creator of the natural world is. But if they want to avoid that conclusion and instead maintain the providence of the Forefather, then they must say that the Pleroma was projected so as to provide a template for creation. But in this case, although the harmony of the cosmos is preserved, the Pleroma exists not for itself but for its image. The Pleroma is then inferior to creation, as if it were a clay model, made only to facilitate the construction of a gold, silver, or brass statue. In sum, if the Pleroma is a template for creation, then the Father’s creation is inferior to what the Demiurge made.

Irenaeus accuses the Valentinians of fostering an infinite regression that wreaks havoc with their arithmetical theology. If they don’t agree that the Pleroma was made for creation, then they must say that it was made for a higher reason or cause (2.16.1). But this is to postulate that Depth used a higher pattern to shape and arrange the Pleroma. A vicious regression begins, since you must ask how and why this super-Pleroma was made. The same line of questioning can lead to super-super-Pleromas, and so on. Irenaeus argues that you must accept that one God, who made the world, took the pattern for creation from his own power and his own self. If you deviate the least bit from monotheism, you end up always asking and seeking out how and from what source the creator patterned his creation, upon what he styled the number of projections, and from where he derived the substance that was used. If they try to argue that Depth perfected the design of the Pleroma from himself, then it should be allowed that perhaps the Demiurge also patterned the world, not from the Pleroma, but from himself. That is, maybe the Demiurge is not so evil after all. But if they insist that creation is an image of the Pleroma, then what is to prevent the Pleroma from also being an image, and so descend into an endless regression of images of images?

Throughout his argument, Irenaeus focuses on Valentinian number symbo-lism. He pursues the numerical patterns and structures central to their theo-logy to test their claims that there are innate, direct connections between creation and the Pleroma. That there are differences between natural and divine patterns raises difficult questions. Why those numbers in particular? Where did they come from? Are they intrinsic to the highest reality, or merely accidental parts? Irenaeus argues that the heretics make number external to the deity, which is why they always try to trump each others’ protologies, since deity is subservient to unbounded, arbitrary arithmetical patterns. And the origin of those patterns is troublesome. Basilides (2.16.2) says that Ineffable based the pattern for the emanation of the heavens upon his dispensation. But where did that dispensation come from? Ineffable had to have created the dispensation either from himself, or from a yet higher power. If the former, then one might as well abandon the entire theological complex of aeons in favor of simply the one God, who created the one world from a numerical pattern of his own design (2.16.3). If the latter, then the endless regression resumes.

Irenaeus mocks his opponents’ increasingly complex systems as symptomatic of their spiritual arrogance (2.16.4). Just as the Valentinians accused less spiritual Christians such as Irenaeus of remaining in the Hebdomad, so the Basilideans could accuse the Valentinians of remaining at the level of the Triacontad, and not ascending to the 45 ogdoads, then the 365 heavens. The higher the number, the better, no? Why not invent a system of heavens or aeons numbering 4,380, the number of daytime hours in a year? And then build upon the nighttime hours an even greater number? This endless one-upmanship means that the Valentinians and Basilideans will always be unable to rise to the highest conception of the number of heavens or aeons. The creation of such tiers above our world is an invitation to descend into endless levels of worlds (2.35.1).

Irenaeus returns to this theme in Book 4 of Against Heresies, where he advises that anyone who seeks a Father beyond the one Father of the Scriptures will need to find a third, a fourth, and so on (4.9.3). Such a person will never rest in the one God, but will drown in a Depth without Limits, until repentance brings him back to the place from which he was cast out, the one God. In his admonition, Irenaeus symbolizes God by the garden of Eden, the place of single simplicity. To develop other gods or aeons is to begin a journey into a bottomless pit of multiplicity, a transience ended only by returning to the garden of God’s unity.

Moreover, if the Valentinians want the twelve apostles to represent Human and Church’s projected twelve aeons, to be consistent they should produce ten more apostles to represent the other Decad of aeons, emitted by Word and Life (2.21.1). How could the Savior provide a type for the youngest (and therefore least significant) aeons, but overlook the elder ten? The same applies to the Ogdoad, which ought to have been numerically signified by the election of eight apostles. Indeed, their system can make nothing of the seventy other apostles the Lord sent after he commissioned the twelve, since seventy prefigures neither an Ogdoad nor a group of thirty. If their reasoning is correct, that the election of the twelve apostles signifies the twelve aeons, then they must hold that the seventy apostles were chosen because of seventy aeons. If this is the case, then the two groups of apostles, twelve and seventy in number, symbolize eighty-two aeons, far beyond the canonical thirty.

To the Valentinian appeal to the numbers in the Mosaic Law as symbols of the Pleroma, Irenaeus offers numerous counterexamples (2.24.3). Their system, he asserts, has nothing to say about the dimensions of vessels in the holy of holies: the ark of the covenant (2½ by 1½ by 1½ cubits), the mercy seat (2½ by 1½ cubits), and the table of the showbread (2 by 1 by 1½ cubits). The seven-branched candelabra, by their scheme, ought to have been made with eight lights, to typify the primal Ogdoad (Exodus 25.31–37). They appeal to the 10 curtains (Exodus 26.1) as a type of the 10 aeons, but they neglect the skin coverings, 11 in total (Exodus 26.7), and the length of the curtains, 28 cubits (Exodus 26.2). Although they say the 10-cubit length of the columns typifies the Decad of aeons, they cannot explain their 1½-cubit width (Exodus 26.16). Furthermore, they cannot account for the oil (500 shekels of myrrh), the cassia (also 500), the cinnamon, and the calamus (both 250). These four items plus the oil make five ingredients, a number that does not fit their scheme.

Irenaeus turns the Valentinians’ technique against them. He notes sarcastically that according to the Scriptures, an exorcised spirit of ignorance finds those who were formerly possessed “striving not after God but after cosmic inquiries, and brings along seven other spirits more wicked than himself” (1.16.3, citing Matthew 12.43). One spirit plus seven others makes eight. By the Valentinians’ own logic, a demon has left them but returned and found them ready to be inhabited, and so has taken along “seven other spirits, thus constituting their Ogdoad of spirits of wickedness.” Their arrogance is so great that, in enumerating seven heavens, they presume to have surpassed the apostle Paul, who ascended only to the third heaven, four short of the highest level (2.30.7, citing 2 Corinthians 12.2).

Number Symbolism in Irenaeus’ Theology and Exegesis

All four of these lines of argumentation boil down to charges of incompleteness, inconsistency, and arbitrariness. But someone must have pressed Irenaeus to offer his own account of how numbers should be used responsibly in theology and biblical interpretation. We get a hint of this when the text asks: Are the placement of names, the election of apostles, and the acts of the Lord and his deeds recorded for no reason whatsoever? Irenaeus replies:

Not at all. Rather, everything God does—whether ancient or anything accomplished by his Word in recent times—is harmonized and well ordered with abundant wisdom and precision. And these things should be yoked not with the number thirty but with the underlying narrative of truth. And they should not undertake an investigation about God on the basis of numbers, syllables, and written letters. (For this is unsound because of their multifaceted and variegated nature, and because any narrative—even one that someone cooks up today—can gather out of the same [numbers, syllables, and letters] proof texts contrary to the truth, in that they can be manipulated to many ends.) Rather, they should fit to the underlying narrative of truth the numbers themselves and the things that have been done. For the rule does not come from numbers, but numbers from the rule (non enim regula ex numeris, sed numeri ex regula). Neither does God come from creation, but that which is made, from God. For everything is from one and the same God.

