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ΕΝ ΑΡΧΗΙ ΗΝ Ο ΛΟΓΟΣ: THE LONG JOURNEY OF GRAMMATICAL ANALOGY

Published online by Cambridge University Press:  28 February 2019

Francesca Schironi
Francesca Schironi*
Affiliation:
University of Michigan
*
[email protected]
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Extract

Grammar as a discipline devoted to the study of language was greatly advanced by the Alexandrian philologists, and especially by Aristarchus, as demonstrated by Stephanos Matthaios. In order to edit Homer and other literary authors, whose texts were often written in archaic Greek and presented many linguistic problems, the Alexandrians had to recognize linguistic grammatical categories and declensional patterns. In particular, to determine the correct orthography or accentuation of debated morphological forms they often employed analogy, which is generally defined as the doctrine that grammatical forms must follow strict rules of declension. Modern scholars have often opposed the Alexandrian doctrine of analogy to the Pergamene doctrine of ‘anomaly’, which favoured spoken usage to determine debated forms. Detlev Fehling and David Blank, however, have shown that this strong opposition never really existed and it is mostly due to Varro. More correctly, ancient grammarians identified inflectional rules as well as forms derived from spoken usage or otherwise aberrant forms—however, respect for spoken usage in the latter case was not labelled ‘anomaly’, which was never a technical term of ancient grammar. Rather, and especially in the Roman period, grammarians used the term ‘pathology’ to account for and explain irregular forms.

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Research Article
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The Classical Quarterly , Volume 68 , Issue 2 , December 2018 , pp. 475 - 497
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Copyright © The Classical Association 2019 

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Footnotes

This is a revised version of a paper I presented (in different versions and research stages) between 2006 and 2007 at the Radcliffe Institute, Harvard University, at New York University, at the Centre Louis Gernet (Paris), at Yale University and at Greek from Alpha to Omega: A Birthday Symposium for Anna Morpurgo Davies, Oxford University. I would like to thank the colleagues present in each of these occasions as well as the anonymous readers for Classical Quarterly for their helpful comments and criticism. Anna Morpurgo Davies enjoyed the talk when I presented it at the symposium in her honour. I do not know if she would still approve of it, but I dedicate this article to her memory: she was an inspirational figure and very enjoyable company when I was Junior Research Fellow at Somerville College from 2001 to 2004.

All translations are mine unless otherwise noted.

References

1 For brief and clear surveys of grammar in antiquity, see Taylor, D.J., ‘Rethinking the history of language science in classical antiquity’, in Taylor, D.J. (ed.), The History of Linguistics in the Classical Period (Amsterdam and Philadelphia, 1987), 1–16CrossRefGoogle Scholar; Kemp, A., ‘The emergence of autonomous Greek grammar’ in Schmitter, P. (ed.), Geschichte der Sprachtheorie 2: Sprachtheorien der abendländischen Antike (Tübingen, 2. verb. Aufl., 1996), 302–33Google Scholar; Matthaios, S., ‘Neue Perspektiven für die Historiographie der antiken Grammatik: Das Wortartensystem der Alexandriner’, in Swiggers, P. and Wouters, A. (edd.), Grammatical Theory and Philosophy of Language in Antiquity (Leuven, Paris and Sterlin, VA, 2002), 161–220Google Scholar; Swiggers, P. and Wouters, A., ‘Description of the constituent elements of the (Greek) language’, in Montanari, F., Matthaios, S. and Rengakos, A. (edd.), Brill's Companion to Ancient Greek Scholarship (Leiden and Boston, 2015), 759–97Google Scholar.

2 Matthaios, S., Untersuchungen zur Grammatik Aristarchs: Texte und Interpretation zur Wortartenlehre (Göttingen, 1999)CrossRefGoogle Scholar.

