James Adam, The Republic of Plato

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ff. The simile of the Line contains perhaps more Platonic teaching than any passage of equal length in Plato's writings, and is of primary and fundamental importance for the interpretation of his philosophy. I have discussed the various difficulties as they occur, partly in the notes and partly in the Appendices to this Book. For a consecutive exposition of the whole simile in its connexion with the simile of the Cave see App. I to Book VII.

αὐτώ: the Sun and the Idea of the Good.

ἵνα μὴ οὐρανοῦ κτλ. “I do not say ‘of heaven,’ lest you should imagine that I am etymologising on the name.” The Sun might well be called βασιλεὺς οὐρανοῦ. Socrates pretends to avoid the word οὐρανός, lest by thus equating it with ὁρατόν (for the contrast with νοητοῦ would suggest that οὐρανοῦ=ὁρατοῦ) he should be accused of deriving οὐρανός from ὁρᾶν, as certain clever people did in Plato's time (Crat. 396 B. The same derivation is given by Philo Jud. de mund. opif. 10). For σοφίζεσθαι in this sense cf. σοφία in Crat. 396 C, D. E. S. Thompson (Proceedings of the Camb. Phil. Soc. 1888 p. 14) takes σοφίζεσθαι simply as ‘pun’ and thinks that the pun is between νοῦ (suggested in νοητοῦ above) and οὐρα-νοῦ, quoting ἀπ᾽ ὄνου πεσεῖν, and the anecdote in D. L. II 118, VI 3: cf. also Isocrates Apophth. Fr. 8 ed. Blass. But such a pun is both far-fetched and pointless, and in view of the passage from the Cratylus there should be no doubt that Plato more suo is merely scoffing at a well-known contemporary etymology. The reading οὐρανόν—see cr. n.—would be fatal to Thompson's theory, but οὐρανοῦ (which most MSS read) is more pointed and idiomatic, and perhaps right, though the accusative is not indefensible.

ἄνισα. It appears from the Scholiast that even ancient critics debated whether ἄνισα or ἴσα (εἰς ἴσα v) should be read. Proclus (in Plat. remp. I p. 288 Kroll) and the author of the third Quaest. Plat. in Plutarch (1001 C ff.) read ἄνισα: ἴσα appears in a grammarian cited by Stallbaum from Villoison Anecd. Gr. II p. 199. The dispute still reigns, Stallbaum and some others preferring ἴσα, others, such as Richter (Fl. Jahrb. 1867 p. 145) and Dümmler (Antisth. p. 80) ἀν᾽ ἴσα, others even ἂν ἴσα (which is certainly not Greek, though found in a few inferior MSS); but there should be no question that Plato wrote ἄνισα. If the line is bisected, all four segments are equal, and the elaborate proportions drawn in 510 A, 511 E, VII 534 A represent no corresponding relations between the different segments of the line. The inequality, as Schneider and Steinhart point out, is intended to represent the difference in σαφήνεια or ἀλήθεια between the δοξαστόν (or ὁρατόν) and the γνωστόν (or νοητόν): cf. σαφηνείᾳ καὶ ἀσαφείᾳ below and 510 A. (So also Benson in Nettleship's Lect. and Rem. II p. 239 note). For this reason the νοητόν should be represented by a longer segment. Others assign the larger part to the ὁρατόν, as being the region of τὰ πολλά (Plutarch l.c. and Espinas in his edition of Book VI), but the length of the two main segments should follow the primary and fundamental principle of Plato's classification. The relevant consideration is not at present multiplicity versus unity, but different degrees of clearness and truth. Beckman's excision of ἄνισα τμήματα (num Plato artefactorum ideas statuerit p. 38) needs no refutation. See also next note.

πάλιν τέμνε κτλ. See Figure 1 on p. 65.

AD : DC :: AC : CB, and CE : EB :: AC : CB.

It follows (1) that AD : DC :: CE : EB, (2) that DC=CE; for

Similarly

But has been proved equal to CE.

therefore DC=CE.

(This last equality—so far as it goes—is a slight though unavoidable defect in the line, for DC is not equal to CE in point of clearness. See last note). Neither of these inferences is expressly drawn by Plato himself; but he appears to make use of the first in 532 A ff.

καί σοι ἔσται κτλ.: ‘and when classified according to their relative clearness and obscurity, the different segments will represent—in the visible sphere, segment 1, Images’ etc. The datives, like ἀληθείᾳ in 510 A, are causal, and state the principle on which the entire classification (of νοητά as well as ὁρατά) rests. With ἐν μὲν τῷ ὁρωμένῳ Socrates begins to describe the contents of the particular segments. This is interrupted by the definition of εἰκόνες, and resumed, in a different form, at τὸ τοίνυν ἕτερον in 510 A. μέν before τῷ ὁρωμένῳ contrasts with σκόπει δὴ αὖ in B, much as τὸ τοίνυν ἕτερον balances the second μέν. On σαφηνείᾳ see below 511 C note