No other passage is as important for understanding Irenaeus’ theology of arithmetic. He argues that numbers, syllables, and letters are unfit to be the foundation of a system because they are composite, they have many different qualities, and they can be used to prove anything one likes. Anyone can dream up a narrative and find numbers and letters to corroborate it. By calling numbers and letters weak, Irenaeus gives priority to Scripture and the rule of faith, which are unchanging. So the Valentinians’ principal fault is in going first not to the Bible but to the world of numbers and letters. Although the Valentinians appeal to the Scriptures and to the order of the natural world, these appeals are based ultimately upon preconceived arithmetical ideas. Scripture is extra.

So much for numbers in Irenaeus’ theology. But what about his Bible interpretation? Irenaeus was quite attracted to the numbers found in the Bible, and he interpreted many of them symbolically. In certain respects he tried to stay close to the rule of faith; in others he was just as arbitrary as the Valen-tinians.

Irenaeus interprets the thirty-, sixty-, and hundredfold fruit in the parable of the sower as three levels of reward in the hereafter (5.36.2, citing Matthew 13.8). The hundred represent those who will be taken up into the heavens, the sixty, those spending time in paradise, and the thirty, those inhabiting the city (i.e. the heavenly Jerusalem). To corroborate this interpretation, Irenaeus claims as his authority the elders who were disciples of the apostles. According to them, those being saved advance by stages, by rank, through the Spirit toward the Son, and through the Son toward the Father. Thus Irenaeus draws from an oral tradition to elucidate a parable whose interpretation is not immediately clear. Unlike the Valentinians, Irenaeus pays no attention to the symbolism of the numbers themselves. Rather he focuses on their structure, that of a tripartite hierarchy.

Eschatological numbers fascinated Irenaeus. I have already mentioned how he takes the seven marches around Jericho to represent the trumpets of the end of time. His most sustained discussion of number symbolism occurs at the end of Book 5 of Against Heresies, where he treats numerous passages in Daniel and Revelation, whose symbolic numbers seem to have attracted as much attention then as they have since. Irenaeus suggests that, because one day is as a thousand years to the Lord, the world must come to an end after six millennia, reflecting the six days in which it was created (5.28.3, citing 2 Peter 3.8). He also addresses the very contentious issue of the interpretation of the number of the beast (Revelation 13.18). He begins by noting that the name of the beast is fittingly 666, since the number shows how he sums up in his person the pervasive spread of wickedness before the deluge (5.29.2). Noah, after all, was six hundred at the time of the flood (Genesis 7.6). And the beast, the sum of idolatry, is symbolized by Nebuchadnezzar’s image, which had a height of sixty cubits and a breadth of six. Six hundred, sixty, and six make 666, QED. This recapitulation, where six recurs in units, tens, and hundreds, signifies the recapitulation of the apostasy at the beginning, middle, and end of history (5.30.1). Staying true to his principles, Irenaeus draws from the Scriptures, choosing verses whose treatment of the number six allows for a broader, moral treatment of Revelation. He does not characterize the number six as a falling short of the perfection of seven, nor does he suggest, at least here (see below), that the beast’s number has anything to do with the psephic value of a name (in contrast to Marcus’ 888, the psephic value of Ἰησοῦς). The first of these explanations would have been a difficult sell, since six was considered a perfect number, and it had only positive connotations in ancient number symbolism. [30] The second explanation would have veered too close to Marcus’ techniques and would have encouraged speculation in gematria, which Irenaeus found exasperating.

