ὅ τι νόησις ‐‐ εἰκασίαν
. That is to say, in the Simile of the Line (see Fig. i on p. 65), (1)
CB :
AC ::
EB :
DC and (2)
CB :
AC ::
CE :
AD. We have already seen that
CE :
EB ::
AD :
DC (VI 509 D note); therefore
componendo
τὴν δ’ ἐφ’ οἷς κτλ.
Liebhold (who also conjectured
καὶ ἔτι νόησις for
καὶ ὅ τι νόησις) makes the extraordinary suggestion
τὴν δ’ ἐφ’ οἶς ταῦτ’ ἂν διέχῃ ἀναλογίαν καὶ διαίρεσιν ἑκατέρου (
Philol. 1876 p. 372). The text is of course quite sound and=
τὴν δὲ <τούτων> ἐφ’ οἷς ταῦτά <ἐστιν> ἀναλογίαν κτλ.: cf. VI 511 E. I cannot agree with Shorey when he says (
Idea of Good etc. p. 235) that Plato “avoids drawing out the proportion
εἴδη: objects of
διάνοια=
σκευαστά etc.:
εἰκόνες, because he is aware that the second member is a blank and the fourth is largely fantastic.” Both of these assertions are in my opinion quite wrong, and if they were true, Plato would have refrained from drawing out the proportions between the faculties themselves for exactly the same reasons. See App. I. As it is, we should take Plato at his word. He may well decline to enter on the tedious and unprofitable task of expounding and illustrating in detail the proportions which may be conjectured to obtain between the different objects of our intellectual powers. It would for example lead to no useful result if we tried to establish a proportion between a particular
ε<*>δος, one of the five
μαθήματα, a particular object of
πίστις, and a particular object of
εἰκασία. Such attempts would certainly involve us in an endless amount of talk, and would hardly result in anything but a series of barren and pedantic formulae and subdivisions.
ἢ ὅσων
. See cr. n.
ὅσων is read by a large majority of MSS, and the confusion of
ο and
ω is common: see
Introd. § 5. The construction (as Schneider points out) is
ἢ ὅσων λόγων οἱ παρεληλυθότες λόγοι ἡμᾶς ἐνέπλησαν: cf. (with Schneider)
παρὰ δόξαν τοῖς νῦν δοκουμένοις VI 490 A. Madvig's
ὅσοι has little probability, although it avoids a certain awkwardness.
ἦ καὶ διαλεκτικὸν κτλ.
Cf. 531 E note As far as words go, this definition of Dialectic might almost have come from the historical Socrates, although of course
λόγον λαμβάνειν, οὐσία and
λόγον διδόναι meant less to him than to Plato.
οὐ φήσεις
=‘negabis.’
οὐ is not here ‘nonne.’ The interrogation is carried on from the last clause.
διορίσασθαι ‐‐ ἀφελών
perhaps suggests the
διαίρεσις, which was an essential part of Plato's dialectical method: see App. III. It is noteworthy however that the
Republic lays far more stress on
συναγωγή than on
διαίρεσις: cf. 537 C, Zeller^{4} II 1. p. 617 note and App. III.
ὥσπερ ἐν μάχῃ κτλ.
: ‘as it were in a battle, exhausting every elenchus, striving to test his view not by that which
seems, but by that which
is’ etc. For
διὰ πάντων—διεξιών cf. Thuc. III 45. 3
διεξεληλύθασί γε διὰ πασῶν τῶν ζημιῶν and
Parm. 136 E
διὰ πάντων διεξόδου. We apply the
ἔλεγχοι ourselves: cf.
ἐξελέγξωμεν in X 610 A. The ordinary interpretation supposes that the
ἔλεγχοι are applied by others (‘running the gauntlet of all questionings’ J. and C.); but in that case we must take
ἐλέγχειν as=
ἐλέγχειν τοὺς τῶν ἄλλων ἐλέγχους, which is difficult, because
ἐλέγχειν is most naturally interpreted by
ἐλέγχων just before, and
ἐλέγχων certainly means tests or elenchi which are applied to the theory which the dialectician is himself maintaining. Plato means that the dialectician tests his view of good not by ‘seeming’ i.e. by what ‘seems’ (good, bad etc.) to the many, but by the Truth i.e. by that which ‘is’ in the Platonic sense of
οὐσία, viz. the Ideas, such as (let us say) the Ideas of
κάλλος, δίκαιον and so forth. The Idea of Good has connexions and relations with all the other Ideas (cf. VI 510 B, 511 B notes); and our knowledge of these may therefore be used to test the accuracy of our conception of Good. Zeller^{4} II 1. p. 620 note rightly compares the present passage with
Parm. 135 C
—136 E: see App. III. It is perhaps unnecessary to notice Liebhold's foolish conjecture
νόησιν for
οὐσίαν.
ὀνειροπολοῦντα κτλ.
533 C note
οὐκ ἂν ἐάσαις κτλ.
: ‘you will not suffer to be mere irrational quantities, if they are to rule in the city and control the higher issues.’
ἄλογοι γραμμαί are irrational magnitudes (cf. Arist.
περὶ ἀτόμων γραμμῶν 968^{b} 18), which Greek mathematicians treated “geometrically through a symbolism of irrational lines,” as in Euclid Bk. X (Gow
Gk Math. p. 78). They are
ἄλογοι or
ἄρρητοι because “nicht aussprechbar” (Cantor
Gesch. d. Math. p. 154 note), whereas rational lines are
ῥηταί, ‘expressible’ (cf. Blass
de Pl. Math. p. 18). In its application to Glauco's ‘children,’
ἄλογοι is active, and means of course
μὴ λόγον ἔχοντες διδόναι (534 B). Has
γραμμάς also any special application? Probably it has: otherwise the witticism seems unnecessarily far-fetched and frigid, even if we make every allowance for Plato's love of a mathematical jest (cf.
Pol. 266 B
), as well as for the interest which the subject of irrationals seems to have excited among the mathematicians of his day (see
Theaet. 147 D
ff. and Cantor l.c. pp. 182, 191, 203). Lucilius (II 20) has the line “vix vivo homini ac monogrammo” (“a dead-alive sketch of an anatomy” Tyrrell
Lat. Poetry p. 175), and Cicero mocks at Epicurus' gods as “monogrammos” (
N. D. II 59: cf. I 123 homunculi similem deum—liniamentis dumtaxat extremis, non habitu solido— praeditum etc., and other passages in Usener
Epicurea p. 234). Perhaps Plato means to suggest that his “airy burgomasters,” as Milton calls them, would in such a case be only as it were mere silhouettes (“Schattenrisse” Bertram
Bilderspr. Pl. p. 46) of rulers moving blindly to and fro in a sort of dreamland (cf.
ὀνειροπολοῦντα 534 C and 533 C note). For other views see App. XVII.
τῶν μεγίστων
. 525 B note
ἐρωτᾶν τε καὶ ἀποκρίνεσθαι κτλ.
Plato concludes by emphasizing the most conspicuous and characteristic feature of the Socratic method: cf.
Crat. 390 C
.
