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It is unclear what Philolaus had in mind with his limiters and unlimiteds: some suggest limiters are atoms, unlimiteds void, in a parallel to atomic theory; others take them as Aristotelian form and matter, respectively; or limiters could be odd numbers, and unlimiteds even numbers.<fnref n="121" /> Perhaps they might be said to correspond to letters and numbers, and drawing a parallel we would think of letters as related to form, conveying meaning, while numbers would correspond to matter, ‘fleshing out’ the forms. Or maybe the distinction is the one between γράμματα and στοιχεῖα, letters and phonemes: letters, written, fixed, would be the limiters, while sounds, ungraspable, would be the unlimiteds. This is not unrelated to the famous passage about letters in *Philebus* (18b6ff.), where Plato seems to be drawing from Philolaus, and where the invention of letters out of the acoustic continuum by Theuth is an example of a science in which by ‘having number,’ that is, consisting of an ordered set of elements (στοιχεῖα, ‘members of a series’), ‘a subject matter can be learned and its elements applied to explain or manipulate the world.’<fnref n="122" />

Other fragments of Philolaus speak of the importance of the monad or the dyad, or number seven, but I shall retain the above selection for our purposes, and consider that in Philolaus we have had contact with the motherlode of ‘arithmetic’ Pythagoreanism. From here onwards I shall not dwell on the details of the transmission through the ‘early Academy and the later tradition of Platonism,’ as mentioned above by Huffman, but concentrate on particularly relevant examples, either because they deal with significant aspects of number theory or because they have been historically influential.

## ‘Pythagorean’ Milestones

In order to trace down the centuries the idea that the intelligibility of the world depends on number, or even that in some way number sustains, rules or constitutes the order of the universe as we know it, and if we are based on the current hypothesis that Philolaus is the earliest representative of such view, the task ahead is to establish, however tentatively, the transmission line, or lines, of this number cosmology.

Let us take as point of departure and at the same time as chart, an illustration from a twelfth-century copy of Boethius’ *Fundamentals of Music*,<fnref n="123" /> where appear depicted, as

<footnote n="121">121. See Graham, *Philolaus*, 52.</footnote>

<footnote n="122">122. More on this below, p. 138. See *ibid.*, 55; cf. also C. Sirat, ‘Les lettres hébraïques, leur existence idéale et matérielle,’ in *Perspectives on Jewish Thought and Mysticism*, ed. A. L. Ivry, A. Arkush, and E. Wolfson, dedicated to the memory of Alexander Altmann (Amsterdam: Harwood Academic Publishers, 1998), 240.</footnote>

<footnote n="123">123. Cambridge University Library Ms. Ii.3.12, fol. 61v.</footnote>
the great milestones in the study of music: Boethius and Pythagoras in the upper half,
and Plato and Nicomachus in the lower half.<fnref n="124" />

<figure><img src="image_10.png" /></figure>

The image captions read as follows:

1-BOETIUS. *Consul et eximiae scrutator philosophiae. Ut videat vocum discrimina per monochordum. Iudicat aure sonum percurrens indice nervum.*

Boethius. Companion and student of the excellent philosophy. In order to observe the
differences between sounds with the aid of the monochord, he slides his finger along
the string and tells the note by ear.

2- *Pythagoras physicus physiceque latentis amicus. Pondera discernit trutinans et dissona spernit. Pulsans aera probat quota quaeque proportion constat.*

Pythagoras, cosmologist and lover of hidden cosmology. He discerns the weights with the balance and discards the dissonant ones. By striking the bells he assesses the quantity and quality of the proportion.

3- *Edocet ipsorum summus Plato philosophorum quomodo disparium paritas sonat una sonorum.*

<footnote n="124">124. See Hicks, 'Pythagoras and Pythagoreanism,' 428.</footnote>
Plato, the greatest of philosophers themselves, is teaching in what way is achieved a consonance of disparate sounds.

4– *Obviat instanti ratione Nicomachus illi.*

Nicomachus confronts him with a pressing argument.

<figure><img src="image_11.png" /></figure>

The iconological analysis is not without interest,<fnref n="125" /> but I shall look at it primarily as a testimony to the association established, over a thousand years after Pythagoras' lifetime, between these figures of the history of philosophy, viewed here in their capacity of masters of music, a very Pythagorean concern and one of the branches of mathematics. In fact, the monochord played in the image by Boethius is one of the basic components of, and thus a direct link with, the earliest layers of Pythagorean legend— the Master himself is said to have discovered with its aid the numerical correspondences of musical intervals.<fnref n="126" />

The manuscript comes from Canterbury, which had associations with the School of Chartres just at the time when knowledge was being received from Byzantium and the doctrines of Plato's *Timaeus* were circulating in Calcidius' translation.<fnref n="127" /> The relation between Pythagoras and Plato, and in particular his *Timaeus*, 'the single most seminal philosophical text to emerge from the whole of antiquity,'<fnref n="128" /> has been mentioned above (p. 67).

Platonic Pythagorean arithmetic would be accrued in post-classical times with the doctrines and refinements of later Academics, including what we now call Middle and Neo-Platonists, to the point that one of them has been judged, with Plotinus and Iamblichus, to postulate a new layer of reality, a new kind of rarified 'number', for every difficulty encountered in the text of the *Timaeus*.<fnref n="129" /> Some have gone so far as to call the Middle Ages an age of 'New Pythagoreanism,' thereby prompting a further specification: it was not just any Pythagoreanism, but the 'mathematical Pythagoreanism' of Nicomachus which 'captured the medieval imagination'.<fnref n="130" /> Indeed,

<footnote n="125">125. See A. Katzenellenbogen, 'The Representation of the Seven Liberal Arts,' in *Twelfth-Century Europe and the Foundations of Modern Society*, ed. M. Clagett (Madison: The University of Wisconsin Press, 1966), 46, and D. Knipp, 'Medieval Visual Images of Plato,' in *The Platonic Tradition in the Middle Ages. A Doxographic Approach*, ed. S. Gersh and M. J. Hoenen (Walter de Gruyter, 2002), 376.</footnote>

<footnote n="126">126. See especially Burkert, *L & S*, 369ff.; also Huffman, *Archytas*, 48.</footnote>

<footnote n="127">127. See E. Poleg and L. Light, eds, *Form and Function in the Late Medieval Bible*, Library of the Written Word—The Manuscript World (Leiden: Brill, 2013), 34.</footnote>

<footnote n="128">128. D. Sedley, 'Hesiod's *Theogony* and Plato's *Timaeus*,' in *Plato and Hesiod*, ed. G. Boys-Stones and J. Haubold (Oxford University Press, 2010), 246.</footnote>

<footnote n="129">129. S. Slaveva-Griffin, 'Number in the Metaphysical Landscape,' in *The Routledge Handbook of Neoplatonism*, by P. Remes and S. Slaveva-Griffin (Routledge, 2014), 209.</footnote>

<footnote n="130">130. See Hicks, *'Pythagoras and Pythagoreanism,'* 418.</footnote>
as we advance down the centuries, it is important to keep in mind that the medieval image of Pythagoras had little to do with the historical Pythagoras, and it was not a novel creation but a direct outcome of the late antique presentations of Pythagoras found in such authors as Boethius (drawing on Nicomachus), Calcidius and Macrobius.<fnref n="131" />

Similarly, the medieval Platonic tradition as a whole is much too complex to be described indiscriminately as either Platonism or Neoplatonism, and ‘often behind a Neoplatonic interpretation, or combined perhaps with an exegesis of Hellenistic provenance, a purely Platonic element is found.’<fnref n="132" /> In this landscape, the figure of Philo of Alexandria marks an important meeting point of traditions: Platonic, Aristotelian, Hellenistic, Jewish, and sets a tendency to harmonisation of diverging schools which would have a wide and lasting impact.<fnref n="133" /> To complete the panorama, especially as I intend to study Semitic derivations, it should be noted that since Alexandrian times the word ‘Hermetic’ is used to refer not just to works associated with the name Hermes, but also to all manner of works with ‘Gnostic’, ‘Neoplatonic’, ‘Neopythagorean’, or ‘esoteric’ tendencies, and eventually practically any early Arabic pseudepigraph.<fnref n="134" />

And this conflation of schools and authors did not stop there. Even Aristotle, through the ascription of some Arabic translations to his name and other similar filtering,<fnref n="135" /> acquired eventually a rather Neoplatonic profile, which would make its way into Latin translations and convey a complex, if not outright baffling doctrinal variety.<fnref n="136" /> Witness to these developments are, for instance, pronouncements such as the first or second century BC Πλάτων πυθαγορίζει—Plato ‘pythagorises’,<fnref n="137" /> or Jerome’s famous ἢ Πλάτων φιλωνίζει, ἢ Φίλων πλατωνίζει, aut Plato Philonem sequitur, aut Platonem Philo, ‘either Plato is a Philonist or Philo is a Platonist.’<fnref n="138" /> The resemblance between Plato and Philo,

<footnote n="131">131. Huffman, *History*, 21.</footnote>

<footnote n="132">132. R. Klibansky, *The Continuity of the Platonic Tradition During the Middle Ages: Outlines of a Corpus Platonicum* Medii Aevi (London: Warburg Institute, 1939), 36.</footnote>

<footnote n="133">133. I shall have occasion to discuss his writings later. See N. S. Gara, ‘Die Rezeption der Philosophie des Aristoteles im Islam als Beispiel die Rezeption der Seelenlehre des Aristoteles bei Ibn Sīnās Buch (‘Ilm al-nafs: Die Wissenschaft der Seele’ (PhD diss., Seminar für Sprachen und Kulturen des Vorderen Orients, der Ruprecht-Karls-Universität Heidelberg, 2003), 167–8.</footnote>

<footnote n="134">134. See K. van Bladel, *The Arabic Hermes: From Pagan Sage to Prophet of Science*, Oxford Studies in Late Antiquity (New York: Oxford University Press, 2009), 19.</footnote>

<footnote n="135">135. See Klibansky, *The Continuity*, 40.</footnote>

<footnote n="136">136. See C. D’Ancona, ‘From Late Antiquity to the Arab Middle Ages: the commentaries and the »harmony between the philosophies of Plato and Aristotle«,’ in *Albertus Magnus und die Anfänge der Aristoteles-Rezeption im lateinischen Mittelalter*, ed. L. Honnefelder, Subsidia Albertina 1 (Münster: Aschendorff, 2005), 54; and also M. Stepaniants and J. Behuniak, *Introduction to Eastern Thought* (Walnut Creek, CA: AltaMira Press, 2002), 6.</footnote>

<footnote n="137">137. Aetius, II, 6, 6; Eusebius, *Prep*. 15, 37.</footnote>

<footnote n="138">138. De vir. ill. 11.</footnote>
both in contents and form, was so strong, that in a humorous anachronism Plato is
suggested to have followed an author born centuries after.

Nicomachus and his *Introduction*

Returning to the picture and as to Nicomachus' Pythagorean credentials, he authored a biography of Pythagoras which proved most influential through Porphyry and Iamblichus.<fnref n="139" /> His *Introduction to Arithmetic*, 'despite its poorness from a mathematical point of view, was the most influential work on arithmetic from the time it was written, sometime between the latter part of the first and the first part of the second centuries AD, until the sixteenth century. The treatise was translated into Latin by Apuleius [lost] and some centuries later by Boethius, and it is the ultimate source of the arithmetical treatises of Cassiodorus, Martianus Capella, and Isidorus of Seville.'<fnref n="140" />

This same *Introduction* was translated into Arabic twice<fnref n="141" /> and it not only provided Avicenna with some arithmetical knowledge for his *Metaphysics*,<fnref n="142" /> but seems to have exercised a powerful influence on later Jewish and Islamic developments. Some scholars have found traces of Nicomachus' *Introduction* in the *Rasā'il* of the Ikhwān al-Ṣafā and even possibly in the *Sefer Yetsirah*.<fnref n="143" /> Through these two major works, countless developments in Islamic and Jewish literature would carry the Pythagorean imprint, including key and long-lived Kabbalistic concepts. Furthermore, in 1317, Qalonymos b. Qalonymos produced a Hebrew translation from the Arabic which would circulate in Andalusia, exerting a non-negligible influence on Jewish thinkers from the fourteenth century onward.<fnref n="144" /> Recalling the previous chapter, the significance of Nicomachus in the field of arithmetic appears very similar to the one of Dionysius Thrax in grammatical tradition.

<footnote n="139">139. Burkert, *L & S*, 98–99. Iamblichus’ *Vita* is said to be ‘the textual locus where a clear relation between Orpheus, Pythagoras and Plato can be found,’ A. Motta, ‘Materia e forma dei miti. Su mimesi platonica e simbologia omerica,’ *Revista Estética e Semiótica* (Brasilia) 5, no. 2 (2015): 23.</footnote>

<footnote n="140">140. Asclepius of Tralles, *Commentary to Nicomachus' Introduction to Arithmetic*, ed. L. Tarán (Philadelphia: American Philosophical Society, 1969), 5.</footnote>

<footnote n="141">141. For details, see G. Freudenthal and M. Zonta, ‘Remnants of Ḥabīb Ibn Bahrīz’s Arabic Translation of Nicomachus of Gerasa’s *Introduction to Arithmetic*,’ in *Adaptations and Innovations: Studies on the Interaction between Jewish and Islamic Thought and Literature from the Early Middle Ages to the Late Twentieth Century*, dedicated to Prof. Joel L. Kraemer* (Louvain: Éditions Peeters, 2007), 67.</footnote>

<footnote n="142">142. D. Gutas, *Avicenna and the Aristotelian Tradition: Introduction to Reading Avicenna's Philosophical Works. Second, Revised and Enlarged Edition, including an Inventory of Avicenna's Authentic Works*, Islamic Philosophy, Theology and Science. Texts and Studies 89 (Leiden, Boston: Brill, 2014), 105, 171.</footnote>

<footnote n="143">143. See S. Wasserstrom, ‘Sefer Yesira and Early Islam: A Reappraisal,’ *Journal of Jewish Thought and Philosophy* 3, no. 1 (1994): 10. Thābit’s mathematical work was known to Sa‘adyā Gaon, the earliest extant commentator of *Sefer Yetsirah*.</footnote>

<footnote n="144">144. Freudenthal and Zonta, *Remnants*, ' 69.</footnote>
Nicomachus’ *Introduction* Tables

To jump finally into the thick of this centuries-long ‘conversation’ outlined above,
whilst tracking in the original texts the course of the concept of the alphanumeric
element, I present in the following pages a Nicomachean *tetrapla* of sorts in seven
tables, comparing the Greek original,<fnref n="145" /> Arabic<fnref n="146" /> and English<fnref n="147" /> translations of it, and
Boethius’ related passages, which are in most cases not translations but elaborations of
the Greek material. I have also had occasion to consult some of the Hebrew manuscripts
of the Qalonymos Hebrew translation,<fnref n="148" /> and thus to have on sight the three languages
of medieval trilingual libraries<fnref n="149" /> facing the Arabic version which was so intimately and
decisively related to the Greek and the Hebrew.

My English translation is based on D'Ooge's translation from the Greek, with
frequent adjustments of key terms with a view to bringing out the literal import and
the possible connections of the text. I have added some highlighting to draw attention
to phrases or concepts which are commented upon after every table. The asterisks * in
the Arabic text indicate those readings judged dubious by Kutsch, whose diplomatic
spelling I have retained throughout, including the absence of hamzas and other such
details. The commentaries by Asclepios<fnref n="150" /> and Philoponus<fnref n="151" /> have been consulted too,
though I have found little in them of much relevance to the passages discussed.

<footnote n="145">145. Nicomachus of Gerasa, *Introduction Arithmétique*, ed. J. Bertier, Histoire des doctrines de l'Antiquité classique 2 (Paris: Vrin, 1978); Nicomachus of Gerasa, *Introductio arithmetica*, ed. R. Hoche (Leipzig: Teubner, 1866).</footnote>

<footnote n="146">146. Nicomachus of Gerasa, *Tābit b. Qurra's arabische Übersetzung der Arithmētikē eisagōgē des Nikomachos von Gerasa: Kitāb al-Madḥal ilā 'ilm al-'adad*, ed. W. Kutsch (Beyrut: Imprimérie Catholique, 1958).</footnote>

<footnote n="147">147. Nicomachus of Gerasa, *Introduction to Arithmetic*, trans. M. D'Ooge, with studies in Greek arithmetic by F. E. Robbins and L. C. Karpinsky (New York and London: Macmillan, 1926).</footnote>

<footnote n="148">148. BnF, Ms Hébreu 1093.</footnote>

<footnote n="149">149. E.g. Corpus Christi, Oxford, or the Collège des trois langues, Paris, or Alcalá de Henares.</footnote>

<footnote n="150">150. Asclepius of Tralles, *Commentary to Nicomachus' Introduction to Arithmetic*.</footnote>

<footnote n="151">151. John Philoponus, *Commentario alla Introduzione aritmetica di Nicomaco di Gerasa*, trans. Giovanna R. Giardina (Catania: CUECM, 1999).</footnote>
<table><caption>TABLE 1</caption><thead><tr><th>Nicomachus 1.1</th><th>Boethius 1.1</th></tr></thead><tbody><tr><td>ταῦτα ἄν εἶη τὰ ἄυλα καὶ ὧν κατὰ μετουσίαν ἔκαστον λοιπὸν τῶν ὁμωνύμως ὄντων καὶ καλουμένων τόδε τι λέγεται καὶ ἔστι. τὰ μὲν γὰρ σωματικὰ δήπου καὶ ὑλικὰ ἐν διηνεκεῖ ρύσει καὶ μεταβολῆ διὰ παντός ἐστι μιμούμενα τὴν τῆς ἐξ ἀρχῆς ἀιδίου ὑλῆς καὶ ὑποστάσεως φύσιν καὶ ἰδιότητα ὅλη γὰρ δι' ὅλης ἦν τρεπτὴ καὶ ἀλλοιωτή· τὰ δὲ περὶ αὐτὴν ἤ καὶ σὺν αὐτῇ θεωρούμενα ἀσώματα, οἰον ποιότητες, ποσότητες (...) πάντα ἀπλῶς, οἰς περιέχεται τὰ ἐν ἑκάστῳ σώματι, ὑπάρχει καθ' ἑαυτὰ ἀκίνητα καὶ ἀμετάπτωτα, συμβεβηκότως δὲ μετέχει καὶ παραπολαύει τῶν περὶ τὸ ὑποκείμενον σῶμα παθῶν.</td><td>These real things would be things immaterial, by sharing in the substance of which everything else that exists under the same name and is so called is said to be 'this particular thing', and exists. For bodily, material things are, to be sure, forever involved in continuous flow and change—in imitation of the nature and peculiar quality of that eternal matter and substance which has been from the beginning, and which was all changeable and variable throughout. The bodiless things, however, of which we conceive in connection with or together with matter, such as qualities, quantities [...] all those things, in a word, whereby the qualities found in each body are comprehended—all these are of themselves immovable and unchangeable, but accidentally they share in and partake of the affections of the body to which they belong.</td><td>Esse autem illa dicimus, quae nec intentione crescunt, nec retractione minuuntur, nec variationibus permutantur, sed in propria semper vi, suae se naturae subsidiis nixa custodiunt. Haec autem sunt qualitates, quantitates (...) et quidquid adunatum quodammodo corporibus invenitur. Quae ipsa quidem natura incorporea sunt, et immutabilis substantiae ratione vigentia, participatione vero corporis permutantur, et tactu variabilis rei, in vertibilem inconstantiam transseunt.</td></tr></tbody></table>
• One of the interests we had was about the precise relation between the divine ‘arch-types’ and the phenomena (see above, p. 49). As regards letters, the interpretations seem to be all rather tropological, ‘a simile, a metaphor’, until we come to the Kabbalistic authors, but for the Pythagoreans, as we have seen and see here, number is more ontological. The relation between the numbers in divinis—which in the Arabic are further described as ‘eternal and everlasting’—and phenomena is expressed by the term μετουσία, consubstantiation, which is a strong one, used by Christian theologians to express the participation in God through Christ, the λόγος. The Arabic gives mushārakah, a ‘partaking’, which is not so substantial etymologically, but which is actually used to speak of the Christian communion. Further down, we have μιμούμενα, ‘represented’, against Thābit’s tashabbahu, which bespeaks a comparison. Boethius, in his adaptation of the text, speaks of the incorporeal reality being adunatum quodammodo corporibus, ‘united somehow to the bodies.’

One of the commentaries has the following to add here, regarding the archetypal relation:

ἄσπερ οὖν ἡμεῖς πρὸς ταῦτα βλέποντες τὰ σκιαγραφήματα ποιοῦμεν τόδε
τι, οὕτω καὶ ὁ δημιουργὸς πρὸς ἐκεῖνον ἀποβλέπων κοσμεῖ τὰ τῆδε· ἀλλ’
ἰστέον ὅτι τὰ μὲν τῆδε σκιαγραφήματα ἀτελῆ εἰσιν, ἐκεῖνος δὲ ὁ λόγος
ἀρχέτυπος.

Just as when we look at blueprints<fnref n="152" /> and we make this or that, just so the Craftsman, by looking at that one [archetype] there, constructs what is here; but it should be known that our blueprints here below are imperfect, while that one over there is the arch-model analogy.<fnref n="153" />

Of course, ὁ λόγος ἀρχέτυπος could be also rendered as the ‘archetypal word’ or the ‘archetypal ratio’.

• Half way down the passage, the incorporeal realities are seen, θεωρούμενα, about and with the ever-totally-changing matter, just as the quality of a thing is seen about it or with it. Thus matter would participate in the ideas as a shirt participates in whiteness. This is also interesting because of the crucial but discreet role played by some prepositions (Ar. hurūf) in these contexts, and I shall keep an eye on them and their interpretation. The Arabic gives maʻahu. A prime example of this kind of metaphysically loaded prepositions is found in the Eucharistic doxology: *per ipsum, et cum ipso, et in ipso... omnis honor et gloria...*<fnref n="154" />

<footnote n="152">152. The word σκιαγράφημα means literally ‘painting with the shadows,’ a suitable description for the action of the *gnomon*.</footnote>

<footnote n="153">153. Asclepius of Tralles, *Commentary to Nicomachus’ Introduction to Arithmetic*, 1, 35.</footnote>

<footnote n="154">154. See H. Dörrie, ‘Präpositionen und Metaphysik: Wechselwirkung zweier Prinzipienreihen,’ *Museum*</footnote>
Finally there occur two more words for the same relation: μετέχει καὶ παραπολαύει. The first one is the more usual Greek root and it has its usual Arabic rendering in *sharika* again, but παραπολαύω means that the incorporeal ‘shares the fruits’ of the matter it qualifies. Thābit resorts to the root *qarana*, which has conjugal associations, while Boethius uses *tactu*.

Perhaps there is no inconsistency in terms, but a variation in points of view: what would appear from a coarser view as ‘comparison’ or ‘imitation’, might be seen as an essential participation from another subtler point of view. Thinking of *qarana*, notably the word used of planets ‘in conjunction’, how do we know if two persons (like a given phenomenon and its incorporeal principle) are married (μετουσία) or if it is just that they share some circumstances (*mushārakah*), or that we see one *with* and *about* the other?

• Another point of note in this passage is the use of the Ar. *ʿunṣur*, a customary translation of στοιχεῖον, which is used here in *al-ashyā’ al-jismāniyah al-ʿunṣuriyah* as a rendering of ὑλικά, and further down in *al-ṭabīʿat al-ʿunṣur* as a translation of τὴν ἐξ ἀρχῆς φύσιν.

<footnote>*Helveticum* 26, no. 4 (1969): 217–228. In Platonic studies this has been called a ‘prepositional metaphysics’, used to indicate nuances in causality in the Platonic corpus. Cf. D. T. Runia, *On the Creation of the Cosmos according to Moses*, Philo of Alexandria Commentary Series 1 (Leiden: Brill, 2001), 139.</footnote>
<table><caption>TABLE 2</caption><thead><tr><th>Nicomachus 1.2</th><th>Boethius 1.1</th></tr></thead><tbody><tr><td>ἐκεῖνα μὲν ἄυλα καὶ ἀίδια καὶ ἀτελεύτητα καὶ διὰ παντὸς ὅμοια καὶ ἀπαράλλακτα πέφυκε διατελεῖν, ὡσαύτως τῇ αὐτῶν οὐσίᾳ ἐπιδιαμένοντα, καὶ ἔκαστον αὐτῶν κυρίως ὄν λέγεται (...) λέγεται μὲν ὁμωνύμως ἐκείνοις ὄντα, καθ' ὅσον αὐτῶν μετέχει, ἔστι δὲ τῇ ἑαυτῶν φύσει οὐκ ὄντως ὄντα.</td><td>Those things are immaterial, eternal, without end, and it is in their nature to persist ever the same and unchanging, abiding by their own essential being, and each one of them is said to be in the proper sense (...) These [other] are also said to be, with the same name, insofar as they partake of them, but they do not really exist by their own nature.</td><td>Haec igitur (quoniam ut dictum est, natura immutabilem substantiam vimque sortita sunt) vere proprieque esse dicuntur.</td></tr></tbody></table>
• In this second passage we find again a characterisation of those incorporeal, eternal true entities, and yet another take on the relation between them and material entities: aside from the pair μετέχει- mushārakah, it is explained that material transitory things can be called ‘beings’ inasmuch as they partake of those eternal. The homonymy is conditional on the degree of participation.