Irenaeus’ most famous use of number symbolism is his argument for there being four and only four Gospels (3.11.8). [35] It is not so much Bible interpretation as meta-Bible interpretation. Responding simultaneously to those who espoused more Gospels (the Valentinians) and to those who held to a much smaller number (Marcion, who accepted only Luke, and an abridged form at that), Irenaeus claims that the Gospels had to have been four, no more and no fewer. There are four regions of the world and four universal winds. [36] The Church is spread throughout the whole earth and the Gospel is the “pillar and support” (1 Timothy 3.15) of the Church and the spirit of life. [37] Because of all these things, the Church fittingly has four columns, breathing incorruption and granting people life from all directions. From this it is evident that the Word, the craftsman of all things, after manifesting itself to humanity, gave a quadriform gospel encompassed by a single Spirit. The Word rests on the cherubim and the cherubim have four faces (Psalms 79.2; Ezekiel 1.6, 1.10). These faces are images of the activity of the Son of God. Following the language and order of Revelation 4.7 (and not Ezekiel 1.10), Irenaeus interprets the lion, ox, man, and eagle as, respectively, John, Luke, Matthew, and Mark, on the basis of the opening lines of each Gospel. [38] The four animal shapes reflect the four activities of the Son of God, and the four Gospels. For the same reason, four covenants were given to humanity, the first before the deluge, the second to Noah, the third to Moses, and the fourth is that which “renews man and recapitulates in itself everything, through the gospel raising and granting wing to men for the heavenly kingdom.” [39] Thus everyone who nullifies the shape of the Gospel and introduces more or fewer faces of the Gospel is foolish and ignorant (3.11.9). Those who have more (the Valentinians) claim they have found something greater than the truth. Those who have fewer (the Marcionites) nullify the dispensation of God. God creates all things to be harmonious and well fitted, so the form of the gospel too had to be harmonious and well fitted. Thus the four gospels alone are true and certain, and admit neither increase nor decrease.

How well does this argument for the four Gospels conform to Irenaeus’ principles? He does not seem to appeal to the rule of faith, and it looks like the argument arises from a predilection for number symbolism. Is Irenaeus com-mitting the Valentinians’ sin of regula ex numeris?

Consistency in Irenaeus’ Thought

But is Irenaeus consistent? How well fitted is his rule of truth to the principles he outlines? He charges the Valentinians with mishandling Scripture, with putting numbers ahead of doctrine. But has he himself committed this very error? Recall the four main lines of Irenaeus’ substantive critique of Valentinian number symbolism, but phrased as principles that Irenaeus must necessarily defend. First, the numbers in one’s taxonomy of the godhead should be consistent. Second, theology should not derive from and depend upon the changing linguistic or mathematical habits of a particular society. Third, numerical patterns of the natural world, if used to justify one’s theology, should be applied consistently. Fourth, numbers in theology should emerge from the entire body of Scripture, and proof texts should be used with regard to their context. This last principle is especially important for him: numbers should emerge from the rule of faith (the Scripture being part of that rule), not the other way around.

As for the third principle, the need for one’s number symbolism to be consistent with nature, Irenaeus is unfair to his opponents. In Irenaeus’ day, the four winds and the four cardinal points were unquestionable, natural phenomena subject to neither change nor social convention. Even if we grant him the science, was it any reason to conclude that there are four and only four Gospels? Recall his criticizing the Valentinians for justifying their various levels of the Pleroma on the basis of inappropriate divisions of time. Irenaeus is just as arbitrary. A Valentinian, for instance, could have argued for the five Gospels—Matthew, Mark, Luke, John, and the Gospel of Truth—on the basis of the five senses, the same basis upon which deutero-Simon argues for the perfection of the Pentateuch. Whose argument is stronger? Are the Gospels more like geography or sensation? And if the Gospels resemble the four winds, as Irenaeus claims, then how does the number of epistles or other biblical books fit into that analogy? Why the specific number of letters by Paul and other apostles? Why the number of Old Testament books? If the Gospels represent the four winds, what do the other books represent? After all, Irenaeus insists that if the Valentinians find evidence for the Dodecad in the calendar year, then they must find chronological divisions that are prototypes of the Decad and Ogdoad as well, to be consistent. By the same token, the numbers of the other books of the Bible should be reflected in the appropriate parts of the natural world. Both Irenaeus and Valentinians depended upon incomplete, ad hoc natural analogies.

In the first and fourth principles, however, Irenaeus is entirely consistent. He keeps numbers subservient to God, their creator, and interprets numbers in conformity with the rule of faith preserved in the churches of Asia Minor, Gaul, and Rome. He is especially careful to preserve inviolate the first principle, that of a consistently numbered godhead. In pursuing his biblical exegesis, Irenaeus tries to apply the fourth principle, making his interpretation come from the Scriptures and the rule of faith itself, or at least remain in conformity with them.

