James Adam, The Republic of Plato

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πίστιν κτλ. If we strictly limit DC to ὁρατά, πίστις must be understood as the state of mind which believes only in visible, palpable (ἐναργῆ) things (τὰ περὶ ἡμᾶς ζῷα καὶ πᾶν τὸ φυτευτὸν καὶ τὸ σκευαστὸν ὅλον γένος 510 A): ‘seeing,’ as we still say, ‘is believing.’ But Plato has already spoken of AC as δοξαστόν (510 A note); so that πίστις should not be confined to the objects of sight. It is in fact a subdivision of δόξα, superior in point of ‘clearness’ (σαφήνεια) to εἰκασία. We may regard it as the normal condition of the average uneducated mind. εἰκασία is the state of mind in which εἰκόνες are held to be true. Here again, if εἰκόνες are strictly limited to images of ὁρατά (cf. 509 E, 510 A), εἰκασία must be similarly confined in its scope, and loses all metaphysical interest and importance: see VII 517 A note But since the εἰκόνες are a lower grade of δοξαστά (510 A note), εἰκασία should be understood as a lower variety of δόξα (as in VII 534 A), viz. the state of mind which accepts as true that which is a copy of a copy (τρίτον πρὸς ἀλήθειαν). In this sense εἰκασία (with a play on εἰκόνες) is a new coinage of Plato's. The translation ‘conjecture’ is misleading, for conjecture implies conscious doubt or hesitation, and doubt is foreign to εἰκασία in Plato's sense. Plato may however have intended to suggest that such a state of mind is in reality no better than conjecture. See also X 598 A note and Bosanquet Companion pp. 261 f. with Nettleship Lect. and Rem. II pp. 242—246.

ὥσπερ ἐφ᾽ οἷς κτλ.: “attributing to them such a degree of clearness as their objects have of truth” J. and C. Liebhold's ἐφ᾽ ὅσον for ἐφ᾽ οἷς is an unhappy suggestion: cf. VII 534 A. A corrector in q changed the first μετέχειν to μετέχει, which, in deference to Schneider's arguments, I formerly printed. But the text is quite sound. Stated categorically, the clause would run ὥσπερ ἐφ᾽ οἷς ἔστιν ἀληθείας μετέχει, οὕτω ταῦτα σαφηνείας μετέχει. Under the government of ἡγησάμενος, the first as well as the second μετέχει becomes μετέχειν; for the accusative with infinitive may be employed even in the subordinate clauses of Indirect. See on 492 C. The jingle μετέχειν— μετέχειν is inoffensive: cf. X 614 A, 621 B.