^{page 190 note 1} My papers appeared in the Classical Quarterly, 1921, pp. 131–52, and 1922, pp. 15–28. Mr. Murphy's was published in the same magazine, April, 1932, pp. 93–102, and escaped my notice at the time. The three papers will be referred to as A, B, and M. I should like to acknowledge again the debt I owe to ProfessorStocks's, J. L. paper on ‘The Divided Line’ in C.Q., 1911Google Scholar. I must also refer especially to ProfessorStenzel's, account of λóγοσ (Zur Theorie des Logos bei Aristoteles, Quellen und Studien zur Geschichte der Mathematik, Abt. B., Bd. I, pp. 34–66)Google Scholar.

^{page 190 note 2} Topica, I. cc. 17–18, p. 108a7, b7.

^{page 190 note 3} The term is Platonic; see Phaedrus, 265d, ε⋯ς μ⋯αν τε ⋯δ⋯αν συνορ⋯ντα ἄγειν τ⋯ πολλαχῇ διεσπαρμ⋯να ἵνα ἕκαστον ⋯ριζóμενοσ κ.τ.λ.; compare συνοπτικóς

^{page 190 note 4} Alexander, , Topica, 59Google Scholar. 2 Wallies.

^{page 190 note 5} Top. 108a10; cf. Eth. 1096b28.

^{page 191 note 1} Op. cit., 124. 15. In an analogy the relation of an illustration to the illustrandum is just that they are ἕν κατ' ⋯ναλογ⋯αν (Met. 1016D34).

^{page 191 note 2} Top. 108a8.

^{page 191 note 3} 250e.

^{page 191 note 4} Rep. 420c; cf. 532C5-dI. In speaking of a similar analogia, that of virtue in the soul and health in the body, Alexander gives the basis of comparison thus: τελειóτητες γ⋯ρ γ⋯ν ὑποκειμ⋯νων αὐταῖς (Top. 118. 14).

^{page 191 note 5} I shall use analogia in the strict sense of a proportion, as Plato used it. In an analogia the important matter is the similar relation between pairs of terms, which are ⋯μο⋯ως ἔχοντα πρòς ἄλληλα (Top. 153b36). It should not be necessary to say this; but the Line is habitually interpreted as if a logos existed between any two terms that are adjacent, and even between a generic term and a term belonging to a subordinate species of the other genus—e.g. π⋯στις and διάνοια, δóζα and διάνοια. The logical rule is:ὅσα μ⋯ν γ⋯ρ διαϕ⋯ρει τ⋯ν γεν⋯ν καΘ' ὐπεροχ⋯ν κα⋯ τῸ μ⋯λλον κα⋯ τῸ ἧττον, τα⋯τα ὑπ⋯ζενκται ⋯ν⋯ γ⋯νει ⋯σα δ' ἔχει ⋯ν⋯λογον, χωρ⋯ς(depart, anim. 644a16).

^{page 191 note 6} Π⋯ντων αὔτη ⋯ ρ Θ ⋯ ν τε κα⋯ κ α λ ⋯ ν α⋯τ⋯α. The simile deals throughout with ⋯ρετα⋯, as we shall see. Compare 601d4: οὐκο⋯ν ⋯ρετ⋯ κα⋯ κ⋯λλος κα⋯ ⋯ρΘΌτης ⋯κ⋯στον… οὡ πρòς ἄλλο τι ἢ τἠν χρε⋯αν (cf. 507d12) ⋯στ⋯ν πρΌσ ἣν ἂν ἔκαστον ἢ πεποιημ⋯νον ἢπεϕυκóσ; cf. 444d13. κ⋯λλος is properly used of the symmetry of a whole (420d4, Tim, 87d, and Ar. Met. 1078a36).

^{page 191 note 7} Oὐ γ⋯ρ ᾗ αῚτιατòν ⋯ ἥλιος, εἴληπται κατ⋯ τ⋯ν ⋯ναλογ⋯αν, ⋯λλ' ᾗ αἴτιον μóνον (Proclus, in remp. I. 274.29 Kroll).

^{page 191 note 8} Proclus Saw this: ἵνα δ⋯ μ⋯ παραδρ⋯μωμεν τ⋯ν δι⋯ τ⋯ς ⋯ναλογ⋯ας διδασκαλ⋯αν, σκòπει π⋯ς ϕησιν τ⋯ μ⋯ν ⋯γαθ⋯ τòν ἵλιον ⋯ναλογεῖν. κατ' ἄλλο μ⋯ν οὐδ⋯ν (λ⋯γω δ⋯ οὐ καθ⋯σον σ⋯μα ἕχει κα⋯ τΌπον σωματικóν, οὐ καθòσον κινητòν), καθ' ἓν δ⋯ μóνον τóνον τò αἴτιον εἶναι ϕωτóς, δι' οὗ τὐ ⋯ρώμενα π⋯ντα ⋯ρατ⋯. (ibid. I. 276. 23). The other view is a κ⋯βδηλος λóγος.

^{page 192 note 1} For the moment I assume that χρ⋯μα, τò ⋯ρατóν, τò ⋯ρώμενον are identical. This is Proclus' list: χρòας ϕ⋯ς ⋯ϕθαλμοὑς ἵλιον (op. cit., I. 278. 3).

^{page 192 note 2} The corresponding verbal forms are qualified: ⋯ρ⋯ν ὅτι κ⋯λλιστα (508a5), σαϕ⋯σ ⋯ρ⋯ν (di). Compare ⋯πíρρυτον (b7) and ⋯λιοειδ⋯ (509a1), and τοȗ σαϕεστ⋯του ⋯ν σώματι πρῸσ τ⋯ν τοȗ ϕανοτ⋯του (θ⋯αν) κ.τ.λ. It may be worth noting that Alcibiades I. also compares the virtue of the eye (⋯ψισ) with the virtue of the soul—σοϕíα (133b-c). Aristotle takes up from the Republic the same illustration: τῇ γ⋯ρ τοȗ ⋯ϕθαλμοȗ ⋯ρετῇ ε⋯ ⋯ρ⋯μεν (Eth. 1106a18).

^{page 192 note 3} 50707, d8.

^{page 192 note 4} Met. 1050a34 gives the basis of our comparison: ὅσων δ⋯ μ⋯ ἄλλο τι ἔργον παρ⋯ τ⋯ν ⋯ν⋯ργειαν, ⋯ν αὐτοîσ ὑπ⋯ρχει ⋯ ⋯ν⋯ργεια (οἷον ⋯ ὅρασις ⋯ν τ⋯ ⋯ρ⋯ντι κα⋯ ⋯ θεωρ⋯α ⋯ν τ⋯ θεωροȗντι…). Here ὅρασις is the ‘power of ⋯ψις,’ and θεωρ⋯α is the regular word for the actuality of knowledge (de anima 412a22), answering to Plato's ⋯πιστ⋯μη or νóησις.

^{page 192 note 5} 508a5, 509b2; cf. 517b3.

^{page 192 note 6} De anima 426a13. As the cutting of an axe and ὅρασις, so the waking state is an entelechy; and as ⋯ψις aud the capacity of a tool, so is the soul (ibid. 412b27), τò ϕ⋯ς πυιεῖ τ⋯ δυν⋯μει ⋯ντα χρώματα ⋯νεργε⋯ᾳ χρώματα (430a16). MrBury, R. G. noted the Academic origin of the distinction between potency and actuality in the Classical Review (1894, p. 298)Google Scholar, although he appears to take δ⋯ναμις here as ‘function’ of either good or bad quality. But the sun actually gives the ‘power’ of being seen (509b2), and the Good actually gives the ‘power’ to the knower (508e2); these are perfections.

^{page 192 note 7} Rep. 601d2, quoted above, p. 191, n. 6.

^{page 193 note 1} Iamblichus, , Protrepticus, 43.20–44.15 (Pistelli). SeeGoogle ScholarJaeger, , Aristoteles, p. 69Google Scholar . The passage is worked over in Met. 980a21, as Jaeger shows. (Perhaps a reminiscence of the myth of the Phaedrus, 250d.) We should compare the terminology of Protr. 34. 17: τοῖ δ' αὖ νοῖ αǶ νο⋯σεις ⋯ν⋯ργειαι, ⋯ρ⋯σεις οὖσαι νοητ⋯ν, ὡς τοῖ ⋯ρατικοȗ ⋯ν⋯ργεια ⋯ ρ ⋯ ν τ ⋯ ⋯ ρ α τ ⋯.

^{page 193 note 2} 507d11–12; so in 518C5 Plato uses the phrase ⋯ ⋯νοῖσα δ⋯ναμις to point the moral of the Cave.

^{page 193 note 3} Nοῖν ἔχειν (or ἴσχειν) is used in 508d6, 511d1, 534b6, always in contrast with knowledge (in the full sense) not in use. The phrase should not be translated ‘to acquire mind’; this suggests the theory exploded in 518b.

^{page 193 note 4} 511d4; cf. 533e4. “Eζιςis the regular word for an art; dialectic is invariably called a δὑναμις

^{page 193 note 5} 532a2.

^{page 193 note 6} De anima, 418a26; the ο⋯κεῖον χ7rho;⋯μα is in question.

^{page 193 note 7} T⋯ τ⋯ ακóτψ κεκραμ⋯νον(508d70); compare 516e4. 7d7, 8c8, 20c3.

^{page 193 note 8} Met. 1022b34: ὂΌρατον δ⋯ κα⋯ τῷ ὃλως μ⋯ ἔχειν χρ⋯μα κα⋯ τῷ ϕαὑλως.

^{page 193 note 9} ⋯π⋯ δ⋯ τ⋯ς ⋯ψεως ⋯ξα⋯ρετοσ ⋯ τοῖ ϕωτῸς χρε⋯α ὂμϕω τελειοῖντος κα⋯ τῸ ⋯ρ⋯ν εῚς τ⋯ ⋯ρ⋯ν κα⋯ τῸ ⋯ρατῸν εῚσ τῸ ⋯ραθ⋯ναι (Procian, , Metaphrasis, 6. 17 BywaterGoogle Scholar). Similarly Proclus calls the perfections caused by the Good τελειΌτητες (in remp., I. 276. 6).

^{page 193 note 10} Proclus Writes: τ⋯ δ⋯ ⋯ρὠμενα τοῖς νοουμ⋯νοις (⋯ναλογεῖν), οὐχ⋯ ὡς ⋯ν τΌπψ ⋯ντα καὐ κινο⋯μενα, ⋯λλ' ὠς ⋯ρώμεα μΌνον (op. cit., I. 277. 4).

^{page 193 note 11} Alexander takes the comparison of sight with other senses as an example of the τΌποσ about seeming similars and real similars: it is different because the object must be under illumination (Topica, 202–203).

^{page 193 note 12} This is conclusive for the sense of δ⋯ναμις.

^{page 194 note 1} I shall use the word ‘field’ for ρΌπος it is not misleading, like ‘world.’.

^{page 194 note 2} Nυκτεριν⋯ ϕ⋯γγη (508c6) should not be taken as luminaries of the night. Aeneas Tacticus, Plato's contemporary, lays down that inhabitants of a threatened city must undress in the dark, and put out all lamps and other υκτεριν⋯ ϕ⋯γγη (X. 25), lest they should signal; this is the most general term for an artificial light. My paper (A. 135) followed the traditional rendering, and softened Plato's fundamental contrast. This sense is carried through by the figure of the fire in the cave—what is the fire but a nocturnal light?—and we avoid the difficulty that the light of the moon and the stars, as well as the sun, is used in the allegory to illustrate the system of the illegible (516a).

^{page 194 note 3} 'Aμβλνώττειν, ⋯γγ⋯ς ϕαíνεσθαι τυϕλ⋯ν) (σαϕ⋯σ⋯ρ⋯ν

^{page 194 note 4} Note the sentence endings: ὥσπερ οὐκ ⋯νο⋯σης καθαρ⋯σ ⋯ψεωσ (508c7), ⋯νο⋯σα' ϕα⋯νεται (d2), νοῖν ἔχειν ϕαíνεται 9d60, νο⋯ν οὐν ἔχοντι (d9), We may recall the common sophistical play on the double meaning of ⋯ψιν ἔχειν. Aristotle defines the distinction between potency and actuality by analogy, because there is no other way; see quotation at the head of this paper. A still better example is the definition of ⋯ ὑποκειμ⋯νη ϕὐσις in Phys. 191a7: it is to οὐσíα as bronze to a statue.

^{page 194 note 5} 506a1, C7, 11.

^{page 194 note 6} 518b6-d1, ⋯νο⋯ς ⋯πιστ⋯μης, τ⋯ν ⋯νο⋯σαν ⋯κ⋯στον δ⋯ναμιν: the language echoes our passage.

^{page 195 note 1} T⋯ν δ⋯ναμιν ⋯ποδιδΌναι (or παρ⋯χειυ 509b3) is Platonic for ‘actualize’.

^{page 195 note 2} The test throughout is value—τιμ⋯; cf.507c7, 508a1, 509a5. So κ⋯λλοσ, πρ⋯σβεια, δ⋯ναμισ(509b9). The mark of τῸ καλΌν is its completeness and definiteness; see p.191, n.6.

^{page 195 note 3} Our text, as it stands, does not make it clear that the μ⋯γιστον μ⋯θημα is known by the mind as the sun is seen by the eye (508b10), and we should expect this; compare 516b7, 517b8, 532a5. It may be taken that this meaning is conveyed by 508e4—ὡς γιγνωσκομ⋯νης διανοοῖ (δι⋯ νοο⋯ D).

^{page 195 note 4} Rep. 596a6, Parmen. 133c8-d5.

^{page 195 note 5} This is imitated by Pseudo-Archytas (Iamblichus, , Protr. pp. 16–17Google Scholar).

^{page 196 note 1} Bασιλε⋯ειν(509d2) belongs to the language of illustration; cf. κ⋯ριος (508a5, 517C3) and επιτροπε⋯ων (516b10).

^{page 196 note 2} The alternative is to refer the comparison of the two ‘kinds,’ visible and invisible, to the contrast between the forms and the many beautifuls and goods, as Mr. Murphy (for example) does. It seems dogmatic to plump for the many beautifuls on the strength of one word—that they are ‘seen’—and to ignore the recurrence of the whole group of terms posited for analogical purposes. I merely ask that the three passages (507b, 508b12, 509c5-d4) should be compared without prepossessions, and that readers should consider how the many beautifuls, in all their variety, can possibly be included within the two subordinate species of the visible kind in the Line—with due regard both for Plato's language and the rules of logic. If I Mr. Murphy aright, he places the many beautifuls in the genus ⋯ρατóν, but not in its species.

^{page 196 note 3} Ar. Top. 108b23m Rhet. 1412a11.

^{page 196 note 4} Oψις is called the ο⋯κε⋯α ⋯ρετ⋯ of the eyes in 353c1; our figure depends on the conception of function and virtue there worked out.

^{page 196 note 5} Mr. Murphy sets aside ray view in thesewords: ‘It seems quite impossible to hold that the visible world in this simile (of the Sun) is only used as a symbol of the intelligible’ (M. 94). It does seem impossible, and therefore Mr. Murphy might have looked again (A. 135). My interpretation of the whole range of these figures depended upon the contention that the visible-in-the-sun stands constantly for the intelligible, and the obscure (which is ‘visible’ in Mr. Murphy's language) for the opinable(which is also ‘visible’ in Mr. Murphy's language); this is the distinction I use above, and my argument is meaningless apart from it. It is unfortunate that his readers should have been led to believe, at the outset, that my theory rested upon an absurdity.

^{page 197 note 1} On the importance of λòγος and πρòς ⋯λληλα in the Platonic mathematics, see Toeplitz, , Quellen und Studien z. Gesch. d. Mathematik, Abt. B, bd. 1, pp. 12sqqGoogle Scholar.

^{page 197 note 2} Scholiast, in Eucl. vol. V, p. 280 HeibergGoogle Scholar.

^{page 197 note 3} Ethics, 1131b1. Aristotle uses a line even to illustrate arithmetical ‘proportion’ in a phrase closely resembling the language of our passage (509d6)—κα⋯ ὥσπερ γραμμ⋯ς ε⋯ς ἄνισα τετμημ⋯νης (Ethics, 1132a25). It is applied to a judge restoring equality.

^{page 197 note 4} Philebus, 24a-b; Ar. Categ. 10b26. See p. 191, n. 5.

^{page 197 note 5} If the procedure he had in mind was geometrical, the general theory of proportion is presupposed, and the conception of similar figures is used in the construction; see Euclid, VI. 10. As Plato used this method in the solution of the Delian problem, there is no reason to exclude the possibility here.

^{page 197 note 6} The differentiation was made in 507c. Compare 478C10 with 510a8. If it is said that the purpose of the Line is to show the relation of opinion to knowledge, the datumfrom which the argument starts is confused with the conclusion in 511e.

^{page 197 note 7} Mr. Murphy raises a question about δ⋯χα τ⋯μνειν (509d6), which should mean ‘bisect’ if interpreted geometrically (M. 99, n. 1). Does it not rather recall the ordinary terminology ofdivision, as the phrase δια⋯ρεσις διχ⋯ suggests? See the Sophist and Politicus passim.

^{page 198 note 1} On the quadripartite theory the classification is in four groups. On Mr. Murphy's theory it is tripartite; this involves giving the ⋯ρατ⋯ν γ⋯νος a content fuller than its constituent species possess.

^{page 198 note 2} Ar. Top. 108b23.

^{page 198 note 3} τ⋯ν δ⋯ ⋯μοιότητα σκεπτ⋯ον ⋯π⋯ τε τ⋯ν ⋯ν ⋯τ⋯ροις γ⋯νεσιν ὡς ἔτερον πρ⋯ς ἕτερ⋯ν τι, οὔτως ἄλλο πρ⋯ς ἄλλο (Top. 108a7).

^{page 198 note 4} See Ar. Top. 157a7, and Philebus 57C10–59C2, quoted at the beginning and the end of this section. This definitory diairesis of the two kinds of knowledge is carried further in Book VII for the mathematical sciences; but Socrates refuses to divide dialectic because Glaucon is not ripe for it (532e). This is evidence of the real purpose of the Line—to discriminate dialectic. See § 4 below.

^{page 199 note 1} Soph. 250e.

^{page 199 note 2} Compare also the formal process of defining human image-making in Sophist, 26–6. In matter, as distinct from form, this discussion is not germane to the Line; for the genera and the fundamentum divisionis are totally different.

^{page 199 note 3} Compare Gorgias, 451C9: π⋯ς πρ⋯ς ἄλληλα τ⋯χους ἔχει (τ⋯ ἄστρα). πρὸς ἄλληλα is the regular Euclidean formula for a ratio; e.g. λ⋯γον ἔχειν πρ⋯ς ἄλληλα μεγ⋯Θη λ⋯γεται κ.τλ. (Book V, def. 4).

^{page 199 note 4} The difficulty of making ε⋯κασ⋯α obscure may be judged from Mr. Murphy. (1) The images are blurred and wavering, in water, for example (M. 101). Plato's surfaces are ‘close-grained, and bright’ (510a2); his usage for watermirrors is unvaried, as I show elsewhere. (2) It is denied that ‘ε⋯κασ⋯α is only obscure (sc. less clear) because it is an imperfect way of apprehending the original object. But this is not Plato's doctrine (cf. e.g. 508d)’ (M. 101). In 508d Plato makes the obscurity depend on the light, not on the object in itself, as Mr. Murphy suggests; in 516b4 Plato means that looking at the object in water is an imperfect (not an obscure) way of seeing the object—and this is his usage. (3) The light is neutral or un qualified (M. 99, 100). This can be said only if the context is completely ignored, and the analogy between ε⋯κασ⋯α and δι⋯νοια forgotten. All this violence to the text is required in order to identify these shadows and reflections with clear, the flickering shadows of the cave in a light itself shadowy (532C2).

^{page 200 note 1} Philebus, 57d1, 58c3, 5911.

^{page 200 note 2} See Ar. Top. 157a7, quoted at the head of this section.

^{page 200 note 3} Timaeus, 46b, and Taylor's, Commentary, p. 286Google Scholar.

^{page 200 note 4} The shadow is the imprinted outline of the object, from which one can at least judge its shape; these shadows are σκια⋯ τ⋯ν ⋯ντων (532C).

^{page 200 note 5} In my paper (A. 144–5) examples from the common usage of πιστ⋯ς, σαϕ⋯ς, β⋯βαιος were collected.

^{page 200 note 6} The illustrative theory advanced above has been thought to deny the ‘metaphysical importance’ of images. The phrase (Adam's) was used to suggest that these images, as described by Plato, are not important enough to rank in a fourfold classification of ⋯ντα. This seems to be right; but the remedy is not to add anything that may be called an image. Their metaphysical importance is given by their use; they are ‘one by analogy’ with the objects of δι⋯νοια, in respect of clearness, as ε⋯κασ⋯α is one with σι⋯νοια (511e3).

^{page 201 note 1} The summary in 533e7 begins with the enumeration of the four states, and concludes with their analogia.

^{page 201 note 2} The phrase in 511e2 (⋯ϕ' οῖς ⋯στιν κ.τ.λ.) is explained by this passage and by the definition of the ‘same power’ in 477d2: τἔν ⋯π⋯ τῷ αὐτῷ τεταγμ⋯νην. Cf. 534a5. On δ⋯ναμις see ProfessorPaton's, paper in Proc. Aristotelian Society, 1921–1922Google Scholar.

^{page 201 note 3} Cf. 516C8, d3, 521d9. It is important to recognize that the allegory deals with a conflict of goods.

^{page 202 note 1} B. 14, 25.

^{page 202 note 2} The relation of the two figures is discussed in section V.

^{page 202 note 3} See II. 6 iii for the difference between the two types of analogia.

^{page 203 note 1} This confusion lurks beneath the parallelist theory, and Mr. Murphy makes it explicit. His theory is a compromise. He agrees with me (though he does not say so) that there are only three substantive states in the Cave—δ⋯ζα. δι⋯νια, ν⋯ησις but he remains a parellelist, because there is a ‘very exact correlation’ between the Line and the Cave (M. 94, 95).

(i) If there are but three states, where is the quadripartite division? It is found by taking four sets of objects—the duplicated images and originals. How are they related to the three states? By assuming that the brief history of a rescue, which begins and ends with the word ‘suddenly,’ is not a history; the ‘conversion to puppets’ and the ascent stand, each in turn, for the transition to mathematics. Succession is interpreted as repetition so that four may be counted as three and still remain four. This view traverses both narrative and symbolism. If the fire stands for the sun (as he assumes), it is incongruous that its light should fall upon forms; the continued ⋯πορ⋯α and unbelief described by Plato (515c6–16a3) is transformed into a duplicated revelation; the revelation should not take place in the darkness of the cave, where the philosopher himself is bewildered on his return by objects that are not forms. But the philosopher must, upon this theory, tell the prisoner that these puppets in firelight are forms, and the bewildered soul ‘fugit indignata sub umbras.’ If Plato meant anything like this, he was bound to explain in his interpretation (517b); but there is no inkling that puppets in firelight stand for forms and their shadows in the same light for sensibles, or that succession stands for repetition.(ii) The ‘very exact correlation’ with the Line depends upon the analogia—shadows: puppets:: divine images: originals—and these are equated to the terms of the Line by position. The equation breaks down because the transition to δι⋯νοια, which is all-important for the allegory, is meaningless in the analogia of the Line. Instead of a common logos (which an analogia must surely have), Mr. Murphy founds upon the vague metaphor of ‘the same stress or rhythm’ (M. 95). He finds this stress in puppet-gazing, which answers by position to π⋯στις and π⋯στις is ‘a “crowning phase” or completion of one kind of activity.’ So it is in the Line, because it is one by analogy with νóησις; but upon the theory puppet-gazing stands for δι⋯νοια, which is not a crowning phase and completes nothing. Mr. Murphy interprets the initial bedazzlement as illumination. It is supposed that the Line gives abstractly the formula of the Cave—the one thing it cannot give; for the logos laid down for the Line cannot be stated with δι⋯νοια as the second term of a ratio, and the thesis requires this. The thesis abandons the common logos, and uses the notion of equivalence ambiguously. If we allow for the moment that the cave as a whole and the lower line as a whole ‘represent’ the ‘lower world’ (the object of δ⋯ζα), it is still untrue that εἰκαδ⋯αis to π⋯τις as δ⋯ζε⋯α to δι⋯νια (M. 98). Nor can ⋯παιδευδ⋯α and παιδε⋯α be substituted for the two last terms (M. 102, n. 1). It is an assumption that ⋯παιδευδ⋯α has the same content as δ⋯ζα (see § 3 below), and παιδε⋯α does not answer to δι⋯νοα it includes the ⋯πορ⋯α, which is still δ⋯, and the whole subsequent progress to the Good. When the theory rejects the obvious symbolism determined by the previous figures, it introduces a polymorphous symbolism, which makes anything stand for anything: puppet-gazing corresponds by position to π⋯δτις shadow-gazing symbolizes δ⋯ζα and puppet-gazing symbolizes δι⋯νοια; puppet-gazing and shadow-gazing together represent δ⋯ζα and puppet-gazing is analogous to gazing at originals in sunlight. The theory multiplies hypotheses, and is still unable to find the logos of the Line in the Cave.

^{page 203 note 2} Mr. Murphy has given me nothing to answer, but much to correct. I take three instances from a single footnote (M. 94, n. 1). He extracts some ‘actual statements’ from my articles to show ‘the difficulties inherent in this type of interpretation.’ They are not actual statements, and they are misconstrued; in two cases I did not recognize what my own meaning could be. (i) A sentence from a correct description of the shadow-play is silently abbreviated and treated as if it were an interpretation; then an interpretation I could accept is used to refute it. (ii) A question at the end of a correct description of the double bewilderment of the prisoner and the philosopher in the cave is eviscerated, turned into a statement, and misunderstood. (iii) A fragment of a sentence about the objects outside the cave, itself unexceptionable, is held to imply that the release, in my view, is not effected by mathematics. I twice said the contrary (B. 23, 26), though I did not explain how, any more than Mr. Murphy does, and stressed the ethical side too much (see p. 205, n. 5).

^{page 204 note 1} The so-called ‘conversion to puppets’ is a phrase wrenched from its context (532b). The question is, What has power to rouse the soul? and the answer is, the mathematical arts—they effect the whole change, release, being turned to puppets and the light, and the ascent—all short of seeing the originals in sunlight. This is a summary of the narrative of rescue as well as an interpretation. It is therefore evident that puppet-gazing is neither a distinct stage of education prior to mathematics nor a consummation within mathematics; it is an initial stage within the activity—being troubled by a problem, not being illuminated by the forms. The prisoners continue to believe their shadows to be truer until they at last accept the divine shadows. This is the only interpretation that fits Plato's narrative. Let me add that the phrase used for turning to puppets (πρ⋯ς μ⋯λλον ⋯ντα—sc. τ⋯ν δκι⋯ν—515d3) should not be construed as if it read πρ⋯ς τ⋯ ⋯ντα. The δκια⋯ τ ⋯ ν ⋯ ν τ ω ν outside are expressly contrasted with the ε ἰ δ ῴ λ ω ν δκια⋯ in a shadowy life (532C1–3)—the puppets are and stand for εἴδωλα, not ⋯ντα.

^{page 204 note 2} The last proposition of this book—to form a square equal to a given area—is the culmination of the Pythagorean algebra.

^{page 205 note 1} In principle this is the subject of the controversy between Speusippus and Menaechmus about the nature of the problem in geometry, as reported by Proclus, In Euclidem 77. 15 Friedlein. Discussion must be left for another occasion. The relevant passages may be found in Stenzel's enlightening article on Speusippus (Pauly-Wissowa, , Real-Encyclopädie, III A 2, 1659–1660Google Scholar).

^{page 205 note 2} Junge, G., quoted in Hasse, and Scholtz, , Die Grundlagenkrisis der Griechischen Mathematih, p. 66Google Scholar.

^{page 205 note 3} This is one reason why it is meaningless speak of a common logos between the two pairs of images and their originals in the Cave. It runs counter to the description.

^{page 205 note 4} It is not the case that the Platonic ‘education’ is represented as putting a man at once in contact with an ideal world. The passage in 524d-e, cited by Mr. Murphy (M. 96), says something quite different. There are things that awaken δι⋯νοια and cause the soul to be at a loss, and to seek; but to be stimulated to ask ‘What is unity ?’ is not finding it.

It should be noted that the puppets that are contrasted with their own distorted shadows arenot merely ethical opinables, as 517d and 520c might lead one to suppose. It is the contrast between the standards of the cave and the ethical forms that bewilders the returning philosopher; so these two passages mention them alone. But the bewilderment of the prisoner might be caused by anything that upsets his ordinary assumptions, though the means used is a question about mathematics.

^{page 206 note 1} The test for the cave is what is valued and sought. The uneducated is the man who has missed something, through environment, insensitiveness, or passion. He is the pedigreed snob (Theaet. 175a1), the average sensual man (Protag. 347C7), the person of vulgar common-sense (Theaet. 17565; ef. 17435), the critic who succumbs to mob standards, having known better (Laws, 659a6), the man bereft of moral standards (Gorg. 527e1), the degenerate tyrant (ibid. 510b8). The locus dassicus for ⋯παιδευσ⋯α and environment is Timacus, 86–87b. The standards by which the uneducated is judged are those of καλοκαγαθ⋯α, ϕρ⋯νησις, ⋯ρετ⋯, and his state is closely connected with the π⋯θη. In the Cave the ultimate standard is knowledge of reality, and those who do not possess it are ