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
In ancient Judaism and Christianity, the fascination with numbers and number symbolism was widespread. Just think of the 12 tribes and 12 apostles, Enoch’s 365 years on earth, and 40-day periods of fasting or mourning. In such patterns, Jews and Christians shared a common vocabulary with all ancient societies, which used numbers to adorn their lore, order their calendars, and frame their cosmology. In the second century, a variety of new Christian movements—among the most prominent one called the Valentinians—developed systems of number symbolism that went well beyond what is found in Scripture and early Jewish and Christian lore, both in meaning and intensity. These Christians described God and interpreted the Bible through the lens of arithmetic. To them God was a ‘unit’ or ‘monad,’ who had self-erupted into a harmonic multiplicity of ‘aeons’ or ‘emanations,’ from there showering down upon all levels of reality, both material and immaterial worlds, an arithmeti-cal structure rooted in the divinity. Scriptural verses were used to justify and explain this theology of arithmetic, and the Bible was treated as a repository of numbers, a cache of proof texts that could be understood only in the light of secret revelation.
The principal impetus for this theology of arithmetic was the Platonic and Pythagorean literary tradition, in which numbers were a driving force of metaphysics, symbolism, and interpretation. Philosophers in the century Jesus lived in argued over the number of principles in the universe, and intellectuals such as Plutarch used numbers and their symbolic meanings to interpret religious myths and to frame the natural world. Platonist and Pythagorean number symbolism provided a credible framework for some second- and third-century Christians to build their new theologies. They continued from neo-Pythagorean deliberations—Do things start with a monad or a dyad? If the latter, what kind?—and put forward a conflicting variety of philosophical myths, intellectual archways erected seemingly ad hoc, both to straddle and to intrude upon the structures of Middle Platonism (today so called) and Christianity.
The ecclesiastical dispute that emerged over the appropriate role of numbers was brief but intense. The Valentinians were fiercely opposed by orthodox apolo-gists such as Irenaeus, a second-century bishop of Lyons whose major work, Against Heresies, is one of the most important sources for this dispute. Irenaeus directly tackled the Valentinians’ use of numbers, and argued that numbers should be subservient to the tradition handed down by the apostles, not vice versa. His argument against the Valentinians was echoed by other Christians at the time, and so Irenaeus’ argument and tone articulately express opposition to Valentinian theology across the Mediterranean. But that reaction belies the widespread use of number symbolism by orthodox Christians. The orthodox culture of number symbolism can be seen in the writings of Irenaeus, and especially of his near contemporary Clement of Alexandria, who opposed the Valentinians for similar reasons, but who was inclined to correct by example, to counter Valentinian errors tacitly. Irenaeus and Clement of Alexandria typified the number symbolism that was to circulate in the Church for centuries, without controversy, into the medieval period.
The second-century Christian debate over numbers eventually influenced the very tradition that inspired it. Platonist philosophy after Plotinus increasingly depended upon a number symbolism that took on the colors painted by early Christians. And in the fourth century, Theodore of Asine was to some fellow Platonists as much a heretic in his number symbolism as the Valentinians were to other Christians. Iamblichus was the Platonists’ Irenaeus and Clement at once, articulating principles for a reasoned use of number symbolism. Although the influence of Christian theology upon the Platonists is not explicitly discussed in our sources, I believe that it is evident in the parallels. Christians were the first to expand the imaginative metaphysical possibilities of number symbolism and the first to engage in a critical discussion about what transgressed their tradition. Both of these Christian trends expanded the cultural horizons of the Mediterranean, and cleared the way for analogous Platonist developments.
That, in outline form, is the argument I advance in this book, written for anyone interested in intellectual history in late antiquity. An astute reader may wonder where Judaism fits into this story. After a substantive look at Philo (chapter 2) and glancing looks at Aristobulus and Hermippus (chapter 7), I say little more about Jewish authors for whom numbers were important, for two reasons. First, the story I tell centers on the role of numbers in the philosophical–theological tradition, particularly metaphysics. That tradition is not attested in the non-Christian Jewish sources that can be reliably dated to the second to fourth centuries. Second, the practice of psephy (see below), discussed so frequently in this book, was developed in Hebrew and Aramaic literature only after it had matured in Greek. That is, Jewish gematria is largely dependent upon, not the cause of, the gematria discussed in this study. This may seem counterintuitive to many readers, especially those who would think the Bible is the source of gematria. It is not. To explain my rationale adequately requires a separate, cultural history of psephic practices and habits, which is in preparation.
Some of my terminology needs a brief explanation. For instance, I tend to avoid the term ‘gnostic,’ which has been greatly abused over the last century. The term as we use it today, as scholars have increasingly recognized, is a modern invention, and does not adequately describe the fractious and polymorphic religious landscape evident in both Irenaeus’ Against Heresies and the Nag Hammadi library.  Hence I avoid the label altogether, except when the sources warrant (for instance, when Irenaeus or Clement of Alexandria use it; but even there it describes a specific group, not all the heresies). But I do use the relatively vague term ‘gnosticizing,’ not to separate groups, but to describe behaviors, as explained in the context of my discussion.
It may seem that by focusing first on Christian groups classified today as gnostic (chapters 3–5), and by setting them in opposition to Irenaeus and his followers (chapters 6 and 7), I uncritically adopt Irenaeus’ distinctions between heretical and orthodox and between gnostic and orthodox. This judgment would be hasty. The opposition between Irenaeus and these various groups is not my premise but my thesis. I argue, not assume, that the two have conflicting views of the role of numbers. The point should become apparent in my account of the differences. Furthermore, this book is not about every second-century Christian group considered deviant. A number of heresies popularly labeled ‘gnostic’ fail to bear consideration, since not all systems of gnosis had an interest in number symbolism. Prominently missing from consideration are Simon Magus, Marcion, Basilides, and “Sethian” texts. This is not to say that they do not use numbers as symbols or literary devices (they do, sometimes profusely), but they do not show a propensity to mathematical theology.
I use the term ‘orthodox’ provisionally, as do most scholars of late antique Christianity who wisely wish to avoid declaring which party was in the right. But despite the good reasons for qualifying the term, ‘orthodox’ can be used justifiably in this study. The Valentinians and the like-minded used novel ideas to advance provocative theses; their opponents, who came from disparate parts of the Roman Empire, sought to articulate principles that were as old and as widespread as the Church. Valentinians cherished private, elite audiences; Irenaeus, Clement, Tertullian, and Hippolytus appealed to the Church at large. So I use ‘orthodox’ of men who appealed to a common, lived experience of the Church—that is, churches that identified themselves with the other churches scattered about the Mediterranean—but I do not mean to comment on how justifiable that claim was.
To describe Valentinian systems I have used ‘protology’ (and derivatives).  The term is helpful because it points to the arithmetical character of Valentinian theories of how everything started from a πρῶτος, a unitary principle. That nuance is missing in synonyms such as ‘metaphysics,’ ‘philosophy,’ and ‘theology.’ But ‘protology’ can be misleading, since it implies that the Valentinians were doing something wholly separate from that which occupied their orthodox counterparts, whose ruminations on the relationship between the Father and the Son we would more comfortably call ‘theology,’ not ‘protology.’ In reality, both groups were vying for the same conceptual space, trying to present a plausible account of what constitutes the highest order of the universe. Therefore I use ‘protology’ only when it refers to the emergence of multitude from the original πρῶτος (or δεύτερος, as we shall see).
I also distinguish in this study between ‘arithmetic’ and ‘mathematics.’ The former, the study of the properties and operations of discrete numbers (e.g. addition and multiplication), is a proper subset of the latter, which is the study of all the numerical sciences. Mathematics comprises arithmetic, geometry, music, and astronomy—the ancient foursome known in Greek as the τέσσαρες μεθόδοι and later in Latin (via Boethius) as the quadrivium. Thus, in antiquity, references to mathematicians (such as in Sextus Empiricus’ Against the Mathematicians) signify those who handle any of the numerical sciences (and who use these sciences to investigate the world), not merely those skilled in computation. This classical distinction between the two words was current in English as late as the eighteenth century. The conceptual overhaul of the sciences in the age of Newton led to our present usage, where ‘arithmetic’ and ‘mathematics’ are often interchangeable. For aspects of this study, however, the ancient distinction is helpful, especially since we often encounter the term μαθήματα, which always implies more than our modern term ‘mathematics’ does.
I use the term ‘numerology’ only of number symbolism intended either to reveal or to keep concealed occult knowledge. Think of it as a correlate to ‘astrology,’ which has similar connotations that distinguish it from ‘astronomy.’ All ancient numerology is number symbolism, but only a part of ancient number symbolism is numerology. Some ancient authors would object, were they to learn that their number symbolism was today conflated with activities such as predicting the outcome of a marriage or determining the date of a person’s death based on the numerical value of his name. Thus I generally prefer the neutral term ‘number symbolism’ unless prognostication is at work, in which case ‘numerology’ is accurate. As a synonym for ‘number symbolism’ Delatte (1915) introduced the term ‘arithmology,’ which he found in the title of a Greek text preserved in an eighteenth-century manuscript. His neologism is anachronistic. In the Athens manuscript he consulted (Bibl. Nat. 65), ἀριθμολογία, a hapax legomenon, describes a late or post-Byzantine collection of numbered lists, and the text has no overt number symbolism. But ‘arithmology’ breaks up the monotony of ‘number symbolism,’ and it has made its way into our vocabulary, so I use it occasionally as a synonym.
I use ‘psephy,’ ‘psephic,’ and ‘isopsephy’ (all derived from ψῆφος ‘pebble’ or ‘vote’) to describe the ancient habit of reckoning the numerical value of names and words based on the arithmetical values of their constituent letters. This is more commonly known in English as ‘gematria,’ but the Hebrew term that this word comes from was not coined until probably the sixth or seventh century. For the cultural and chronological scope of this study, the first three terms are more appropriate.
In general, references to the Hebrew Scriptures follow the Septuagint, ex-plicitly marked when a difference in content (not just chapter and verse numera-tion) is salient. Uncredited translations are my own.
This is the first in-depth exploration of early Christian number symbolism. Certainly, there have been dozens of studies about the individual texts and ideas I discuss, and I signal many of these in the notes and bibliography. But no one, to my knowledge, has tried to describe and explain as a whole the late antique Christian and Platonist debates over number symbolism. Although this is the first word, I hope it is not the last. There is much work to be done on this topic. I have not, for instance, analyzed number symbolism in the Barbeliotes, the Peratae, the Apocryphon of John, the so-called Ophites, the Books of Jeu, the untitled text from the Bruce codex, or Pistis Sophia. Closer to orthodox circles are the Shepherd of Hermas, the Sybilline Oracles, and various apocalyptic texts, which frequently indulge in number symbolism. And the later Christian tradition of number symbolism is rich and understudied. On the Platonist and Pythagorean side, number symbolism is abundant in numerous texts, including the Nag Hammadi treatise Marsanes; the numerous commentaries on Plato from late antiquity; and the namesake of my book, the Theology of Arithmetic, a bestiary-like collection of numerical lore dating from late antiquity and before. I hope my study stimulates others to explore ancient number symbolism further.
[ back ] 1. For more on the artifice of the term see M. Williams 1996.
[ back ] 2. Orbe 1976:484n198, reinforced throughout in Thomassen 2006.