James Adam, The Republic of Plato

σοφή -- δικαία. This is apparently the earliest passage in Greek literature where the doctrine of four cardinal virtues (if by cardinal virtues we mean those which make up the sum of perfect goodness) is expressly enunciated. The doctrine may of course be Pythagorean, but evidence is wanting, and it is doubtful whether Pindar's τέσσαρες ἀρεταί Nem. III 74 are to be interpreted as the cardinal virtues: see Bury ad loc. The nearest approach to the doctrine before Plato is in Xen. Mem. III 9. 1—5 (as Krohn has pointed out Pl. St. p. 372), with which compare IV 6. 1—12, where Justice, Wisdom, and Courage are named, as well as other virtues, including εὐσέβεια. Cf. also Aesch. Sept. 610 σώφρων δίκαιος ἀγαθὸς εὐσεβὴς ἀνήρ. From other passages in Plato, none of which are so precise and technical as this, it would seem that ὁσιότης made a good fight for a fifth place: Prot. 329 C, Lach. 199 D, Men. 78 D, Gorg. 507 B. In Phaed. 69 C and Laws 631 C σωφροσύνη, δικαιοσύνη, ἀνδρεία and φρόνησις (not σοφία) are named together, without ὁσιότης, which in the Euthyphro (12 D ff.) is a subdivision of δικαιοσύνη. From Adimantus' ready assent (cf. V 476 A note), we may reasonably infer that the doctrine of four cardinal virtues was already a familiar tenet of the Platonic school. Schleiermacher thinks it may have been taken over “aus dem allgemeinen Gebrauch” (Einleitung p. 26). There is however no evidence to shew that these four virtues and no others were regarded as the essential elements of a perfect character before Plato. If the theory was originated by Plato himself, it is possible enough that in restricting the number to four, Plato was not uninfluenced by the sacred character of the number four in Pythagoreanism, just as Aristotle has been supposed to have limited his categories to ten on similar grounds. An interesting conjecture is suggested by the remarks of Schleiermacher (l.c. p. 21). Our city is ex hypothesi perfectly virtuous. Its constituent elements are Rulers, Auxiliaries, Farmers and Artisans. Now the virtues which are exhibited in the lives and mutual relationship of these classes are, as Plato holds, Wisdom, Courage, Temperance, and Justice. Consequently these virtues are the component factors of moral perfection; in other words they are the cardinal virtues. We may admit that there is no petitio principii in such a method of investigation, which is, in fact, akin to the perfectly legitimate method described in Men. 86 E: cf. also V 458 A. If this suggestion is correct, the doctrine of four cardinal virtues will be directly descended from the arrangements of Plato's ideal city. But it is clear from what Plato himself says, both here and in 429 A, 430 D, 432 B, 433 B f., that the doctrine is already an accepted part of his ethical system, and not merely a provisional hypothesis which is intended to be confirmed by what follows. For the relative value and importance of the four cardinal virtues in Plato's way of thinking see Laws 630 D ff.

οὐκοῦν -- ηὑρημένον. Essentially the same method is used by Aristotle to reach his conclusion that virtue is a ἕξις (Eth. Nic. II 4). Cf. also (with J. and C.) Lys. 216 D, E. Jowett observes that the true function of “this half-logical, halfmathematical method of residues” is in dealing with “abstract quantity” and “the laws of Nature.” It is undeniable that this method is much more likely to lead us astray in ethics than in mathematics or the natural sciences, owing to the nature of the subject; but it is valid if our analysis of the phenomena is exhaustive and exact. A similar method was frequently employed in the Eleatic school: see II 380 D note Plato not unfrequently extends the methods of mathematical reasoning beyond what we should consider their proper sphere: the whole of the preliminary studies, for example, in Book VII are to be pursued according to the methods of pure mathematics. See on VII 528 E ff. and the Appendix to Book VII “On the propaedeutic studies of the Republic.”