αὕτη ἡ ἐπιστήμη κτλ.
: ‘the nature of this science is in precise contradiction to’ etc.
πᾶν τοὐναντίον is adverbial, and
ἔχει intransitive. In what follows Plato is not (as Stallbaum strangely supposes) censuring contemporary geometricians, “sed vitium quoddam ipsius scientiae” (Schneider, who refers to VI 510 B—511 A), for even those
ὅσοι καὶ σμικρὰ γεωμετρίας ἔμπειροι agree with him. It is however probable on other grounds that Plato himself was afraid lest his pupils should depend too much on geometrical figures and instruments; and Plutarch tells us that he reproved Eudoxus and others for this very fault:
ἀπόλλυσθαι γὰρ οὕτω καὶ διαφθείρεσθαι τὸ γεωμετρίας ἀγαθὸν αὖθις ἐπὶ τὰ αἰσθητὰ παλινδρομούσης, καὶ μὴ φερομένης ἄνω μηδὲ ἀντιλαμβανομένης τῶν ἀϊδίων καὶ ἀσωμάτων εἰκόνων, πρὸς οἷσπερ ὢν ὁ θεὸς ἀεὶ θεός ἐστι (
Conv. Disp. VIII 2. 718 F: cf. also
Vit. Marc. 14. 5—7. The anecdote refers in particular to stereometrical instruments, but its moral applies equally to the study of plane geometry). See Rothlauf l.c. pp. 66 ff. and Gow
Gk Math. p. 181.
ἀναγκαίως
‘in beggarly fashion’ (“nothgedrungenen Weise” Prantl). They are ‘hard up’ for words to express their meaning, and must consequently use language which does not: cf. VI 510 D. J. and C.'s explanation “with merely practical needs in view” is quite wrong; nor does the word appear to me to contain “a facetious allusion to geometrical necessity” (in the sense of V 458 D), as they assert. Madvig's
ἀκάκως for
ἀναγκαίως is a singularly unhappy suggestion.
παρατείνειν
= ‘to apply,’ e.g. a parallelogram to a given line: cf.
Men. 87 A
(
παρὰ τὴν δοθεῖσαν—γραμμὴν παρατείναντα κτλ.) with E. S. Thompson's note. Blass takes the same view (
de Pl. math. p. 19). Euclid's expression for this is
παραβάλλειν (X 18 ff. and
passim: cf. Cantor l.c. p. 145). The ordinary translation ‘produce’ (as e.g. a line) has no authority, and Euclid's word for ‘producing’ a line is
ἐκβάλλειν or
προσεκβάλλειν (I 5, 17 and
passim. So also in Aristotle: see the
Ind. Arist. s.v.).
προστιθέναι
: ‘to add,’ sc. one
μέγεθος to another in any geometrical construction: cf. Nicom.
Introd. Ar. II 12. 2. Euclid uses
συντιθέναι, σύγκειμαι (X 16 and
passim) of such an operation.
φθεγγόμενοι
is said “non sine eleganti quadam irrisione” (Stallbaum): cf. VI 505 C note
τὸ δέ
: ‘whereas’: cf. I 340 D note
τοῦ ἀεὶ ὄντος
. Plato held the objects of mathematical study to be
ἀΐδια καὶ ἀκίνητα ‘eternal and unchangeable’ (Arist.
Met. A 6. 987^{b} 16: cf. VI 510 C ff., VII 526 A note), but not Ideas. The Platonic meaning of
τοῦ ἀεὶ ὄντος is certainly not exhausted by the observation that “the truths of every science are always true” (Bosanquet).
ὄντος implies substantial existence, independently of our thoughts, and independently also of particulars. The existence of
τὰ μαθηματικά as
μιμήματα τῶν ὄντων or copies of the Ideas, ‘moving in and out of’ the material substance of the Universe, which they stamp with an infinite diversity of forms and shapes, is a cardinal doctrine of Plato's physics (
Tim. 50 C
al.), and Bosanquet appears to me to rob the words of Plato of half their significance, in the fruitless attempt to find in his ontology nothing but what commends itself to certain schools of philosophy in the present day. See V 476 E and App. I.
τοῦ ποτέ κτλ.
: ‘that which at some particular time is a particular instance of becoming and perishing.’
