Bryn Mawr Classical Review

BMCR 2014.01.21 on the BMCR blog

Bryn Mawr Classical Review 2014.01.21

Joel Kalvesmaki, The Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity. Hellenic studies, 59.   Washington, DC:  Center for Hellenic Studies, Trustees for Harvard University, 2013.  Pp. vi, 231.  ISBN 9780674073302.  $22.95 (pb).  

Reviewed by Dirk Baltzly, University of Tasmania (

This short paperback investigates parallels in the treatment of number symbolism between Neo-Pythagorean writers and Christian gnostics. It returns to pagan Platonists in a final chapter on Theodore of Asine and Iamblichus. If you have struggled to see how the number and structure of Aeons in Valentinian theology is anything other than arbitrary, this book is for you. If you didn’t understand the previous sentence, it is not. This book is for specialists and presupposes a good grasp of theology and philosophy in the first to fourth centuries CE.

The central thesis of Kalvesmaki’s book is summarised with admirable clarity on the first two pages of the first chapter. Arithmology in the second- and third-century gnostic theologies found its impetus in the Platonic and Pythagorean literary tradition. Kalvesmaki locates the apogee of Christian numerology in the Valentinian Marcus “Magus”. These developments within Christianity came under attack by writers such as Irenaeus and Clement, who sought to establish the orthodox limits of number symbolism in theology and scriptural interpretation. In the concluding chapter, Kalvesmaki considers Iamblichus’ criticism of the metaphysics and Platonic interpretations advanced by Theodore of Asine. He argues that Iamblichus stands to the Neoplatonic tradition as Clement stands to Christian gnosticism. Each is the defender of a more conservative approach to number symbolism.

Terminology in these inquiries matters. Kalvesmaki’s most general term is ‘number symbolism’ which he uses interchangeably with ‘arithmology’ (though he notes that the latter term is of late- or post-Byzantine origin). He reserves the term ‘numerology’ for that branch of number symbolism that attempts to foretell the future (p. 4). Another specific branch of number symbolism is ‘psephy’ (sometimes called ‘gematria’ in the Hebrew context). This is the practice of drawing inferences on the basis of the use of letters to represent numbers in both Greek and Hebrew. Thus Kalvesmaki notes the passage in Barnabus Epistle 9.7-9 where the fact that Abraham had 318 servants (Gen. 14.14) was thought to foreshadow the crucifixion of Jesus on the basis of the manner in which the number would be written in Greek: τιή. (Equating the τ with the cross and ιη with Jesus.) On Kalvesmaki’s use of the word, this is number symbolism or arithmology.

Recent scholarship on Pythagoreanism, however, has sought to impose tighter parameters on arithmology. Thus Zhmud reserves the latter term for the more narrow category that draws parallels between concepts and numbers in ways that rely on the properties of the decad or the first ten numbers.1 So in the Theology of Arithmetic we find the identification of the number seven with Athena on the grounds that she is both born from Zeus and has no children (just as seven has no factor among the first ten numbers save 1 and is itself not a factor for any of the numbers in the decad). Kalvesmaki’s notion of number symbolism is wider and must be learnt from examples. Readers may well wonder whether his concept is not just a bit too capacious so that historical precision is sacrificed. Clearly Neopythagoreans, Valentinians and Neoplatonists took numbers to symbolise things. They also used the idea of the generation of numbers from the unit as an analogy for the emanation of all things from the One. Throughout the book I found myself a little concerned that the identification of parallels between these groups sometimes depended a bit too much on the vagueness associated with the idea of number symbolism or arithmology. It is, however, a very good start to sorting out these issues and Kalvesmaki’s exegesis of passages from individual authors is clear and illuminating.

After a brief introduction, Chapter 2 sets the context for the discussion of gnostic number symbolism by looking at Neopythagoreanism. Kalvesmaki concentrates on Eudorus and argues that a close reading shows that there were both monistic and dualistic version of Pythagorean metaphysics circulating in the first century CE. By dualistic, he means systems that accord the indefinite dyad or some other source of plurality an existence that is independent of the source of unity. A monistic version of Pythagoreanism, by contrast, treats all things – including the source of plurality – as products of a single first principle. The monistic metaphysics, he concludes, combined with widespread interest in number symbolism, provided the foundation for early Christian arithmology.

Chapter 3 charts the rise of the early Christian theology of arithmetic and focuses on Valentiniansim. Kalvesmaki does a good job of showing the numerical patterns that structure the various Valentinian systems of Aeons. The most complex of these is the Triacontad which consists of a basic eight Aeons (the Ogdoad), an additional ten (the Decad), and then twelve more (the Dodecad). This system of Aeons – the Pleroma – is held together by a Limit that is hexagonal and thus associated with the number six. Each of these groups consist of pairs, one male and one female. The males correspond to odd numbers, the female to even ones. In this respect the gnostic system resembles the Pythagorean assignment of oddness to male and evenness to female (p. 50). The system encodes the key proportions discussed by Neopythagoreans. The Ogdoad, Decad, Dodecad is an arithmetic proportion, while the hexagonal Limit, together with the Ogdoad and Decad forms a harmonic proportion. Kalvesmaki does not explain how the authors of the Valentinian systems might have been acquainted with Neopythagorean ideas. Presumably too little is known of these people to hazard any guesses. Rather, Kalvesmaki stresses that the gnostic number symbolism would have given gnostic ideas a properly intellectual or philosophical air.

Chapter 4 pursues this project further with specific reference to the number symbolism found in Irenaeus’ account of the Valentinian Marcus. This takes us into the obscure realms of psephy. To take but one of the examples discussed by Kalvesmaki, in the contemporary conventions for writing numerals, the letters in the name Ἰησοῦς correspond to the following numbers: 10 + 8 + 200 +70 + 400 + 200. This sums to 888 and, according to Marcus, thus illustrates the interplay of the Ogdoad and the Decad. This takes us far, far beyond the number symbolism that we find in Neopythagoreanism, as Kalvesmaki acknowledges.

Chapter 5 considers alternatives to the Valentinian theology of arithmetic in the form of two other heresies discussed by Hippolytus: Monoïmus and the Paraphrase of Apophasis Megale. Kalvesmaki argues that these two arithmological traditions are independent of one another and of Valentinianism. They are linked, according to Kalvesmaki, in being ‘inspired by’ Neopythagorean and Platonist ideas and propounded in order ‘to provoke and persuade both churchmen and the cultural elite of a transcendent vision’ (p. 102). To my mind the most convincing evidence for a connection to Pythagoreanism in this chapter involves the Monoïmus’ attempt to account for the origins of the Platonic solids in his account. In other respects, it seems to me that – as with Marcus – we are a long way from the kind of material found in the Neopythagorean associations with the decad preserved in Theology of Arithmetic.

Chapter 6 turns to the defenders of (what turned out to be) Christian orthodoxy. Kalvesmaki reads Irenaeus’ attack on Valentinianism in On Heresies both for what it says about the alleged mistakes of this gnostic theology of arithmetic, but also for what Irenaeus regards as the proper limits of number symbolism in the interpretation of the scriptures. Irenaeus thinks that the Valentinians go wrong by beginning from relations among numbers and then reading scripture in light of this. It should be the other way round. This is not to say that the ‘Bible first’ principle always leads to sober and modest results. Since a thousand years are as a day to the Lord (2 Peter 3:8) and since it took six days for the Lord to create the world, the world will come to an end after six millennia (p. 118, citing Irenaeus 5.28.3). In fact, Kalvesmaki argues that Irenaeus is inconsistent: he himself makes use of the very exegetical principles that he criticises in the Valentinians.

Chapter 7 concerns the other defender of orthodoxy: Clement of Alexandria. Kalvesmaki argues that Clement differs from Irenaeus in at least two respects. First, his criticisms of Valentinian number theology and hermeneutics are more subtle, for he wishes to co-opt heretical number symbolism for orthodox ends. Second, he does not confine his attention to Christian gnostics but engages with Platonist and Stoic ideas as well in order to show that Christian theology surpasses even the best of the previous pagan philosophers. Clement sometimes uses number symbolism in this latter task, as when he argues for an expansion of the Stoic’ parts of the soul from eight (hegemonikon, five senses, voice, and the reproductive power) to a more numerologically satisfying ten (by the inclusion of the formed spirit and the mark of the Holy Spirit).

Chapter 8 concludes the book with a sequel to the dialectic between Christian gnostic number symbolism and the defenders of what turned out to be Christian orthodoxy. Kalvesmaki notes that the dispute about number symbolism within Christianity mostly went quiet after the late second century. Gnostic writings that evince a fascination with number symbolism continued on into the fourth century, but subsequent defenders of orthodoxy do not rival Irenaeus or Clement. However from the late second through the early fourth century a parallel debate took place within Platonism: ‘speculative number symbolism, controversy, an attempt to articulate principles, and out of that a sense of what was acceptable in the Platonist tradition’ (p. 152). The principal players here are the little-known Theodore of Asine and Iamblichus. Kalvesmaki provides a lengthy exegesis of the cryptic testimonia about Theodore in Proclus’ Timaeus Commentary before turning to the criticisms preserved from Iamblichus’ essay Against the circle of Amelius found in the same source.

There are two appendices with the Greek text of passages that Kalvesmaki treats in details, a bibliography, and an index. ​


1.   L. Zhmud, Pythagoras and the Early Pythagoreans, Oxford: OUP, 2012.

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