Irenaeus held to four Gospels not because of the weather patterns but because of the churches’ tradition (Against Heresies 3.1). He learned from the elders of Asia Minor, who themselves preserved what the apostles taught them, that there are but four Gospels. This is the apostolic rule of faith, and Irenaeus treats it as having the authority of Scripture. The rule of faith preserves four and only four books, and this unalterable fact enlightens other, more obscure parts of the tradition. The four Gospels explain the meaning of the four faces of the cherubim, as well as of the four covenants God gave throughout human history. Such numbers are drawn exclusively from the tradition.

We might imagine the Valentinians’ objecting, claiming that they too were working from within a tradition, albeit a specially revealed one. Irenaeus’ counterargument, however, would be strong. Doctrine respects the narrative structures of the Scriptures, and it engages in the entire breadth of the tradition. It flows out of the tradition, not into it. The tradition does not depend on any one person, school, movement, or special revelation, but is the possession of all the churches. The Valentinians cannot justifiably claim to be following this rule. If they could, they would be able to point everywhere to churches that preserve their tradition from the apostles (3.1–4), they would have a place for the sacred number five, and their system would harmonize with the Scriptures taken in their broader context.

Irenaeus’ fourth principle is his chief axiom. The rule of faith is a constant, consisting of the Scriptures, the oral tradition, and the life and teaching of the churches founded by the apostles. Numbers should be treated as a part of that rule, and numbers from another rule should not force their way in. For Irenaeus, the various numbers in Scripture are not so much proofs as implications of his system. The four animals of Ezekiel 1 and Revelation 4 do not justify the claims that there are exactly four Gospels; rather, these verses are explained by that part of the tradition. Irenaeus’ phrases of inference—“for also” (καὶ γάρ), “and because of this” (καὶ διὰ τοῦτο)—do not look backward, to a basis for belief, but forward, to its implication. Throughout Against Heresies, Irenaeus uses inferential language for two purposes: one for proof, and the other to show off a doctrine’s explanatory power. When interpreting the four Gospels, he uses only the second technique. His clause of inference “for since” (ἐπεὶ γάρ;–177) explicates rather than justifies. He is, in the end, not proving the number of Gospels but rather explaining the coherence of that number. He cloaks his explanation in clauses of inference to strengthen the persuasive power of his rhetoric, albeit at the expense of clarity.

Irenaeus responded thoroughly to the Valentinian theology of arithmetic by setting down strictures and principles that applied to all of Christian theology and exegesis. He carefully upheld the principles he most cared about. In his exegesis, he maintained his commitment to orthodoxy as a driving principle, but he used some of the same arithmological techniques the Valentinians, Philo, and Plutarch used. Irenaeus was typical of many orthodox writers in his day, but his approach, with its ideals and inconcinnities, is only one example of the orthodox approach to number symbolism. A more complete picture requires us to consider Irenaeus’ near contemporary, Clement of Alexandria.


[ back ] 1. Irenaeus Against Heresies 3.3.4.

[ back ] 2. See DECL, s.v. “Irenaeus”; Eusebius Church History 5.4, 7–8, 20, 26.

[ back ] 3. Eusebius preserves the closing words of the treatise: Church History 5.20.2.

[ back ] 4. The preserved text is muddled here. My paraphrase follows the conjecture of Rousseau et al. 1965–1982:1.260.

[ back ] 5. See p. 55 and n81 above.

[ back ] 6. This may be Irenaeus’ invention, or it may reflect an analogy the Valentinians themselves made between the Dodecad and the gods or the zodiac. The latter possibility should not be discounted, given the Valentinian penchant for Pythagorean symbolism.

[ back ] 7. The logic is similar to that employed by Hippolytus’ Valentinians, who derive the same number by excluding the Forefather from the class of aeons.

