Acerbi ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 Article copyright held by the author(s) and made available under the Creative Commons Attribution License CC-BY https://creativecommons.org/licenses/by/4.0/ Ψευδαριθµός Fabio Acerbi HE LIDDELL-SCOTT-JONES lexicon records the noun ψευδαριθµός “false number” as a hapax, occurring only in a scholium to Tht. 191B. It has long been known that the word is not attested in the manuscripts, but it has been considered until recently a correct emendation of the actual reading. The story of such an error, and the surprising inertia to ψευδαριθµός being replaced by the correct term, is worth telling. The Theaetetus has reached the point where Socrates and Theaetetus have just concluded that false judgement exists, by rejecting three objections against it. In particular, concerning the third objection, Socrates acknowledges (191A8) that he and Theaetetus “were wrong to agree that it is impossible for a man to be in error through judging that things he knows are things he doesn’t know.” To confirm this view, Theaetetus (191B2–6) relates an experience of his as an example: he does know Socrates but, seeing in the distance someone who is unknown to him, he happened to think that that person was Socrates. A scholium commenting on Theaetetus’ example claims at this point that “the conjunction of perception and opinion” is the key to solving such puzzles.1 Socrates replies that they already 1 Schol. 191B4, now best read as scholium no. 230 in Tht. in D. Cufalo, Scholia Graeca in Platonem I (Rome 2007) 70. The scholium was already printed in W. C. Greene, Scholia Platonica (Haverford 1938) 37.21–22 and 444.1–2 (here and in the next note I print line numbers for clarity’s sake). In Greene’s edition the “scholia Arethae” (namely, the ones, among those con- tained in Bodl.Clark. 39, in the hand of the renowned Byzantine scholar) are T 318 ΨΕΥΔΑΡΙΘΜΌΣ ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 “recoiled from this suggestion,” and concludes (191B10): “Then let us not put the case in that way.” A subsequent scholium, after a short paraphrasis of the Platonic lemma, tries to explain briefly why the proposal contained in the preceding scholium runs into difficulties:2 µὴ οὕτω τιθῶµεν, φησίν, ὡς ἔµπροσθεν, καὶ ἡµῖν συγχωρήσει τις εἶναι δυνατὸν ἃ οἶδέν τις δοξάσαι αὐτὰ ἄττα εἶναι ὧν οὐκ οἶδεν, ἴσως δὲ ἀντιτενεῖ. καὶ γὰρ τοῦτο προσέθηκεν, εἰδὼς ὅτι κἂν ἐν µίξει τοῦ εἰδέναι πρὸς τὸ αἰσθάνεσθαι δείξωµεν ψευδῆ δόξαν ἐνοῦσαν, οὐχ ἕξοµέν τι λέγειν πρὸς τὸν ἀποροῦντα περὶ τούτων, ἐπειδὰν ἡµᾶς ἐρωτᾷ περὶ τῶν ἔξω τῆς αἰσθήσεως, εἰ δυνατὸν συστῆναι ψευδοδοξίαν, οἷον ἐπὶ τῶν παρὰ τοῖς γεω- µέτραις καλουµένων ψευδαρίων. οὐ γὰρ διὰ µίξιν αἰσθήσεως ψευδογραφοῦσιν. “Let us not put the case in that way,” he says, as before, and one might agree with us that it is possible for someone to judge that what he knows is among what he doesn’t know—but perhaps he will resist. For he added this because he knows that, even if we were able to show that there is false judgement in the commix- ture of knowing and perceiving, we would not have anything to say to someone raising an objection about this, whenever he asks us, concerning the things that are outside the sensible, whether it is possible for a false opinion to come to be, for example, in the case of those called pseudaria by the geometers. For they do not propose false proofs by commixture with the sensible. The scholium appears to refer to the lost Euclidean Pseudaria; the treatise is mentioned by a number of ancient sources, mainly late commentators with a strong Neoplatonic bent.3 In his collection of Euclidean Fragmenta, Heiberg asserts that ___ printed separately from the scholia vetera. As a consequence, identical scholia to Theaetetus, Sophist, and Alcibiades I are printed twice. 2 Schol. 191B10: scholium no. 232 in Tht. at Cufalo, Scholia Graeca 70 (= Greene, Scholia Platonica 38.1–9 and 444.5–13). 