• We can start to see here how the sectioning of Boethius’ work is far from following to the letter Nicomachus’ original. He sometimes merges several Greek sections into one Latin, sometimes he develops one point or other in a detail not found in the Greek. In spite of the occasional collating difficulties, it is possible in most cases to see the ‘threads’ of Nicomachus’ original discourse. The Arabic, by contrast, is close to the Greek, with occasional changes in the order of the words.
<table><caption>TABLE 3</caption><thead><tr><th>Nicomachus 1.3</th><th>Every diagram, system of numbers, every scheme of harmony, and every law of the movement of the stars ought to appear one to him who studies rightly; and what we say will properly appear if one studies all things looking to one principle, for there will be seen to be one bond for all these things [...] and if anyone attempts philosophy in any other way he must call on Fortune to assist him. For there is never a path without these; this is the way, these the studies, be they hard or easy; by this course must one go, and not neglect it (...) It is clear that these studies are like ladders and bridges that carry our minds from things apprehended by sense and opinion to those comprehended by the mind and understanding, and from those material, physical things, our foster-brethren known to us from childhood, to the things with which we are unacquainted, foreign to our senses, but in their immateriality and eternity more akin to our souls, and above to what is intellectual in them.</th><th>Boethius 1.1</th></tr></thead><tbody><tr><td>ἀπαν διάγραμμα ἀριθμοῦ τε σύστημα καὶ ἀρμονίας σύστασιν ἀπασαν τῆς τε τῶν ἄστρων φορᾶς τὴν ἀναλογίαν μίαν ἀναφανῆναι δεῖ τῷ κατὰ τρόπον μανθάνοντι, φανήσεται δ' ἀν ὅ λέγομεν ὀρθῶς, εἴ τις εἰς ἐν βλέπων πάντα μανθάνει· δεσμὸς γὰρ ἀπάντων τούτων εἶς ἀναφανήσεται [...] εἰ δέ τις ἄλλως μεταχειριεῖται φιλοσοφίαν, τύχην δεῖ καλεῖν συνεργόν· οὐ γὰρ ἄνευ τούτων ἡ ὁδός ποτε, ἀλλ' οὖτος ὁ τρόπος, ταῦτα τὰ μαθήματα εἴτε χαλεπὰ εἴτε ῥάδια, ταύτη ἰτέον, ἀμελεῖν δὲ οὐ δεῖ [...] δῆλον γάρ, ὅτι κλίμαξι τισι καὶ γεφύραις ἔοικε ταῦτα τὰ μαθήματα διαβιβάζοντα τὴν διάνοιαν ἡμῶν ἀπὸ τῶν αἰσθητῶν καὶ δοξαστῶν ἐπὶ τὰ νοητὰ καὶ ἐπιστημονικὰ καὶ ἀπὸ τῶν συντρόφων ἡμῖν καὶ ἐκ βρεφῶν ὄντων συνήθων ὑλικῶν καὶ σωματικῶν ἐπὶ τὰ ἀσυνήθη τε καὶ ἑτερόφυλα πρὸς τὰς αἰσθήσεις, τῇ δὲ ἀυλίᾳ καὶ ἀιδιότητι συγγενέστερα ταῖς ἡμετέραις ψυχαῖς καὶ πολὶ πρότερον τῷ ἐν αὐταῖς νοητικῷ.</td><td>كل جَدْوَل من جَدَاوَل جماعات العدد وجماعات التاليف فانه يجب ان مشاكلا لحركات الكواكب ضربا من المشكلة اذا تفهم الانسان وهذا شي يظهر للانسان ويتين ان هو فهم ما يقول فهما صحيحا فنظر في جميع هذه الاشيا نظرة الى شي واحد بعينه وذلك ان رباط جميع هذه الاشيا يرى رباطا واحدا [...] فان رای احده انہ یقدر ان یاخذ في علم الفلسفة من غیر هذه الجهة فینبغي ان یسله اسعاون * بذلك وليس ینبغي في وقت من الاوقات ان یسلکی غیر هذه السبیل لكن ینظر في العلوم التعليمية على هذه الجهة ان صعب ذلك وان سهل فيترك ویسلك هذه السبیل ولا یغفل عنها (...) فهو بین ان هذه العلوم التعليمية تشبه المعابر والدرج والجسور وذلك انها تنقل افهامنا وتصير بها من الاشيا المظنونة الى الاشيا المعقولة المعلومة ومن الاشيا التي هي ربايب لنا ونابتة معنا منذ الصبا مالوفة عندنا هيولانية جسمانية الى الاشيا الغير مالوفة والتَّي هي مباينة للحواس فاما الاشيا السرمدية التي ليست هيولانيت فهي شديدة المجانسة لانفسها والقرب منها ومجانستها للقوة العقلية التي هي في الانفس اقدم واسبق.</td><td>Sed hinc sumpsit sibi ipsa ratio, in quibus possit indagaticem veritatis exercere solertiam. Delegit enim de infinitae multitudinis pluralitate, finitae terminum quantitatis, et interminabilis magnitudinis sectione reiecta, definita sibi ad cognitionem spatia depoposcit [...] Constat igitur quisquis haec praeterniserit, omnem philosophiae perdidisse doctrinam. Hoc igitur illud quadrivium est, quo iis viandum sit, quibus excellenter animus a nobiscum procreatis sensibus, ad intelligentiae certiora perducitur. Sunt enim quidam gradus certaeque progressionum dimensiones, quibus ascendi progrediente possit.</td></tr></tbody></table>
• Having just quoted Archytas, Nicomachus starts this famous passage with a quotation from Plato's *Epinomis* (991d-e), which is the first clear mention of the quadruple way of study, here in particular a fourfold designation for a limited collection (*jamāʻah*) of fundamentals which reveal the unity of the cosmos, constitute the only right way to learn (οὖτος ὁ τρόπος, ταῦτα τὰ μαθήματα), and which are likened to stairs and bridges from the sensible to the immaterial. The four names are διάγραμμα, *jadwal*, a geometrical proposition, a paradigm or table; ἀριθμοῦ σύστημα (*jamāʻat al-ʻadad*), a numerical assemblage; ἀρμονίας σύστασις, a composition of harmony (*jamāʻat al-taʼlīf*), referring to music; and τῶν ἄστρων φορᾶς ἀναλογία, the collation of the movements of the heavenly bodies (*mushākalah harakāt al-kawākib*, a rather too literal ‘analogy of the movements of the heavenly bodies’). Thābit equated σύστασις with σύστημα, translating both as *jamāʻah*. His translation here may indicate a slightly different text from the Greek we have.

Notwithstanding the *Epinomis* citation, in a chapter entitled ‘The Origin of the Quadrivium’, Merlan observes and explains how ‘closely the quadrivium is connected with the interpretation of the *Timaeus*.’<fnref n="155" />

• These basic ‘diagrams’ are pontifical, as mentioned above: κλίμαξι καὶ γεφύραις, and Thābit has one more term, *al-maʻābir wa-al-daraj wa-al-jusūr*, ‘fords, a stairway and bridges’, *gradus certaeque progressionum dimensiones*. But they are not only the passageways: they also actively carry the rational mind across, διαβιβάζοντα τὴν διάνοιαν, *tanqulu afhāmanā*, *animus perducitur*, towards the intellective and the epistemic, τὰ νοητὰ καὶ ἐπιστημονικὰ, *ad intelligentiae certiora*.

• Boethius gives an adaptation of the passage, explaining that reason needed a determination of finite quantity through which it could seek the truth, and this is ‘the fourfold way’, his *quadrivium*, thus giving a unitary name to what in Nicomachus is simply a list of the four ways.

<footnote n="155">155. P. Merlan, *From Platonism to Neoplatonism*, 3rd ed., revised (The Hague: Martinus Nijhoff, 1975), 88ff.</footnote>
<table><caption>TABLE 4</caption><thead><tr><th>Nicomachus 1.4</th><th>Boethius 1.1</th></tr></thead><tbody><tr><td>基 άριθμητική (...) ἔφαμεν αὐτὴν ἐν τῇ τοῦ τεχνίτου θεοῦ δια- νοίᾳ προυποστῆναι τῶν ἄλλων ὡσανεὶ λόγον τινὰ κοσμικὸν καὶ παραδειγματικόν, πρὸς ὃν ἀπερειδόμενος ὁ τῶν ὅλων δη- μιουργὸς ὡς πρὸς προκέντημά τι καὶ ἀρχέτυπον παράδειγμα τὰ ἐκ τῆς ὕλης ἀποτελέσματα κοσμεῖ καὶ τοῦ οἰκείου τέλους τυγχάνειν ποιεῖ.</td><td>وهو صناعة علم العدد (...) انها سابقة في علم الله صانع الاشيا متقدمة للعلوم الباقية بمنزلة الشي الجميل الذي قياسه الى الاشيا الباقية قياس المثال فجعله مثالا لساير الاشيا التي خلق وحذوا عليها وعلى حسبه خلقها وسواها وزين ما خلقه من العنصر وبلغ به الامر الافضل الموافق في كل واحد من الاشيا.</td><td>Arithmetic (...) existed before all the others in the mind of the artisan God like some universal and exemplary plan [λόγος], relying upon which as a design and archetypal example the creator of the universe sets in order his material creations and makes them attain to their proper ends.</td><td>Haec autem est arithmetica. Haec enim cunctis prior est, non modo quod hanc ille huius mundanae molis conditor Deus, primam suae habuit ratiocinationis exemplar, et ad hanc cuncta constituit, quaecunque fabricante ratione, per numeros assignati ordinis invenere concordiam; sed hoc quoque prior arithmetica declaratur, quod quaecunque natura priora sunt, his sublatis simul posteriora tolluntur.</td></tr></tbody></table>
• In this cosmogonic passage, arithmetic is the divine pattern for creation, reminding us strongly of Philo's terms, and God is a craftsman or builder, τεχνίτης, ṣāni‘ al-ashyā’, *conditor*, and an artisan, δημιουργὸς, khāliq. The Arabic ‘ilm is in this context more sensitive than the English ‘mind’ to the range of meanings of διάνοια.

• The model is like a cosmic logos, a ‘word of order’, or ‘embellishment’, a notion picked up by Thābit lines below with emphasis on the aspect of beauty implicit in κοσμικός and κοσμέω: wa-‘alā ḥasabihi khalaqahā wa-sawāhā wa-zayyana mā khalaqahu min al-‘unṣur, ‘and what He made from the original raw material, He made and regulated and embellished according to it.’

• This logos is used by the creator as προκέντημα and ἀρχέτυπον παράδειγμα, mithāl and ḥadhw.156 Of these terms, two have very practical crafts associations: the rare Greek προκέντημα echoes immemorial methods used to transfer a design by pricking (κεντέω),157 while the Arabic ḥadhw, defined as taqdīr and qaṭf,158 a measuring and a ‘cut’ in the sense of a cutting pattern, has to do especially with shoe making, as in a pair of sandals (na'l), implying the mirroring pattern of the two complementary sides.159

• The other key Arabic term used for the comparison between the model and the world is qiyās, also with the basic meaning of ‘measuring’, and perhaps best rendered as an ‘analogical relation’. Qiyās means also the premises of a syllogism, or the syllogism itself. This would make the relation between the archetypal realities and the world a ‘logical’ relation, as if the world were an inference from the noetic realm.

• In this case, a detailed translation of Boethius’ Latin sheds some additional light on the main ideas:

Arithmetic is prior to all, not only because the builder God of the multiplex structure of the world had it as exemplar of his own ratiocination, and established by it all things which through the crafting apportioning through numbers came into the concord of the assigned order, but arithmetic is said to be first for this reason also, that whatever by nature are first, if they are removed, later things are also removed.

Masi<fnref n="160" /> and others tend to translate *ratio* as ‘logic’ or ‘reason’, but it is clear in most cases that the meaning verges towards mathematics. Here, D’Ooge’s ‘plan’ for λόγος

<footnote n="156">156. See direct references to this passage in the online *GALex* filecards *Nicom.Arithm.0725* and *Nicom.Arithm.0722*.</footnote>

<footnote n="157">157. Cf. the medieval ‘pricking of the quires,’ R. W. Clement, ‘Medieval and Renaissance book Production,’ *Library Faculty & Staff Publications* (Utah State University), no. 10 (1997): 10.</footnote>

<footnote n="158">158. Ibn Manẓūr, *Lisān al-‘arab* (Cairo: Dār al-Ma‘rif, 1981), 814b (hereafter cited as *Lisān*).</footnote>

<footnote n="159">159. The usage of ḥadhw for such an exalted term as the ‘archetypal paradigm’ casts a remarkable light on the veneration of the sandal pattern of the Prophet na‘l al-nabī so common through Islamic lands.</footnote>

<footnote n="160">160. Boethius, *Boethian Number Theory: A Translation of the De Institutione Arithmetica* (*with Introduction and Notes*), ed. M. Masi et al. (Amsterdam: Rodopi, 1983), 74.</footnote>
is satisfactory only if understood as the plan of a craftsman, a set of proportioned
measures, a design, almost like a formula, a recipe, culinary or alchemical, in which
strict proportions and procedures are specified (cf. above, p. 60), or as a musical score
(cf. above, p. 70).
<table><caption>TABLE 5</caption><thead><tr><th>Nicomachus 1.6</th><th>Boethius 1.2</th></tr></thead><tbody><tr><td>Πάντα τὰ κατὰ τεχνικὴν διέξοδον ὑπὸ φύσεως ἐν τῷ κόσμῳ διατεταγμένα κατὰ μέρος τε καὶ ὅλα φαίνεται κατὰ ἀριθμὸν ὑπὸ τῆς προνοίας καὶ τοῦ τὰ ὅλα δημιουργήσαντος νοῦ διακεκρίσθαι τε καὶ κεκοσμήσθαι βεβαιουμένου τοῦ παραδείγματος οἶον λόγον προχαράγματος ἐκ τοῦ ἐπέχειν τὸν ἀριθμὸν προυποστάντα ἐν τῇ τοῦ κοσμοποιοῦ θεοῦ διανοίᾳ, νοητὸν αὐτὸν μόνον καὶ παντάπασιν ἄυλον, οὐσίαν μέντοι τὴν ὄντως τὴν ἀίδιον, ἵνα πρὸς αὐτὸν ὡς λόγον τεχνικὸν ἀποτελεσθῇ τὰ σύμπαντα ταῦτα, χρόνος, κίνησις, οὐρανός, ἄστρα, ἐξελιγμοὶ παντοῖοι.</td><td>All that has been arranged in the universe by nature following a skilful way seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things; for the pattern was fixed, like a preliminary sketch, by the domination of number preexistent in the mind of the world-creating God, number intellectual only and immaterial in every way, but at the same time the true and the eternal essence, so that with reference to it, as to an artistic plan, should be created all these things, time, motion, the heavens, the stars, all sorts of revolutions.</td></tr></tbody></table>
• κατὰ τεχνικὴν διέξοδον — Things are arranged in the world following a τεχνικὴ διέξοδος, which could be read as a ‘technical method’. However, thinking of the similarity with the *Sefer Yetsirah*, where God creates along/through thirty-two ‘marvellous ways of wisdom’ (*netivot peli’ot hokhmah*),<fnref n="161" /> I would rather keep ‘way’, which happens to be closer to the usual meaning of διέξοδος, a pathway, like an orbit, also a detailed narrative. Naturally, given the composition of the word itself, δι-εξ-οδος, it implies the passage through and outward of something. The Heb. *hokhmah*, notably unlike its Ar. cognate *hikmah*, has also the meaning of technical skill. So a Hebrew rendering of this phrase could very easily read: *netivah hokhmah*. Thābit gives *tarīq ṣanāʿī*.

• διακεκρίσθαι τε καὶ κεκοσμῆσθαι — What the numbers bring about in the world is this determination and ordering, an idea which acquires a nuance and development in the Arabic as *mayyazahā wa-sawwāhā ‘alā hāl al-maḥmūda al-jamīla*, ‘He determined and regulated them in a praiseworthy and beautiful condition,’ adding ‘praiseworthy’ to the qualities of the universe, and once again bringing out the aspect of beauty implicit in κοσμέω.

• κατά — Coming back to the cosmological role of the prepositions, here we have this opening κατά, which I have translated as ‘following’ to suit διέξοδος, rather as a **perrelative**,<fnref n="162" /> and which could be akin in its function to the opening ב of the Torah (*Bere’shit*) and of the most common version of *Sefer Yetsirah*. Thābit’s **علی** shows even more possibilities: ‘upon a skilful pathway’, ‘along a way of craft’...

Further down, κατὰ ἀριθμὸν shows a somehow **instrumental** use of the preposition, and this aspect is disclosed partially in the Latin by saying *numerorum ratione*. The Arabic shows yet another facet of this κατά by saying ‘alā nasabi al-a‘dād, ‘in the lineage’ or ‘in relation to’, as if ‘under the parentage’ of numbers.

• *mutuata* — Again on the relation between number or the noetic realities and the transient world, the Latin uses an image not found before: the four natural elements *borrow* from numbers their *multitudo*—the fact that they are four, or perhaps the pattern of their proliferation?

• προχάραγμα — This word for the nature of the divine paradigm had not been used. It is related to engraving, like γράμματα, and it also makes me think about the inversions between the superior and lower realms that characterise the process of divine stamping and typing.<fnref n="163" /> It is related in its usage to προκέντημα, mentioned earlier, and it belongs very clearly to architecture. The corresponding Arabic is *rasm mutaqaddim sābiq*, a

<footnote n="161">161. See Chapter 7 below.</footnote>

<footnote n="162">162. The perrelative case expresses movement through or along a referent noun. For Greek examples, its synthetic causal meaning, and links to ‘the extensive and manifold uses of Hebrew ב’, cf. P. Bortone, *Greek Prepositions: From Antiquity to the Present* (Oxford University Press, 2010), 158, 192–3.</footnote>

<footnote n="163">163. Cf. below, p. 120.</footnote>
‘previous prepared sketch’.

• ἐπέχειν — Yet another facet of the ‘participation’ is made explicit when the sketch is said to have been established ἐκ τοῦ ἐπέχειν, ‘by the domination’, ‘due to the control’ of pre-sup-posed (προυποστάς) number. This domination seems not to have been conveyed into the Arabic or the Latin. Perhaps it might be better, especially given the syntax, to use the intransitive meaning of ἐπέχω, which is frequent with διανοία and νοῦς, meaning ‘attend to’, ‘direct one’s mind’; as if the divine number were in-tended or directed toward the constitution of the heavenly paradigm.

• The other points of note here simply reprise themes mentioned earlier, like the supernal ‘location’ of the models (ἐν θεοῦ διανοίᾳ, fī ‘ilmi Llāh, in animo conditoris), or their immaterial and eternal quality.
<table><caption>TABLE 6</caption><thead><tr><th>Nicomachus 1.11</th><th>Boethius 1.14</th></tr></thead><tbody><tr><td>αὐτῶν μέντοι συντεθέντων ἑαυτοῖς δύναιντ' ἄν ἄλλοι γενέσθαι ἀπὸ πηγῆς ὡσανεὶ καὶ ῥίζης αὐτῶν τούτων ἀρχόμενοι, διόπερ πρῶτοι καλοῦνται ὡσανεὶ ἀρχαὶ ἐκείνων προυποκείμενοι· ἀρχὴ δὲ πᾶσα στοιχειώδης καὶ ἀσύνθετος, εἰς ἤν πάντα ἀναλύεται καὶ ἐξ ἦς πάντα συνίσταται, αὐτὴ δὲ εἰς οὐδὲν καὶ ἐξ οὐδενός.</td><td>وما اذا رُكب هذا النوع الذي ذكرنا مع نفسه فأنه يتولد منه غيره وكان ساير الأعداد انّما يبتدئ من هذه فتكون هذه الأعداد لها بمنزلة الينبوع والاساس الذي منه ابتدأها ولهذا السبب سميت اعداد اولّ لانّها كمبادي المتقدمة لتلك واما الابتدأ الذي ليس بمركّب والذي هو بمنزلة العنصر الجميعها فهو الواحد وهو الذي اليه ينحل جميعها على طريق العنكّر* ومنه تركب واما الواحد فليس ينحل الى شي ولا هو مُركب من شي.</td></tr><tr><td colspan="2">When they are combined with themselves, other numbers might be produced, as from a fountain and a root, having them as principles, wherefore they are called 'prime', because they exist beforehand as the principles of the others. For every principle is elementary and incomposite, into which everything is made, but the principle itself cannot be resolved into anything or constituted out of anything.</td></tr><tr><td colspan="2">Hi autem in semetipsos multiplicati faciunt alios numeros velut primi, eosque primam rerum substantiam vimque sortitos, cunctorum a se procreatorum velut quaedam elementa reperies, quia scientificet, et incompositi sunt, et simplici generatione formati, atque in eos omnes quicunque ex his prolati sunt numeri resolvuntur, ipsi vero neque ex aliis producuntur, neque in alia reducuntur.</td></tr></tbody></table>
• συντεθέντων — this paragraph speaks of the prime numbers. Their productive ‘combination’, changed in Latin to *multiplicatio*, but retained in Arabic as *rukkiba maʿa nafsahu*, is reminiscent of *Sefer Yetsirah* §19–21, where the combination (Heb. *hamir*, *tsaraf*) of the letters brings about the world. Συντίθημι is often used for addition, whereas multiplication is expressed by πολλαπλασιάζειν or simply the preposition ἐπί. E.g. τὰ ἡμίσηα ἐπ’ ἄλληλα = ‘the halves multiplied by each other.’<fnref n="164" />

• The primes are called ‘roots’ (*al-asās*) as were the elements by Empedocles. They are also compared to a fountain, πηγή, yanbūʻ.

• ἀρχὴ πᾶσα στοιχειώδης — ‘every principle is elementary’, is modified in Ar. to *al-ibtidā’ alladhī huwa bi-manzilat al-‘unṣur*, ‘the beginning in lieu of element’, recalling the phrase τὰ καλούμενα στοιχεῖα. The relation between ἀρχή and στοιχεῖον, at times verging on synonymity, is of interest, as we had seen by the grammarians, in that it shows how the latter term was far from being exclusively used for the material components.

• Prime numbers have an elemental aspect which makes them very interesting for this research—each one is ‘unique’ and through their combination it is possible to produce all numbers. However, the primes are infinite, which is at odds with the limited number of letters in an alphabet. An alphabet cannot be infinite, since its power lies partly in the small, easy to grasp, number of its components. The question then remains open: in what way, if at all, are the primes ‘elementary’? This is precisely the topic of the next and last passage.

<footnote n="164">164. M. Bakker, ‘A Papyrus with Mathematical Problems,’ *The Bulletin of the American Society of Papyrologists* 44 (2007): 18.</footnote>
<table><caption>TABLE 7</caption><thead><tr><th>Nicomachus 2.1</th><th>Boethius 2.1</th></tr></thead><tbody><tr><td>Ἐπειδὴ στοιχεῖον λέγεται καὶ ἔστιν, ἐξ οὖ ἐλαχίστου συν- ίσταταί τι καὶ εἰς ὁ ἐλάχι- στον ἀναλύεται οἶον γράμ- ματα μὲν τῆς ἐγγραμμάτου φωνῆς στοιχεῖα λέγεται, ἐξ αὐτῶν τε γὰρ ἡ σύστασις τῆς συμπάσης ἐνάρθρου φω- νῆς καὶ εἰς αὐτὰ ἔσχατα ἀνα- λύεται· φθόγγοι δὲ μελωδίας ἀπάσης, ἀφ' ὦν ἄρχεται συγ- κρίνεσθαι καὶ εἰς οὖς ἀναλύ- εται· κοινὴ δὲ τοῦ κόσμου τὰ λεγόμενα τέσσαρα στοιχεῖα ἀπλᾶ ὑπάρχει σώματα, πῦρ, ὕδωρ, ἀήρ, γῆ· ἐκ γὰρ πρωτί- στων αὐτῶν ἡ σύστασις τοῦ παντὸς φυσιολογεῖται καὶ εἰς αὐτὰ ἔσχατα ἐπινοεῖται ἡ ἀνά- λυσις.</td><td>An element is said to be, and is, the smallest thing which enters into the composition of an object and the least thing into which it can be analysed. Letters, for example, are called the elements of inscribed speech, for out of them all articulate speech is composed and into them finally it is resolved. Sounds are the elements of all melody; for they are the beginning of its composition and into them it is resolved. The so- called four elements of the universe in general are simple bodies, fire, water, air, and earth; for our of them in the first instance we account for the constitution of the universe, and into them finally we conceive of it as being resolved.</td><td>Sed quae rerum elementa sunt, ex eisdem principaliter omnia compo- nuntur, et in eadem rursus resolu- tione facta resolvuntur. Ut quoniam articularis vocis elementa sunt litte- rae, ab eis est syllabarum progressa coniunctio, et in eadem rursus ter- minatur extremas, eamdemque vim obtinet sonus in musicis. Iam vero mundum corpora quattuor non igno- ramus efficere. Namque (ut ait Lu- cretius) Ex imbri terra atque anima gignuntur et igni; sed in haec rursus eius quattuor elementa fit postrema resolutio. Ita igitur, quoniam ex ae- qualitatis margine cunctas inaequali- tatis species proficisci videmus, om- nis a nobis inaequalitas ad aequali- tem rursus, velut ad quoddam ele- mentum proprii generis resolvatur.</td></tr></tbody></table>
• Nicomachus opens the second part of his book looking for the στοιχεῖον of arithmetic, and in order to do so he defines the word, and he certainly does not have in mind a material principle. There is indeed a remarkable subtlety in the use of the word: there is an emphatic καὶ ἔστιν at the beginning which only appears in a clearer light when the four cosmic τὰ λεγόμενα στοιχεῖα are mentioned (al-ajsām allatī yuqālu lahā al-‘anāṣir). So these four are only called elements, but at the beginning, speaking in general, he had specified that the smallest components of something not only are called but *are indeed* elements. The comparison with the letters and the sounds only brings up more questions, as the relation between written letter and sound is brought in as a sort of *topos* and left unexplored. The strain put on the Arabic translation is patent when ḫurūf, ‘letters’, has to be used in the middle of the paragraph, before returning to ‘anāṣir, ‘elements’.