3 E.g. Steinthal, H., Geschichte der Sprachwissenschaft bei den Griechen und Römern mit besonderer Rücksicht auf die Logik, 2 vols. (Berlin, 1890–12), II 71–146, esp. 127–46Google Scholar; Collart, J., Varron, grammairien latin (Paris, 1954), 135–49Google Scholar; Collart, J., ‘Analogie et anomalie’, in Brink, C.O. et al. , Varron: six exposés et discussions (Vandoeuvres-Genève, 1963), 117–40Google Scholar; Pfeiffer, R., History of Classical Scholarship. From the Beginnings to the End of Hellenistic Age (Oxford, 1968), 203Google Scholar (but see 245); Siebenborn, E., Die Lehre von der Sprachrichtigkeit und ihren Kriterien. Studien zur antiken normativen Grammatik (Amsterdam, 1976), 97–104Google Scholar; Robins, R.H., ‘Varro and the tactics of analogist grammarians’, in Davies, A. Morpurgo and Meid, W. (edd.), Studies in Greek, Italic, and Indo-European Linguistics Offered to Leonard R. Palmer on the Occasion of his Seventieth Birthday, June 5, 1976 (Innsbruck, 1976), 333–6Google Scholar; Baratin, M. and Desbordes, F., L'analyse linguistique dans l'antiquité classique, 1. Les théories (Paris, 1981), 43–6Google Scholar; Ax, W., ‘Sprache als Gegenstand der alexandrinischen und pergamenischen Philologie’, in Schmitter, P. (ed.), Geschichte der Sprachtheorie 2: Sprachtheorien der abendländischen Antike (Tübingen, 2. verb. Aufl., 1996), 275–301, at 294Google Scholar.

4 Fehling, D., ‘Varro und die grammatische Lehre von der Analogie und der Flexion’, Glotta 35 (1956), 214–70Google Scholar; Blank, D.L., Ancient Philosophy and Grammar: The Syntax of Apollonius Dyscolus (Chico, CA, 1982), 1–5, 11–12, 24–8Google Scholar; Blank, D.L., ‘Analogy, anomaly and Apollonius Dyscolus’, in Everson, S. (ed.), Language (Cambridge, 1994), 149–65, at 151–8Google Scholar; Blank, D.L., Sextus Empiricus. Against the Grammarians (Adversus mathematicos I) (Oxford, 1998), xxxiv–xlGoogle Scholar.

5 Yet, while Fehling, D. (‘Varro und die grammatische Lehre von der Analogie und der Flexion. Schluß’, Glotta 36 [1957], 48–100, at 95–6 and 99)Google Scholar, rather unconvincingly, concluded that the anomaly-analogy controversy was entirely Varro's creation, Blank (n. 4 [1998], xxxvi–xl) suggests that the source for the anti-analogical arguments was an empiricist, either Epicurean or Sceptic.

6 See Fehling (n. 4), 267; Blank (n. 4 [1994]), 152–4; and Blank (n. 4 [1998]), 254. The term ‘anomaly’ occurs in a treatise by Chrysippus, Περὶ τῆς κατὰ τὰς λέξεις ἀνωμαλίας πρὸς Δίωνα (Diog. Laert. 7.192 = SVF II fr. 14), but indicates the ‘inconsistency’ that sometimes occurs between the signified and the signifier (Varro, Ling. 9.1 = SVF II fr. 151).

7 See Blank (n. 4 [1982]), 41–9 and Lallot, J., ‘Analogie et pathologie dans la grammaire Alexandrine’, Lalies 15 (1995), 109–23Google Scholar.

8 On Aristarchus’ methodology in his Homeric studies, see Schironi, F., The Best of the Grammarians: Aristarchus of Samothrace on the Iliad (Ann Arbor, 2018)CrossRefGoogle Scholar. Aristophanes of Byzantium, too, used analogy; see Callanan, C.K., Die Sprachbeschreibung bei Aristophanes von Byzanz (Göttingen, 1987), 107–22CrossRefGoogle Scholar and Ax, W., ‘Aristophanes von Byzanz als Analogist. Zu Fragment 374 Slater (= Varro, de lingua Latina 9, 12)’, Glotta 68 (1990), 4–18Google Scholar. On analogy in Aristophanes and Aristarchus, see also Pagani, L., ‘Language correctness (Hellenismos) and its criteria’, in Montanari, F., Matthaios, S. and Rengakos, A. (edd.), Brill's Companion to Ancient Greek Scholarship (Leiden and Boston, 2015), 798–849, at 806–12CrossRefGoogle Scholar.

