Counting the Letters of the Alphabet . A Reading of Plutarch , Quaestiones convivales 9

The last book of Plutarch’s Quaestiones convivales contains several discussions of literary and grammatical topics. The present article focuses on Quaest. conv. 9.3, which deals with the number of the letters in the alphabet. This question is raised by ‘Plutarch’ to Hermeias the geometer. It is first argued that this qualifies as an excellent sympotic question (according to Plutarch’s own standards). Then, attention is given to the solution proposed by ‘Plutarch’ himself (738DE), to the learned reply by Hermeias (738EF), and to the final critical evaluation by Zopyrio (738F-739A). This detailed interpretation of the Quaestio should help in revealing the argumentative dynamics of Plutarch’s philosophical approach in the Quaestiones convivales. Key-words: Plutarch, Table Talk, alphabet, ζήτησις.


ISSN 0258-655X
Ploutarchos, n.s., 18 (2021) 57-70 T he last book of Plutarch's Quaes tiones convivales is ex cep tional in several respects. Whereas all other books consist of ten questions and deal with different dinner parties, book nine contains the account of the rich and learned conversation during one banquet. As a result, the number of questions goes beyond the usual ten 1 . Plutarch explains the reason for this va riation in a short rhetorical proem. The occasion of the conversation mentioned in this ninth book was the Festival of the Muses and he cannot make a selection of topics but should render to the Muses all that belongs to them 2 . This sounds reasonable enough, but if we take Plutarch's statement at face value, it has important implications for the historicity of the Quaestiones convivales (or at least for the historicity of this book). It indeed suggests that these conversations had really taken place and that the anomaly in the structure is simply rooted in a historical context 3 .
The historicity of the Quaestiones con vivales, however, is a difficult pro blem that has entailed extreme views 4 . As so often, much is to be gained from a cautious aurea mediocritas. Scholars now rightly underline Plutarch's autho rial input: he holds the pen and has elaborated, polished and completed the argu ments of the different speakers. It would be quite naïve, then, to believe that we are reading the verba ipsissima that were uttered by the different spea kers during the symposium. Yet it would be hypercritical to deny all the histo rical basis and consider the whole work as pure fiction. I agree with the wellbalanced view of Titchener: Historians care 'what' happe ned, and biographers care 'how'. What the Table Talk presents us with is something a little in bet ween: what might have happened, could have happened, and perio dically had in fact happened 5 .
This basically holds true for Book 9 as well. In my view, the book has inde ed a historical fundamentum in re, yet Plutarch has elaborated this ma terial, drawing 1 The book contains 15 questions, although the questions 711 are no longer extant, and 6 and 12 are incomplete. 2 Quaest. conv. 736C. 3 An alternative explanation is suggested by Teodorsson 1996, 300: "The number 15 has nothing symbolic about it. Perhaps we may suppose that Plutarch, when setting out to write book IX, happened to see that he had a number of interesting questions left which he could not refrain from including." 4 See on this quaestio vexata, e.g., Ziegler 1951, 886887;Teodorsson 1989Teodorsson , 1215Pordomingo Pardo 1999;Sirinelli 2000, 379382;Titchener 2009;Roskam 2010, 4648;Klotz -Oikonomopoulou 2011, 312;Meeusen 2016, 162165. 5 Titchener 2011 from the storehouse of his own erudition and embellishing it with the honey of his literary talents. It is no longer possible to recover what is historical and what is not, nor does it greatly matter. The picture we get is historically credible and throws an in teresting light on the philosophical and literary interests of the elite of pe pai deu me noi in Plutarch's day. That, I think, is mo re than enough to deserve a careful reading and interpretation.