[ back ] 8. cum sit velut adfectio eius. Here, adfectio probably represents διάθεσις. See SC 293, index, s.vv. ‘διάθεσις’ and ‘adfectio.’ To describe the female aeon as the διάθεσις of the male is characteristic of the “more knowledgeable” Ptolemaeans discussed at Against Heresies 1.12.1. See pp. 35–37 above.

[ back ] 9. μεταγενέστερον δὲ καὶ σαυτοῦ· σὺ γὰρ μόνος <εἰς> εἴδωλον κατήγαγες τὴν ὑπὸ σοῦ λεγομένην Ἀλήθειαν.

[ back ] 10. See Pliny the Elder Natural History 7.192, Tacitus Annales 11.14, and many others cited at Förster 1999:238–242 and Teodorsson 1989–1996:3.318. Irenaeus’ report resembles that of Plutarch’s Table Talk 9.3 (738–739). For modern approaches to the history of the Greek alphabet, see OCD s.v. “Alphabet, Greek.”

[ back ] 11. This is my interpretation of Against Heresies–46, a convoluted passage poorly preserved in the Latin: Ipsae enim antiquae et primae Hebraeorum litterae et sacerdotales nuncupatae x quidem sunt numero: scribuntur autem quaeque per xv, nouissima littera copulate primae. Et ideo quaedam quidem secundum subsequentiam scribunt, sicuti et nos, quaedam autem retrorsum a dextera parte in sinistram retorquentes litteras. As we have it, the text states that Hebrew has ten letters, each written “through fifteen, the more recent letters joined with the first.” The text also seems to appeal to the direction of writing, from right to left. The earlier part of 2.24.2 deals with two numerical practices regarding names: the number of letters in a word, and its psephic value. Irenaeus dispenses with the first notion by highlighting the peculiar way (he says) letters are counted in Hebrew. This muddled and unparalleled explanation of the structure of the Hebrew alphabet must then refute Marcus’ claims by showing that his dependence upon Greek psephy has no logic in the Hebrew alphabet.

[ back ] 12. Treated passim in Irenaeus Against Heresies 1. See pp. 42–44 and 52 above.

[ back ] 13. See p. 45 above.

[ back ] 14. See p. 46 above.

[ back ] 15. See p. 46 above.

[ back ] 16. Recall Irenaeus’ analogy of the relationship between a clay model and the gold statue upon which it is made (2.15.2, discussed at p. 110 above). The two objects have different material causes, but share an identical form.

[ back ] 17. See pp. 30 and 80 above.

[ back ] 18. Marcus’ differentiation between numbers greater than and less than 100 resembles techniques in second-century dream interpretation, which treated 100 as an auspicious number and evaluated the names of things occurring in dreams accordingly. Artemidorus Dream Book 2.70, 3.34, says that numbers should be reduced to 100 to be suitable for interpretation, and that the number 100 is especially auspicious. But Artemidorus does not consider numbers less than 100 to be inherently unlucky.

[ back ] 19. Irenaeus’ list: infancy, childhood, youth, adulthood, and old age, is shorter than Solon’s (fragment 19 Diehl 1971) and Hippocrates’ (On Hebdomads 5) more famous model, of seven phases in human life. But cf. Theon of Smyrna Mathematics Useful for Reading Plato 98.13–14, which divides human life into four, a τετρακτύς.

[ back ] 20. Note how Irenaeus’ proofs move from the New Testament to the natural world to the Old Testament. This mirrors the order and sequence of the Valentinian exegesis Irenaeus presents in Book 1, where the New Testament proof texts for the Pleroma are at chaps. 1–3 and 8, natural world proofs are at chap. 17, and Old Testament proof texts at chap. 18. This is evidence both for the sequence of Irenaeus’ source and for the basic integrity of the authorship and sequence of Against Heresies 1.1–22.2, which may constitute Irenaeus’ first draft of Book 1. See Kalvesmaki 2007b.