9 Lloyd, G.E.R., Polarity and Analogy: Two Types of Argumentation in Early Greek Thought (Cambridge, 1966), 175Google Scholar.

10 Cf. Matthaios (n. 2), 288–9, 409.

11 See Schironi (n. 8), 394–7.

12 The last two scholia discussed derive from Aristonicus, who is generally considered to preserve Aristarchus’ notes from the commentary. Thus, even if Aristarchus is not expressly quoted in those scholia, the scholarly consensus is that they preserve Aristarchean views.

13 Pace Siebenborn (n. 3), 71, according to whom Aristarchus was generally concerned with simple comparisons (i.e. two-term analogies) and used them mostly to discuss questions of prosody and not to determine inflectional patterns. Cf. also Matthaios (n. 2), 28–30.

14 The seminal studies on this regard are Regenbogen, O., ‘Eine Forschungsmethode antiker Wissenschaft’, in Dirlmeier, F. (ed.), Kleine Schriften (München, 1961), 141–94Google Scholar, originally published in Quellen und Studien zur Geschichte der Mathematik 1.2 (Berlin, 1930), 131–82Google Scholar, and Lloyd (n. 9).

15 Cf. Regenbogen (n. 14), 150–6 and 168 (‘Beweisanalogie’).

16 Cf. OED s.v. ‘analogy’ (8). On analogy and analogical change, see Hock, H., Principles of Historical Linguistics (New York, 1991 2), 166–209CrossRefGoogle Scholar and Campbell, L., Historical Linguistics: An Introduction (Edinburgh, 2013 3), 91–105Google Scholar.

17 Cf. Ritter, J., Historisches Wörterbuch der Philosophie (Basel, 1971–2007), Band 1Google Scholar, s.v. Analogie, 214–29, at 214–15.

18 On this fragment, see Huffman, C.A., Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King (Cambridge and New York, 2005), 166–81CrossRefGoogle Scholar.

19 Cf. Heath, Th.L., A History of Greek Mathematics, 2 vols. (Oxford, 1921), 1.322–34, esp. 1.325–7Google Scholar (on Eudoxus’ theory of proportion).

20 On Euclid's biography, see Heath (n. 19), 1.354–7; Heath, Th.L., The Thirteen Books of Euclid's Elements, Translated from the Text of Heiberg, with Introduction and Commentary, 3 vols. (Oxford, 1926 2), 1.1–6Google Scholar; Vitrac, B., ‘Euclide’, in Goulet, R. (ed.), Dictionnaire des philosophes antiques, vol. 3 (Paris, 2000), 252–5Google Scholar.

21 On Eudoxus and the fifth book of the Elements, see Acerbi, F., ‘Drowning by multiples. Remarks on the fifth book of Euclid's Elements with special emphasis on Prop. 8’, Archive for History of Exact Sciences 57 (2003), 175–242, at 220–37 (esp. 227–37)CrossRefGoogle Scholar.

22 Transl. Heath (n. 20), 2.114. Cf. Heath (n. 20), 2.116–19.

23 Cf. also Heron, Def. 136.31, p. 134.12–13 Heiberg: ἀναλογία ἐστὶν ἡ τῶν λόγων ὁμοιότης.

24 On these definitions of analogy, cf. Heath (n. 20), 2.120–9, 2.292–3.

25 This is one of the most debated problems in the Elements. On this question, see Vitrac, B., Euclide d'Alexandrie, Les Éléments. Traduction et commentaires. Vol. 2. Livres V–VI: proportions et similitude, Livres VII–IX: arithmétique (Paris, 1994), 507–38Google Scholar.

26 The link between mathematics and grammatical analogy was already hinted at by Siebenborn (n. 3), 56–62. I will now develop this idea further and examine it diachronically.

27 On analogy in Plato and Aristotle, see Lloyd (n. 9), 360–80, 389–414. ‘Weak’ analogy occurs also in the Hellenistic period: the empirical school of medicine used the μετάβασις κατ’ ἀναλογίαν, ‘analogical transition’, to understand and cure hitherto unknown diseases by equating them to similar (and known) conditions; cf. Deichgräber, K., Die griechische Empirikerschule, Sammlung der Fragmente und Darstellung der Lehre (Berlin, 1930), 48.9–10Google Scholar (fr. 10b).