The setting
The conversations that are recorded in Book 9 take place at the house of Plutarch's teacher Ammonius. Dur ing the Festival of the Muses in Athens, Ammonius indeed attended a de monstra tion in the school of Dio ge nes and afterwards invited the success ful teachers to dinner. His house was fill ed with a large company, for apart from these teachers, many scholars and friends were present as well. In short, we are dealing with the kind of company that we often find in the Quaes tiones convivales: a circle of erudite pepaideumenoi, well versed in literature and culture.
At the moment of this banquet, Plu tarch was probably still young. His bro ther Lamprias, in any case, appears as a boy (παῖς) 6 . The central figure of Book 9 is Ammonius, the host and symposiarch. He did not organize the banquet in his capacity of school teacher but as the strategos of Athens, supervising the edu cation of ephebes. In that sense, this banquet does not give us a glimpse in to Ammonius' private Academy, al though the school context makes its influence felt in the conversation, given the presence of the different teachers and the members of his own circle (the συνήθεις), including Plutarch.

The preceding conversation
The third question of Book 9, which will be discussed in this article, focuses on the number of letters in the alphabet 7 . It opens, however, with the remark of Hermeias the geometer that he accepts both explanations (ἀμ φο τέ ρους ἀποδέχεσθαι τοὺς λό γους) 8 . This evaluation obviously refers back to the previous question. Such smooth transitions between two successive questions occur more than once in the ninth Book 9 and add to the coherence and unity of the Book. Hermeias has asked the reason why the alpha was put first in the alphabet and now comments on the answers he has received. Since his generous acceptance of both expla 6 Quaest. conv. 747B. 7 The Greek title of the Quaestio that has come down to us is not entirely accurate; cf.

ISSN 0258-655X
Ploutarchos, n.s., 18 (2021) 57-70 na tions characterizes him very well and is in fact relevant for his own way of think ing, it is worthwhile to pause for a brief moment and have a quick look at the previous question 10 .
The two λόγοι to which Hermeias refers are two different explanations of the initial position of the letter alpha. The grammarian Protogenes proposes the standard theory of the school, which rests on three argumentative steps: (1) vowels precede semivowels and consonants, (2) ambiguous vowels (α, ι and υ) precede vowels that are either short or long, and (3) of these ambiguous vowels, the alpha is the one that is prefixed to iota and upsilon and suffixed to neither 11 . The young 'Plutarch' 12 , adopting the view of his grandfather Lamprias, explains that the alpha is the easiest natural sound, uttered by a mere opening of the lips, and is also used by babies 13 . This theory gains further support from a few etymological observations and from the fact that nearly all mutes (except pi) have names that employ an added alpha. Hermeias considers both these theories to be correct, and in fact, both can indeed be combined to a certain extent, as they both reveal complementary characteristics and powers of the alpha. Moreover, both explanations also show the same blind spot, that is, they both ignore the question of the origin. Neither Protogenes nor 'Plutarch' mentions the concerns of the στοιχειώτης 14 . They ra ther prefer an ahistorical approach that explains the position of the alpha by means of a posteriori rationalizations. This kind of approach will also be followed by Hermeias in the third Quaestio. In that sense, his approval of both hypotheses is not merely the re sult of his concern for symposiastic conviviality and friendship 15 but also reflects his own way of thinking. 10 I deal with this Quaestio in detail in Roskam (2020

The question
'Plutarch' then raises a question to Hermeias: what is the reason for the number of letters in the alphabet 16 ? In several respects, this is an ex cellent question that illustrates the intelli gen ce of the young 'Plutarch'. The program matic first question of the Quaestiones convivales deals with the place of philosophy at a banquet and in this context also discusses the kind of questions that should be raised over wine 17 . 'Plutarch' there argues that we should first of all bear in mind the character of those present. If they lack culture and erudition, we better avoid philosophical topics, but if the majority of them is well educated, philosophy should have its place in the conversation 18 . Since Ammonius' banquet is attended by a company of learned men, philosophical issues are not forbidden, and as a matter of fact, several philosophical questions will be raised later on 19 , although the majority of subjects has to do with literary or cultural issues. Next to the character of the guests, attention should be given to the kind of topics. Historical matters or current events are suitable for banquets: they should not be overtechnical but should contain elements that can sti mulate philosophical reflection. The questions themselves should be 'fluid' (ὑγρο τέρας) and uncomplicated so that less learned guests may not be turned away 20 . In other words, the topics should easily spread over the company. Everybody should be interested in the question and eager to learn the answer. In this respect, the present question raised by the young 'Plutarch' is a direct hit indeed: it raises wonder and is not technical at all. In short, it has everything to capture the attention of the listeners.
The question of 'Plutarch' regarding the number of letters in the alphabet, then, perfectly qualifies as a 'fluid' question. It also has an obvious link with the previous discussion and thus keeps the conversation going. Moreover, 'Plutarch' also takes into account Hermeias' expertise. He neither bothers him with philosophical problems that pass the competence of the geometer nor addresses technical geometrical issues with which he is not familiar himself 21 . He has rather found an intriguing question that is sufficiently general to arouse everybody's interest and that is at the same time in line with Hermeias' expertise.

'Plutarch' making the first move
The latter claim, though, may seem strange at first sight. What, after all, is the connection between geometry and the number of letters of the alphabet? That both have more in common than we may be inclined to think, appears from the clarification that 'Plutarch' adds: Well then, I said, isn't it time you expounded to us any reason there may be for the number of letters in the alphabet? I am sure there is one, and find evidence in the fact that the mutes and semi vowels stand in no chance nume rical relation either to one another or to the vowels, but are in pri mary, or as you geometers call it, arithmetical proportion: since they are nine, eight, and seven, they have the property that the middle number exceeds the one extreme by the same amount as that by which it falls short of the other. Next, the largest number has the same relation to the smallest as that of the Muses to that of Apo llo, the number nine being, as we know, assigned to the Muses and seven to their Leader. Then if we add together these extremes, they are twice the middle number, rea sonably so, since the semivowels in a sense share the quality of both vowels and mutes 22 .
In this way, 'Plutarch' already gives a rough sketch of the answer to his own question and thus precisely does what his teacher Ammonius did for him in the previous discussion. There, Ammonius indeed suggested that the initial place of the alpha can be explained by its Phoenician origin 23 . This of course made the task of 'Plutarch' quite easy: in principle, he had only to develop the readymade answer provided by Ammonius. In the present talk, 'Plu tarch' imitates his teacher. At the sa me time, he suggests that his question does not stem from ignorance but that he is familiar with the issue and can propose his own view. Yet all this is not merely a matter of subtle selfdisplay: it can also be seen as a genuine help. 'Plutarch' does not want to get Hermeias into trouble. If the geometer happens to be at a loss for an answer, 'Plutarch' gives him an easy way out, by orienting his question towards a geometrical perspective. This is a clever move indeed: 'Plutarch' does not break off the conversation about the alphabet but closely connects it with the domain of the geometer by introducing the notion of the arithmetical proportion. The theory proposed by 'Plutarch' may strike the contemporary reader as rather awkward. He entirely ignores the gradual evolution of the alphabet and instead merely focuses on the final result. Thus he adopts basically the same approach as Protogenes and he himself in the previous discussion. His point of departure is the final number of 24 letters, which can be subdivided into three groups, viz. seven vowels, eight semivowels, and nine consonants 24 . This observation entails some number speculations that seem to be typical of the young 'Plutarch'. In a famous passage from De E apud Delphos, Plutarch indeed recalls how he was fond of such mathematical theories in his youth 25 . The young 'Plutarch' there gives a lengthy speech in which he explains the mysterious E on Apollo's temple in Delphi as a reference to the number five. Here, Apollo is rather connected with the number seven, whereas the Muses are linked to the number nine 26 . This enables 'Plutarch' to establish a parallel between Apollo and the seven vowels. The suggestion apparently is that the vowels can bring forward their own sound 27 , just like Apollo is himself the origin of the inspiration. The consonants, on the other hand, are mute by themselves and need the help of the vowels, just as the Muses need the inspiration of the leader, the Μουσηγέτης 28 . This theory 'explains' the number of vowels and consonants. The number of semivowels can then easily be connected with their intermediate position 29 . This explanation is quite clever but also smells of the sophistic ingenuity (εὑρησιλογία) for which Plutarch some times blames other speakers or au thors 30 . After all, the connection between the numbers and the gods is rather artificial 24 Cf. Dionysius Thrax,6,9.7 and 11.512 Yes he did. This appears from seve ral interesting parallels from other au thors. In the Scholia Londinensia on Dio nysius Thrax, the scholiast links the number of letters to the number of hours in a day and argues that the power of the letters resembles that of the lunar cycle. Full moon is connected with the vowels, half moon with the semivowels, and gibbous moon with the consonants 31 . Alexander of Aphrodisias alludes to a theory that connects the 24 letters with the totality of the universe, that is, with the twelve Signs of the Zodiac, the eight planetary spheres, and the four elements 32 . 'Plu tarch' keeps silent about these views, but it is clear that they contain interesting complementary information and provide Hermeias with many starting points for further discussion. Along these lines, he could even have considered the number of letters as a telling indication that God is always doing geometry 33 or he could have pointed to other arithmetical means 34 .

