James Adam, The Republic of Plato

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528E - 530C Astronomy will accordingly be fourth in order, and Stereometry third. Yes, says Glauco; for assuredly Astronomy compels the soul to look ‘on high.’ On the contrary, Socrates replies, as studied at present, Astronomy turns the soul's eye down, though the bodily eye looks upward. True astronomy is not observation of the visible heavens, which are, like all things seen, imperfect and subject to change; it is a mathematical science, which studies the true movements of intelligible stars and uses the visible firmament as its orrery. We shall therefore pursue Astronomy by making use of problems and leave the heavens alone.

ff. We have seen that the study of Stereometry, the science which deals with τρίτη αὔξη, naturally follows the study of Geometry, in which δευτέρα αὔξη is investigated (526 C note). Astronomy, like Stereometry, is still concerned with bodies of three dimensions, but in Astronomy we have one additional element, viz. Motion, so that the study of Astronomy, as Plato conceives it, is a degree more complicated than Stereometry, and forms its natural sequel: cf. 528 A, B. Plato's conception of ἀριθμητική and γεωμετρική would have commended itself in the main to the mathematicians of his day (cf. 525 D ff., 527 A), although they might not have accepted his view of the ontology of these sciences; but in the two remaining subjects of his curriculum, Astronomy and Harmonics, he consciously and deliberately parts company with his contemporaries (see 529 A—530 C, 530 E—531 C). After every allowance has been made for the perfervid enthusiasm of Plato's style, it must be confessed that the application of the principles laid down in this chapter would have checked the progress of astronomical science. Both Astronomy and Harmonics are treated by Plato as branches of pure rather than applied mathematics; and in each of these sciences Plato either discredits or altogether prohibits observation. It must be remembered, on the other hand, that Plato's object is not to promote the study of physical science for its own sake, but to provide a suitable προπαιδεία for those who are to crown their lives by the contemplation of the Idea, from which every element of sense-perception is far removed. The astronomy which Plato sketches in this chapter is a unique compound of poetry, metaphysics and mathematics. Besides the powerful appeal which it makes to the poetical imagination, it has a permanent value even in the history of Astronomy as a passionate protest against mere empiricism, and an emphatic if exaggerated vindication of the theoretical side of the science. See also on 529 C, D and App. II.

528E - 529A 31 ᾗ σὺ μετέρχει: lit. ‘in respect of that, in respect of which you pursue it,’ i.e. ‘in the way in which you pursue it,’ no longer for its practical uses, as I did before (527 D), but because it leads the soul ‘on high,’ and from things here yonder (“from the things of this world to the next,” say D. and V., quite wrongly). The object of ἐπαινῶ is not ᾗ σὺ μετέρχει, but astronomy. Glauco has assimilated the phraseology of Socrates without its meaning. ‘On high’ and ‘yonder’ mean to Glauco the material heavens, not the νοητὸς τόπος: and he thinks the soul looks upwards if the bodily eye is turned aloft! The essence of Glauco's error consists in materializing the spiritual; and Plato here warns us against a danger which is responsible for countless errors, not only in Platonic criticism, but in every department of human thought and dogma. See also on 529 B, C.