28 The questions of how the line is divided and oriented, as well as what the ratio between the members of the proportion is, are still debated; see, for example, Smith, N.D., ‘Plato's divided line’, AncPhil 16 (1996), 25–46Google Scholar.

29 See Arist. Top. 1.17 (108a7–17). On Aristotle and analogy, see Einarson, B., ‘On certain mathematical terms in Aristotle's logic’, AJPh 57 (1936), 33–54 and 151–72Google Scholar; Hesse, M., ‘Aristotle's logic of analogy’, PhilosQ 15 (1965), 328–40Google Scholar; Olshewsky, T.M., ‘Aristotle's use of analogia’, Apeiron 2 (1968), 1–10CrossRefGoogle Scholar. In particular, Hesse (this note), 333 distinguished between ‘substantive analogy’ (= possession of common properties) and ‘formal analogy’ (= similarity of relation). On this distinction, see Nagel, E., The Structure of Science: Problems in the Logic of Scientific Explanation (New York, 1961), 110–11Google Scholar. On the value of mathematical models for Aristotle, see Acerbi, F., ‘Osservazioni sulle origini aritmetiche della teoria aristotelica del sillogismo’, in Alessandrelli, M. and de Vincentis, M. Nasti (edd.), La logica nel pensiero antico. Atti del colloquio, Roma, 28–29 novembre 2000 (Naples, 2009), 77–104Google Scholar.

30 On Aristotle's definition, see Huffman (n. 18), 180.

31 Corrective justice, on the other hand, is an arithmetic proportion (i.e. progression) of the type: A – B = B – C. On this passage, see Dirlmeier, F., Aristoteles, Nikomachische Ethik (Berlin, 1999), 100–5Google Scholar; Keyt, D., ‘Aristotle's theory of distributive justice’, in Keyt, D. and Miller, F.D. Jr. (edd.), A Companion to Aristotle's Politics (Oxford and Cambridge, MA, 1991), 238–78, at 240–2Google Scholar; Young, C.M., ‘Aristotle's justice’, in Kraut, R. (ed.), The Blackwell Guide to Aristotle's Nicomachean Ethics (Malden, MA and Oxford, 2006), 179–97, at 184–6Google Scholar. A similar ‘proportional’ concept of justice is to be found again in Aristotle (Pol. 1301b29–1302a8) as well as in Plato (Leg. 744b1–c4 and 757a5–758a2; Grg. 507e5–508b3).

32 Arist. Hist. an. 486b17–21 ἔνια δὲ τῶν ζῴων οὔτε εἴδει τὰ μόρια ταὐτὰ ἔχει οὔτε καθ' ὑπεροχὴν καὶ ἔλλειψιν, ἀλλὰ κατ' ἀναλογίαν, οἷον πέπονθεν ὀστοῦν πρὸς ἄκανθαν καὶ ὄνυξ πρὸς ὁπλὴν καὶ χεὶρ πρὸς χηλὴν καὶ πρὸς πτερὸν λεπίς. ὃ γὰρ ἐν ὄρνιθι πτερόν, τοῦτο ἐν τῷ ἰχθύι ἐστὶ λεπίς (‘some animals have parts which are not the same in form, nor by excess or by defect: but they [are identical] by analogy; for example, bone has the same [analogical] relationship to spine, nail to hoof, hand to claw, and scale to feather; for what the feather is in a bird, the scale is in a fish’). For a discussion on analogies in Aristotle's biological works, see Wilson, M., ‘Analogy in Aristotle's biology’, AncPhil 17 (1997), 335–58Google Scholar.

33 As Janko, R., Aristotle Poetics I, with The Tractatus Coislinianus, A Hypothetical Reconstruction of Poetics II, The Fragments of the On Poets (Indianapolis and Cambridge, 1987), 130Google Scholar says: ‘It corresponds to “metaphor” in our sense, and depends on discerning likenesses between pairs of things.’

34 So Geus, K., Eratosthenes von Kyrene: Studien zur hellenistischen Kultur- und Wissenschaftsgeschichte (Munich, 2002), 149–51, 164–5Google Scholar.