Hermeias' reply
Hermeias, however, does not need the helping hand of 'Plutarch'. He indeed ignores the latter's suggestion and immediately comes up with his own solution -not unlike 'Plutarch', who likewise ignored Ammonius' suggestion in the previous conversation and there preferred to follow his own course. This illustrates, once again, that we have to do with erudite independent thinkers who, though appreciating such help in a symposiastic context, do not feel obliged to repeat another's opinion and rather develop their own point of view. Hermeias comes straight to the point: Hermes, said Hermeias, was, we are told, the god who first in vented writing in Egypt. Hence the Egyptians write the first of their letters with an ibis, the bird that belongs to Hermes, although in my opinion they err in giving precedence among the letters to one that is inarticulate and voi celess.  Ferrari 2009. 34 Such as the one lurking in the theory mentioned by Alexander of Aphrodisias (8 being the arithmetical means of 12 and 4).

Ploutarchos, n.s., 18 (2021) 57-70 ISSN 0258-655X
four is particularly associated with Hermes; and many writers record that his birthday was ac tually on the fourth day of the month. Now not only did four multiplied by four provide the original letters of the alphabet, named the 'Phoenician letters' because of Cadmus, but also four of those that were invented later were added by Palamedes, and subsequently the same number once more by Simonides. A fur ther point is this. It is clear that in the series of numbers the first perfect number is three, as having a beginning, a middle and an end, or six, as being equal to the sum of its factors. Now of these, six multiplied by four, or three, the first perfect number, multiplied by eight, the first cube, has given our total of twentyfour 35 . This is a particularly learned discussion which builds on much traditional ma terial. Hermeias thus shows that he knows the scholarly debate on the origin of the alphabet quite well and this throws a new light on his question to Protogenes regarding the initial position of the alpha. We now see that this question was not merely motivated by his concern to take into account Protogenes' own expertise as a grammarian but also reflects his own interests. By starting a conversation about the alphabet, he thus stayed within his own comfort zone.
As a matter of fact, Hermeias does not only answer the question of 'Plutarch' but he also adds a critical note to the previous discussions. We have seen that he ac cepted, at the beginning of this talk, the explanations put forward by Protogenes and 'Plutarch', yet he here briefly returns to the problem of the first letter, though in a roundabout way, by focusing on the Egyptian alphabet. In Hermeias' view, the Egyptians are wrong because they began their alphabet with a mute letter. Like Protogenes and 'Plutarch', he thus uses the quality of the letters as his criterion and ignores the historical perspective on which Ammonius' explanation was based. This helps to explain why Hermeias accepts both theories (ἀμφοτέρους τοὺς λόγους) although the previous conversation in fact involves three alternative explanations: his basic hermeneutic approach is fun damentally in line with that of Protogenes and 'Plutarch'.
Nevertheless, Hermeias, unlike Pro to genes and 'Plutarch', also places the previous discussion in a broader histo rical perspective. In this, he indeed resembles Ammonius, but whereas the latter only dealt with one cog in the wheel, Hermeias now provides us with a full panorama. The discovery of the al phabet, so he argues, was made by the god Hermes in Egypt. This claim is in line with Plato's position. Near the end of the Phaedrus, Socrates indeed relates how the Egyptian god Theuth 35 Quaest. conv. 738EF.

ISSN 0258-655X
Ploutarchos, n.s., 18 (2021) 57-70 invented the letters and introduced them to the king 36 . Plutarch of course knew (this passage from) the Phaedrus very well. The Platonic dialogue was a major source of inspiration for his Amatorius 37 and its concluding section on the problem of writing repeatedly makes its influence felt in his works 38 . Against this background, Hermeias returns to the problem of the first letter of the alphabet: the Egyptians, so he says, begin their alphabet with an ibis, the bird that belongs to Hermes. This recalls Ammonius' her meneutic approach of explaining the choice of the first letter by pointing to the philosophical or religious convictions of the original inventors 39 . Yet Hermeias also adds that their choice was wrong, since the quality of the letter should be decisive in such matters. This argument is a return to the ad hoc speculations of Protogenes and 'Plutarch': a historical approach may throw additional light on the problem but does not offer the most important normative clue.
In what follows, Hermeias combines the historical perspective with number speculations that rest on the number four as the number of Hermes. The product of four and four is sixteen, the number of the original letters, also called Phoenician letters "because of Cadmus" (διὰ Κάδμον). The precise meaning of his passing reference to Cadmus can be derived from Herodotus' account. The historian relates how the Phoenicians who accompanied Cadmus brought the alphabet to Greece. This story was often accepted by later authors and Ammonius has also alluded to it in the previous conversation 40 . In that sense, Hermeias' reference to Cadmus is also a subtle and tacit correction of Ammonius' position. Cadmus should not be regarded as the πρῶτος εὑρετής (for this honour should be granted to the god Hermes) but as one of the figures that played an intermediary role at a later stage of the evolution. Moreover, this evolution did not end with Cadmus, for Palamedes and Simonides both added another four to the list. Palamedes was often considered as the inventor of the entire Greek alphabet or, alternatively, of some letters, and several sources also ascribe an active role to 36 Phdr. 274c7d2. Socrates there does not identify Theuth with Hermes, but this identification was common in Plutarch's day; see, e.g., Festugière 1944, 6970. 37 Billault 1999. 38 See Zadorojhnyi 2007 Cf. Teodorsson 1996, 317: "As regards the order of the hieroglyphic signs, about 700 in number, there is no evidence that there existed any fixed order, but if a series of signs was to be enumerated for some purpose, it would have been natural to begin with the holy sign designating Thoth." 40 Herodotus 5.58. This view is often accepted by later authors; see esp. Schneider 2004, 126133. Simonides in the later development of the alphabet 41 . Such parallels show that Hermeias uses traditional material, which he then moulds on the number four, the number of Hermes. This results in a coherent theory in which smart number speculations are supported by a historical perspective.
Hermeias then adds a further point (καὶ μήν), which provides an alternative for the view of the young 'Plutarch'. Whereas the latter interpreted the num ber 24 as the sum of 7, 8 and 9, Hermeias now sees 24 as the product of 3 and 8, or 6 and 4. Here too, he thus sticks to Hermes' number, multiplied by 6 (a perfect number, being the sum of its factors), or to the first cube (8 = 4 + 4) multiplied by 3 (another perfect number, having a beginning, middle and end). The historical perspective thus again fades into the background. It indirectly remains relevant through the importance of Hermes' number 4 but the emphasis is here clearly on the theory of numbers rather than on the role of the god.
As a whole, Hermeias' hypothesis surpasses that of 'Plutarch' in several res pects. He succeeds in harmoniously com bining an a posteriori explanation, based on number speculations, with an historical perspective that takes in to ac count the gradual genesis of the alphabet. Moreover, the connection between both perspectives, through the number 4, is much closer than in Plutarch's theory. All this makes Her meias' theory an intelligent, well considered, comprehensive and plau sible attempt to explain the number of letters in the alphabet.

In cauda venenum: the reaction of Zopyrio
Yet Hermeias does not speak the last word, for Zopyrio the grammarian still wants to have his say: While he was still talking, Zopyrio the schoolmaster was obviously laughing at him and kept on making audible com ments; when he came to an end, he let himself go and stigmatized all such talk as complete nonsen se. Both the number of the letters of the alphabet and their order, he said, were what they were by coincidence, and not for any re ason, just as it was an accidental consequence of chance that the number of syllables in the first line of the Iliad was the same as that in the first line of the Odys sey, while the same thing was again true of their last lines 42 . This is a remarkable intervention. We have just seen that Hermeias has given 41 A good overview of the ancient sources can be found in Schneider 2004, 121124 (on Palamedes) and 139140 (on Simonides). The closest (though not perfect) parallel to our Quaestio is Pliny, Nat. 7,192.

ISSN 0258-655X
Ploutarchos, n.s., 18 (2021) 57-70 a wellbalanced, erudite and ingenious answer to the question of 'Plutarch', and now, Zopyrio brushes this all aside as utter nonsense. Moreover, Zopyrio has the last word on this topic, so that this discussion ends on a strikingly negative note. How should this be understood?
We may understand Zopyrio's reac tion as a testimonium paupertatis that cha racterizes him as a schoolmaster with a blinkered mind, unable to sur pass the boundaries of his own domain. Tell ingly enough, the parallel with Ho mer's Iliad and Odyssey also comes from the grammarian's field. If Zopyrio refuses to consider the possible relevance of theoretical speculations about numbers or a posteriori justifications and instead prefers to explain everything away as mere coincidence, this only illustrates his own intellectual limitations. Furthermore, such a negative evaluation of Zopyrio's reaction is in line with the general ima ge of grammarians in Plutarch's works (and notably in the Quaestiones con vi vales) 43 . Indeed, grammarians there often appear in a negative light. They more than once transgress the proprieties by their inopportune interventions. Here too, Zopyrio flatly refuses to join the dynamics of looking for explanations, that is, of philosophical ζήτησις. In the next Quaestio, Maximus the teacher of rhetoric will ask him a question about Homer, and even on this topic, that has to do with his own expertise, he will be at a loss for an answer 44 . This obviously suggests that Zopyrio is not the most penetrating thinker.
Although there is much to be said in favour of such an interpretation, yet Zopyrio's reaction to Hermeias' answer should not be dismissed as a mere testi mo nium paupertatis. On further con si deration, Zopyrio's intervention also shows a critical mind. Significant in this respect is that he also rejects the previous theories about the initial place of the letter alpha as utter nonsense (φλυαρίαν ... πολλήν). He thus also disagrees with the standard view of the school exposed by his fellow grammarian Protogenes 45 . This suggests at least a certain independence, in which he apparently surpasses his colleague.
Moreover, Zopyrio's view is placed at the very end, and that is the place where we usually find the view that Plutarch considers the most plausible! This throws new light on the relevance and value of the previous number speculations. An interesting parallel in this respect can be found in the second part of De animae procreatione in Timaeo. There, Plutarch refers to the view of those who say that we can limit ourselves to observe the ratios and can ignore the numbers. This position is rejected by Plutarch because, "even 43 See Horster 2008 andEshleman 2013. 44 Quaest. conv. 739B. 45 Quaest. conv. 737E. if it is true (κἂν ἀληθὲς ᾖ), it debars us from another speculation that has a charm not unphilosophical" 46 -and this other speculation indeed has to do with num bers. This key passage, together with Zo pyrio's reaction at the end of this con versation, reveals a great deal about Plutarch's position towards the solutions proposed here. He was fond of such number speculations and found in them "a charm not unphilosophical", yet at the same time, he realized their limitations. He knew indeed that such speculations were not compelling at all and that the whole issue could equally well be explained as a matter of pure coincidence. Zopyrio's intervention, then, is ultimately a signal of caution that shows intellectual honesty. In that sense, it even shows the spirit of sincere and authentic philosophical ζήτησις and a love of the truth that is so typical of Plutarch himself.