τι γιγνομένου=
ὄντος (the copula)
γιγνομένου τινός, but
γιγνομένου itself involves the copula, the presence of which would here be intolerable. Cf. V 473 D note and
Euthyph. 10 C
εἴ τι γίγνεται ἤ τι πάσχει, οὐχ ὅτι γιγνόμενόν ἐστι, γίγνεται, ἀλλ’ ὅτι γίγνεται, γιγνόμενόν ἐστι. Here
τι is indeclinable like
τι in
Lach. 200 B
,
Menex. 247 B
(
οἰομένῳ τι εἶναι),
Euthyd. 303 C
(
δοκούντων τι εἶναι),
οὐδέν, μηδέν etc. tolerably often in tragedy, and the adverbial use of
ἀμφότερα and
τἀναντία (e.g.
Lach. 185 A
ὑέων γὰρ που ἢ χρηστῶν ἢ τἀναντία γενομένων κτλ.): cf. also (with Schneider
Addit. p. 57) Procl.
in Tim. 136 E
τοῦ—ἀδιαιρέτως πάντα ὄντος et al. The indeclinable form adds to the emphasis, and indeed
τινὸς (if placed after
ποτέ) could hardly stand at all. Schneider translates “des etwas werdenden und vergehenden,” apparently taking
τι predicatively with
γιγνομένου. But the expression ‘that which becomes something’ suggests a substratum underlying
γιγνόμενον, whereas the only correct antithesis to
ὄν (
τοῦ ἀεὶ ὄντος) is
γιγνόμενον itself. Stallbaum wrongly explains
τι as “aliqua ratione.” A few inferior MSS omit the word. I believe the text is sound, though possibly
τι should be accented, as in the exactly similar Aristotelian usage of
τις “ad significandam
τὴν ἀτομότητα” (Bonitz
Ind. Ar. p. 763) e.g.
ὁ τὶς ἄνθρωπος. The use of
ποτέ also reminds us of the
ποτέ of the Categories.
γεωμετρική
is an adjective (Schneider).
σχεῖν
. The tense is inchoative or ingressive, as usual: see 516 E note
καλλιπόλει
. Socrates rallies Glauco on his ‘braif toun.’ The word, as J. and C. point out, is full of tenderness and affection. Callipolis was the name of several cities in Greece (PapeBenseler
Gr. Eigennam. s.v.), a fact which sufficiently refutes Herwerden's doubts as to the formation of the word: see also (with Schneider) Lobeck's
Phrynichus pp. 600—607. Herwerden ought not to have revived the tasteless and prosaic conjectures
καλῇ πόλει (
Π^{2}) and
καλλίστῃ πόλει (
Ξ).
αὐτοῦ
: viz.
τοῦ μαθήματος.
καὶ δὴ καὶ κτλ.
See on 526 B.
ἡμμένος τε
. Herwerden excises
τε, comparing 526 D; but the MSS are a safer guide.
ἐμοὶ γοῦν
. Schneider and others write
ἔμοιγ’ οὖν (see cr. n.), but
οὖν is too strongly illative for this passage. Cf. I 335 E note
τὸ γὰρ περὶ κτλ.
Cf. 526 C note and Xenophon there quoted, esp. § 4
ἐκέλευε δὲ καὶ ἀστρολογίας ἐμπείρους γίγνεσθαι, καὶ ταύτης μέντοι μέχρι τοῦ νυκτός τε ὥραν καὶ μηνὸς καὶ ἐνιαυτοῦ δύνασθαι γιγνώσκειν κτλ. and infra
τὰς ὥρας τῶν εἰρημένων διαγιγνώσκοντες. The ana logy of this passage suggests that in Plato
καὶ (‘both’)
μηνῶν καὶ ἐνιαυτῶν depends on
ὥρας, which is the accusative plural: cf.
Laws 812 B
εὐαισθήτους δεῖν γεγονέναι περί τε τοὺς ῥυθμοὺς κτλ. Practical astronomy will enable one to tell both the time of month and the time of year by looking at the moon and the sun. For
ὥρας μηνῶν cf. also, besides the passage of Xenophon just quoted,
Eur.
Alc. 449
f.
Σπάρτᾳ κυκλὰς ἁνίκα Καρνείου περινίσσεται ὥρα |
μηνός κτλ. Schneider and the English translators take
ὥρας as genitive and parallel with
μηνῶν κτλ., but it is difficult to see what
εὐαισθητοτέρως ἔχειν περὶ ἐνιαυτῶν can mean: for
ἐπιμέλειαν ποιεῖσθαι ἐνιαυτοῦ καὶ ὡρῶν in VI 488 D is quite different. Schleiermacher translates the passage correctly.
εὐαισθητοτέρως
. For this form of the comparative adverb see I 343 E note
ἡδὺς εἶ
: ‘you amuse me.’ See I 337 D note
μὴ δοκῇς κτλ.