[ back ] 21. Non quidem, sed cum magna sapientia et diligentia ad liquidum apta et ornata omnia a Deo facta sunt, et antiqua et quaecumque in novissimis temporibus Verbum eius operatum est. Et debent ea, non numero xxx, sed subiacenti copulare argumento sive rationi, neque de Deo inquisitionem ex numeris et syllabis et litteris accipere—infirmum est enim hoc propter multifarium et varium eorum, et quod possit omne argumentum hodieque commentatum ab aliquo contraria veritati ex ipsis sumere testimonia, eo quod in multa transferri possint—sed ipsos numeros et ea quae facta sunt aptare debent subiacenti veritatis argumento. Non enim regula ex numeris, sed numeri ex regula, neque Deus ex factis, sed ea quae facta sunt ex Deo: omnia enim ex uno et eodem Deo.” Rousseau et al.’s reconstruction of the Greek (1965–1982), with my own conjectures in angle brackets: Οὐ μὴν ἀλλὰ μετὰ μεγάλης σοφίας καὶ ἀκριβείας εὔρυθμα καὶ ἐγκατάσκευα πάντα ὑπό τοῦ Θεοῦ ἐγένετο, τά τε ἀρχαῖα καὶ τὰ ὅσα ἐν ἐσχάτοις καιροῖς ὁ Λόγος αὐτοῦ ἔπραξεν· ὀφείλουσι δὲ αὐτὰ μὴ τῷ ἀριθμῷ τῶν τριάκοντα <τῷ τριακοντάδι?>, ἀλλὰ τῇ ὑποκειμένῃ συνάπτειν <συνεικειοῦν?> ὑποθέσει τῆς ἀληθείας, μηδὲ περὶ τοῦ θεοῦ ζήτησιν ἐξ ἀριθμῶν καὶ συλλαβῶν καὶ γραμμάτων ἀναδέχεσθαι—ἀσθενὲς γὰρ τοῦτο διὰ τὸ πολυμερὲς καὶ πολυποίκιλον αὐτῶν καὶ τὸ δύνασθαι πᾶσαν ὑπόθεσιν καὶ σήμερον παρεπινοουμένην ὑπό τινος ἀναλήθεις ἐξ αὐτῶν λαμβάνειν μαρτυρίας ἅτε εἰς πολλὰ μεθαρμόζεσθαι δυναμένων—ἀλλ ᾽ αὐτοὺς τοὺς αριθμοὺς καὶ τὰ γεγονότα ἐφαρμόζειν ὀφείλουσι τῇ ὑποκειμένῇ τῆς ἀληθείας ὑποθέσει. Οὐ γὰρ ὑπόθεσις ἐξ ἀριθμῶν, ἀλλ ᾽ ἀριθμοὶ ἐξ ὑποθέσεως, οὐδὲ Θεὸς ἐκ γεγονότων, ἀλλὰ γεγονότα ἐκ Θεοῦ· πάντα γὰρ ἐξ ἑνὸς καὶ τοῦ αὐτοῦ Θεοῦ. For my first conjecture, see, where xxx numerus is a duplicated translation of ἡ Τριακοντάς. There is no “number of the thirty” in Valentinian theology, but rather a Triacontad, within which are many numbers. On my second conjecture, see The sexual connotation of copulare, alluding to the Valentinian syzygies, suggests a word stronger than συνάπτειν. What I translate as “narrative,” ὑπόθεσις, can equally well be translated “plot,” “argument,” or “doctrinal system.” Irenaeus uses the same word frequently at 1.9.4 to describe the narrative structures of the Iliad and Odyssey, and to this discussion he no doubt alludes here, at 2.25.1. See Rousseau et al. 1965–1982:1.296–299.

[ back ] 22. The extended argument is at Against Heresies 2.15–16.

[ back ] 23. Against Heresies 1.9.2: Τοῦ γὰρ Ἰωάννου ἕνα Θεὸν παντοκράτορα καὶ ἕνα Μονογενῆ Χριστὸν Ἰησοῦν κηρύσσοντος. Cf. Proof of the Apostolic Preaching 5.

