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1 Cf. Laws 653 B-C, where Plato defines education by this principle. Aristotle virtually accepts it (Ethics ii. 3. 2). The Stoics somewhat pedantically laid it down that reason entered into the youth at the age of fourteen.
2 Plato often employs letters or elements (στοιχεῖα) to illustrate the acquisition of knowledge (Theaetetus 206 A), the relation of elements to compounds, the principles of classification (Philebus 18 C, Cratylus 393 D), and the theory of ideas (Politicus 278 A. Cf. Isocrates xiii. 13, Xenophon Memorabilia iv. 4. 7, Blass, Attische Beredsamkeit, ii. pp. 23 f., 348 f., Cicero De or. ii. 130).
3 It is of course possible to contrast images with the things themselves, and to speak of forms or species without explicit allusion to the metaphysical doctrine of ideas. But on the other hand there is not the slightest reason to assume that the doctrine and its terminology were not familiar to Plato at the time when this part of the Republic was written. Cf. Unity of Plato's Thought, pp. 31 ff., 35. Statistics of the use of εἶδος and ἰδέα(Peiper's Ontologica Platonica, Taylor, Varia Socratica, Wilamowitz, Platon, ii. pp. 249-253), whatever their philological interest, contribute nothing to the interpretation of Plato's thought. Cf. my De Platonis Idearum Doctrina, pp. 1, 30, and Class Phil. vol. vi. pp. 363-364. There is for common sense no contradiction or problem in the fact that Plato here says that we cannot be true “musicians” till we recognize both the forms and all copies of, or approximations to, them in art or nature, while in Book X (601) he argues that the poet and artist copy not the idea but its copy in the material world.
4 Plato, like all intellectuals, habitually assumes that knowledge of principles helps practice. Cf. Phaedrus 259 E, 262 B, and 484 D, 520 C, 540 A.
5 Liberality and high-mindedness, or rather, perhaps, magnificence, are among the virtues defined in Aristotle's list (Eth. Nic. 1107 b 17), but are not among the four cardinal virtues which the Republic will use in Book IV. in the comparison of the indivdual with the state.
7 Music and beauty lead to the philosophy of love, more fully set forth in the Phaedrus and Symposium, and here dismissed in a page. Plato's practical conclusion here may be summed up in the Virgilian line (Aeneid v. 344): “Gratior et pulchro veniens in corpore virtus.”
8 Extravagant pleasure is akin to madness. Cf. Philebus 47 A-C, Phaedo 83 C-D.
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