3 The main testimonies come from Proclus (In Eucl. 70.1–18 and 59.2–7 Friedlein) and from several Aristotelian commentators. An analysis of the testimonies can be found in F. Acerbi, “Euclid’s Pseudaria,” AHES 62 (2008) 511–551. FABIO ACERBI 319 ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 ψευδαρίων is Ruhnken’s correction, and that the manuscripts have ψευδαριθµῶν.4 This claim is false, and was already cor- rected in Greene’s edition of the Platonic scholia: Greene prints “ψευδαρίων (lege ψευδαριθµῶν)” in the text and “ψευδαρίων B T W: ψευδαριθµῶν recte vulg. ex Proclo ut videtur” in the appara- tus, contradicting Heiberg’s indications.5 Greene’s “vulgata” is Hermann’s text,6 which in turn stands on the shoulders of earlier editions of the Platonic scholia. In their order of pub- lication, these editions are: Siebenkees’ Anecdota graeca (1798),7 Ruhnken’s Scholia in Platonem (1800),8 Gaisford’s catalogue of the Clarkian manuscripts in the Bodleian Library (1812),9 and Bekker’s edition of the Platonic dialogues supplemented with scholia (1823).10 Hermann’s own edition of the Platonic scholia appeared in 1853 as an appendix to the dialogues.11 Of those scholars, Gaisford alone did not print the scholium.12 4 Heiberg writes “ψευδαριθµῶν codd., corr. Ruhnken”: Euclidis Opera omnia VIII (Leipzig 1916) 236 in app. 5 See n.22 below for the MSS. that correspond to Greene’s sigla. The reasons why Greene claims that Proclus supported ψευδαριθµῶν remains a mystery. 6 Cf. Green, Scholia Platonica XII; see below for Hermann’s edition. 7 Anecdota graeca ex praestantissimis Italicar. Bibliothecarum codicibus de- scripsit Ioann. Philipp. Siebenkees. Edidit et praefatus est Ioann. Adam. Goez (Nuremberg 1798). The volume contains also Libanius’ Pro Olympio, a writing of Georgius Gemistus Pletho where he corrects a few passages in Strabo, and extracts from Theophrastus’ Characters. 8 Σχόλια εἰς Πλάτωνα. Scholia in Platonem, Ex codicibus mss. multarum bibliothecarum primum collegit D. Ruhnkenius (Leiden 1800). 9 Catalogus sive Notitia manuscriptorum qui a Cel. E. D. Clarke comparati in Biblio- theca Bodleiana adservantur, Pars prior, Inseruntur scholia quaedam inedita in Platonem et in Carmina Gregorii Nazianzeni (Oxford 1812). 10 Immanuelis Bekkeri in Platonem a se editum commentaria critica, Accedunt scholia, Tomus alter (Berlin 1823). 11 Starting at 223 in Platonis Dialogi secundum Thrasylli Tetralogias dispositi, ex recognitione C. F. Hermanni, VI (Leipzig 1853). 12 The description of Bodl.Clark. 39 runs on Catalogus 68–71; the scholia are printed at 72–93. 320 ΨΕΥΔΑΡΙΘΜΌΣ ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 Siebenkees prints ψευδαριθµῶν without comment (other terms in the scholium have textual notes).13 Siebenkees died two years before his Anecdota graeca was printed, but in the preface he is quoted by the editor Goez as follows: “Platonis scholiasten descripsi e Codd. Venetis in Catalogo, quem Zanet- tius edidit N. 186 et 189 notatis, et e Cod. Biblioth. Angel.”14 Bekker follows Siebenkees in printing ψευδαριθµῶν without apparatus or comment,15 but declares that his scholia are “col- lata ad codices,” and his sigla correspond to Bodl.Clark. 39, to Par.gr. 1808 and 1812,16 and to Marc.gr. 184. As was usual with him, Hermann simply employed the pre- ceding editions as sources (apparently, Bekker excepted),17 con- sistently did not print any apparatus, and retained Siebenkees’ reading ψευδαριθµῶν without comment.18 Only Ruhnken’s edition of the Platonic scholia retains ψευδαρίων as the text. This edition is a small 8vo volume of 256 pages (this is an integer number of quires) + 4 of preface; the scholium to Tht. 191B10 is on page 32. The text has no ap- paratus and presents such variant readings as to suggest that Ruhnken resorted to a manuscript in the family of Marc.gr. IV.1.19 In the preface, no indications are provided as to the manuscripts employed: it is only stated, most generically, that the scholia are drawn “ex Codicibus MSS, qui servabantur in Bibliothecis Vindobonensi [sic], Florentinis, aliisque.” The author of the preface could not be more precise, as he was not 13 Anecdota graeca 19–20. 14 Anecdota graeca VII. The last-named MS. is Angel.gr. 107, listed as item 162 in N. G. Wilson, “A List of Plato Manuscripts,” Scriptorium 16 (1962) 386– 395; cf. Cufalo, Scholia Graeca XV. 15 In Platonem commentaria critica 366. 16 Actually, Par.gr. 1807 is also mentioned, but this manuscript contains only the dialogues of the last two tetralogies. 17 Hermann himself recognizes this at Platonis Dialogi VI XXXI. 18 Platonis Dialogi VI 248. 