[ back ] 24. See e.g. Against Heresies 2.1.1, 2.11.1, 2.16.3, 4.38.3.

[ back ] 25. Irenaeus uses this early credal practice against the Valentinians, who “confess with the tongue one God the Father,” Creator of all things (4.33.3) and “one Lord Jesus Christ, the Son of God,” yet they split up Christ into assorted entities. Thus, according to Irenaeus, when at church they profess faith in the unity of God and his Son they pay mere lip service. Easter creeds through the fourth century tend to follow Irenaeus. See Kelly 1950:167–204, esp. 195.

[ back ] 26. See Theophilus of Antioch To Autolycus 2.15, dated to just after 180. On Irenaeus’ Trinitarian theology, see below and, e.g., Against Heresies 4.38.3; Proof of the Apostolic Preaching 4–8.

[ back ] 27. Irenaeus Proof of the Apostolic Preaching 9.

[ back ] 28. Joshua 2, Joshua 6; Irenaeus Against Heresies 4.20.12. Joshua 2 (MT and LXX) mention only two spies. Joshua 6.5 (LXX) speaks of only one trumpet, whereas Irenaeus speaks of seven (and he calls them “final”: 1 Corinthians 15.52). Irenaeus seems to take the trumpets at Jericho to foreshadow the end-times trumpets of Revelation 8.2, 6.

[ back ] 29. Judges 6.27 (LXX Vat., not Alex.); Irenaeus, fragment 18 (Harvey). The syntax of much of this passage is unintelligible, despite its attestation in three manuscripts.

[ back ] 30. Theology of Arithmetic, s.v.

[ back ] 31. Along with Irenaeus’ testimony, several New Testament fragments confirm this variant reading. See Nestle et al. 2004, s.v. Rev. 13.18.

[ back ] 32. Or a copyist may have inserted this comment, Harvey’s suspicion (1857: s.v.).

[ back ] 33. See Rousseau et al. 1965–1982:1.331–333.

[ back ] 34. At Against Heresies 2.27.1–2.28.2–3, Irenaeus says that the more veiled, opaque passages of Scripture should not be used to decipher parables. The passages that are clearest should be the interpretive key for the more obscure. That there are Scriptures we don’t understand is to be expected. After all, we do not understand many things in the natural world.

[ back ] 35. Cf. an Armenian abridgement, fragment 6 at Ter Mĕkĕrttschian and Wilson 1919:737. Irenaeus’ is the first attested argument for the four canonical Gospels, but we should not infer from this that it is his invention. Irenaeus regularly reproduces, even verbatim, the thought of his predecessors without attribution. See Hill 2006.

[ back ] 36. Cf. Theology of Arithmetic 24.10, 29.15.

[ back ] 37. Πνεῦμα ζωῆς. The pun and intent in relating the Scripture to world geography is better seen by translating the phrase “wind of life.”

[ back ] 38. For the larger patristic tradition see Stevenson 2001.

[ back ] 39. τετάρτη δὲ ἡ ἀνακαινίζουσα τὸν ἄνθρωπον καὶ ἀνακεφαλαιοῦσα τὰ πάντα εἰς ἑαυτήν, ἡ διὰ τοῦ εὐαγγελίου ἀνιστάσα καὶ ἀναπτεροῦσα τοὺς ἀνθρώπους εἰς τὴν οὐράνιον βασιλείαν.

[ back ] 40. Cf. Perkins 1992:279.

[ back ] 41. John 1.3 and, e.g., 1 Thessalonians 2.13.

[ back ] 42. See e.g. Aelius Herodianus (fl. second c. CE), Περὶ ἀριθμῶν (TLG no. 87.42).

[ back ] 43. Save for a rare early example—a coin from the reign of Alexander Jannaeus (103–76 BCE)—Hebrew alphabetic numerals are known to have been widely used only after 66 CE; Lieberman 1987:193–198.