Conclusion

From Nicomachus' days (first–second century AD) until the sixteenth century, he was honoured for his *Introduction to Arithmetic* among Greeks, Latins, Jews and Arabs, who considered his work to be the basis of the science of numbers.<fnref n="165" /> He was considered a pivotal thinker between early Pythagorean and Platonist authors and the new developments in Neoplatonic and other groups.

Boethius' writings, dating from the sixth century were so decisive in defining the intellectual currents of the twelfth century that it is often called the *aetas Boethiana*.<fnref n="166" /> He was also considered a pivotal figure, frequently described as 'the last of the Romans and the first of the scholastic philosophers', between the end of Antiquity and the beginning of the Middle Ages.

Thābit ibn Qurra was one of the most accomplished scholars active in Baghdad during the ninth century, and his contributions encompass not only arithmetic but also astronomy, mechanics, geography and medicine.<fnref n="167" /> As a Sabian from Harran and a Syriac speaker, Thābit was among the scholars destined to contribute to one of the most important cultural transfers in the history of Europe, the translation of the Greek heritage into Arabic at the heart of Islamic civilisation.

The continued and authoritative unanimity of these three scholars through the centuries is testimony to the shared set of basic cosmological tenets found with little variation from Greek antiquity to the late Mediterranean Middle Ages, in what was

<footnote n="165">165. See Nicomachus of Gerasa, *Introduction to Arithmetic*, 124.</footnote>

<footnote n="166">166. M. Konik, ‘A reception of the idea of the music of the spheres in the music theory of the twelfth and thirteenth centuries,’ *Musica Iagellonica* (Cracow) 6 (2012): 5–50.</footnote>

<footnote n="167">167. J. J. O’Connor and E. F. Robertson, ‘Al-Sabi Thabit ibn Qurra al-Harrani.’</footnote>
effectively not only a trilingual but a quadrilingual world. We have here an example
of what Curtius calls ‘a community of great authors throughout the centuries’, who
‘by a series of interconnections across time’ held together the Mediterranean cultural
continuum.<fnref n="168" /> In fact, by the comparison above of the three versions of the *Introduction*,
we have plunged into the Middle Ages, leaping across centuries and yet as if stationary
in a scholarly community of shared doctrines.

In the following chapter I shall return to late antiquity and the early Middle Ages, to
follow a closely parallel thread of Pythagorean arithmetic in a world transformed by
the advent of the Abrahamic faiths.

◆

But before proceeding, I will close this chapter with some verses from Boethius’
*De consolatione philosophiae* (3, 9) which have been said to ‘summarise in less than
thirty verses the entire first part of the *Timaeus*, as if suspended between Platonism
and Christianity.’<fnref n="169" /> In doing so, they recapitulate the time span between the most
‘Pythagorean’ pages of Plato and the Abrahamic monotheistic discourse which would
be adopted by European philosophy from Boethius on.

O qui perpetua mundum ratione gubernas
Terrarum caelique sator qui tempus ab aevo
Ire iubes stabilisque manens das cuncta moveri,
Quem non externae pepulerunt fingere causae
Materiae fluitantis opus, verum insita summi
Forma boni livore carens, tu cuncta superno
Ducis ab exemplo, pulchrum pulcherrimus ipse
Mundum mente gerens similique in imagine formans
Perfectasque iubens perfectum absolvere partes.
Tu numeris elementa ligas [...]

O you who rule the world with steady reckoning,
father of lands and heaven, who from eternity
ordered time to advance, and who unmoving set everything in motion,
you whom no external causes forced to give shape
to a work from unsteady matter, but rather the inner form
of the highest good, free of any envy. You who bring forth
all things after the exalted heavenly pattern, producing in your mind

<footnote n="168">168. Curtius, *European Literature and the Latin Middle Ages*, 18, 397</footnote>

<footnote n="169">169. A. Lernould, ‘Boèce. Consolation de Philosophie III, *metrum* 9,’ in *Plato Revived: Essays on Ancient Platonism in Honour of Dominic J. O’Meara*, Beiträge zur Altertumskunde 317 (Berlin/Boston: Walter de Gruyter, 2013), 376, 388; see also A. J. Hicks, *Composing the World: Harmony in the Medieval Platonic Cosmos* (Oxford University Press, 2017), 258–9.</footnote>
a beautiful world as you are beautiful, and shaping it in faithful resemblance,
ordering that its perfection be accomplished in every one of its parts.
You bind with numbers the elements [...)

These verses follow only a few lines after Lady Philosophy has explained: *Sed cum,
ut in Timaeo Platoni nostro placet, in minimis quoque rebus divinum praesidium debeat
implorari*—‘since, as in the *Timaeus* it pleased our Plato, in the smallest things too one
should invoke divine guidance.’ The connection to the Platonic dialogue is thus explicit,
and the verses quoted echo the demiurgic work and several of the cosmogonic stages
described in *Timaeus*. At the end of the quotation, we can see how the arrangement of
the elements in the world, literally a binding up (*ligas*), is accomplished by the power
of number.<fnref n="170" />

<figure><img src="image_12.png" /></figure>

Hardly a better illustration of this tight geometric knot of the elements in the cosmos
could be found than the ‘Mundus-Annus-Homo rota’ below,<fnref n="171" /> where the elements and
their qualities are tied (*ligati*) within and by a perfectly rigorous geometric pattern
(*numeris*). Moreover, the *rota* in the text of Isidore accompanies a quotation from
the *Hexameron* of St Ambrose (3, 5) which describes the intricate, ‘conjugal’ (*iugales*)
relations between elements and qualities, and finishes explaining how

*per hunc circuitum et chorum quendam concordiae societatisque conueniunt.*
*unde et graece στοιχεία dicuntur quae latine elementa dicimus, quod sibi*
*conueniant et concinant.*

<figure><img src="image_13.png" /></figure>

Through this circle and dancing round of sorts they are united in concord
and fellowship. And this is why what we call ‘elements’ in Latin, are called
στοιχεία in Greek, because they unite and are in accord with one another.

<footnote n="170">170. Cf. *Timaeus* 31b and 53a-b. See Lernould, *Boèce. Consolation III, 9*,’ 377.</footnote>

<footnote n="171">171. From a woodcut in the edition of the *De natura rerum* of Isidore of Seville, printed in 1472.</footnote>
The next steps in my investigation will explore further the particulars and various manifestations of this cosmogonic and cosmological concert and chorus of the στοιχεία.
Part II

Alphanumeric Cosmology in the
Abrahamic Scriptures
Introduction · Change and Continuity

Following the evolution of our concept through late ancient and early medieval
philosophy, I need to take stock of two major contextual shifts which in many ways will
determine every intellectual endeavour for at least fifteen centuries after Nicomachus
of Gerasa: the cultural diversification of Classical Graeco-Roman civilisation, and the
spreading and establishment of a monotheistic worldview.

The conquests of Alexander the Great in the fourth century BC and the eventual
Roman imperial expansion had as a most lasting combined result the gradual emergence
of a cosmopolis quite foreign in practice to any classical Attic or Roman republican
polity. By the turn of the era, just after the time of Dionysius Thrax, the main cultural
centre of this 'Mediterranean' cosmopolis was Alexandria, where Roman citizens and
foreigners of all origins coexisted in a cultural melting pot that never ceased to hark
back to the glories of Classical Greece and Rome, and yet never stopped evolving into
new forms. While the eventual division of the Roman empire (285 AD), the adoption of
Christianity as official imperial religion (380 AD), and the advent of Islam in the early
seventh century altered completely the socio-political panorama, it only took decades
in each of these cases for a remarkable and deep scholarly continuity to be reaffirmed
through the surface changes of peoples, languages and religions.<fnref n="1" />

A figure like Nicomachus, whose influence we started studying in the previous
chapter, is a testimony to this ongoing cultural integration. Nicomachus hailed from
the Roman East as did also, in later times, several of the greatest Platonists. Iamblichus
came from an illustrious Emesan family boasting Aramaic, Arabic, Greek and Latin
names. One could also mention Proclus, who was born in Constantinople, or his disciple
Marinus, who is thought to have been a Jew from Syria Palaestina.<fnref n="2" />

Here we have indeed one of the most remarkable facts in the history of philosophy.
As famously happened to the mighty Romans when they became disciples of their
Athenian subjects, just so, wave after wave of new political, social and religious
superstructures would eventually adopt and appropriate the same pool of ultimate
philosophical concerns and questions brought together by Aristotle, effectively the
great coordinator of early Greek philosophy.

The idea of one almighty and beneficent deity was not foreign to classical antiquity,
where the boundaries between ‘monotheism’ and ‘polytheism’ were fluid within a

<footnote n="1">1. This is all closely related to the view summed up by Guy Stroumsa when he speaks of a ‘connected religious history’ across a ‘scriptural galaxy’; see G. G. Stroumsa, ‘The Scriptural Galaxy of Late Antiquity,’ in *A Companion to Religion in Late Antiquity* (Hoboken, NJ: Wiley Blackwell, 2018), 563, 566.</footnote>

<footnote n="2">2. See P. Merlan, ‘Zur Zahlenlehre im Platonismus (Neuplatonismus) und im *Sefer Yezira*,’ *Journal of the History of Philosophy* 3, no. 2 (1965): 181.</footnote>
continuum, and did not determine exclusive domains.<fnref n="3" /> In fact, the idea of a *summum bonum* was already in the Platonic dialogues and was abundantly elaborated upon by Plato's followers. Through all the upheavals and in spite of all the conflicting beliefs, this idea became the great unifying doctrinal factor of the post-Classical *cosmopolis*, as is evinced by the shared Abrahamic ancestry professed by all three mainstream religions, Judaism, Christianity and Islam, which would witness, assimilate and transmute the demise of Classical civilisation in so many ways.<fnref n="4" />

More specifically within our field of interest, one major common doctrine shared by the Abrahamic faiths was the primacy of the Divine Word, either as the cosmogonic *fiat* —the ten creative Jewish *ma'amarot*, the Islamic creative command, *amr*— or as a cosmological manifestation of the divine as λόγος, aurally as recitation, Ar. *qur'an*, and as the letters (Heb. *otot*) and the verses (Ar. cognate *āyāt) of the Holy Book. I shall repeatedly come back to these fundamental terms in the coming pages, examining in detail how they relate to our sought-after 'elements' in their phonetic, graphic and logical dimensions, when and how they may recall one or another of the many facets of the στοιχεία found in previous pages, and in what ways our concept moved through languages and cultures.

Trying to organise the wealth of material pertaining to this chapter opens up many possibilities: to be strictly chronological, or work at a time on each of the linguistic/religious domains, or attempt a thematic sectioning, but given that the main interest is to bring into relief the correspondences and connections, and to show how our basic concept disregards time, languages and subject boundaries, I shall continue as I started in previous chapters, placing the emphasis on the semantic analogies and connections rather than on a very linear timeline: I shall take points of departure arranged in chronological order of works and authors, but within each particular section I will allow for as much time travelling as is required by this comparative procedure. Having said that, the four chapters in this second part will move approximately, allowing for exceptions, between the beginning of the Christian era and the eighth century.

<footnote n="3">3. Cf. G. Bohak, 'The Impact of Jewish Monotheism on the Greco-Roman World,' *Jewish Studies Quarterly* 7, no. 1 (2000): 13, 21.</footnote>

<footnote n="4">4. In this regard, cf. S. Noegel, J. Walker, and B. Wheeler, eds, *Prayer, Magic, and the Stars in the Ancient and Late Antique World*, Magic in History (Pennsylvania State University, 2003), 5.</footnote>
# Chapter 3

## Jewish Sources and Exegesis

### Tanakh and Translations

Honouring ancient methodology, I shall start by having a look at the Jewish scriptures themselves, bringing in for comparison the most influential translations used throughout the Middle Ages by most communities of the Abrahamic faiths:<fnref n="1" /> the early Greek translation or *Septuagint*, Latin renderings from Jerome's *Vulgate*, and some medieval Arabic versions. In each of these forms, the text of the *Tanakh* was to exercise a lasting and powerful cultural influence, not only in religious environments, but also in various scholarly fields, given that scriptural authority provided the epistemological foundation of every discipline.

### Genesis—Creation by Speech

The prominence of language in Jewish cosmogony, of the spoken word in particular, is at first sight evident from as early as the third verse of Genesis, *wa-yoʻmer elohim...*, 'and God said...'<fnref n="2" /> This expression, which occurs nine other times in the first chapter, is added to the opening *be-reʼshit* to total what are called the 'ten maʼamarot', 'the ten utterances' through which everything was created.<fnref n="3" /> There will be occasion to return to these ten afterwards, but the remarkable status of the first 'utterance' (*be-reʼshit*), which

<footnote n="1">1. The important Syriac, Armenian, Ge'ez and Georgian textual traditions exceed my competence and will not be treated in this work.</footnote>

<footnote n="2">2. Cf. Psalms 33: 6, 'By the word of the Lord were the heavens made; and all their hosts by the breath of His mouth.'</footnote>

<footnote n="3">3. Talmud *Megillah* 21b:10, 'The Gemara asks: What are these ten utterances? Presumably, they are the utterances introduced by the words "and God said" in the story of Creation in the first chapter of Genesis. However, there are only nine of these utterances and not ten. The Gemara answers: The expression: "In the beginning" is also considered an utterance... which indicates that the first utterance of Creation was the general creation of the entire universe.'</footnote>
seems to not be one at all, should not escape our attention as we ascertain the role of
letters and numbers in this cosmogony.

According to several rabbinical authorities, the Torah itself was created before the
universe,<fnref n="4" /> and Rashi comments that ‘God created the world for the sake of the Torah.’
In the *Midrash Tanḥuma*’ (Bere’shit 1:1), we find that ‘when the Holy One, blessed be
He, was about to create this world, He consulted (*hityaʿets*) the Torah before embarking
upon the work of creation.’ This ‘consultation’ is specified further in *Tanḥuma*’ Buber
(Bere’shit 5:1), ‘While God was creating the world, he was looking at the Torah,’ which
was like a trusted model (*amon*), a word cognate to the liturgical *amen*.<fnref n="5" /> And a few
lines below, ‘How was the Torah written? It was written with letters of black fire on a
surface of white fire.’ In *3 Enoch*,<fnref n="6" /> it is specified that these letters, ‘by which’ or ‘through
which’ were created heaven and earth, mountains and hills, seas and rivers (and a long
list...), were ‘engraved with a flaming style on the Throne of Glory’ (*haquqot beʿeṭ
shelahevet al kise ha-kavod*).<fnref n="7" /> Summing up then, we have, even before the creation
of the universe, the Torah as a model for divine creation, as a template constituted by
letters of fire. Odeberg puts it succinctly in his edition of *3 Enoch*, ‘all possible *otiyyot*
and *shemot* [letters and names] are represented as contained in the Torah. “The letters
of the Torah” is the technical term for the cosmical letters.’<fnref n="8" />

Now, there is an alternative letter-related exegesis of the first verse which does not
have to do with the entire alphabet but only with the letters of the divine name.<fnref n="9" /> The
letters of the Divine Name are the constituents of the world, especially the letters of
YHWH and ‘EHYE (...), and even more exclusively the letters *Yod* and *He*. A convoluted
explanation commences involving several passages, as follows.

We start with Gen. 1:1, *בראשיתבראالוהים*. This verse is normally parsed as *be-re’shit bara’ elohim*, ‘In principle God created’, but the reading reported from several Mishnaic sources uses a different vocalisation: *bara’ shet*, ‘God created six,’ referring

<footnote n="4">4. *Bere’shit Rabbah* 1:4, “In the beginning of God’s creating...” — Six things preceded the creation of the world [...] The Torah and the Throne of Glory were created. See also J. L. Kugel, *Traditions of the Bible: A Guide to the Bible As It Was at the Start of the Common Era* (Harvard University Press, 1998), 46-7, for references to the Torah as Wisdom personified.</footnote>

<footnote n="5">5. Note also here the related word *aman*, a workman or artificer. In V. Armenteros Cruz, ‘Midrás Tanhuma Buber a Génesis: traducción, notas y análisis estructural-hermenéutico’ (PhD diss., Universidad de Granada, Departamento de Filología Semítica, 2006), 93, other meanings of *amon* are reported from *Midrash Rabbah*, like a ‘tutor’ and a ‘pedagogue’—all having to do with the basic idea of ‘trust’. Reference is also made to Philo’s doctrinal parallel, which I shall be discussing soon.</footnote>

<footnote n="6">6. H. Odeberg, *3 Enoch: Or, The Hebrew Book of Enoch* (Ktav Publishing House, 1973), pp. 54–55 Heb.</footnote>

<footnote n="7">7. The ‘engraving’ method corresponds exactly to the Gr. γραφεῖν and its production, γράμματα.</footnote>

<footnote n="8">8. Odeberg, *3 Enoch*, 172.</footnote>

<footnote n="9">9. See *Bere’shit Rabbah* 12, 2; *The Letters of Rabbi Akiba* (Washington DC: Government Printing Office, 1897), 713, and for other references, Odeberg, *3 Enoch*, 34-5.</footnote>
ביה יהוה, to the six letters of a holy name. This is then compounded with Is. 26:4,
צור עולמים, which is usually read as *be-yah YHWH tsur ‘olamim*, ‘in Jah Jehovah is a
rock of the worlds,’ but becomes *be-YHYHWH tsawar ‘olamim*, ‘He formed the worlds
by YHYHWH,’ so the ‘six letters’ mentioned in Gen. 1:1 would be YHYHWH, what
translators make into ‘Jah Jehovah’ or ‘the LORD GOD’ or ‘the LORD, the LORD’. Finally,
to round off and support this interpretation, Gen. 2:4 is given an unusual reading too:
the verse speaks of ‘the generations of heaven and earth when they were created (*be-
hibar’am*),’ but this last word בהיבראם is read instead as *be-HY bara’am*, ‘He
created them by HY.’

What is clear at the end of this complex explanation, rather Kabbalistic *avant la lettre*, is that the ‘letters of creation’ would be the six letters י, ה, יִ, הִ, וִ, הִ, and not necessarily the entire alphabet. It will be noted how this special status of a subset of letters is comparable to the special cosmological status of some Greek letters, like the vowels which are identified with the seven planets.<fnref n="10" />

Another frequent and relevant association to the primordial *re’shit* and the
hexameron is that of the construction of the tabernacle (*mishkan*) or the pitching of
a tent (*ohel*), because ‘the Tabernacle is equal to the creation of the world itself.’<fnref n="11" /> The
image is architectonic, and is found with the alternative association to the building of
a house—‘May our master teach us the benediction one should offer upon the building
of a new home!’ (*ha-boneh bayt hadash*).<fnref n="12" /> One of the relevant scriptural associations
is Psalm 119:90–91, ‘Thou hast established the earth, and it standeth’ (*konanta erets
wa-ta‘amod*).

Here we may remember how in one of the Greek commentaries the letters were
compared to building blocks, and how the crucial term *στοῖχος* designates a course of
bricks in building.

Finally, from a numerical point of view, there is a notable explanation in *Midrash Tanhuma*' (Bere’shit 5), as to why the account of creation opens with a *bet*: 'The letter *bet* is employed in order to teach man that there are two worlds, this world and the hereafter.' This explanation is based on the numerical value of *bet*, two, and it seems clear that the question is equivalent to saying 'Why does the Torah open with two?' The identity between letter and number is a matter of fact.

<footnote n="10">10. See above, pp. 45 and 46.</footnote>

<footnote n="11">11. *Midrash Tanhuma*, Pekudei 2:3. See also *Bemidbar Rabbah*, 12:13.</footnote>

<footnote n="12">12. *Midrash Tanhuma*, l.c., and Bere’shit 4:1.</footnote>
Psalm 33:6

A passage often mentioned in the Talmud when discussing the creation is Psalm 33:6,<fnref n="13" />
By the word of the Lord were the heavens
made; and all the host of them by the breath of his mouth. This is said to indicate ‘that
all of creation came into existence through a single utterance, after which all matter
was formed into separate and distinct entities by means of the other nine utterances,’
since ‘the first utterance of Creation was the general creation of the entire universe.’<fnref n="14" />
And specifying, ‘the hosts of heaven are the angels, who are created from the mouth
of God.’<fnref n="15" /> This concept of a primordial moment in divinis, from which all reality is
later ‘expanded’ or ‘elaborated’, reminds of the cosmogonic primacy accorded to the
monad among the Pythagoreans, and to the related grammatical exegeses about the
alpha among Greek grammarians. In one of the above pages,<fnref n="16" /> we had a glimpse into
the relation between letter-numbers and angels, but here this relation may be specified:
the first letter-number belongs as if to a different order altogether, while the rest of the
decad-alphabet would be formed by ‘angelic’ beings. In fact, it is a common doctrine<fnref n="17" />
that from every one of God’s utterances an angel is created. I shall have occasion to
dwell further on this angelic comparison in later sections.

Exodus—Bezalel

In Exodus 31:2–5, we find this remarkable testimony when on top of Sinai Moses is
told:

See, I have called by name Bezalel the son of Uri, son of Hur, of the tribe
of Judah, and I have filled him with the Spirit of God, with proficiency and
intelligence, with knowledge and all craftsmanship (mal'akhah), to design
designs (lahshov mahshavot), to work in gold, silver, and bronze, in carving
(haroshet) stones for setting, and in carving wood, to work in every craft
(mal'akhah) [highlighting mine].

רְאֵה קְרָאתי בְּשֵׁם בְּצַלְאֵל בֶּן אוּרی בֶּן חֹר לְמַטֶה יְהוּדָה: וָאֲמַלָּא אֹתוֹ רוֹחַ אֱלֹהִים
בְּחָכְמָה וּבְתִבּוֹנָה וּבְדַעַת וּבְכָל מְלָאכָה: לַחֲשַב מַחֲשָׁבָת לַעֲשָׂת בַּנָּהּב וּבְכֶסֶף וּבְנַחֲשֶׁת:
וּבַחֲרֻשֶּׁת אֶבֶן לְמַלֵּאת וּבַחֲרֻשֶּׁת עֵץ לַעֲשָׂת בְּכָל מְלָאכָה:

This is repeated almost verbatim at 35:30, when Moses engages Bezalel to do the job,
and it is later referred to in ch. 36 when the building work is undertaken.

<footnote n="13">13. Cf. for instance, Ro'sh Hashanah 32a:19 and Megillah 21b:10.</footnote>

<footnote n="14">14. Megillah 21b:10.</footnote>

<footnote n="15">15. *Hagigah* 14a:3.</footnote>

<footnote n="16">16. See p. 40.</footnote>

<footnote n="17">17. See *Hagigah* 14a:71, and also Odeberg, *3 Enoch*, 34.</footnote>
The crucial beginning of verse 4, with the cognate accusative **לחשב מחשבת**, which I translate as ‘to design designs’, was paraphrased in the *Septuagint* as διανοεῖσθαι καὶ ἀρχιτεκτονῆσαι, bringing out both the epistemological and technical aspects of **חשב**, which has an arithmetic basic meaning of computation and calculation. The same expression was rendered into the Latin of the Vulgate as *ad excogitandum*, which, like ‘design’, does not imply necessarily the idea of calculation in the original—the arithmetic nuance was lost in the Latin.

I have highlighted above the terms used in this passage for carving and craft because of the relation they have with the creating, or rather shaping, power of number we encountered above in Nicomachus’s description of the cosmogonic role of number, but what is really relevant for us is what the Talmud (Berakhot 55a3) has to comment on this passage:<fnref n="18" />

> Rab Judah said in the name of Rab: Bezalel knew how to combine the letters by which the heavens and earth were created. It is written here (Ex. 35), ‘And He hath filled him with the spirit of God, in wisdom and in understanding, and in knowledge.’

> אמר רב יהודה אמר רב יודע היה בצלאל לצרף אותיות שנבראו בהן שמים וארץ כתיב הכא (שמות לה) וימלא אותו רוח אלהים בחכמה ובתבונה ובדעת

Following the *Exodus* text, we would have expected to see that the heavens and earth were ‘designed, calculated, devised’ (all translations of *hashav*),<fnref n="19" /> but instead it is remarkable how the verb used here for creation is נבראו *nivra'*u, passive of *bara*', usually reserved in theology for *creatio ex nihilo*. In addition to this, on the same Talmud page, Rashi comments that this is said of the letters, ‘regarding their combination as mentioned in *Sefer Yetsirah*.’ This further complicates the determination of the kind of creative act envisaged in this demiurgic text, by establishing a link to *yatsar*, yet another alternative for crafting from pre-existent matter, as is also the idea of ‘combining’, *tsaref*.

Something else worthy of note is the etymology and ancestry of Bezalel. He is ‘by

<footnote n="18">18. See *Midrash Rabbah*, ed. H. Freedman, M. Simon, and J. J. Slotki, 10 vols (London: Soncino Press, 1939) and *Talmud Bavli: the Schottenstein edition: the Gemara: the classic Vilna edition*, with an annotated, interpretive elucidation, as an aid to Talmud study, ed. Y. S. Schoor, C. Malinowitz, and H. Goldwurm, 72 vols, ArtScroll Series (New York: Mesorah Publishers, 1990-2005). Also valuable references in M. L. Munk, *The Wisdom in the Hebrew Alphabet: the Sacred Letters as a Guide to Jewish Deed and Thought*, ArtScroll Series (New York: Mesorah Publications, 1983), and a most helpful online resource, *Talmud Bavli* (*Soncino Babylonian Talmud*), ed. I. Epstein (July 20, 2016).</footnote>

<footnote n="19">19. Cf. B. Davidson, *The Analytical Hebrew and Chaldee Lexikon*, Regency Reference Library (London: Samuel Bagster & Sons, 1848), s.v. *hashav*.</footnote>
the shade of God', *be-tsel-El*,<fnref n="20" /> and he is son of *Uri*, 'my light', providing a new reference to the luminous nature of the letters, which 'make the mind bright' as we had found earlier.

## Counting the Glory

An important occurrence of *ספר safar*, a crucial triliteral root in our research, which combines the meanings of writing and counting, is found at the beginning of Psalm 19,

The heavens recount the glory of God, and the sky tells of the work of His hands.

### השמים מספרים כבויד אל ומעשה ידיו מגיד הרקיע

What I would single out here is that the semantic complexity at the basis of *mispar*, 'number', and *mesaper*, 'to recount', is strictly analogous to the one found in English and other Indo-European languages when we speak of giving an account or doing accounts, like Fr. *compter/raconter*, Sp. *un cuento/la cuenta, por favor*.<fnref n="21" /> There is also the same ambiguity of the verb 'to tell', as in 'telling a story', or in a 'teller machine', and even stronger, that is, harder to distinguish, in 'telling our beads', which finds an inverse of sorts in the expression to 'count prayers'.

Another relevant passage on this topic is Gen. 5:1, 'This is the record of Adam's line,' a verse considered by Ben Azzai 'the major principle of the Torah,'<fnref n="22" /> in which the word *sefer* is a major object of commentary and is explained as meaning a 'record' or a 'list' rather than a book. Luzzatto explains succinctly: זה ספר: 'This is the record of Adam's line,' a tally [sefirah] and a narrative (*sippur*).<fnref n="23" />

All this is meant to point out that there is hardly any disagreement here from a Pythagorean-Platonic cosmological point of view. In *Epinomis* 978b7ff., the answer to the question πῶς ἐμάθομεν ἀριθμεῖν, 'How have we learnt to count?' is precisely the order and regularity of the celestial movements. Referring to the psalm above, Ibn Ezra comments that 'no one can understand this passage who has not the science of the stars.'

Rashi's commentary to this first verse brings together some of the different meanings:

<footnote n="20">20. For this interpretation and later developments, cf. M. Idel, 'Reification of Language in Jewish Mysticism,' *Mysticism and Language*, 1992: 46.</footnote>

<footnote n="21">21. For more examples and detailed analysis in the context of narratology, see J. García Landa, 'Narrating Narrating: Twisting the Twice-Told Tale,' in *Theorizing Narrativity*, ed. J. Pier and J. García Landa (Berlin/Boston: Walter de Gruyter, 2008), 420-21.</footnote>

<footnote n="22">22. Cf. the *Torat Kohanim Parshat Kedoshim*.</footnote>

<footnote n="23">23. Shadal on Genesis 5:1. The *s-f-r* root of *sippur*, inasmuch as it refers to a narrative, brings to mind the classical Greek term στοιχηγορέω, 'to tell a story in regular order,' 'with στοιχος.'</footnote>
The Psalmist himself explains the matter below: 'There is neither speech
nor words' [19:4]. They do not speak with the creatures [they are inaudible]
except in the sense that 'their radiation goes forth throughout the earth'
[19:5] and they give light to the creatures, and thereby the creatures
recount the glory of God and give thanks and bless [Him] for the
luminaries.

המשורר עצמו פירש את הדבר "אין אומר ואין דברים" - אינן מדברים עם הבריות אלא מתוך ש"בכל הארץ יצא קום" ומאירים לבריו מתוך כך מספרים הבריות כבוד אל ומודים ומברכין על המאורות

Aside from other aspects, here we encounter again the luminosity of the letter-numbers, this time made explicit in an astronomical fashion: the heavenly bodies like a supernal writing which recounts the glory of God; when the creatures perceive this radiation, they in turn do the recounting.

## The Potter of Light

Another important Tanakh passage is Jeremiah 18:6,

O house of Israel, cannot I do with you as this potter? saith the Lord. Behold, as the clay is in the potter's hand, so are you in my hand.

הַכִּוֹצֵר הַזֶּה לֹא־אֹכַל לַעֲשָׂות לָכֶם בֵּית יִשְׂרָאֵל נָֽאֵם־יְהוָה הִנֵּה כַחֹמֶר בְּיִד הַיּוֹצֵר
כָּן־אַתָּם בְּיָדִי

This verse is directly related to Isaiah 45:7, part of a formidable self-characterisation of God,

I form light and create darkness; I make peace and create evil; I am the Lord, who does all these things.

יֹצֵר אוֹר וּבוֹר אַ חֹשֶׁךְ עֹשֶׂה שָׁלוֹם וּבוֹר אַ רָע אֲנִי יְהוָה עֹשֶׂה כָּל אֵלֶּה

The relevance of these verses for us has to do with the use of the above-mentioned root *צֹר yatsar*, ‘to shape, fashion, form’, or in a general sense ‘to create’ as a craftsman does. This imagery became incorporated into liturgical life in the *Yotser Or*, ‘Creator of Light’, also known as *Birkat Yotser*, ‘Blessing of Creation’, the first of the two blessings recited before the *Shema* during the morning religious services.

Blessed are you, Lord our God, King of the universe, who forms light and
creates darkness, who makes peace and creates all things. Blessed are you
Lord, who forms the luminaries.
בָּרָךְ אַתָּה וְיִֽאֱלֵהנוּ מָלֶךְ הָעוֹלָם, יוֹצֵר אוֹר וּבוֹרֵא חָשָׁךְ, עֹשֶׂה שָׁלוֹם וּבוֹרֵא אֶת הַכֹּל.
בָּרָךְ אַתָּה, וְיִֽ, יוֹצֵר הַמָּאוֹרֹת

The יוצר yotser as a particular type of craftsman is here implicitly referring to craftsmen and their arts in general, but the synecdoche became explicit centuries later in the piyyut Ka-homer, still sung at Yom Kippur, in which God is invoked as a potter, a stonecutter, a blacksmith, a sailor, a glass-blower, an embroiderer and a silversmith.<fnref n="24" />

## Acrostics

A literary device in the *Tanakh* which is significant for this research is the alphabetic acrostic or *abecedarium*, a series of verses or stanzas in which every unit starts with a letter of the alphabet in sequential order. The origin of acrostics is attributed by Rabbinic tradition to Solomon,<fnref n="25" /> but this kind of composition is found already in Akkadian poetry, and it was common in Syriac, Greek, Roman and later Byzantine literature.<fnref n="26" /> The best known biblical example is Psalm 119, where from *alef* to *taw*, every letter presides over eight successive verses, for a total of 176 verses. Other important alphabetic acrostics include Psalm 145, the eulogy of the good wife in Proverbs 31, and the first four chapters of Lamentations. In this last example, the alphabet is set out complete four times, one after another.<fnref n="27" />

But beyond compositional details, what is of main value in the light of my research is the meaning, the purpose of the alphabetic acrostic. This formal structure used to appear as an oddity to modern scholars, who tried to justify its use mostly as a didactic mnemonic device,<fnref n="28" /> on the assumption that aesthetic grounds alone could not justify such ‘an impediment to artistic and poetic expression.’<fnref n="29" /> Now contemporary scholarship has been consistently widening its views regarding these acrostics, bringing

<footnote n="24">24. For an erudite treatment of this multiple demiurgic symbolism, see J. Hani, *Les Métiers de Dieu: préliminaires à une spiritualité du travail* (Paris: Jean-Cyrille Godefroy Editions, 2010); see also L. Roche, ‘Dieu créa l’artiste à son image : Le thème du Dieu-artiste dans la théorie artistique moderne (XVe-XVIIIe siècle)’ (master’s thesis, Sorbonne, Paris IV, 2012), 18ff.</footnote>

<footnote n="25">25. Song of Songs Rabbah 1:7.</footnote>

<footnote n="26">26. For specific references and general bibliography, see R. Marcus, ‘Alphabetic Acrostics in the Hellenistic and Roman Periods,’ *Journal of Near Eastern Studies* 6, no. 2 (1947): 109–115, A. Kadelbach, ‘Das Akrostichon im Kirchenlied: Typologie und Deutungsansätze,’ *Jahrbuch für Liturgik und Hymnologie* 36 (1996): 176, and R. Van der Spuy, ‘Hebrew Alphabetic Acrostics — Significance and Translation,’ *Old Testament Essays* 21, no. 2 (2008): 513–532.</footnote>

<footnote n="27">27. See Lamentations Rabbah 5.</footnote>

<footnote n="28">28. Cf. Marcus, ‘Alphabetic Acrostics,’ 110.</footnote>

<footnote n="29">29. See L. D. Maloney, ‘A Word Fitly Spoken: Poetic Artistry in the First Four Acrostics of the Hebrew Psalter’ (PhD diss., Dept of Religion, Baylor University, 2005), 188-9, for a wealth of relevant sources, and an overview of the current shift in the appreciation of the acrostic in Biblical scholarship.</footnote>
in explanatory theories from cognitive sciences<fnref n="30" /> and allowing for more comprehensive and historically-aware literary judgements.<fnref n="31" /> I shall simply add here some remarks from the very particular angle of my research, hoping to contribute to the effort at understanding these acrostics in their own historical context. I would like to suggest that we have enough testimonies and comparative data to allow for more than a resigned guess.<fnref n="32" />

First we have some old testimonies:

The expression ‘from *alef* to *taw*’ is found repeatedly in Rabbinic literature to mean ‘from A to Z’, ‘entirely’, as in ‘Abraham performed the law from *alef* to *taw*,<fnref n="33" /> and as in the commentaries to Daniel 9:11, ‘Israel has transgressed your law’ *עִבּרוּ אֶת־תּוֹרָתךְ*. Lamentations Rabbah (1:20) and 3 Enoch (44:9), among other sources, explain that it means ‘they have transgressed all the letters in the Torah,’ reading the accusative preposition of *et toratekha* as the abbreviation of the alphabet. A correct translation of Daniel’s verse would accordingly be ‘Israel has transgressed the A–Z of your law.’ In later literature, the expression is also found referring to the blessings of God upon earth.<fnref n="34" />

The relation between this expression and the Greek ‘alpha and omega’ has been studied and associated to Isaiah 44:6, ‘the Lord of hosts, I am the first and I am the last’ *יהוה צבאות אני ראשון ואני אחרון* we had encountered in the first chapter, and I shall leave the Christian parallels for a later section. One noteworthy commentary to this verse is the following dialogue,

‘What is the seal of God?’

‘Truth [אמת].’

‘And why truth?’

‘Because “truth” has three letters: *alef*, the first letter; *mem*, the middle one; and *taw*, their end.’<fnref n="36" />

<footnote n="30">30. See Van der Spuy, ‘Hebrew Alphabetic Acrostics,’ 516.</footnote>

<footnote n="31">31. Cf. Kadelbach, ‘Das Akrostichon,’ 205, ‘When games are understood not simply as pointless activities, but rather as the satisfaction of a primal human need which brings the *homo ludens* into harmony with himself, God and the World, only then can acrostic poetry also be perceived as a playful fulfilment of the human ideal.’</footnote>

<footnote n="32">32. See Van der Spuy, ‘Hebrew Alphabetic Acrostics,’ 515.</footnote>

<footnote n="33">33. See *Midrash Tehillim* 112; *Yalquṭ Shim'oni*, remez 871.</footnote>

<footnote n="34">34. *Chidushei Agadot* to Bava Batra 88b (part of Vilna edition).</footnote>

<footnote n="35">35. R. H. Charles, *A Critical and Exegetical Commentary on the Revelation of St. John* (Edinburgh: T. & T. Clark, 1920), 20. Also a rare source used by Charles, J. C. Schöttgen, *Horae Hebraicae et Talmudicae in universum Novum Testamentum* (Leipzig: Hekel, 1733), 1086.</footnote>

<footnote n="36">36. Devarim Rabbah 1:10. Regarding this conclusive image of the seal, and also in its ‘protective’ aspect, cf. M. B. Sendor, ‘The Emergence of Provençal Kabbalah: Rabbi Isaac the Blind’s *Commentary on Sefer Yeşirah*. Vol. 2, translation and annotation’ (PhD diss., Near Eastern Languages and Civilizations, Harvard</footnote>
Now, considering the dual character of the letter-numbers we have been studying, it seems evident that an acrostic is not only a way of alphabetically sorting lines or paragraphs, but also *and simultaneously* an enumeration. Considering the qualities of the στοιχεία we have already listed, it is easy to agree with the cognitive scientists when they note how the alphabetic acrostic communicates 'a well-defined *order*, a *finite structure* and the sense of a complete unit and *wholeness*'.<fnref n="37" /> Considering the elevated cosmological rank of letters and numbers, it is hard to ignore that such an enumeration, in the liturgical context of the scripture, would not only serve a sort of cataloguing purpose, but that it is also a direct reference to the cosmic order and its attributes.

Drawing again from the *Timaeus* (32c5ff.), we can recall how, in the composition of the world, the Composer uses up every one of the four (*sc. elements*), leaving nothing unused. This is related to what Lovejoy considered a major philosophical principle, his 'principle of plenitude',<fnref n="38" /> according to which the universe is a *plenum formarum* in which the range of conceivable diversity is exhaustively exemplified, since the extent and abundance of the creation must be commensurate with the productive capacity of a 'perfect' and inexhaustible Source. This also gives us an opening onto a new field of correspondences, if we compare this principle with the Evangelic and Gnostic concept of a fullness *in divinis*, in Greek a πλήρωμα, 'like a completely coherent and comprehensive matrix, timeless, ungenerated, immaterial and perfect, of the physical cosmos'.<fnref n="39" /> A key term related to this Pleroma in Gnostic literature is τύπος,<fnref n="40" /> a 'stamp', an 'imprint' or simply a 'model', used either to describe entities within the Pleroma as *types* (models) of lower entities, or to describe the lower phenomena of this world as *types* (impressions) of entities in the Pleroma—this has to do with the same fundamental ambiguity inherent to the craft of printing that we have in the English term 'impression', and to which I shall soon have occasion to return.<fnref n="41" /> After this consideration, it is easier to see to what extent there is a connection between 'the seal of God' of the previous page and the plenitude of the alphabet.

<footnote>University, 1994), 15f.</footnote>

<footnote n="37">37. Van der Spuy, *'Hebrew Alphabetic Acrostics,'* 516, my italics.</footnote>

<footnote n="38">38. See A. O. Lovejoy, *The Great Chain of Being: A Study of the History of an Idea*, 2001 reprint (Cambridge, MA/ London: Harvard University Press, 1964), 65.</footnote>

<footnote n="39">39. J. Dillon, *'Pleroma and Noetic Cosmos: A Comparative Study,'* in *Neoplatonism and Gnosticism*, ed. R. T. Wallis and J. Bregman, Studies in Neoplatonism: Ancient and Modern 6 (SUNY Press, 1992), 100. I should note that for the purpose of this work, and *pace* Dillon, the Talmudic and other Rabbinic references discussed in previous sections will be considered enough evidence of a 'purely Jewish' idea of 'a whole, articulated archetypal world, by reference to which, as a pattern, God makes this one.'</footnote>

<footnote n="40">40. 'A virtual synonym for the more Platonic *eikon*, see *ibid*., 107.</footnote>

<footnote n="41">41. For a renowned typographer's perspective and reflections on the relation between stamp and printing press, see J. Tschichold, *Der chinesische Stempel. Ursprung des Buchdrucks* (Basel: Bucherer, Kurrus & Co, 1972).</footnote>
## Summary

What stands out very clearly from the above pages is that the *Tanakh* and all its commentaries through the centuries not only include as a major theme the cosmogonic power of speech, or at least of divine speech, but also that the attention to the relevance of the elements of that speech is embedded formally in the form of *abecedaria* and has also been commented upon from very early, like in the Talmud passage regarding Bezalel, and the passages of *3 Enoch*, estimated to date between the fourth and seventh centuries AD.

Later in this chapter, I shall introduce very important Jewish textual traditions which, although not so explicitly connected to the *Tanakh*, shed more light on our central topic.

For the time being let us retain from the above quotations: the consideration of a divine speech or script, the inextricable unity between the concepts of telling and counting, the cosmogonic aspect of the letters of the divine name, the connection between technical creativity and light, and the relation between a certain angelology and the basic elements of creation.

## Philo

As mentioned in the previous chapter (see above, p. 82), Philo stands as a crucial figure in the development of Hellenistic and Jewish philosophy and exegesis. It is as if from his particular intellectual vantage point, being conversant with both the Greek tradition and the Jewish scriptures, he had been able to bring the characteristically autonomous philosophical discourse to bear on Biblical hermeneutics, while at the same time enriching Greek Hellenistic cosmology with elements of Jewish origin. All this from a distinctly 'Platonic' doctrinal position which gave rise to the Pythagorean associations, as evident, among other works, in his Περί τῆς κατά Μωϋσέα κοσμοποιίας, *The Making of the World according to Moses (De opificio mundi)*,<fnref n="42" /> which discusses the creation of the world according to the Genesis hexaemeron. It is perhaps because of this middle ground he occupied—he has been dubbed 'a concordist between the Bible and *Timaeus'*—<fnref n="43" /> that he was neither incorporated into the roster of Greek philosophers nor to the Jewish rabbinical authorities, and even his supposed Hebrew name, Jedediah ('ידידיהו'), seems

<footnote n="42">42. See E. Filler, 'תאור הבריאה על-ידי פילון לאור תורת המספרים הניאופיתגוראית' (Description of the Creation by Philo in the Light of The Neopythagorean Theory of Numbers), 'Daat: A Journal of Jewish Philosophy & Kabbalah', no. 62 (2008): 5–25.</footnote>

<footnote n="43">43. See G. González Rabassó, 'Subtilitates naturae: Continuïtats i ruptures a la cosmologia d'Hildegarda de Bingen' (PhD diss., Facultat de Filosofia, Universitat de Barcelona, 2015), 96.</footnote>
οὖ γέγονεν, ὕλην δὲ τὰ τέσσαρα στοιχεῖα ἐξ ὧν συνεκράθη, ὅργανον
δὲ λόγον θεοῦ δι’ οὖν κατεσκευάσθη, τῆς δὲ κατασκευῆς αἰτίαν τὴν
ἀγαθότητα τοῦ δημιουργοῦ.

Moving on from these particular fixtures, consider now the greatest house or city, namely, this world: you will find that God is its cause (αἴτιον), by whom it came into being, that the materials (úlhn) are the four elements (στοιχεῖα), of which it is composed (συνεκράθη); that the instrument (ὕργανον) is the word [or reckoning] (λόγος) of God, by means of which it was set up (κατεσκευάσθη—furnished, arranged); and the object of the building you will find to be the display of the goodness of the Craftsman.47

The ‘elements’ are mixed like ingredients in a recipe, and the ‘word’ is the instrument. Now, that Word-Reckoning surely is also formed by stoicheia (letter-sounds, numbers) of another level. We have here again, more clearly, two implicit levels of stoicheia, the material meaning, and the ‘noetic’ uncreated one, or perhaps ‘formed not yet created’. It is worth remembering how we had found in the first chapter that the letters were a representation of the heavens, whereas now, with the world elements modelled on a ‘primordial printout’ (ἀρχέτυπον) in divinis, there would seem to be an inversion. As mentioned above, this would fit with the alternation between mould and cast which characterises printing techniques.

In another passage, Philo asks the reader to think of God’s creation as that of an architect,

ώς ἄρα τὴν μεγαλόπολιν κτίζειν διανοηθεὶς ἐνενόησε πρότερον τοὺς τύ-
πους αὐτῆς, ἐξ ὧν κόσμον νοητὸν συστησάμενος ἀπετέλει καὶ τὸν αἰσθη-
τὸν παραδείγματι χρώμενος ἐκείνῳ. καθάπερ οὖν ἡ ἐν τῷ ἀρχιτεκτονικῷ
προδιατυπωθεῖσα πόλις χώραν ἐκτὸς οὐκ εἶχεν, ἀλλ’ ἐνεσφράγιστο τῇ
τοῦ τεχνίτου ψυχῇ, τὸν αὐτὸν τρόπον οὐδ’ ὁ ἐκ τῶν ἰδεῶν κόσμος ἄλλον
ἀν ἔχοι τόπον ἤ τὸν θεῖον λόγον τὸν ταῦτα διακοσμήσαντα.

Just as when he thought through the construction of a great city, and he
conceived first its **types/characters** [a blueprint or mould], from which
he would compose and bring to completion a noetic world, which he
would then use as a paradigm for the perceptible world, similarly, just as
the city, **previously impressed** (*προδιατυπωθεῖσα*) **in the architectonic
paradigm**, was not situated anywhere, but **was stamped** solely in the
soul of the craftsman, neither could the world of the ideas have any

<footnote n="47">47. *De cherubim*, 127, 1.</footnote>
other location except the divine reckoning (λόγος) which had devised
(διακοσμήσας) them.<fnref n="48" />

We find here again in several instances the important image of the ‘impression’ or
‘stamping’ related to the word τύπος, with the addition of σφραγίς, ‘seal’, to the same
semantic group.<fnref n="49" /> The origin of this imagery goes back to the Timaeus (cf. 39e7, 50c-d),
with further developments in Middle Platonism under the influence of the Stoa.<fnref n="50" />

Another important aspect of the divine design is order, τάξις, an ‘arrangement’,
which in the first chapter I have shown to be, according to the Greek grammarians,
essential to the concept of στοιχεῖον. The following passage makes explicit once again
the relation between τάξις and ἀριθμὸς, but now in a cosmogonic context.

“Εξ δὲ ἡμέραις δημιουργηθῆναι φησι τὸν κόσμον, οὐκ ἐπειδὴ προσεδεῖτο
χρόνων μήκους ὁ ποιῶν (...) ἀλλ' ἐπειδὴ τοῖς γινομένοις ἔδει τάξεως.
τάξει δὲ ἀριθμὸς οἰκεῖον.

He [Moses] says that the world was crafted in six days, not because the
Maker needed any length of time (...) but because the new things required
arrangement [order]; and number is akin to arrangement.<fnref n="51" />

Given the features of Philo's cosmogony, it should be clear that the usual translation of κοσμοποιία as 'creation of the world', though perhaps not inaccurate in view of the Greek, would benefit from a more nuanced approach. What the texts contain is the description of the 'making', the 'fashioning', or the 'crafting' of the world from the point of view of a master craftsman, especially an architect, while the word 'creation' carries with it, especially in this context, the connotation of an *ex nihilo* process.<fnref n="52" />

## Archetype and Noetic Creation

The word ‘archetype’, which was current as a model, and had also been used in
philosophical contexts in that general sense, acquires in Philo a meaning which seems

<footnote n="48">48. *Opif.*, 19–20. Cf. Runia, *On the Creation*, 139, ‘the seal or mould (σφραγίς) first has to be engraved or marked out with markings (τύποι or χαρακτήρες) before it can be used to imprint form on receptive material. Because it is the prime source of the transferred design, it is also called the ἀρχέτυπον (literally “first or chief marking”)’, and see below.</footnote>

<footnote n="49">49. According to Chantraine, the origin of this word remains unclear in spite of various hypotheses, cf. P. Chantraine, *Dictionnaire étymologique de la langue grecque: histoire des mots* (Paris: Klincksieck, 2009), s.v. σφραγίς (hereafter cited as DELG).</footnote>

<footnote n="50">50. Cf. Runia, *On the Creation*, 139.</footnote>

<footnote n="51">51. *Opif.*, 13.</footnote>

<footnote n="52">52. About this very controversial topic in Philo studies, see Runia, *On the Creation*, 152-3.</footnote>
to reflect the influence of his Jewish background.<fnref n="53" /> We may not owe to Philo the first
ever occurrence of the word ‘archetype’ in a metaphysical sense, for it had been used
by some contemporary Platonists and by Stoic authors,<fnref n="54" /> but it is particular to Philo
that the ‘archetype’ is used with the full import of its printing connotation, with the
notion of ‘type’ in the sense of imprint—the idea of stamping, or etching as explained
above. Further down in *Opif.*, 25, we find,

δῆλον ὅτι καὶ ἡ ἀρχέτυπος σφραγίς, ὃν φαμεν νοητὸν εἶναι κόσμον, αὐτὸς
ἀν εἴη [τὸ παράδειγμα, ἀρχέτυπος ἰδέα τῶν ἰδεῶν] ὁ θεοῦ λόγος.

It is plain that the archetypal seal, which we affirm to be the intelligible
cosmos, would itself be the model and archetypal idea of the ideas, the
Logos of God.

[transl. Runia]

To complete this topic, I would like to present another passage,

προλαβὼν γὰρ ὁ θεὸς [...] ὅτι μίμημα καλὸν οὐκ ἄν ποτε γένοιτο δίχα
καλοῦ παραδείγματος οὐδέ τι τῶν αἰσθητῶν ἀνυπαίτιον, ὃ μὴ πρὸς
ἀρχέτυπον καὶ νοητὴν ἰδέαν ἀπεικονίσθη, βουληθεὶς τὸν ὁρατὸν
κόσμον τουτονὶ δημιουργῆσαι προεξετύπου τὸν νοητόν, ἵνα χρώμενος
ἀσωμάτω καὶ θεοειδεστάτω παραδείγματι τὸν σωματικὸν ἀπεργάσηται,
πρεσβυτέρου νεώτερον ἀπεικόνισμα, τοσαῦτα περιέξοντα αἰσθητὰ γένη
ἶσαπερ ἐν ἐκείνῳ νοητά.

God, apprehending beforehand [...] that there could not exist a good
imitation without a good model, and that of the things perceptible to the
external senses nothing could be faultless which was not fashioned with
reference to some archetypal idea conceived by the intellect, when he
had determined to create this visible world, cast first that one which is
perceptible only to the intellect, in order that so using an incorporeal model
formed as far as possible on the image of God, he might then make this
corporeal world, a younger likeness of the elder creation, which should
contain as many different perceptible genera as there are intelligible ones
in the other world.<fnref n="55" />

In these lines the notion of likeness, model, copy and imitation stand out, all in
relation to the first 'noetic' creation. Nothing comes to be directly, but rather mediated

<footnote n="53">53. See TDNT, s.v. λέγω.</footnote>

<footnote n="54">54. Cf. Runia, *On the Creation*, 151.</footnote>

<footnote n="55">55. *Opif.*, 16.</footnote>
by this intermediary creation, whose author and crafting are described in demiurgic
and ‘poietic’ terms. We also encounter here again the notion of a quantitative
correspondence between the ideal and the material realms, the ‘principle of plenitude’.

The Model is Λόγος

This ideal noetic model is often referred to by Philo as the λόγος, a word that in his
works expresses forcefully his own singular position between Hellenism and Judaism,
as I have mentioned.<fnref n="56" /> In the following passage, Philo explicitly lays bare what had
remained implicit in previous paragraphs.

εἰ δέ τις ἐθελήσειε γυμνοτέροις χρή-
σασθαι τοῖς ὀνόμασιν, οὐδὲν ἄν
ἔτερον εἴποι τὸν νοητὸν κόσμον
εἶναι ἤ θεοῦ λόγον ἤδη κοσμοποι-
οῦντος· οὐδὲ γὰρ ἡ νοητὴ πόλις
ἔτερόν τί ἐστιν ἤ ὁ τοῦ ἀρχιτέκτο-
νος λογισμὸς ἤδη τὴν νοητὴν πόλιν
κτίζειν διανοουμένου [...] τὴν γοῦν
ἀνθρώπου γένεσιν ἀναγράφων [...]
όμολογεῖ, ὡς ἄρα κατ' εἰκόνα θεοῦ
διετυπώθη. εἰ δὲ τὸ μέρος εἰκὼν εἰ-
κόνος, δῆλον ὅτι καὶ τὸ ὅλον· εἰ δ'
ό σύμπας οὖτος ὁ αἰσθητὸς κόσμος,
      ὅς μείζων τῆς ἀνθρωπίνης ἐστίν, μί-
μημα θείας εἰκόνος, δῆλον ὅτι καὶ
      ἡ ἀρχέτυπος σφραγίς, ὃν φαμεν νο-
ητὸν εἶναι κόσμον, αὐτὸς ἄν εἴη τὸ
παράδειγμα, ἀρχέτυπος ἰδέα τῶν
ἰδεῶν ὁ θεοῦ λόγος.

If you should wish to use words at their most
naked, you would say that the noetic world
is nothing but the **Logos** of God as he is
actually engaged in making the world;<fnref n="57" /> and a
city too, when only perceptible to the intellect,
is nothing but the **reason/reckoning/counting**
of the architect, who is then and there designing
to build another one perceptible to the external
senses, on the model of that which is so
only to the intellect [...] Accordingly Moses,
when recording the creation of man [...] asserts
expressly that he was **cast** in the image of
God—and if the part is **image of an image**,
then manifestly this is the case too for the
whole. And if this entire perceptible world,
which is greater than the human image, is a
**representation of the divine image**, it is clear
also that the ‘archetypal seal’, what we call the
intelligible world, would itself be the paradigm,
the archetype, the idea of ideas, the *Logos* of
God.<fnref n="58" />

In this disclosure, the making of man and the world are compared, both in the image
of the noetic reality, and finally a single name is given to that reality, the *Logos* of
God. I shall soon have an opportunity to explore the developments of this Greek term
in Christian theology, but it is important to point out that in this context, in which

<footnote n="56">56. See TDNT, s.v. λέγω, B-4.</footnote>

<footnote n="57">57. See Runia, *On the Creation*, 148–51, and p. 94 for the last part of the Greek paragraph.</footnote>

<footnote n="58">58. *Opif.*, 24–5.</footnote>
the discourse is about the divine all-possibility, the word is rife with its manifold senses, meaning inclusively, among others: collection, reckoning, calculation, account, consideration, enumeration, catalogue, narrative, word, speech.

Finally, in *De mutatione*, 135, we find the same motifs further detailed and forcefully put as a rhetoric question,

τίνος ὁ δακτύλιος, ἡ πίστις, ἡ τῶν ὅλων σφραγίς, ἡ ἀρχέτυπος ἰδέα, ἥ τὰ πάντ’ ἀνείδεα ὄντα καὶ ἄποια σημειωθέντα ἐτυπώθη; [...] ἄρ’ οὐχὶ μόνου θεοῦ;

Whose is the signet, the pledge, the stamp of all things, the archetype idea by which all things lacking form and quality were imprinted as meaningful signs [...] if not God's alone?

## Numbers: the Tetrad and the Decad

Philo's usage of numerology pervades his works. It is not that he uses isopsephy, but that he constantly appeals to the arithmetical properties of numbers in order to advance his explanations, and so, even though his Περὶ ἀριθμῶν is not preserved, we can have a very clear picture of the number doctrines he espoused. 'His testimony, in brief, is that the Greek *arithmetica*, as Nicomachus knew it and compiled it, existed also in Philo's day, and was accessible to and generally known by the well-educated man, even if he were not a professional mathematician.'<fnref n="59" />

As an example of his numerology, which gives also an insight into his arithmetic views, here is an important passage (*Opif. 47*) where he extols the virtues of numbers four and ten,

οἱ δ' οὐρανὸς διεκοσμεῖτο αὖθις ἐν ἀριθμῷ τελείῳ τετράδι, ἥν δεκάδος τῆς παντελείας οὐκ ἂν διαμάρτοι τις ἀφορμὴν εἶναι λέγων καὶ πηγήν· ὃ γὰρ ἐντελεχείᾳ δεκάς, τοῦτο τετράς, ὡς ἔοικε, δυνάμει· εἰ γοῦν οἱ ἀπὸ μονάδος ἄχρι τετράδος ἑξῆς συντεθεῖν ἀριθμοί, δεκάδα γεννήσουσιν, ἥτις ὅρος τῆς ἀπειρίας τῶν ἀριθμῶν ἐστι, περὶ ὃν ὡς καμπτῆρα εἰλοῦνται καὶ ἀνακάμπτουσι.

Heaven in its turn was ordered with a perfect number, the four. You would not go astray in affirming that it is the principle and source of the all-perfect number ten; for what the ten is in actuality, the four, it would seem, is potentially. If the numbers from the unit to the four are added up, they will produce the ten. It forms the boundary for the infinitude of numbers,

<footnote n="59">59. F. E. Robbins, 'Arithmetic in Philo Judaeus,' *Classical Philology* 26, no. 4 (October 1931): 361. See also Runia, *On the Creation*, 25ff.</footnote>
which wind around it like a turning post and turn back.

[transl. Runia]

It is important to observe here that such a view of number ten as the axis on which revolves the 'infinitude of numbers' is what lies at the basis of the concept of Pythagorean 'roots' (πυθμένες) and the calculations based on them,<fnref n="60" /> and it is, even more significantly for this research, a testimony to the vitality of the reverence accorded to the decad.

Finally, in the following reference are combined numeric symbolism and arithmetic understanding, to give an insight into the metaphysics of number at the basis of Philonian thought,

διαφέρει δὲ μονὰς ἑνὸς ἦ διαφέρει ἀρχέτυπον εἰκόνος· παράδειγμα μὲν γὰρ ἡ μονάς, μίμημα δὲ τῆς μονάδος τὸ ἕν.

The monad differs from one like the archetype from its image, for the monad is the model, and one is the **representation** of the monad.<fnref n="61" />

It is clear that the monad, the dyad, the triad and so on up to the decad—which are the objects of arithmetic speculation—are only called numbers by extension, figuratively. In reality they are something different, and they belong to a paradigmatic level from where the numbers draw their appearance.

## Chapter Summary: Philo in Perspective

Philo is at a cultural crossroads, explaining the *beri'ah* (*creatio ex nihilo*) of the hexaemeron in the symbolic language of a *yetsirah*, or to put it in Greek terms, he is putting a *genesis* in the terms of a *poetic*. At the heart of his exegesis there is λόγος, combining in its many facets the basic order and hierarchy of the alphabet, and also its semi-divine nature and its intermediary function. It is doubtlessly in the order intrinsic to this λόγος where we find in Philo the closest functional equivalent to our alphanumeric στοιχεῖα.<fnref n="62" /> When Philo uses the word itself στοιχεῖον, it refers to the 'material' elements, and not to the cosmogonic principles which inform the visible world. The brief grammatical passages where he uses the term exhibit the same basic

<footnote n="60">60. See above p.64.</footnote>

<footnote n="61">61. K. Staehle, *Die Zahlenmystik bei Philon von Alexandreia* (Leipzig: Teubner, 1931), fr. 2.</footnote>

<footnote n="62">62. I may also mention in this regard the 'spermatic substances' and 'invisible patterns', σπερματικά οὐσία which contain ἄδηλοι λόγοι (*Opif. 43*), mentioned on occasion of the creation of plants. Some scholars draw here clear parallels to the Stoic doctrine of *spermatikoi logoi*; see Runia, *On the Creation*, 56 and 184.</footnote>
alternation between the meaning of phoneme and written character which is found in
other authors.<fnref n="63" />

As Philo constitutes a first monumental point of contact in cosmological doctrines
between the Greek world and the Jewish tradition, I shall now move to another instance
of the same conjunction, but one which would become incomparably more widespread
and would begin not as a scholarly endeavour but as a religious movement, I mean the
advent of Christianity.

A connection between Philo and Middle Platonist and Stoic philosophers has
been mentioned, opening an entire new vista towards more or less contemporary
developments in the Hellenic world.<fnref n="64" /> However interesting these developments can
be, I shall for the moment concentrate on pursuing the alphabetic thread into the
early Christian literature, and only afterwards return to Greek philosophy in order to
examine the fate of our concept in Late Platonic authors.

<footnote n="63">63. *Agr. 137; Det. 7; Her. 210; Leg. 3,121; Mut. 63; Opif. 126; Sacr. 76*</footnote>

<footnote n="64">64. For the relevant references, see Runia, *On the Creation*, esp. 33, 139 and 184, where are treated topics related to this research.</footnote>
Chapter 4

Christian Sources and Exegesis

Letters-Numerals of the Christic Word-Number

After the previous pages, and after the insights obtained in the second chapter about
the root meaning of λόγος, it will hardly be surprising that we proceed to study how
our concept appears in Christian doctrine and exegesis, given that at the very heart
of this religion, the figure of Christ himself is identified since the earliest times with a
cosmic divine λόγος. The first and most important testimony to this in the Christian
scriptures is the beginning of the Gospel of St John, which gave rise over the centuries
to commentaries and doxological developments of all sorts.

Έν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν, καὶ θεὸς ἦν ὁ λόγος.

In the beginning was the logos, and the logos was with God, and the logos
was God.

Given the present context, the best option is to leave λόγος untranslated, and thus
to allow for the full import of its polysemy. By doing so, this Johannine cosmogonical
account reveals with clarity its resemblance to a Pythagorean-Platonic creation with
number, or *through* the word, as in the Genesis *ma'amarot*, or *by means of* a pattern
as in Philo's architectural cosmogony. The semantic richness is aptly expressed by the
Greek Fathers when they appeal to the text itself and affirm that 'no one can grasp the
sense (voũς) of this Gospel who has not reclined his head on Jesus' chest and who has
not received his mother Mary from him as his own mother.'<fnref n="1" /> Another interesting note
in the *Catenae* is that the verb ἦν should be understood as indicative of an eternal and
everlasting being (τοῦ ἀεὶ καὶ ἀπείρως εἶναι).<fnref n="2" />

<footnote n="1">1. J. Cramer, ed., *Catenae Graecorum patrum in Novum Testamentum*, repr. 1967 (Oxford University Press, 1841), 179.</footnote>

<footnote n="2">2. *Ibid*., 180.</footnote>
In any case, Augustine famously noted how *quod graece λόγος dicitur latine et rationem et verbum significat*, ‘what is expressed by λόγος in Greek, is expressed in Latin by *ratio* and *verbum*.’<fnref n="3" /> Quoting this very passage in his commentary to *De divinis nominibus*, Aquinas delves one step further into the meaning, explaining how *ratio* has four meanings: 1) *cognoscitiva virtus*, hence that God may be called *ratio*, comprehending ‘every cognition, either reason, mind or wisdom and of everything in every way’; 2) *causa*, and God is so called not only as being *the* cause of everything, but—and this is Dionysius—as ‘having gathered in himself primordially the causes of all things in a uniform way (μονοειδῶς)’;<fnref n="4" /> 3) *computatio*, a calculation or reckoning, as in Matt. 18:23–4, where a king is said to ‘settle accounts’;<fnref n="5" /> and 4) *aliquid simplex abstractum a multis*, used precisely because the divine *ratio* is the most simple above all simplicity, and the most separate or abstracted from all things.<fnref n="6" />

I barely need to refer the reader to the correspondences in Philo above, and to other previous similar findings. I shall instead concentrate on the remarkable second point to steer my argument towards my main concern in the alphanumeric elements. The ‘containing of the causes of all things’ is specified by Aquinas, *non per modum compositionis, sed per modum uniformitatis et simplicitatis*,<fnref n="7" /> ‘not as they are within composites, but inasmuch as they are unidimensional and simple,’ which in view of the divine στοιχεῖα can easily be thought to refer to the elemental quality of those secondary causes, as if on a list or row of simples. If this were so, we might expect to find elsewhere in the Christian tradition exegetical developments that pointed in this direction. And indeed we have several such developments, the first and most directly relevant of which I shall present in the following pages.

**Mysteria litterarum: Textual History**

The *Mysteria litterarum* was known from a Coptic-Arabic bilingual manuscript studied since the late nineteenth century.<fnref n="8" /> A French translation of the Coptic was published by

<footnote n="3">3. Augustine, *De diversis quaestionibus*, §63.</footnote>

<footnote n="4">4. For another passage in Aquinas which edges even closer to the demiurgic understanding of *ratio*, much in the manner of Philo, ‘as a ratio or *type* that preexists in the mind of the craftsman’, see E. Pattaro, *A Treatise of Legal Philosophy and General Jurisprudence (Volume 1: The Law and The Right)* (Dordrecht: Springer, 2005), 322-3.</footnote>

<footnote n="5">5. *Rationem ponere*, transl. NRSV.</footnote>

<footnote n="6">6. See Aquinas, Saint Thomas, *In librum beati Dionysii De divinis nominibus expositio*, ed. C. Pera O.P. (Torino: Marietti, 1950), 277.</footnote>

<footnote n="7">7. *Ibid*.</footnote>

<footnote n="8">8. Bodleian Ms. Huntington 393, dated 1393. For the most complete and recent history of the text, see Bandt, *Vom Mysterium*, and G. G. Stroumsa, ‘*The Mystery of the Greek Letters: a Byzantine Kabbalah?*’, *Historia religionum* 6, no. 6 (2014): 35–44. There is also a recent online translation from the Coptic by Anthony Alcock.</footnote>
Hebbelynck in 1900/01.<fnref n="9" /> Although a Greek Ms was known to be in Paris and mentioned by some authors who were interested in particular aspects of the text, it was only in 1980 that Paramelle studied this Greek witness and wished for an edition of the three versions together, Greek, Coptic and Arabic.<fnref n="10" /> Bandt has now partially fulfilled his wish; she has established that the original is Greek, that it was translated into Coptic, and from there into Arabic. Her 2007 monograph includes a Greek text based on all known Greek and Coptic/Arabic Mss., a rich preliminary study and German translation. The final pages of the text are only extant in Arabic, and apparently go rather off topic ('obscure jusqu'au rebus', says Paramelle).

The authorship is attributed by a Greek Ms. to John of Damascus, by the Coptic to an Apa Seba (Saba in Ar.). Based on this, Amélineau had attributed this to St Sabas of Jerusalem (439–532), and others, even more specifically, to an author within the monastic community of St Sabas, namely Saint Eustathius of Galatia, who was a calligrapher by profession.<fnref n="11" /> What all these conjectural authors have in common is their monastic life at the Great Lavra of St Sabas (Mar Saba), which continues to function to this day near Bethlehem. It has become conventional to speak of Ps.-Sabas as the author.

Being an original Greek work, it is quite remarkable that most parallels to its ideas are found in Jewish literature.<fnref n="12" /> Bandt singles out three works in particular where the idea of creation related to the twenty-two letters is found, and each of them is related to a Prophet:

1. *The Book of the Palaces* (Sefer hekhalot—henceforth SH) or 3 Enoch

2. The *Sefer Yetsirah* (SY)—Abraham

3. The *Book of Jubilees* (BJ)—Moses

I have already quoted before several passages from the *SH*. As for the *BJ*, Bandt describes it as the ‘earliest occurrence of the idea of relation between the Hebrew alphabet and the divine work of creation.’<fnref n="13" /> She also observes that whereas in *ML* the relation between the shapes of the letters and the cosmic realities is metaphoric, the Hebrew letters are seen in Jewish tradition as the actual material of the creation; Hebrew is indeed the language of creation, the cosmogonic language, and the divine act of creation is equalled to an act of writing.

<footnote n="9">9. A. Hebbelynck, ‘Les Mystères des lettres grecques,’ texte copte, traduction, notes, *Le Muséon*, nos. 19/20 (1900/1901): 5–36, 105–136, 269–300 and 5–33, 369–414.</footnote>

<footnote n="10">10. J. Paramelle, ‘Christianisme byzantin,’ *Annuaire de l’École pratique des hautes études. Vᵉ section, Sciences religieuses* 88 (1979): 379–386.</footnote>

<footnote n="11">11. Bandt, *Vom Mysterium*, 8.</footnote>

<footnote n="12">12. How much so is evident also from Stroumsa's mention of a 'Byzantine Kabbalah'.</footnote>

<footnote n="13">13. Bandt, *Vom Mysterium*, 51. The ref. is to *BJ* 2:1–25.</footnote>
Regarding SY and Abraham,<fnref n="14" /> attention is first drawn to the astronomical connections of Abraham, who came from Ur of the Chaldaeans (=astronomers). Abraham, however (and quite in agreement with Qur'anic material),<fnref n="15" /> is special in that he submitted his astronomy to the power of the One God. Bandt quotes a remarkable passage of the BJ in which Abraham's metanoia is described in terms almost identical to the Qur'anic account. But I shall have occasion later to return in more detail to the significance of SY.

Regarding Moses, what is paramount is his ‘authorship’ relation to the Torah. Bandt cites familiar Jewish traditions according to which the Torah is considered the ‘blueprint’ of the cosmos and, even more specifically, the particular letters each have a cosmogonic function. According to a tradition already cited,<fnref n="16" /> ‘The Holy One, praised be He, said, “I need workers.” The Torah said to Him, “Let me provide you with twenty-two workers, the twenty-two letters which are in the Torah, and I give each of them its due.”’

*Mysteria litterarum—the text*

The larger part of ML is dedicated to a letter by letter exegesis, including symbolic interpretations of the letter shapes, which are outside our ken, but the opening paragraphs, fortunately near where the extant Greek begins, contain the cosmological gist of the book. The author starts by describing how it was upon reading two New Testament passages that he was brought to understand that there was a great mystery hidden in the alphabet: ‘I am the alpha and the omega,’ (Rev. 1:8 and 22:13)<fnref n="17" /> and ‘Not an iota, not a dot, will pass from the Law until all is accomplished’ (Mt. 5:18).

In response to his prayers for his understanding to be opened to this mystery, he was granted a vision in which he stood on Mount Sinai and saw the lordly power (δεσποτικὸν κράτος), from which he heard and learnt about the letters. This same power, or an undetermined ‘untaught teacher’ (ἀδίδακτος διδάσκαλος), starts by explaining the relation between στοιχεῖα and γράμματα:

στοιχεῖα λέγονται ταῦτα τὰ γράμ-
ματα, οὐχ ὅτι στοῖχόν τινα καὶ τάξιν
ἀποτελοῦσιν, ὡς οἱ μάταιοι τῶν Ἐλ-
λήνων σοφοὶ ἐνόμισαν, ἀλλ' ὅτι τῶν
στοιχεῖων τῶν κτισμάτων τοῦ κόσμου
τοὺς τύπους καὶ τὰ σχήματα ἐν ἑαυ-

These letters are called ‘elements’ not because
they evince some **elemental sequence and order,** as the silly scholars among the Greek
thought, but because they contain in them-
selves and they trace (ὑπογράφουσι) the im-
prints (τύπους) and configurations (σχήματα)

<footnote n="14">14. Bandt, *Vom Mysterium*, 62ff.</footnote>

<footnote n="15">15. Qur'ān 6:76–79.</footnote>

<footnote n="16">16. See above p.26. *Tanhuma Yelammedenu*, (ed. Urbach, 1966), quoted in Bandt, *Vom Mysterium*, 73.</footnote>

<footnote n="17">17. Cf. above p. 116 and below p. 144.</footnote>
τοῖς ἔχουσι καὶ ὑπογράφουσι. of the elements that build this universe.<fnref n="18" />

A few lines later, after giving some examples, he explains that such a mystery was
carved precisely in the Greek letters so that the former idolaters would acknowledge
and submit to god-worship. Since ‘every human hand which by writing imprints these
letters (γράφουσα τοὺς τύπους τῶν γραμμάτων), thereby retraced/ratified (ὑπέγραψε)
and confirmed, either willingly or unwillingly, that the universe was not uncreated
as it seemed to the atheist among the Greek sages, but that there is the Divinity, and
that it made (ἐποίησε) in the beginning heaven and earth…’ Then, after giving a Genesis
summary, and after reminding us that Christ himself is the alpha and omega, he explains
a little further the process of creation:

Αὕτη ἡ νομιζομένη εὐτελὴς ἀλφάβητος τὸ μυστήριον περιέχει· διδά-
σκουσα ἡμᾶς ἐν τοῖς σχήμασι καὶ ἀριθμοῖς τῶν στοιχεῖων αὐτῆς τήν τε
τοῦ θεοῦ λόγου ἐξ οὐρανοῦ κατάβασιν.

This alphabet in its apparent simplicity contains the mystery: it teaches us,
through the configurations **and the numbers** of its elements, the descent
of the word (λόγος) of God from heaven.

Then the author goes on to give a list of all the other points of Christian doctrine taught
by the individual letters, a detailed elaboration which actually fills the rest of the book.

I have highlighted the association to the numbers, which must rank among the
first such texts in Greek literature, where attention to the alphanumeric duality of the
στοιχεῖα is drawn in this explicit way. The ‘elements’, according to it, have an intrinsic
‘number’ which is taught by the alphabet.

Later and throughout the treatise, it becomes hard to discern how the author chooses
when to use γράμματα or στοιχεῖα. Mostly γράμματα is used in the many instances in
which the shape of the written letter is being discussed, but cf. §25, when the author
asks about God:

Ποῖον τῶν κτισμάτων ἢ τῶν στοιχεῖων ἢ τῶν γραμμάτων ἐστὶ κύριος;

Over which of the creatures or elements or letters does he rule?

In §20 it is said of the letters: θεοτύποτα τυγχάνουσι καὶ οὐδεὶς ἀνθρώπων ἢ
φιλοσόφων ταῦτα διετύποσεν, ‘they are stamped/modelled by God, and there is no
man or sage who has stamped them.’ We could almost translate, ‘they are typed by
God,’ and in doing so, we are reminded of similar images in Philo’s writings, all about
divine printing or divine typography.

<footnote n="18">18. Bandt, *Vom Mysterium*, 106, emphasis mine.</footnote>
## 22 or 24 Letters

Another remarkable novelty we find in *ML* is the frequent occurrence of the feminine noun ἀλφαβήτος, used again and again as a sort of independent entity. In this regard, a puzzling feature of this work is how the author chooses to dismiss rather offhand the letters χ and ψ, and thus to deal with a 22-letter alphabet, just like the Hebrew. Indeed, one of the points of contact with the Jewish mystical tradition is the assignment of correspondences between the 22 letters and the 22 works of God, as recounted in the *Book of Jubilees* mentioned above.

In the end, the doctrine becomes rather puzzling between the rejection and the adoption of Hebrew and Greek letters and their respective interpretations and overlapping correspondences. This unclear borderline between the two traditions, as well as its doctrinal implications, has been fully appreciated by Stroumsa,<fnref n="19" /> who also confirms several of the developments I shall be discussing in later pages.

## Apocryphal Gospels

This Hebrew-Greek alphabetic melange is found again in some of the apocryphal gospels, in which the ‘alphabetic’ nature and wisdom of Christ is brought out in a remarkable way. In the *Infancy Gospel of Thomas*, a child Jesus challenges several school masters about the meaning and power of the letters of the alphabet, ‘If you are indeed a teacher, and if you know the letters well, tell me the power of *alpha* and I will tell you that of *beta*,’<fnref n="20" /> and also, ‘Hypocrite! How dare you teach the *beta*, when you have not even known the *alpha* in its original nature (κατὰ φύσιν)?’<fnref n="21" />

Immediately after, Jesus adds some more detail,

‘Listen, teacher, and observe the disposition (τάξις) of the first letter (στοιχεῖον), how it has two guiding strokes and a middle stroke crossing both lines which you see, how they converge with the top projecting and turning back as dancers (χορεύοντας)...’<fnref n="22" />

The puzzling description of the letter seems to refer to a cursive technique of joining

<footnote n="19">19. Stroumsa, *The Mystery*, 42–3.</footnote>

<footnote n="20">20. A. de Santos Otero, *Los evangelios apócrifos*, 9th ed. (Madrid: Biblioteca de Autores Cristianos, 1996), 292. There is a reference to this in Irenaeus, *Adv. haer.* 1, 20, 1; cf. C. A. Frilingos, ‘Parents Just Don’t Understand: Ambiguity in Stories about the Childhood of Jesus,’ *Harvard Theological Review* 109 (2016): 39.</footnote>

<footnote n="21">21. Santos Otero, *Los evangelios apócrifos*, 284, §§6 and 14.</footnote>

<footnote n="22">22. Cf. B. Ehrman and Z. Plese, eds, *The Apocryphal Gospels: Texts and Translations* (Oxford University Press, 2011), 41ff. and especially *The Infancy Gospels of James and Thomas*, vol. 2, ed. by R.F. Hock (Santa Barbara, CA: Polebridge Press, 1995), 117–18, for all the textual problems of this passage.</footnote>
the three constituent movements of the capital *Alpha*.<fnref n="23" /> The mention of the ‘dancing’ strokes, which has particularly baffled interpreters, does not look so strange if we recall the associations with dance found in the first chapter.<fnref n="24" /> We must likewise observe here, as the meaningful recurrence of a trait, the notion of the alphabet in its pedagogical dimension, and the letters as a preserve of childhood. This association, which is so obvious within the practical context of schooling, acquires here, in the narrative of the childhood of the Logos incarnate, a remarkable symbolic dimension.<fnref n="25" />

Similar exchanges are found in the *Arabic Infancy Gospel*,<fnref n="26" /> where *aleph* and *bet* (not Arabic, but Hebrew letter names in spite of the context) substitute the Greek letters, and in a number of other sources which attest to a complex and early transmission.<fnref n="27" />

It is interesting that there is no mention of any such text in the *Mysteria litterarum*; perhaps this could be considered a safe indicator that its text predates the infancy gospels, but the dating of these works is very uncertain, possibly as early as the second century, with variants in different languages found until the ninth century and later.

## A Spiritual ABC in Monastic Literature

Another later text related indirectly to these gospels is a peculiar alphabetic acrostic found in monastic correspondence, a list of virtues and vices that was used for meditative introspection as part of the teachings of religious communities, in particular as used by the hermit Barsanuphius (c. sixth century) to educate his disciples.<fnref n="28" /> The sacrality inherent to the στοιχεία was an integral part of this method, and it was taken for granted with all its connotations. Because στοιχεία meant letters and sounds as well as cosmic elements, their combination was understood to create a meaningful universe.<fnref n="29" /> By relating every letter-element to God, Barsanuphius was sacralizing his teaching. The use of the alphabet was in itself a sacramental practice, punctuating the ascetic progress, or an itinerary through the stations of the spiritual life.

In order to explain more satisfactorily the intension of the concept of such letters,<fnref n="30" />

<footnote n="23">23. Ehrman and Plese, *The Apocryphal Gospels*, 1094.</footnote>

<footnote n="24">24. See above, p. 29.</footnote>

<footnote n="25">25. See above, p. 36.</footnote>

<footnote n="26">26. Also called *Syriac Infancy Gospel*, §§48 and 49. See also the Arabic text in H. Sike, ed., *Evangelium infantiae, vel Liber apocryphus de infantia Servatoris* (apud Franciscum Halmam, 1697), 144ff.</footnote>

<footnote n="27">27. See B. McNeil, 'Jesus and the Alphabet,' *The Journal of Theological Studies*, 1976: 126-128, and also R. Aasgaard, *The Childhood of Jesus: Decoding the Apocryphal Infancy Gospel of Thomas* (Cambridge: James Clarke & Co Ltd, 2009), Greek text 219ff., and a valuable introduction.</footnote>

<footnote n="28">28. B. Bitton-Ashkelony, 'Counseling Through Enigmas,' chap. 5 in *The Monastic School of Gaza*, by B. Bitton-Ashkelony and A. Kofsky, Supplements to Vigiliae Christianae 78 (Brill, 2006), 119.</footnote>

<footnote n="29">29. *Ibid.*, 119-20.</footnote>

<footnote n="30">30. I use the term 'intension' both in its Scholastic and logical sense, referring to the intensity of semantic compression and to the sum of the attributes contained in the word (*OED*, s.v.).</footnote>
Bitton-Ashkelony makes use of a Hebrew binomial prominently attested in later times, the expression *otiyot yesod*. Meaning literally ‘letters of foundation’, this is how the twenty-two letters are once and again called in the *Sefer Yetsirah*; given the semantic correspondence, what we have in her expression is quite possibly *an original and native Hebrew translation of our stoicheia*.
# Chapter 5

## Hermetica, Magic and Gnostic Sources

From around the same time that the four canonical Gospels and the Pauline epistles were being recognised as authoritative in the second century AD,<fnref n="1" /> we have the first evidence of the Greek writings attributed to Hermes Trismegistus,<fnref n="2" /> a hybrid Egyptian-Greek mythical figure which represents the very rich and complex intellectual and religious landscape of late Hellenistic Alexandria, including the coexistence and multi-layered relations between Egyptian, Greek and Roman religions, Judaism and a burgeoning Christianity, so much so that the *Hermetica*, as this literature came to be called, has been viewed as a direct response to this very complex milieu, or more specifically as a result of the cross-cultural exchange and dialogue between Greek and Egyptian symbolic universes,<fnref n="3" /> a cultural and intellectual exchange much older than what took place during the Hellenistic period, and thus ultimately inextricable in historical terms.<fnref n="4" /> Hermetism has also been considered an example of the attempt to retain both philosophy and religion, and in this it has been compared to the writings of Neoplatonists and Neopythagoreans.<fnref n="5" />

Originally a collection of philosophical and soteriological contents, the Hermetic

<footnote n="1">1. See G. H. van Kooten, 'Christianity in the Graeco-Roman World: Socio-political, philosophical, and religious interactions up to the Edict of Milan,' in *The Routledge Companion to Early Christian Thought*, ed. D. J. Bingham (Routledge, 2009), 6.</footnote>

<footnote n="2">2. Hermetic collections of some kind circulated as early as the second or third centuries. See B. P. Copenhaver, *Hermetica: the Greek Corpus Hermeticum and the Latin Asclepius* (Cambridge: Cambridge University Press, 1992), xlii.</footnote>

<footnote n="3">3. J. Dieleman, *Priests, Tongues, and Rites: The London-Leiden Magical Manuscripts and Translation in Egyptian Ritual (100-300 CE)*, Religions in the Graeco-Roman World 153 (Leiden, Boston: Brill, 2005), 2, and more recently R. Gurgel Pereira, 'The Hermetic Λόγος: Reading the Corpus Hermeticum as a Reflection of Graeco-Egyptian Mentality' (PhD diss., Philosophisch-Historischen Fakultät der Universität Basel, 2010), 14.</footnote>

<footnote n="4">4. *Ibid*., 80.</footnote>

<footnote n="5">5. A. E. Affifi, 'The Influence of Hermetic Literature on Moslem Thought,' *Bulletin of the School of Oriental and African Studies* 13, no. 4 (1951): 841.</footnote>
literature<fnref n="6" /> grew over the centuries to include an enormous and uneven body of works which includes many astrological, magic and alchemical works of all origins, including eventually Latin and Arabic works.<fnref n="7" /> Two major strands are usually distinguished in this literature: one more ‘practical’, ‘magical’ or ‘theurgical’, and one more ‘theoretical’, ‘philosophical’ or ‘theological’, but the boundaries are difficult to decide, and the evidence seems to indicate that the two kinds of writings were related aspects of a single practical spiritual way,<fnref n="8" /> and that the dichotomy between technical and philosophical *Hermetica* is a modern classification.<fnref n="9" />

In the following pages, I will be taking into account the larger selection of *Hermetica* found in the Colpe-Holzhausen edition,<fnref n="10" /> which includes the Stobaeus fragments and some Coptic and other material, but I shall draw mainly from some passages of the *Corpus Hermeticum*<fnref n="11" /> and the *Asclepius*<fnref n="12" /> where there is question of the elements and of the power of phonemes.

First, however, I shall take the opportunity afforded by the *Hermetica* to look into the character of their eponymous deity, starting from the Greek myth which is related to this research very deeply and in many ways.

## Who is Hermes?

Whereas the names of most Greek gods have fallen into disuse and are relegated to mythological specialised literature, the name of Hermes has shown an extraordinary persistence through the centuries, partly due to the development of the *Hermetica*, but

<footnote n="6">6. I shall use here a wide meaning of ‘Hermetism’, including not only the philosophical *Hermetica* and its commentaries, but allowing also for later non-Greek sources, alchemical, magical and others, and I shall reserve for early modern material the useful terminological distinction found in W. J. Hanegraaff, *Dictionary of Gnosis & Western Esotericism* (Leiden: Brill, 2006), ix-x (hereafter cited as DGWE). Cf. also in this regard the important caveat in van Bladel, *The Arabic Hermes*, 17-22.</footnote>

<footnote n="7">7. A useful outline of what is included can be found in F. Ebeling, *The Secret History of Hermes Trismegistus: Hermeticism from Ancient to Modern Times* (Ithaca, NY: Cornell University Press, 2007), 10-11. Cf. Copenhaver, *Hermetica*, xxxii and the preface in extenso.</footnote>

<footnote n="8">8. G. Fowden, *The Egyptian Hermes: a Historical Approach to the Late Pagan Mind* (Princeton University Press, 1993), 95ff. and comments in Copenhaver, *Hermetica*, xxxvi.</footnote>

<footnote n="9">9. Gurgel Pereira, ‘The Hermetic Λόγος,’ 96.</footnote>

<footnote n="10">10. *Das Corpus Hermeticum* Deutsch, 2 vols, Clavis Pansophiae, 7, 1-2 (Stuttgart: Frommann-Holzboog, 1997).</footnote>

<footnote n="11">11. Hereafter *CH*, a group of eighteen Greek treatises historically considered as a distinct body of writing, Copenhaver, *Hermetica*, xxxii.</footnote>

<footnote n="12">12. This dialogue, preserved entirely only in Latin translation, was for centuries the only available representative, the ‘tip of iceberg’, of Hermetic literature in Europe; see I. Parri, ‘Tra ermetismo antico ed ermetismo medievale: l’Asclepius,’ in *Adorare caelestia, gubernare terrena. Atti del Colloquio Internazionale in onore di Paolo Lucentini*, ed. P. Arfé, I. Caiazzo, and A. Sannino (Turnhout, 2011), 53.</footnote>
also from the very original nature of the god.<fnref n="13" /> Indeed, this enduring power of Hermes is as clear testimony as could be to the attributes of the god, and even to his metallic symbol, quicksilver, whose ‘mobility makes it especially suitable for transformations,’ such as in its unique capacity to form amalgams with most other metals.<fnref n="14" /> The image of Hermes amalgamated into other traditions to the point that over the centuries he became identified, among others, to the prophets Moses and Elijah or to Enoch,<fnref n="15" /> to the Egyptian god Thoth,<fnref n="16" /> to St Paul of Tarsus,<fnref n="17" /> and to the Islamic prophet Idris.<fnref n="18" />

In the pre-modern Arabic world in particular, attributing a work to 'Hermes' was to ascribe it to an extremely ancient wisdom transmitted from many centuries ago, long before the revelation of Islam, but at some point in history, in early classical Baghdad, the 'thrice-great' Hermes became 'the triplicate Hermes' (Hirmis al-muthallath).<fnref n="19" /> Subsequent references to 'Hermes' sometimes deal accordingly with one of three different individuals: 'the first all-wise Hermes lived in Egypt before the flood, and is identical with Enoch; the second Hermes lived in Babylon and revived the sciences after the flood; the third Hermes is, once again, in Egypt. He taught alchemy and passed on his wisdom to Asclepius. This third Hermes corresponds to the Hermes of the Corpus Hermeticum.'<fnref n="20" /> However, true to the character of the god who moves at ease across boundaries, this triple distinction was far from consistent through the middle ages.

Going back to the origin, there is evidence of the name of Hermes in Greek from Mycenaean inscriptions, and the origin of the name refers clearly to a specific object, the ἔρμα, a cairn or heap of stones used to demarcate boundaries.<fnref n="21" /> Hermes is primarily a god of boundaries and intersections, and only later the consecrated messenger (ἀγγελος) of the gods. He was born at dawn, further emphasising his liminal nature,

<footnote n="13">13. Cf. the current use of 'hermeneutics'; see W. Burkert, *Greek Religion*, trans. J. Raffan (Oxford: Blackwell/Harvard University Press, 1985), 158.</footnote>

<footnote n="14">14. P. Enghag, *Encyclopedia of the Elements: technical data, history, processing, applications* (John Wiley & Sons, 2008), 797, includes a reference to Vitruvius, 7,8, the first recorded mention of amalgamation.</footnote>

<footnote n="15">15. Patai, *The Jewish Alchemists*, 33-4; K. Lindbeck, *Elijah and the Rabbis: Story and Theology* (New York: Columbia University Press, 2010), 74ff.</footnote>

<footnote n="16">16. This is the *interpretatio graeca*, Herodotus, 2, 67; see Fowden, *The Egyptian Hermes*, 22ff.</footnote>

<footnote n="17">17. Acts 14:12, and comment in Cramer, *Catenae*, 235, 'he was taken for Hermes by the unbelievers, because of his command of speech (λόγος).’</footnote>

<footnote n="18">18. O. El Daly, *Egyptology: the Missing Millennium. Ancient Egypt in Medieval Arabic Writings* (London: UCL Press, 2005), 84-5, 113-4, the earliest Arabic source is al-Mas‘ūdī. See also Y. Erder, ‘The Origin of the Name Idrīs in the Qur’ān: A Study of the Influence of Qumran Literature on Early Islam,’ *Journal of Near Eastern Studies* 49, no. 4 (1990): 341.</footnote>

<footnote n="19">19. van Bladel, *The Arabic Hermes*, 121-63.</footnote>

<footnote n="20">20. C. Burnett, ‘The Legend of the Three Hermes and Abū Ma‘shar’s *Kitāb al-Ulūf* in the Latin Middle Ages,’ *Journal of the Warburg and Courtauld Institutes* 39 (1976): 231.</footnote>

<footnote n="21">21. Burkert, *Greek Religion*, 156-7.</footnote>
and as patron of trade, he mingles with mortals and immortals alike.<fnref n="22" /> From very early
times, his most common representations were ithyphallic figures, initially placed on top
of cairns, and later incorporated into single stone pillars, many of which are preserved,
and which occasionally evolved into square pillars devoid of any obvious sexual
association.<fnref n="23" /> These pillars, regardless of their geometric abstraction, were still called
Hermes (whence the English ‘herm’), and they retained the connotations combining
demarcation, communication and generative power. It is not hard to see how in all
these aspects the association with language is natural, but instead of dwelling on this
symbolism, I would like to examine in detail a passage in *Philebus* which seems to sum
up very neatly, through the intervention of Theuth (Thoth, as the Egyptian Hermes),
the complex and wide-ranging significance of Hermes for this research.

Thoth and the Letters in *Philebus*

The context of this passage is important. It is introduced as one among other examples
(like music) of a 'doctrine of principles' which is both epistemological and ontological—
a 'tale of the people of old who were superior to us and living in closer proximity to the
gods, that whatever is ever said to exist consists of one and many' (16d1)—explaining
how knowledge and cosmic order are enacted 'by the action of the One structuring the
indeterminate plurality of the Dyad.'<fnref n="24" />

ἐπειδὴ φωνὴν ἄπειρον κατενόησεν
εἴτε τις θεὸς εἴτε καὶ θεῖος ἄνθρωπος—
ώς λόγος ἐν Αἰγύπτῳ Θεῦθ τινα
τοῦτον γενέσθαι λέγων—ὸς πρῶτος
τὰ φωνήεντα ἐν τῷ ἀπείρῳ κατενό-
ησεν οὐχ ἕν ὄντα ἀλλὰ πλείω, καὶ
πάλιν ἔτερα φωνῆς μὲν οὖ, φθόγ-
γου δὲ μετέχοντά τινος, ἀριθμὸν δέ
τινα καὶ τούτων εἶναι, τρίτον δὲ εἶ-
δος γραμμάτων διεστήσατο τὰ νῦν
λεγόμενα ἄφωνα ἡμῖν· τὸ μετὰ τοῦτο
διήρει τὰ τε ἄφθογγα καὶ ἄφωνα μέ-
χρι ἑνὸς ἑκάστου, καὶ τὰ φωνήεντα
καὶ τὰ μέσα κατὰ τὸν αὐτὸν τρό-

When someone, whether some god or even
divine human—tradition in Egypt reports that
this someone was Theuth—observed that vocal
sound (φωνή) is unlimited (ἄπειρον), he first
observed that the vowel sounds (φωνήεντα)
in the unlimited were not one but many, and
again that others partake not of voice (φωνή),
but of some sound (φθόγγος), and that there
are a certain number of those; and he set
apart a third form of letters, which we now
call stops (ἄφωνα). After that, he distinguished
the voiceless stops (τά ἄφθογγα καὶ ἄφωνα),
up to each one, and the vowel sounds and
the intermediates (τὰ μέσα) in the same way.

<footnote n="22">22. *Homeric Hymn to Hermes*, 17, 572ff.</footnote>

<footnote n="23">23. Burkert, *Greek Religion*, 156.</footnote>

<footnote n="24">24. C. H. Kahn, ‘Dialectic, Cosmology, and Ontology in the Philebus,’ in *Plato’s Philebus: Selected Papers from the Eighth Symposium Platonicum*, ed. J. Dillon and L. Brisson (Sankt Augustin: Academia Verlag, 2010), 59ff. gives a careful and insightful reading.</footnote>
πον, ἔως ἀριθμὸν αὐτῶν λαβὼν ἑνί
τε ἑκάστω καὶ σύμπασι στοιχεῖον
ἐπωνόμασε· καθορῶν δὲ ὡς οὐδεὶς
ήμῶν οὐδ' ἃν ἐν αὐτὸ καθ' αὐτὸ ἄνευ
πάντων αὐτῶν μάθοι, τοῦτον τὸν δε-
σμὸν αὖ λογισάμενος ὡς ὄντα ἔνα
καὶ πάντα ταῦτα ἔν πως ποιοῦντα
μίαν ἐπ' αὐτοῖς ὡς οὐσαν γραμματι-
κὴν τέχνην ἐπεφθέγξατο προσειπών.

When he had grasped their number, he applied
the name ‘letter’ (στοιχεῖον) to each one and
all together. And observing that none of us
would ever learn (μανθάνω) one apart by itself
(ἔν αὐτὸ καθ' αὐτὸ) without all of them, and
having reckoned in turn that this bond was
one (ἔνα) and made all these [letters] somehow
one (ἔν), he pronounced it the ‘art of letters’
(γραμματικὴ τέχνη), as being one [art] set over
them.<fnref n="25" />

MINIMAL SKETCH OF ANCIENT GREEK PHONOLOGY

The twenty-four letters were classified in Greek grammar as seven vowels (φωνήεντα) α ε η ι ο υ ω and seventeen consonants (σύμφωνα) β γ δ ζ θ κ λ μ ν ξ π ρ σ τ φ χ ψ. These were in turn classified as eight semivowels (ήμίφωνα) ζ ξ ψ λ μ ν ρ σ and nine voiceless (ἄφωνα) β γ δ κ π τ θ φ χ, of which three are smooth (ψιλά) κ π τ, three rough (δασέα) θ φ χ, and three medial (μέσα) β γ δ.<fnref n="26" />

It is not quite clear how closely Plato meant to remain to the linguistic classification sketched above, and it is not of much consequence to my present argument, though other contexts will afford the opportunity to mention it later. I also shall not go into the obvious and significant bearings that this extended passage has on the theory of the ideas and their liminal status, but I will draw attention to the fact that the officiating deity is Theuth, identified traditionally with Hermes, and by Ficino more specifically with Hermes Trismegistus.<fnref n="27" /> The invention of the alphabet, or more specifically the phonetic repertoire of the Greek language,<fnref n="28" /> as a selection or recognition of elements from a continuum is naturally ascribed to the god of language and communication. It is important to note too the emphasis on the *delimitation*—setting boundaries—as the method to establish the elements of language that will make possible learning

<footnote n="25">25. 18b6–d2, transl. Gill, *The Divine Method*, 44, slightly modified. Highlighting mine.</footnote>

<footnote n="26">26. Dionysius Thrax, *Dion. Thrax*, 10–13; D. Thrax, *The Grammar of Dionysios Thrax*, trans. T. Davidson, reprinted from the *Journal of Speculative Philosophy* (St. Louis: George Knapp, 1874), 5–6; for the corresponding passage in the *Poetics*, with a useful commentary, Aristotle, *On the Art of Poetry*, ed. I. Bywater (Oxford University Press, 1909), 56, 262 (1456b20ff.).</footnote>

<footnote n="27">27. M. Ficino, *The Philebus Commentary*, ed. M. Allen, Information and Interdisciplinary Subjects (Arizona Center for Medieval / Renaissance Studies, 2000), 273.</footnote>

<footnote n="28">28. Cf. the valuable reference to the International Phonetic Alphabet in Gill, *The Divine Method*, 45.</footnote>
(μανθάνειν), making of the elements in effect μαθήματα, 'mathematicals', and making all knowledge derived from the alphabet 'mathematical' in a way.

‘A certain number’ has to be recognised in the continuum, which then becomes an arithmeticised set of infimae species or intelligibilia prima. Phoneme and number thus stand together, inextricably joined at the root of language, and the same is applicable to music—it will be remembered that the invention of the lyre is also attributed to Hermes.<fnref n="29" />

Two lexical items of note are the use of διεστήσατο, ‘set apart’—a ‘demiurgic’ verb often used in the cosmogony of Timaeus—in establishing part of the alphabet, and the recognition of the unitary bond (δεσμός) which corresponds to our unitary concept of an alphabet or a complete system.

Among the epithets of Thoth in Egyptian literature are found ‘Lord of the words’, ‘The one with great Spell craft’, ‘Lord of the sacred words’ and he who ‘created the world by thought and utterance.’ I shall now move on to examine a few passages of the *Corpus Hermeticum* where these and the above facets of Hermes can be discerned again.

## The Creation Elements in the Hermetica

There are approximately forty occurrences of the word στοιχεῖον/elementum in the CH and the other Hermetica considered. Most of these refer to the four elements of the material world, to their origin and cosmological status.

The first example is found in Poimandres (CH I), 8,<fnref n="30" /> where the origins of the elements is discussed.

Τὰ στοιχεῖα τῆς φύσεως πόθεν ὑπέστη; [...] —Ἐκ βουλῆς θεοῦ ἡ φύσις λαβοῦσα τὸν λόγον καὶ ἰδοῦσα τὸν καλὸν κόσμον ἐμιμήσατο, κοσμοποιηθεῖσα διὰ τῶν ἑαυτῆς στοιχείων καὶ γεννημάτων ψυχῶν.

‘The elements of nature—whence have they arisen?’ [...] And he answered: ‘Nature, by the will of god having received the logos, having observed the beautiful cosmos and imitated it, thus being made itself a cosmos through its own elements and its progeny of souls.’<fnref n="31" />

<footnote n="29">29. *Homeric Hymn to Hermes*, 46ff. Cf. A. Vergados, *The Homeric Hymn to Hermes: introduction, text and commentary*, Texte und Kommentare 41 (Berlin/Boston: Walter de Gruyter, 2013), 88-90, 134ff. for astronomical associations to the seven strings and relevant literature; and see above p. 47.</footnote>

<footnote n="30">30. I cite following the Nock-Festugière text when possible, otherwise Colpe-Holzhausen.</footnote>

<footnote n="31">31. I follow Holzhausen's reading; see his translation, *Corpus Hermeticum Deutsch*, 13, and more specifically J. Holzhausen, 'Natur und Gottes Wille im Hermetischen Traktat 'Poimandres'', *Hermes* 120, no. 4 (1992): 485, where Büchli's reference to *Timaeus* 48 is noted, quite in line with my observations above.</footnote>
The correction introduced by Holzhausen (ή φύσις λαβοῦσα instead of ἥτις λαβοῦσα) solves satisfactorily longstanding textual problems, and it brings to light neatly the relation between the supernal logos and the στοιχεῖα, once again allowing for an alphanumeric interpretation. Here is an alternative and strictly valid translation: 'The letters of nature—whence have they arisen?' [...] 'Nature, by the will of god, received the Word, observed the beautiful cosmos and imitated it, thus becoming itself a cosmos through its own letters and its progeny of souls.'

If the metaphysical model for creation is a word or speech or language, it is only to be
expected that its component parts are letters or sounds. In an analogous way, we could
also translate λόγος as ‘reckoning’ or ‘calculation’—exactly as in the calculations made
by a craftsman during the creative process—and the στοιχεῖα would be the ‘numerals’
or simply the ‘numbers’ of the cosmos. The similarity with the intermediary role of the
λόγος in Philo is quite clear.<fnref n="32" />

It is important to note that the above text seems to imply the notion of a set
of 'beautiful' or heavenly elements which would have as counterpart the material
elements. In fact, this implication is unfolded and made explicit in other passages where
there is question of τὰ ἀνωφερῆ and τὰ κατωφερῆ στοιχεῖα, the 'ascending' and the
'descending' elements, or simply the 'upper' and 'lower' elements. In most contexts,<fnref n="33" />
including some passages of the CH,<fnref n="34" /> these terms refer to the pairs of fire-air and water-
earth respectively, meaning more precisely 'ascending' and 'descending', but in this
passage (I, 10), as in some other similar contexts, there is a clear distinction between
two sets of elements, superior and inferior. A few lines after the above quotation, the
material elements are in fact described as τὰ ἄλογα τὰ κατωφερῆ—they are logos-less
and inferior elements. Another mention of the inferior elements is found further down
in I, 11, and also in Asclepius where the contrast between the elementa inferiora and
superiora is found in sections 9 and 10.

This doctrine is later found explicitly in Aquinas,<fnref n="35" /> in universo elementa superiora dicuntur esse ut forma inferiorum, ‘the higher elements are said to be in the universe like a pattern for the lower ones,’ and it is exactly what is adumbrated by a contemporary philosopher who, elaborating on a passage of Theaetetus, says, ‘We must first discover the noetic elements, the universal letters ABC, and the universal system of the alphabet.’<fnref n="36" />

<footnote n="32">32. Cf. Holzhausen, *Natur und Gottes Wille*, 486.</footnote>

<footnote n="33">33. E.g. Cornutus (ca. 60 AD), *De natura deorum*, 48, 14.</footnote>

<footnote n="34">34. E.g. XIII, 6, and fragment 26.</footnote>

<footnote n="35">35. *Qu. disp. de veritate*, 1 qu.13, art. 5.</footnote>

<footnote n="36">36. J. D. Wild, *Plato's Theory of Man* (Harvard University Press, 1946), 281.</footnote>
Magic Phonemes

In treatise XVI of the CH we find for the first time in our survey another facet of the stoicheia in what came to be known as voces magicae, voces mysticae ('magic' or 'mystical utterances') or nomina barbara ('foreign names'). While addressing his interlocutor, Hermes explains how the translation of this treatise into Greek would render it inefficacious, since 'the very quality of the speech and the (sound) of Egyptian words have in themselves the energy of the objects they speak of,' whereas 'the Greeks have empty speeches ... that are energetic only in what they demonstrate.' 'We, by contrast, use not speeches (λόγοι), but sounds (φωναί) that are full of action (ἔργα).'<fnref n="37" />

The Egyptian language is here presented as a ‘primordial language’ whose sounds correspond directly to reality, independently of their semantic import, and the utterance itself is assigned a power which seems to bear no correspondence with the meaning of the words. The hermeneutical complication introduced by the fact that this text is preserved only in Greek has naturally been noted and commented upon.<fnref n="38" />

Earlier in Greek history, from around the fifth century BC, there is evidence of similar formulas of legendary foreign origin, the so-called ‘Ephesian letters’ (Ἐφέσια γράμματα),<fnref n="39" /> and of ‘meaningless names’ (ἄσημα ὀνόματα),<fnref n="40" /> deemed to possess apotropaic powers.<fnref n="41" /> Under another label, defixa nomina, they are common in amulets and talismans, both pagan and Christian,<fnref n="42" /> and in the also early attested defixiones, curse tablets, ‘inscribed pieces of lead intended to influence, by supernatural means, the actions or the welfare of persons or animals.’<fnref n="43" />

<footnote n="37">37. *Corpus Hermeticum*, ed. A. D. Nock and A.-J. Festugière, 4 vols (Paris: Les Belles Lettres, 1972), II, 232 (hereafter cited as Nock-Festugière). The opposition λόγος-ἔργον was customary; see *Corpus Hermeticum Deutsch*, I, 206. Cf. also Dieleman, *Priests, Tongues, and Rites*, whose first pages are based on this passage, and J. Ritoré Ponce, *La teoría del nombre en el neoplatonismo tardío* (Cádiz: Universidad de Cádiz, 1992), 198.</footnote>

<footnote n="38">38. See *Corpus Hermeticum Deutsch*, 200–201, and also Dieleman, *Priests, Tongues, and Rites*, 4. For possible Jewish influence, see Bohak, ‘The Impact of Jewish Monotheism,’ 8ff.</footnote>

<footnote n="39">39. The form reported by Hesychius is ασκι κατασκι λιξ τετραξ δαμναμενευς αασια; see D. Jordan, ‘Ephesia Grammata at Himera,’ *Zeitschrift für Papyrologie und Epigraphik*, no. 130 (2000): 106.</footnote>

<footnote n="40">40. See Jamblichus, *De mysteriis*, 7, 4–5, where the expression is used and the matter discussed in detail. Cf. also S. Crippa, ‘Les marges du langage dans les contextes sacrés: φθόγγος, φθέγγομαι,’ chap. 18 in *Manières de penser dans l’Antiquité méditerranéenne et orientale: Mélanges offerts à Francis Schmidt*, ed. C. Batsch and M. Vârtejanu-Joubert, *Supplements to the Journal for the Study of Judaism* 134 (Brill, 2009), 269.</footnote>

<footnote n="41">41. Cf. Plutarch, *Quaest. Conv*. 706e1.</footnote>

<footnote n="42">42. See I. Velázquez, ‘Intersección de realidades culturales en la antigüedad tardía: el ejemplo de defixiones y filacterias como instrumentos de la cultura popular,’ *An Tard*, no. 9 (2001): 159ff. and Luz, *Technopaignia*, 213. Cf. Ernout-Meillet, s.v. figo.</footnote>

<footnote n="43">43. D. Jordan, ‘A Greek Defixio at Brussels,’ *Mnemosyne* 40, nos. 1/2 (1987): 162.</footnote>
Magical Papyri

All those powerful unsemantic utterances are a major component of what has come to
be called generically the ‘Magical Papyri’, a collection of very early texts in Demotic,<fnref n="44" />
Coptic or Greek, preserved in Egypt and representing very clearly the Hellenistic
syncretism between Egyptian, Greek and Jewish religions. As with Hermetism in
general, they are still associated primarily with Greek culture, and still often referred to
as ‘Greek Magical Papyri’, in spite of the recurrent coexistence of Greek and Demotic
texts on the same pages, which attests to a very developed synthesis between Egyptian
and Greek literature.<fnref n="45" />

It may be useful to point out that this ‘influence by supernatural means’ is not quite so
‘supernatural’, but rather ‘natural’ within the worldview under study in the preceding
pages; or perhaps what should be made clear, in due fairness to our contemporary views,
is that the ancient concept of nature was more ‘supernatural’ altogether. The power of
the phonemes of a given ‘primordial’ language—which could be other than Egyptian—<fnref n="46" />
is a concomitant of the essential correspondence between human language and cosmic
language.

These different kinds of magical unsemantic utterances are also related directly
to the Greek literary texts comprised by the term τεχνοπαίγνιον—all manners of
wordplay and jeux d'esprit, including acrostics, palindromes and pangrams—<fnref n="47" /> as has
been observed by Luz in her comprehensive monograph.<fnref n="48" />

The main traits of these magical formulas are readily apparent in the several epithets
applied to them which we have given above. That they are called voces refers to the
importance of their enunciation: they are normally to be uttered aloud, even though in
some exceptional cases a personal silent 'saying' is asked for.<fnref n="49" /> This may partly explain
why the vowels occupy such a prominent place in this magical literature, reminding us
of the special cosmological status accorded to vowels by the Greek grammarians. We
find in the papyri, for instance, instructions for the recitation of 'the heptagram', the
seven vowels αεηιουω in many complex variations.<fnref n="50" />

<footnote n="44">44. A later stage of the Egyptian language.</footnote>

<footnote n="45">45. See H. D. Betz, ed., *The Greek Magical Papyri in Translation, including the Demotic Spells* (University of Chicago Press, 1986), xlv; E. Suárez de la Torre, 'Himno(s)-plegaria a Hermes en los papiros mágicos griegos,' in *Ex Pluribus Unum*, ed. C. Scibonae and A. Mastrocinque (Edizioni Quasar, 2015), 193.</footnote>

<footnote n="46">46. See Betz, *Magical Papyri in Translation*, xlv, for mention of Greek and Hebrew as two examples.</footnote>

<footnote n="47">47. A pangram or holoalphabetic sentence is a sentence using every letter of a given alphabet at least once.</footnote>

<footnote n="48">48. Luz, *Technopaignia*, 213–22.</footnote>

<footnote n="49">49. Cf. K. Preisendanz and A. Henrichs, eds, *Papyri Graecae Magicae. Die griechischen Zauberpapyri*, 4 vols (Leipzig/Berlin: Teubner, 1928–1941) (hereafter cited as PGM), 3, LXXVII, 5, θυμῷ μηδὲν λαλήσας, ‘in the heart, saying nothing aloud.’</footnote>

<footnote n="50">50. See Betz, *Magical Papyri in Translation*, 190.</footnote>
Voces, like the Greek φθόγγοι ἐναρμόνιοι ‘harmonic utterances’,<fnref n="51" /> also indicates that they are not necessarily words, but merely vocal sounds, ἄσημα, unsemantic, as shown by another epithet. Sometimes they are instead called γράμματα, letters, referring to the graphic aspect which is such a remarkable feature of the magical papyri, where page after page is filled with all sorts of geometric letter arrangements: mirroring layouts which play on palindromes of varying extension, diminishing lines which form pyramids and triangles, and many other graphic devices.<fnref n="52" />

<figure><img src="image_14.png" /></figure>

Another remarkable use of the vowels, and an additional example of the significance of the symbolism of *alpha* and *omega* is the following array which in the original concludes with the exclamation ‘Jesus Christ, help!’<fnref n="53" />

<figure><img src="image_15.png" /></figure>

With regard to the pairing of *alpha* and *omega*, and further to my previous comments, it has been noted<fnref n="54" /> that among the most distinctive features of the magical papyri is a strong tendency towards ‘circularity’, towards closing strings of letters in the manner of a palindrome,<fnref n="55" /> joining beginning and end to thus symbolically encircle and subdue the object of the spell. Once again, as with the acrostics, it can be seen that the magic power (in other contexts cosmogonic) is related to a ‘catalogue’ of the creative elements, to reciting as one would recite the alphabet, without omitting any element. There seems

<footnote n="51">51. See Crippa, *Les marges du langage*, 269.</footnote>

<footnote n="52">52. See Dornseiff, *Alphabet*, 63–7, and Luz, *Technopaignia*, 215. The following example is from *Suppl. Mag.* 7.</footnote>

<footnote n="53">53. D. Wortmann, ‘Neue magische Texte,’ *Bonner Jahrbücher* 168 (1968): 106.</footnote>

<footnote n="54">54. E. Szepes, ‘Magic Elements in the Prayers of the Hellenistic Magic Papyri,’ *Acta Antiqua Academiae Scientiarum Hungaricae Budapest* 24, nos. 1-4 (1976): 215–16, 222. Cf. above, p.116 for the Hebrew equivalent.</footnote>

<footnote n="55">55. *ibid.*, 216, with a reference to the Ouroboros.</footnote>
to be a creative power in the self enclosing totality of the *system* of elements. In the case of Christ it seems obvious, as perceived by the author of the *Mysteria litterarum*, that when he is called *alpha* and *omega*, the remaining letters of the alphabet are to be understood as well—he is *all* the letters.

The recourse to the Christian invocation, insofar as it has to do with an organised religion, can be related to the epithet of *mysticae*, for this adjective refers to the mysteries of Greek and Roman religion. The religious status of magic, between marginal superstitious and mainstream respectable practice, cannot in most cases be decided clearly, especially in the Egyptian context in which some of the practices later associated exclusively with magic were part of the priestly duties.<fnref n="56" /> Initiation, religion and magic meet inextricably in the use of these ‘utterances’ and ‘letters’.

That they are ‘Ephesian’ typifies their being perceived as foreign, as alien. According to many scholars over the centuries, it is in great part due to this feature that they retain an aura of mystery and that their utterance commands awe and reverence. ‘Ephesian’ also, and more particularly, meant ‘Eastern’, or at the very least open to the East, and indeed, one of the most repeated linguistic traits of these *voces* is the abundance of Semitic word endings like -ηλ and -ωθ.<fnref n="57" />

When they are called *defixa*, what is emphasised is their irrevocability, for there is no reversing an utterance, and in this we find again the image of the seal and the *fixity* of its imprint. Related meanings of *defigo* include ‘to bind’ and ‘to impress’. In a primary and very practical sense, the spells relate to a menial action: to fix or attach something with nails, stakes, ‘to plant’ something, like determining boundaries on a field (*defigere terminos*), or like carving letters on a monument (*defixa monumentis nomina*).<fnref n="58" />

## The Twenty-Four Alphabetic Names of Gods

That they may be called also ὀνόματα, ‘names’, refers to how the utterances of power can be considered as concepts which are simultaneously viewed in their elementary quality. In Orphic literature, as also in Jewish rabbinical texts, it is not uncommon to find long lists of the names of God or a god, or the names of Metatron.<fnref n="59" /> In the papyri we

<footnote n="56">56. See E. Suárez de La Torre, M. Blanco Cesteros, and E. Chronopoulou, ‘A la vez igual y diferente: notas sobre el vocabulario “religioso” de los textos mágicos griegos,’ in *Estudios sobre el vocabulario religioso griego*, ed. E. Calderón Dorda and S. Perea Yébenes, Monografías de Antigüedad Griega y Romana 49 (Madrid–Salamanca: Signifer Libros, 2016), 210, 228.</footnote>

<footnote n="57">57. Respectively the Hebrew name of God, as in *Isra-El*, and the Heb. feminine plural ending as in Rehov-ot; see Luz, *Technopaignia*, 214.</footnote>

<footnote n="58">58. *OLD*, s.v. *defigo*.</footnote>

<footnote n="59">59. See Odeberg, *3 Enoch*, I, 170 and II, 160, but these lists go back to at least the second millenium BC in both Indo-European and Semitic texts; cf. J. Myerston, ‘Divine Names in the Derveni Papyrus and Mesopotamian Hermeneutics,’ *Trends in Classics* 5, no. 1 (2013): 74–110, for refs. to * Enuma Elish* and</footnote>
have one particular example where the name-letter conjunction comes into focus very strikingly, namely in a fifth-century love charm<fnref n="60" /> where the ‘daimons’ are conjured by ‘the true one’ named with an alphabetic acrostic list of names, i.e., twenty-four names, each starting and ending (with two exceptions) successively with the Greek letters; it starts,

Ἀκραμμαχαμαρι Βουλομεντορεβ Γενιομουθιγ Δημογενεδ Ἐνκύκλιε...

*Akrammachamari Boulomentoreb Geniomouthig Demogened ...*

Wortmann calls them the ‘Gods of the Twenty-Four Letters’ and the ‘Twenty-Four Gods of the Alphabet’,<fnref n="61" /> while drawing attention to the unique nature of this spell, and observing that some of the names, e.g. Θωθουθωθ, read like palindromes, while others are just short of being palindromes, e.g. Φιμεμαμεφ. A fair inference of a hypothetical model for this kind of construction would be an acrostic list of twenty-four palindromes, beginning and ending with each letter of the alphabet.

One final example from the papyri shows clearly the ambiguity and the cosmic status of *stoicheia* which are central to this research. It is a love charm that begins with an impressive letter geometrical arrangement and is followed by this,

Ἐξορκίζω σε τῶν δώδεκα στοιχεῖων τοῦ οὐρανοῦ καὶ ἰκοσιτέσσερα στοιχεῖων τοῦ κόσμου...

‘I adjure you by the twelve stoicheia (constellations) of heaven and the twenty-four stoicheia (elements) of the world...’<fnref n="62" />

We had seen that *stoicheia* could be used for the constellations, but what to make of those ‘twenty-four elements of the world’?<fnref n="63" /> They are normally four only, or five, but due to a slip perhaps, or due to what was an all too easy assimilation, the number of the letters of the alphabet is transposed to that of the superior elements. The other possibility might be that the ‘world’ mentioned here were referring to an abstract conceptual world, but in that case the contrast between heaven and world would not be easy to explain.

<footnote>relations to Orphic hymns. Cf. also in general Dornseiff, *Alphabet*, 145–6, and A. Uždavinys, *Philosophy as a Rite of Rebirth* (Westbury, UK: The Prometheus Trust, 2008), 23–24, for Egyptian parallels.</footnote>

<footnote n="60">60. Cologne, Papyrussammlung P. 3323; Wortmann, ‘Neue magische Texte,’ 88, 98–9, including photographs of the text. Translation in Betz, *Magical Papyri in Translation*, 308, no. 101; this is not in PGM.</footnote>

<footnote n="61">61. Wortmann, ‘Neue magische Texte,’ 87, 98.</footnote>

<footnote n="62">62. PGM, 2, XXXIX, 18; Betz, *Magical Papyri in Translation*, 279.</footnote>

<footnote n="63">63. ‘World’ is a more apt translation of κόσμος here in contrast to heaven; cf. Jn. 13:1 ἡ ὥρα ἵνα μεταβῆ ἐκ τοῦ κόσμου τούτου πρὸς τὸν Πατέρα, ‘the time for him to depart from this world towards the Father.’</footnote>
In the context of magical literature, this usage of the ‘twenty-four letters’ also
reminds us strongly of the influential magical *materia medica* entitled *Kyranides*, also
ascribed to ‘Hermes Trismegistos the god’,<fnref n="64" /> and also exhibiting most of the features
mentioned above, wherein stones, herbs, fish and birds are grouped under the Greek
letters in alphabetic order. In this arrangement, the letters act as an intermediary
ordered array between the ‘alphabet in heaven’ and the ‘alphabet of things’.<fnref n="65" />

Trying to sum up the findings in the papyri and their formal relations to Hermetism,
it may be noted that among the most important characteristics of the spells and
invocations are their oriental character, the rhythmic repetition of certain words or
sounds and the listing, often exhaustive, of the divine attributes,<fnref n="66" /> which are all common
features of the more ‘practical’ Hermetica.<fnref n="67" /> Letter ‘acrobatics’, graphic and phonetic,
and isopsephic arrangements are found all over the texts and go hand in hand with
the above features, as in a display of craftsmanship, of the mastery of order and
rhythm, moving from a discursive ‘logic of concatenation’ to an ‘iconic expansive
logic’, transmitting meaning simultaneously on several levels through the ‘semiotic
superposition’<fnref n="68" /> characteristic of ancient poetry as in Greek calligrams, Roman *carmina
figurata* and all sorts of ‘pattern’ or ‘concrete’ poetry.<fnref n="69" />

There is a clear specular relation between the pattern complexity of the magic
formula and the complexity of the reality that is to be altered—in one as in the other,
the basis of the intelligibility and of the constitution on every level is order,<fnref n="70" /> which, as
we had found in the first two chapters, is the most prominent of the characteristics of
the *stoicheia* and is directly related to its numeric aspect.

<footnote n="64">64. D. Kaimakis, ed., *Die Kyraniden* (Meisenheim am Glan: Hain, 1976), prologue, l. 5.</footnote>

<footnote n="65">65. See C. F. Fraker, 'Hermes Trismegistus in the *General Estoria II*,' in *Medieval Iberia: Changing Societies and Cultures in Contact and Transition* (Tamesis Books, 2007), 96–7; also I. Toral-Niehoff, *Kitāb Ġiranīs: Die arabische Übersetzung der ersten Kyranis des Hermes Trismegistos und die griechischen Parallelen*, Quellen und Forschungen zur antiken Welt 43 (München: Herbert Utz Verlag, 2015), 11.</footnote>

<footnote n="66">66. H. Björklund, 'Invocations and Offerings as Structural Elements in the Love Spells in *Papyri Graecae Magicae*,' *Journal for Late Antique Religion and Culture*, no. 9 (2015): 46–7.</footnote>

<footnote n="67">67. 'The Hermetic authors felt no obligation to respect the boundaries drawn around their writings by modern critics,' Copenhaver, *Hermetica*, xxxix.</footnote>

<footnote n="68">68. Cf. P. G. Leal, 'O espelho dos hieróglifos: da ruína das letras egípcias à sua reinvenção quimérica entre os séc. XV e XVII' (PhD diss., Universidade Federal do Rio Grande do Norte, Brazil, 2008), 106; and S. Lojkine, «Dans le moment qui précède l'explosion...» — Temporalité, représentation et pensée chez Diderot,' in *Zeitlichkeit in Text und Bild*, ed. F. Sick and C. Schöch (Heidelberg: Universitätsverlag Winter, 2007), 57.</footnote>

<footnote n="69">69. See A. Pappas, 'The Treachery of Verbal Images: Viewing the Greek *technopaegnia*,' in *The Muse at Play: Riddles and Wordplay in Greek and Latin Poetry*, ed. J. Kwapisz, D. Petrain, and M. Szymański, Beiträge zur Altertumskunde 305 (Walter de Gruyter, 2013), 199.</footnote>

<footnote n="70">70. A. Mastrocinque, 'Le pouvoir de l'écriture dans la magie,' *Cahiers « Mondes anciens* », no. 1 (2010): 37.</footnote>
Regarding the relation between Hermetism and these magic texts, there is on one hand the fact that many of the texts are explicitly related to Hermes,<fnref n="71" /> and it is true that ‘the magician who intends to enter the mysteries by means of the voice and the name, recognises Hermes Psychopomp and Hermes Thoth as his master, as god of gnosis, incarnation of the logos,’<fnref n="72" /> but beyond the explicit mention of the Graeco-Egyptian deity, there is no way to ignore that all this magical literature is Hermetic in substance: it is after all, and here I refer at once to several previous sections of this work, a **communication** established by the **mediation of language** with the purpose of **generating** change. Such manipulation of concepts and numbers, and the concomitant mirroring just mentioned, as foundations of a method of influencing the world, are very close to the foundation of scientific *and* religious endeavours, and most likely the reason why at times magic and science, and at times religion and science, have been considered to be two sides of one coin.<fnref n="73" />

## Gnostic Writings

As in the case of the Hermetic writings, the label of ‘Gnostic’ developed into an umbrella term that has been considered ‘highly problematic’, ‘obscuring distinctive characteristics’, and finally ‘a term that lost its utility.’<fnref n="74" /> This extreme syncretic ‘Gnosticism’ is however one end of a spectrum ranging between two main meanings: first, one narrow and more strictly historical which is the name given, often deprecatingly, to ancient Christian sects, the γνωστικοί or ‘gnostics’, literally ‘the ones acquainted’ (sc. with God); and second, that broader, problematic and variegated meaning, which ranges from Christian heterodoxy to Orphic, Hermetic, Mandaean, Jewish, and Islamic texts.<fnref n="75" /> What most Gnostic writings have in common, and it is

<footnote n="71">71. See Suárez de la Torre, *‘Himno(s)-plegaria a Hermes en los papiros mágicos griegos,’* 199–201.</footnote>

<footnote n="72">72. See Ritoré, *La teoría del nombre*, 196.</footnote>

<footnote n="73">73. See C. Webster, *From Paracelsus to Newton: Magic and the Making of Modern Science*, The Eddington Memorial Lectures (Cambridge University Press, 1982), 1, 57.</footnote>

<footnote n="74">74. A thorough monograph on this topic is M. A. Williams, *Rethinking ‘Gnosticism’: an argument for dismantling a dubious category* (Princeton University Press, 1996). See also, more recently, J. Lahe, *Gnosis und Judentum: alttestamentliche und jüdische Motive in der gnostischen Literatur und das Ursprungsproblem der Gnosis*, Nag Hammadi and Manichaean Studies 75, originally presented as a PhD thesis–University of Tartu (Leiden: Brill, 2012), 11ff. and K. van Bladel, ‘Gnosticism,’ *Encyclopaedia of Islam, THREE*:83.</footnote>

<footnote n="75">75. B. Layton, *The Gnostic Scriptures*, The Anchor Bible Reference Library (New York: Doubleday, 1987), 49; Williams, *Rethinking ‘Gnosticism’*, 42–3. ‘Some texts of magical prayers show a conflation of tendencies, or at least vocabulary analogies between Hermetic gnosis and Judeo-Christian gnosis,’ M.-T. D’Alverny, review of La Révélation d’Hermès Trismégiste. I: L’astrologie et les sciences occultes by A.-J. Festugière, *Bibliothèque de l’École des chartes* 105, no. 1 (1944): 268.</footnote>
in this that they are related to Hermetism, is in what their name itself points to, a direct approach to ‘salvific esoteric knowledge’ (γνῶσις),<fnref n="76" /> to initiatic mysteries.<fnref n="77" /> This Gnostic claim to ‘real knowledge’ comes often in the form of a distinctive cosmology, and it is among such doctrinal writings that the alphanumeric symbolism is occasionally found. With the exception of Marcus the Valentinian<fnref n="78" /> (second century AD) however, there is nothing like a systematic cosmology, but fragmentary evidence gained mostly from Coptic translations of hypothetical original lost Greek texts, or in some cases of possible Syriac origin.<fnref n="79" /> I shall now comment on passages from two works of the Nag Hammadi Library (NHL),<fnref n="80" /> before introducing Marcus’ text. I shall refrain from entering into the details, and especially from trying to make sense of the cosmological complexities of the texts in this section, which are of a bewildering oneiric nature, continually challenging the experts, and which are in general beyond the ken of the present research. I shall instead limit myself to draw attention to the interesting aspects of alphanumeric symbolism found in them.

## Evangelium Veritatis

The *Gospel of Truth*,<fnref n="81" /> approximately dated between 140 and 180 AD, begins with a so-called ‘Litany of the Word’,

> This is the knowledge of **the living book** which he revealed to the aeons, at the end, as his letters, revealing how they are not vowels nor are they consonants, so that one might read them and think of something foolish, but **they are letters of the truth** which they alone speak who know them. Each letter is a complete (thought) like a complete book, since they are letters written by the Unity, the Father having written them for the aeons in order that by means of his letters they should know the Father. While his

<footnote n="76">76. DGWE, vii–viii.</footnote>

<footnote n="77">77. ‘Gnostic and Hermetic texts pullulate with the words *mysteria* and *mystikos*,’ W. Burkert, *Antike Mysterien, Funktionen und Gehalt* (München: Verlag C. H. Beck, 1990), 57.</footnote>

<footnote n="78">78. The followers of Valentinus (d. ca. 160), particularly given to theological speculation, constituted one of the largest and best known Gnostic schools, active throughout the Roman Empire. Marcus and the Marcosians after him should not to be confused with fellow Valentinian and famous heresiarch Marcion of Sinope and the Marcionites; cf. Layton, *The Gnostic Scriptures*, 217ff.</footnote>

<footnote n="79">79. *The Nag Hammadi Library in English*, ed. J. M. Robinson (New York: HarperCollins, 1990), 12; *Nag Hammadi Deutsch: Studienausgabe. NHC I–XIII, Codex Berolinensis 1 und 4, Codex Tchacos 3 und 4*, 3rd ed., de Gruyter Texte (De Gruyter, 2013), 19.</footnote>

<footnote n="80">80. This all-important treasury of Gnostic literature was only discovered in 1945, and it was thus unavailable to Dornseiff. About the non-Gnostic contents of NHL, see G. Quispel, *Gnostica, Judaica, Catholica. Collected Essays of Gilles Quispel*, ed. J. Oort, Nag Hammadi and Manichaean Studies 55 (Brill, 2008), 212.</footnote>

<footnote n="81">81. Nag Hammadi Codex I (henceforth NHC I). *Nag Hammadi Deutsch*, 18ff.</footnote>
wisdom contemplates the Word, and his teaching utters it, his knowledge
has revealed it.<fnref n="82" />

Most Gnostic texts elaborate profusely on various aspects of the Christic nature,
hence on the nature of the logos and its relation to God the Father. Particularly
interesting here is the clear identification between the incarnate Son of God and a
linguistic reality which is not limited to being defined as Word, but also as book and
as utterance. The aeons (from αἰών, an 'age, lifetime, era') constitute 'an entourage
of mythopoetically personified eternal divine attributes'<fnref n="83" /> varying in number and in
ontological status in the different Gnostic mythologies. Some speak of 365 aeons; other
sources specify eight, twelve or, as we shall see later, twenty-four like the number of
letters of the Greek alphabet.

The identification between letters and names which we had encountered previously
is here expanded: each letter may be viewed not only as a word and as a name, but
also as a book, and more precisely as a living book. They are also clearly distinguished
from ordinary vowels or consonants, these are 'letters of the truth' or, we might say,
symbolic letters.

This is the perfection in the thought of the Father, and these are the words
of his meditation. Each one of his words is the work of his one will in the
unveiling of his Speech. While they were still depths of his thought, the
Logos, which was first to come forth, revealed them along with a mind that
speaks, the one Logos and a silent grace [...] Now the name of the Father is
the Son [...] It is possible for him to be seen. The name, however, is invisible
because it alone is the mystery of the invisible which comes to ears that
are completely filled with it by him. For indeed, the Father's name is not
spoken, but it is apparent through a Son [...] This name does not belong to
words, nor does it consist of appellations, but it is invisible.<fnref n="84" />

Let us retain some of the above cosmogonic statements, rather as an imagery that
we may have later occasion to compare: the 'thought' of the Father is an intermediary
locus where the word/name of the Son is uttered beyond language, for it is 'invisible',
'not spoken'. Like in the previous passage, what stands out here is the affirmation of a
symbolic usage of the linguistic imagery.

<footnote n="82">82. I, 22ff.; *Nag Hammadi Library*, 43, highlighting mine.</footnote>

<footnote n="83">83. Williams, *Rethinking 'Gnosticism'*, 10.</footnote>

<footnote n="84">84. I, 37ff.; *Nag Hammadi Library*, 48–50; I have slightly edited Robinson’s in view of the German translation.</footnote>
Marsanes

*Marsanes* (after the name of a gnostic prophet) is one of the so-called ‘Sethian’<fnref n="85" /> Gnostic treatises in the Nag Hammadi corpus. Probably written in the third century AD, its metaphysics and ritual references have been related to those of Iamblichus.<fnref n="86" /> In fact, one of the reasons for supposing that the text is originally Greek is the occurrence of letter symbolism<fnref n="87" /> and of ritual nomenclature of gods and angels.<fnref n="88" />

The text of this treatise is very damaged, but fortunately the section devoted to letter speculation is in relatively good condition. In the following lines I try to reconstruct the meaning of a few isolated passages, following mostly Funk’s German rendition.<fnref n="89" />

> The soul too has its shape, and of a different kind. The shape of the
> soul, which came to be on its own, has the following form: the shape is
> a secondary spherical part around which lies a primary part, ε η ι ο υ,
> and for the self-begotten soul, α ε η ι ο υ ω. The second shape ε η ι ο υ
> comes to be through the diphthongs... Know that the sublime ones exist
> among the vowels, and the diphthongs are next to them... The sounds of
> the semivowels are superior to the voiceless, and those that are double are
> superior... They constitute the names of gods and angels, not because they
> blend with each other according to every form, but in order to produce a
> beneficial effect.<fnref n="90" />

It would be irresponsible to elaborate much on this text without examining the
Coptic original, which is beyond my competence, but what is clear once again is that
the internal structure of the alphabet and its phonetic divisions have a cosmological
value, in other words, that the classification of the phonemes reflects an ontological
hierarchy. In particular, we find here again the combinations of the vowels that we
had encountered in the magical papyri, pointing once again to a fundamental relation
between phonetics, magic and cosmogony. Further down (29-30), the length of the
vowels is also taken into account, and there is question of the consonants in some more
detail:

The consonants exist together with the vowels, and indeed as independent
too; they are placed before them and after them; they serve as names of the

<footnote n="85">85. For the special role of Seth in Gnostic literature, see Lahe, *Gnosis und Judentum*, 283; and Williams, *Rethinking ‘Gnosticism’*, 90–93.</footnote>

<footnote n="86">86. NHC X. See *Nag Hammadi Library*, 460ff.</footnote>

<footnote n="87">87. *Nag Hammadi Deutsch*, 498.</footnote>

<footnote n="88">88. *Nag Hammadi Library*, 462.</footnote>

<footnote n="89">89. Nag Hammadi Deutsch, 505.</footnote>

<footnote n="90">90. X, 26–28. *ibid.*; *Nag Hammadi Library*, 466–67.</footnote>
angels; they exist on their own and they differentiate, and they lead and are
led by the hidden gods by means of stress, pitch, quiescence and point of
articulation; they summon the semivowels...

At this point, it is perhaps possible to start seeing a pattern in the broader distinctions
between vowels and consonants. Let us, for the time being, simply retain the fact that
*the consonants are said to ‘differentiate’*, and that in spite of their name of con-sonants,
they are metaphysically considered to be capable of certain autonomy.

A few lines below (32–33), there is question of numerical cosmology, with the
cosmogonic correspondences of the monad, the dyad, the tetrad and so on, culminating
with the decad ‘which has laid bare all things’, and with Eleven and Twelve ‘which have
completed the traverse through to the unlimited.’ Due to the state of the manuscript it
is not possible to clarify what is the relation between the numerical and the alphabetic
series, but I shall have occasion to reexamine this in the following pages.

The vowels are connected to the consonants either externally or internally
[...] they were numbered four times, they were engendered three times,
and they became twelvefold... (39) Whether he is gazing at the two or he
is gazing at the seven planets or at the twelve signs of the Zodiac or at
the thirty-six Decans..., whether those in heaven or those upon the earth,
together with those that are under the earth... they stand alone...

There seems to be a progression from the abstract alphabetic symbols and the
numerical hierarchy to the cosmic correspondences, but as mentioned above the state
of the text does not warrant further speculation, and is instead illuminated by similar
passages found elsewhere. The *Gospel of the Egyptians* (NHC III, 2; IV 2) and the
*Interpretation of Knowledge* (NHC XI,1), for instance, contain descriptions of the ‘self-
originating Word’, its origin in ‘heavenly Silence’ and its relation to the Son.

Marcus the Valentinian

Marcus ‘the Magician’ (*ca*. second century AD), morally criticised and doctrinally
preserved by Irenaeus of Lyon, and after him by other early church authorities, is
customarily viewed as a ‘Neo-Pythagorean’ among Gnostic authors,<fnref n="91" /> and is thus an
obligated reference for alphanumeric symbolism; this is why in a previous chapter
we found him mentioned as a parallel to the speculations of the *Mysteria literarum*.<fnref n="92" />
It has been the case, however, that most material related to Marcus focused on the

<footnote n="91">91. D. Bueno Donadon, ‘Adversus haereses de Ireneu de Lyon: tradução e comentários’ (PhD diss., Universidade Estadual de Campinas, Instituto de Estudos da Linguagem, 2011), 44.</footnote>

<footnote n="92">92. Bandt, *Vom Mysterium*, 83–5.</footnote>
first part of Irenaeus’ critique in *Adversus haereses* (I, 13–21),<fnref n="93" /> where there is question of the debauchery of the Marcosians, until Förster’s comprehensive monograph was published,<fnref n="94" /> taking into account the full critique of Irenaeus, his followers, and later Syriac and Arabic sources. I shall make use of Rousseau’s critical edition (1979) to present a slightly modified translation based on Harvey (1857), all in the light of Förster’s monograph.

Τὰ γὰρ Ἀναξιλάσου παίγνια τῇ τῶν λεγομένων μάγων πανουργίᾳ συμμίξας,
δυνάμεις ἐπιτελεῖν δοκεῖ.

Combining the pranks of Anaxilaus with the craftiness of so-called magicians, he gives the impression of accomplishing wonders.<fnref n="95" />

Anaxilaus of Larissa was a Pythagorean philosopher famous for his magical exploits, and particularly for a sort of alchemical transmutation.<fnref n="96" /> It may be noted how the first influence in Marcus’ picture is that of the παίγνια, which has a general meaning of divertissement but which can refer more specifically to word plays, as in the term τεχνοπαίγνιον which we had already encountered.

Starting from the general Gnostic principle that the upper world has its reflection in our lower world, Marcus develops a complex cosmogonic system based on the initial silence, on words, ‘syllables’ and letters arranged in groups of varying quantity. ‘When Father, who is without a father, unthinkable and immaterial in substance, who is neither male nor female, first wished that the unspeakable be spoken and the invisible be given form, he opened his mouth and brought forth the Word similar to himself.’<fnref n="97" />

Ἐρωδότης ἀρχῆς ἀνὴρ ἀνόματος τοῦ ὀνόματος ἐγένετο
τοιαύτη· ἐλάλησε λόγον τὸν πρῶτον
τοῦ ὀνόματος αὐτοῦ, ἥτις ἦν ἀρχὴ, καὶ
ἐν ἡ συλλαβὴ αὐτοῦ στοιχείων τεσ-
σάρων. Ἐπισυνῆψε τὴν δευτέραν· καὶ
ἐν καὶ αὐτὴ στοιχείων τεσσάρων. Ἐξῆς
ἐλάλησε τὴν τρίτην· καὶ ἦν καὶ αὐτὴ
στοιχείων δέκα. Καὶ τὴν μετὰ ταῦτα
ἐλάλησε· καὶ ἦν καὶ αὐτὴ στοιχείων δε-
καδύο. Ἐγένετο οὖν ἡ ἐκφώνησις τοῦ

The utterance of the name developed in the following manner. He pronounced the first **word** of his name, which is a **principle**: it was a combination of its four **phonemes**. He joined a second to it which was also a combination of four phonemes. Next he pronounced the third: this too consisted of ten phonemes. And the combination that he pronounced after these had twelve phonemes. So the pronunciation of the

<footnote n="93">93. That is, starting from I, 7 in Harvey’s numeration. I follow henceforth Rousseau’s sectioning.</footnote>

<footnote n="94">94. N. Förster, *Marcus Magus: Kult, Lehre und Gemeindeleben einer valentinianischen Gnostikergruppe*, Wissenschaftliche Untersuchungen zum Neuen Testament 114 (Tübingen: Mohr Siebeck, 1999).</footnote>

<footnote n="95">95. I, 13, 1.</footnote>

<footnote n="96">96. See Förster, *Marcus Magus*, 62.</footnote>

<footnote n="97">97. Irenaeus of Lyon, *St. Irenaeus of Lyons Against the Heresies*, ed. D. J. Unger and J. J. Dillon, vol. 1 (New Jersey: The Newman Press, 1992), 59.</footnote>
ἔλου ὀνόματος στοιχείων μὲν τριάκοντα,
συλλαβῶν δὲ τεσσάρων. Ἕκαστον δὲ
τῶν στοιχείων ἵδια **γράμματα**, καὶ ἵδιον
**χαρακτῆρα**, καὶ ἰδίαν ἐκφώνησιν, καὶ
σχήματα, καὶ εἰκόνας ἔχειν.

whole name consisted of thirty phonemes,
but only four combinations, and each of
the phonemes had its own **letters**, its own
**tracing**, its own pronunciation, shapes, and
representations.

This ‘alphabet’ of thirty letters, which Marcus considers the sum of the aeons of the pleroma, is arrived at through different additions. We may remember that the full Greek alphanumeric system used twenty-seven signs: the twenty-four letters plus the three *episema* or supplementary signs, *digamma ε* (or *stigmaς*), *qopa ό*, and *sampi ᾿*. If we add these three and then also count the three existing double letters (ζ, ξ, ψ) as doubles, we arrive at thirty. Alternatively, it is explained later that ‘the name of Saviour which can be uttered, that is, Jesus (IHSOU&Sigma;), has six letters, but his name which cannot be uttered has twenty-four letters. The name “Christ the Son” (YI&uacute;O&Sigma; XREI&Uacute;ST&uacute;O&Sigma;) has twelve letters; but the name of Christ that is unutterable (A&rsquo;RP&rsquo;HTOV) has thirty letters. And for this reason he asserts that he is alpha and omega in order to indicate the dove (&pi;ERI&Uacute;STERPA), since this bird had that number.’ Indeed, by isopsephy, the numerical value of &pi;ERI&Uacute;STERPA is 801, like the sum of alpha and omega—this equivalence is often used by Marcus and it is found in other similar literature.

The defining characteristics of each στοιχείον, such as its tracing and shape, had been mentioned in the grammatical scholia,<fnref n="98" /> and here again, as in previous texts, they are given a cosmological significance that I shall not expand on at the moment.

Another remarkable image of Marcus' cosmology is the famous passage regarding the 'Body of Truth', wherein the Tetraktys personified, who has been revealing all these matters to Marcus, speaks thus:

θέλω δέ σοι καὶ αὐτὴν ἐπιδεῖξαι τὴν
Αλήθειαν. Κατήγαγον γὰρ αὐτὴν
ἐκ τῶν ὕπερθεν δωμάτων, ἵν' ἐσίδης
αὐτὴν γυμνὴν, καὶ καταμάθοις τὸ
κάλλος αὐτῆς· ἀλλὰ καὶ ἀκούσης
αὐτῆς λαλούσης, καὶ θαυμάσῃς τὸ
φρόνημα αὐτῆς. Ὅρα οὖν κεφαλὴν
ἄνω, τὸ ἄλφα καὶ τὸ ω, τράχηλον
δὲ β καὶ ψ, ὥμους ἄμα χερσὶ γ καὶ
χ, στήθη δ καὶ φ, διάφραγμα ε καὶ
υ, νῶτον ζ καὶ τ, κοιλίαν η καὶ
σ, μηροὺς θ καὶ ρ, γόνατα ι καὶ

I also wish to show you Truth itself. I have
brought her down from the dwellings on high
that you might look on her naked and examine
closely her beauty, and indeed that you may also
hear her speak and marvel at her wisdom. See,
then, *alpha* and *omega* are her head on high;
*beta* and *psi* are her neck; *gamma* and *chi* are
her shoulders and hands; her breast is *delta* and
*phi*; *epsilon* and *upsilon* are her diaphragm; *zeta*
and *tau* are her stomach; *eta* and *sigma* are her
private parts; *theta* and *rho* are her thighs; *iota*
and *pi* are her knees; *kappa* and *omicron* are her

<footnote n="98">98. See above, p. 41, and Förster, *Marcus Magus*, 198–99.</footnote>
π, κνήμας κ καὶ ο, σφυρὰ λ καὶ ξ, legs; lambda and xi are her ankles; mu and nu are πόδας μ καὶ ν. her feet.<fnref n="99" />

This reduction of the twenty-four letters to twelve duplets, in this case following the *atbash* order,<fnref n="100" /> is a variation of the Hellenistic astrological correspondence which followed the *albam* order.<fnref n="101" /> Both are kinds of *melothesia*, the correspondence between parts of the body and zodiacal signs.<fnref n="102" /> The alphabet would seem to perform a mere numerical function as an ordered set that lends itself to distributive ordering, but given the cosmological background, it is rather safe to assume that something more was at play, and that the alphabet here performed yet again a fully alphanumeric function. Through the alphabet, that is, through the elements, the ‘human’ figure is tallied with the duodecad of the heavenly sphere.<fnref n="103" />

Every few paragraphs along these explanations, Irenaeus takes an opportunity to condemn Marcus and even openly mock and ridicule the convoluted doctrine. He does so after this alpha-anatomical passage, and then continues: ‘When that Tetrad had spoken these things, Truth looking at Man and opening her mouth uttered a word. The word became a name, and the name was the one that we know and speak, *Christ Jesus*.’

Jesus is defined in many ways, interchangeably with his name and many numerical possibilities: ‘the name of Jesus, according to the number to which the letters correspond, is eight hundred and eighty-eight. And so you have clearly [stated] also the supercelestial origin of Jesus. For this reason the Greek alphabet has eight units, eight decades, and eight hundreds. Thus it reveals the number eight hundred eighty-eight, that is Jesus, who was composed of all the numbers.’<fnref n="104" />

In view of such taxing explications, it is no great wonder that one can occasionally sympathise with Irenaeus’ rants, which unexpectedly can even help us to have a concise look at the exposition, e.g.,

> Who will put up with you who confine the Builder, Craftsman and Maker (Κτίστης καί Δημιουργός καί Ποιητής) of all things, the Word of God, to figures and numbers—now thirty, now twenty-four, now only six—and then chop Him up into four combinations and thirty characters? With you, who reduce to the number eight hundred and eighty-eight the Lord of all things who established the heavens, as if He had become like the alphabet?

<footnote n="99">99. I, 14, 3; Unger/Dillon (eds), *Against the Heresies*, 61.</footnote>

<footnote n="100">100. From the Hebrew equivalent of pairing *alef-taw*, *bet-shin*, etc.</footnote>

<footnote n="101">101. Also named after a Hebrew pairing *alef-lamed*, *bet-mem*, etc. or, rather common, α-ν, β-ξ, γ-ο etc. See Dornseiff, *Alphabet*, 84–6.</footnote>

<footnote n="102">102. See Förster, *Marcus Magus*, 224–25, for references to iatromathematical texts.</footnote>

<footnote n="103">103. See above p. 47.</footnote>

<footnote n="104">104. I, 15, 2; Unger/Dillon (eds), *Against the Heresies*, 65.</footnote>
With you who subdivide into a Tetrad, Ogdoad, Decad, and Dodecad the Father who comprehends all things, but is Himself incomprehensible. With you, finally, who by the multiplications of these numbers explain the Father's nature, which, as you say, is unutterable and unthinkable?<fnref n="105" />

The complaint is essentially on two grounds: first, the seemingly unwarranted complexity, nay, confusion, of the teachings, and second and most important, the perceived metaphysical absurdity, in the proper sense of dissonance, between two levels of reality—‘as if He had become like the alphabet?’

Though it is not my intention to defend the Marcosian doctrine in any way, it must be pointed out that the three names of God used here by Irenaeus refer to professions whose practice is entirely based on design, hence on the use of figures and numbers (σχήματα καὶ ἀριθμούς). Perhaps, invectives aside, if we examine closely an earlier crucial paragraph of the exposition, we can have a glimpse of what this apparently muddled cosmology is conveying in its dizzying symbolism or, as Irenaeus puts it, in its ‘abyss of letters’.<fnref n="106" />

At the beginning of I, 14, 2, there is mention of τὰ ὀνόματα τῶν στοιχείων τὰ κοινὰ καὶ ῥητὰ, ‘the common and utterable names of the phonemes’, which are called by the revealing Tetraktys by the names of aeons, *logoi*, roots, pleromes, etc., giving in effect a list of synonyms of στοιχεῖον, making clear that it does not refer to speech in any mere linguistic sense, but that this is about cosmology, and implicitly also that there are some ‘names’ of elements/phonemes which are exclusive and unutterable.

I shall refrain from translating the entire passage, which would take me away from my point now,<fnref n="107" /> but there are some additional remarkable outcomes from the careful parsing of the succeeding lines which it will be useful to keep in mind:

* this cosmogony distinguishes carefully four instances of the linguistic image: there is στοιχεῖον and γράμμα, and there is the utterance (φωνή) and the sound (ήχος).<fnref n="108" /> The relations between them span the cosmos, and it is the resonance, as an echo, of a superior kind of phoneme which institutes order (διακοσμεῖ) in the lower world and which generated **what had been before the universe**.

* the ‘names’ of the ‘letters’ are infinitely divisible internally, meaning that every letter is an infinite in potency.

<footnote n="105">105. I, 15, 5, my highlighting; Förster, *Marcus Magus*, 358ff.</footnote>

<footnote n="106">106. I, 14, 2; βυθός τῶν γραμμάτων.</footnote>

<footnote n="107">107. Detailed analysis and notes in Förster, *Marcus Magus*, 206–16, and Irenaeus of Lyon, *Irénée de Lyon: Contre les hérésies. Edition critique d’après les versions arménienne et latine*, ed. A. Rousseau and L. Doutreleau, 9 vols (Editions du Cerf, 1979), 1, 2, 211ff.</footnote>

<footnote n="108">108. This was a technical term in Greek phonetics, but in the context there is an obvious implication of its basic meaning of reverberation.</footnote>