19 Siebenkees’ text has the same variant readings, and others almost surely due to misprints (the whole booklet is full of misprints). FABIO ACERBI 321 ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 Ruhnken, but the printer: the volume was in fact published two years after Ruhnken’s death.20 At the very end of the volume there are only two pages of notes to the scholia, ending with the notes referring to page 3 of the text. The notes are apparently in their final, polished form: although the author of the preface complains that almost all of Ruhnken’s animadversiones are miss- ing because of his death, I strongly suspect some dirty trick on the printer’s side, maybe to keep the volume within a reason- able size: it is implausible that Ruhnken had produced a hand- ful of perfectly accomplished notes and then nothing more at all; nor is the hypothesis that most of the notes got lost reason- able. Anyway, what is important for our purposes is that Ruhnken prints ψευδαρίων. It follows that Heiberg, probably lacking manuscript evidence to check the actual reading, had to choose between trusting Ruhnken’s edition or following the others, all of them without a critical apparatus. He chose the wrong alter- native. Heiberg argued21 that no sensible meaning could be attached to the reading ψευδαριθµῶν in its context, and noted that the word does not appear elsewhere; thus, ψευδαριθµῶν, printed by all other editors, must be the (corrupt) reading of the manuscripts, and ψευδαρίων a (good) emendation. Heiberg should have suspected instead that it was more likely for pro- fessional philologists to print a conjecture like ψευδαριθµῶν (not recognised as such) than for the eclectic Ruhnken cleverly to amend to ψευδαρίων the reading ψευδαριθµῶν supposedly found in the manuscripts. What is puzzling is that, even if amending to ψευδαριθµῶν might be expected from Siebenkees, Bekker should have done it too, and done so independently of Sie- benkees. Even if this possibility seems remote we should never- theless hesitate to conclude that Bekker simply lifted his text 20 This fact explains the doubtful verb form “servabantur” and the typo “Vindobonensi” in the quotation above. 21 He explains his reasoning in Litterargeschichtliche Studien über Euklid (Leip- zig 1882) 38 n.1. 322 ΨΕΥΔΑΡΙΘΜΌΣ ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 from Siebenkees, contrary to what he states about his scholia, namely, that they are “collata ad codices.” In fact, as the 18th- or 19th-century editors of the Platonic scholia did not employ the same manuscripts as the 20th-century editors, there is the possibility that some of the former manuscripts actually have the reading ψευδαριθµῶν.22 As the context is mathematical, and those editors may have been unaware of the lost Pseudaria of Euclid and little acquainted with Proclus’ commentary on Ele- ments Book 1, the reading ψευδαριθµῶν may not have sounded more absurd than ψευδαρίων.23 The only way to settle the issue is to check all the manu- scripts used by Siebenkees and Bekker. Now, Angel.gr. 107, f. 77v marg. ext., has ψευδαρί(ων) by compendium, with accent; Marc.gr. Z. 184, f. 72v marg. ext., has ψευδαρίων in full, ac- cented ψευδαριῶν; Marc.gr. Z. 186, f. 81v marg. inf., has ψευδαρί(ων) by compendium, with accent; Marc.gr. Z. 189, f. 78r marg. inf., has ψευδαρίων in full, with accent; Par.gr. 1808, f. 83v marg. inf., has ψευδαρί(ων) by compendium, with accent; in Par.gr. 1812 the scholium is absent. The conclusion to be drawn is that Siebenkees amended the text and that Bekker copied to a large extent the scholia from him, maybe collating them with his own manuscripts whenever he suspected problems—problems that apparently he did not suspect in our case. Hermann did the same, and in this way Siebenkees’ bad conjecture—actually, the only printed occur- rence of ψευδαριθµῶν that is directly grounded on a manuscript reading (albeit incorrectly emended)—became in this way the 22 The readings of the main manuscripts now used for editing the scholia are as follows: B (Bodl.Clark. 39, f. 105v): ψευδαρίων in majuscule and in full, with accent; W (Vind.suppl.gr. 7, f. 133r): ψευδαρίων in minuscule and in full, with accent; D (Marc.gr. Z. 185, f. 92v): ψευδαρί(ων) in minuscule and by compendium, with accent; T (Marc.gr. IV.1, f. 52v): ψευδαρί(ων) in majus- cule and by compendium, in ligature with the accent. 23 The possibility that both Siebenkees and Bekker independently (and on different manuscripts—see the lists above) misread the text of the scholium is too remote to be envisaged seriously. FABIO ACERBI 323 ————— Greek, Roman, and Byzantine Studies 60 (2020) 317–323 vulgata. Thus, the lemma ψευδαριθµός in LSJ should be elim- inated, or at least adjusted in accordance with this note.24 April, 2020 CNRS, UMR8167 Orient et Méditerranée, Paris fabacerbi@gmail.com 24 The perceptive remarks of the referee and of the editors have improved my argument.