35 Indeed, Eratosthenes is the first to claim to be a φιλόλογος (Suet. Gram. et rhet. 10). See Pfeiffer (n. 3), 158–9.

36 In fact, μάθημα is sometimes used with the more generic meaning of ‘knowledge’ (Ar. Nub. 1231, Av. 380, Thuc. 2.39.1) and of ‘science’ in the broadest sense (Pl. La. 182b6–7; Isoc. Panath. 27).

37 It is debated whether the Τέχνη Γραμματική, attributed to Dionysius Thrax, is authentic; see Taylor (n. 1), 8–11; Kemp (n. 1), esp. 307–15; V. Law and I. Sluiter, Dionysius Thrax and the Technē Grammatikē (Münster, 1995). However, this first paragraph certainly is, as Sextus Empiricus quotes it almost verbatim and attributes it to him (Math. I § 57 and § 250).

38 Pace Pfeiffer (n. 3), 203, n. 1, according to whom grammatical ἀναλογία ‘is hardly derived from the mathematical and philosophical term ἀναλογία (= proportion) used by Eratosthenes, the Platonist, in his Platonicus’.

39 For another connection between mathematics and Dionysius Thrax, see P. Berrettoni, ‘On the geometrical background of Dionysius Thrax’ definition of comparatives’, in R. Petrilli and D. Gambarara (edd.), Actualité des anciens sur la théorie du langage (Münster, 2004), 17–36.

40 On this definition and also on other criteria for analogy, especially among Latin grammarians, see Garcea, A., ‘César et les paramètres de l'analogie’, in Basset, L., Biville, F., Colombat, B., Swiggers, P. and Wouters, A. (edd.), Bilinguisme et terminologie grammaticale gréco-latine (Leuven, Paris and Dudley, MA, 2007), 339–57Google Scholar and Garcea, A., Caesar's De Analogia: Edition, Translation, and Commentary (Oxford and New York, 2012), 167–79Google Scholar. See also Siebenborn (n. 3), 72–83, Pagani (n. 8), 834–8 and Schironi (n. 8), 383–6.

41 Taylor, D.J., ‘Varro's mathematical models of inflection’, TAPhA 107 (1977), 313–23Google Scholar; Garcea, A., ‘Varron et la constitution des paradigmes flexionnels du latin’, Histoire, Épistémologie, Langage 30 (2008), 71–89CrossRefGoogle Scholar.

42 While Taylor sees Varro's mathematical model mostly as his original contribution, Garcea (n. 41), 78 more correctly states that Varro was actually not the first to use four-term analogies; rather, he developed this mathematical model already used by the Alexandrian grammarians into a more complex system (for example with the idea of formula, as discussed by Garcea [n. 41], 78–81). The goal of the present study is to ideally complement Garcea's study of Varro's analogy and to explore how this method started before Varro and developed after him, especially in the Greek world.

43 Book 8 is dedicated to the arguments against analogy and in favour of anomaly, Book 9 to the arguments in favour of analogy and against anomaly, and Book 10 presents Varro's attempt to mediate between these two approaches to language.

44 I would like to thank Wolfgang de Melo, who kindly allowed me to use his new text of Varro's De lingua Latina before its publication (de Melo, W., Varro: De lingua Latina. Introduction, Text, Translation, and Commentary [Oxford, 2019]Google Scholar).

45 Yet, I agree with Garcea (n. 41), 83, when he claims (contra Taylor) that Varro did not take this model from Aristotle but rather from mathematical treatises which were circulating in Rome at his time and which were probably similar to the preserved Introduction to Arithmetic by Nicomachus of Gerasa (c.100 c.e.).

46 See Sch. Il. 1.86 (reported above, at p. 4).

47 Cf. Matthaios (n. 2), 326–51.

48 A further example of such a development is Caesar's De analogia; see now Garcea (n. 40 [2012]), who correctly observes (at 15–18) that the aim of Caesar's treatise is not purely grammatical or philological but rather rhetorical.

49 See also Sch. Il. 17.539b (Hrd.) <καταπέφνων:> Ἀρίσταρχος ὡς τέμνων (καταπέφνων: Aristarchus [reads it] like τέμνων).

50 There are countless examples of the different approach of Herodian compared to Aristarchus in the Homeric scholia; see e.g. Sch. Il. 6.244; 11.495; 24.228a.

51 On this scholium, see Erbse, H., ‘Zur normativen Grammatik der Alexandriner’, Glotta 58 (1980), 236–58, at 237–9 and Matthaios (n. 2), 330, 343, 344–5, 409–10, 411, 421Google Scholar.

52 On the different meaning of analogy in Herodian (i.e. a quality of certain words as well as a method and an activity of a technical grammarian), see Sluiter, I., ‘A champion of analogy: Herodian's On Lexical Singularity’, in Matthaios, S., Montanari, F. and Rengakos, A. (edd.), Ancient Scholarship and Grammar: Archetypes, Concepts and Contexts (Berlin and New York, 2011), 291–310Google Scholar.

53 Also in Euclid's Elements the noun ἀναλογία is seldom used (14 times)—despite a pervasive use of the indeclinable adjective ἀνάλογον (395 occurrences).

54 The same happens in Sch. Il. 14.464a (ex.) Ἀρχέλοχος: Ἀρίσταρχος ἀναλογώτερον τοῦ Ἀρχίλοχος, ὡς φερένικος, ‘Μενέλαος’ (Il. 2.408 al.).

55 Siebenborn (n. 3), 63–7 recognizes three kinds of analogy: 1) the ‘zweigliedrige Vergleichungen’, which I call the ‘two-term proportions’; 2) the ‘viergliedrige Flexions- und Derivationsanalogien’, which I call ‘four- or more term proportions’ and 3) the κανόνες, which I consider the ‘descriptive’ analogy, as conceived by Herodian. As we saw in n. 13 above, according to Siebenborn ([n. 3], 71), Aristarchus mostly employed the first type of analogy, but I have tried to show that he also used the second type (but not the third).

56 On analogy among Latin grammarians, see C. Woldt, De analogiae disciplina apud grammaticos Latinos (Regimonti, 1911). More modern studies are those by Garcea (n. 40 [2007]) and (n. 40 [2012]), which also provide additional bibliography.

57 See Schironi, F., ‘Ἀναλογία, analogia, proportio, ratio: loanwords, calques and reinterpretations of a Greek technical word’, in Basset, L., Biville, F., Colombat, B., Swiggers, P. and Wouters, A. (edd.), Bilinguisme et terminologie grammaticale gréco-latine (Leuven, Paris and Dudley, MA, 2007), 321–38Google Scholar.

58 E.g. Quint. Inst. 1.6.4 (eius [sc. analogiae] haec uis est, ut id quod dubium est ad aliquid simile, de quo non quaeritur, referat et incerta certis probet); Gell. NA 2.25 (ἀναλογία est similium similis declinatio); Pompeius, GL V 197.22 (quae est analogia? comparatio similium); Servius, GL IV 435.15–16 (analogia dicitur ratio declinationis nominum inter se onmi parte similium).

59 In Tim. 4 § 13: quae Graece ἀναλογία, Latine (audendum est enim, quoniam haec primum a nobis nouantur) conparatio proportioue dici potest (‘what in Greek is ἀναλογία can be called “proportion” or “comparison” in Latin [for we must be bold, since we are the first to coin these terms]). Here the Greek context of ἀναλογία is purely mathematical (Pl. Tim. 31c3–32a7). On Cicero's translation of the Timaeus, see Sedley, D., ‘Cicero and the Timaeus’, in Schofield, M. (ed.), Aristotle, Plato and Pythagoreanism in the First Century BC: New Directions for Philosophy (Cambridge, 2013), 187–205Google Scholar.

60 See Schironi (n. 57), 322–3.

61 See Schironi (n. 57), 326–8.

62 Just like his colleagues, aside from this passage, Diomedes never uses the word proportio but only analogia (e.g. GL I 307.22; 375.18; 377.22; 378.14–15; 384.21; 386.passim; 387.4).