The usefulness of ‘useless’ studies is a fundamental principle in Plato's theory; and (as Schneider points out)
ὅτι ἐν τούτοις κτλ. is intended to shew that liberal studies
are in the highest and truest sense useful.
τὸ δ’ ἔστιν
. I 340 D note
χαλεπόν
. Cobet's
παγχάλεπον (after Nicom.
Introd. Ar. III 7) is a wholly gratuitous change: see App. VII.
ἑκάστου
.
Every human being has an
ὄργανον ψυχῆς viz.
νοῦς: it is indeed the possession of
νοῦς which makes him at once truly human and therewithal divine (VI 501 B note). The genitive is much more expressive than
ἑκάστῳ, which Herwerden proposes: cf. 518 C note, and for the combination of genitives V 449 A note
ἐκκαθαίρεται κτλ.
: ‘is purged and rekindled.’ In passages like this Plato hurls his metaphors about with Shakespearian vehemence and profusion. Cf. II 365 C note, and see the admirable remarks on metaphor by the author of the treatise
περὶ ὕψους 32. 4
πλήθους καὶ τόλμης μεταφορῶν—τὰ εὔκαιρα καὶ σφοδρὰ πάθη καὶ τὸ γενναῖον ὕψος εἶναί φημι ἴδιά τινα ἀλεξιφάρμακα, ὅτι τῷ ῥοθίῳ τῆς φορᾶς ταυτὶ πέφυκεν ἅπαντα τἄλλα παρασύρειν καὶ προωθεῖν, μᾶλλον δὲ καὶ ὡς ἀναγκαῖα πάντως εἰσπράττεσθαι τὰ παράβολα, καὶ οὐκ ἐᾷ τὸν ἀκροατὴν σχολάζειν περὶ τὸν τοῦ πλήθους ἔλεγχον διὰ τὸ συνενθουσιᾶν τῷ λέγοντι. The eye of soul is purged of its blindness: its smouldering fires flame forth afresh. To translate “‘is polished’ like a soiled mirror” (J. and C.), besides being wrong, falls far below the level of Plato's
ὕψος. The chiasmus in
ἐκκαθαίρεται—τυφλούμενον adds to the literary effect. On other readings in this passage see App. VII.
οἷς μὲν οὖν κτλ.
The logical sequence is somewhat difficult. Do not (says Socrates) be so anxious to persuade
οἱ πολλοί of the usefulness of our curriculum. Its
true utility is difficult to understand, and
οἱ πολλοί will not easily be persuaded of it. Those who agree with us about its
true utility will highly approve of your proposals; but
οἱ πολλοί will not, for they can see no
practical advantage (worthy of mention) accruing from them.
δόξεις λέγειν attributes the proposals to Glauco as in D
μὴ δοκῇς—προστάττειν, and
ἄλλην is said with reference to
τούτου. To the
ὠφελία of intellectual salvation such persons are blind; and they cannot see any other, i.e. any
practical
ὠφελία worth mentioning in Plato's studies.
ἄλλην cannot be understood as “beyond their practical applications” (D. and V.) unless we refer it to Glauco's remark
τὸ γὰρ περὶ κτλ. in D, to the detriment both of grammar and of sense.
σκόπει οὖν κτλ.
‘Very well: make up your mind once for all with which of these parties you are discoursing: or are you not addressing your remarks to either, but’ etc.? Glauco's insistence on the practical uses of astronomy may be all very well with a popular audience, but are out of place in a philosophical discussion. For this peremptory
αὐτόθεν cf. Symp. 213 A.
οὐ πρὸς οὐδετέρους lit. ‘not to neither’: cf. the familiar
μᾶλλον ἢ οὐ for
μᾶλλον ἤ (Kühner Gr. Gr. II pp. 771—773). I understand
ἢ—ὄνασθαι (with Ast) as an independent question: for it is difficult to supply ‘whether.’ Schneider's objections to this view are based on the idea that
ἢ οὐ (if interrogative) must have an affirmative answer; but
οὐ has nothing to do with
ἤ, and only balances
ἀλλά: cf. Ar. Plut. 372
μῶν οὐ κέκλοφας, ἀλλ’ ἥρπακας; Plato makes this clear by placing the two contrasting clauses in close juxtaposition.
οὐ is omitted by
Ξ and some inferior MSS. The text is, however, sound, and none of the proposed corrections—
σὺ for
οὐ (Schneider),
εἰ πρὸς οὐδετέρους (Madvig),
οὐδὲ πρὸς ἑτέρους (Cobet),
εἰ οὐδὲ πρὸς ἑτέρους (Baiter),
ἦ που πρὸς οὐδετέρους (Liebhold)—will bear examination, though Cobet's deserves the praise of elegance.