63 E.g. Donatus, GL IV 379.3–4; Ps.-Palaemon, GL V 539.21.

64 Ps.-Probus, GL IV 47.23–4 (ratio recta perseuerans per integram declinationis disciplinam).

65 On Donatianus and the Donatiani fragmentum, cf. Kaster, R.A., Guardians of Language: The Grammarian and Society in Late Antiquity (Berkeley, 1988), 274–5Google Scholar.

66 Charisius 149.22–6 Barwick offers a very similar definition, including the Greek phrasing (analogia est, ut Graecis placet, συμπλοκὴ λόγων ἀκολούθων, … ἀναλογία ἐστὶν συμπλοκὴ λόγων ἀκολούθων ἐν λέξει).

67 On this definition, see Blank (n. 4 [1982]), 26–7, who states: ‘now συμπλοκή is a word often used for syntactic construction, while ἀκόλουθος describes the sentence whose construction is consequent or whose words are in proper agreement with one another. Hence the words συμπλοκὴ λόγων ἀκολούθων themselves would seem to indicate that analogy is consequent syntactic construction.’ (27) This is true if we read this definition from a purely linguistic point of view. I have tried, however, to show that the same phrase can also have a mathematical meaning, and that it was used in this sense by the first Greek grammarians. At the time when Donatianus or Charisius used the term, it indeed meant what Blank argues that it did. Blank himself, though, readily acknowledges the ‘scientific background’ of grammatical ἀκολουθία (n. 4 [1982], 16–17).

68 My point is limited to the study of grammar. Mathematical proportions as heuristic tools were in fact used in the Latin world until late. For example, Calcidius (second half of the fourth century c.e.) in his commentary to Plato's Timaeus applies proportions to the analysis of daemons (Comm. in Tim. 131); see Somfai, A., ‘The nature of daemons: a theological application of the concept of geometrical proportion in Calcidius’ Commentary to Plato's Timaeus (40d–41a)’, in Sharples, R.W. and Sheppard, A.D.R. (edd.), Ancient Approaches to the ‘Timaeus’ (London, 2003), 129–42Google Scholar.

69 The borrowing of methodologies from different disciplines as well as the crossing of disciplinary boundaries in ancient Greece (and China) has been recently highlighted by Lloyd, G.E.R., Disciplines in the Making. Cross-Cultural Perspectives on Elites, Learning, and Innovation (Oxford, 2009), esp. 179–82CrossRefGoogle Scholar. However, he does not discuss grammar—in this paper I have tried to add this field to the interdisciplinary group of technai of Greek antiquity.

70 The Alexandrians’ application of a mathematical model to language is not isolated; even before them, Plato used a (meta)mathematical model to define logos in the sense of ‘statement’, ‘proposition’: see Berrettoni, P., ‘A metamathematical model in Plato's definition of logos’, Histoire, Épistémologie, Langage 30 (2008), 7–19CrossRefGoogle Scholar.

71 Indeed, accentuation and prosody more generally were particularly problematic, because there was no written record; see Probert, P., Ancient Greek Accentuation: Synchronic Patterns, Frequency Effects, and Prehistory (Oxford, 2006), 14–45CrossRefGoogle Scholar. As she notes (at 45), sometimes grammarians might have accessed a tradition which preserved some archaic accentuation; yet, even in such cases, grammarians ‘proved’ the chosen accent by using an analogy with a similarly accented form. One such case (Sch. Il. 12.158, mentioned above) is discussed in Schironi (n. 8), 405–7.

72 Ax, W., ‘Aristarch und die “Grammatik”’, Glotta 60 (1982), 96–109Google Scholar, esp. 108–9; Ax (n. 3), esp. 276 and 288.

73 Modern linguistics, perhaps ironically, employs the concept of ‘proportional analogy’ opposed to ‘non-proportional analogy’: the very need to specify that an analogy is ‘proportional’ (a tautology, from an etymological point of view!) is evidence that the original meaning of Greek ἀναλογία is lost in modern linguistics; see Hock (n. 16), 171; Campbell (n. 16), 92–3; Kiparsky, P., ‘Analogy’, in Bright, W. (ed.), International Encyclopedia of Linguistics (New York and Oxford, 1992), 1.56–61, at 56Google Scholar.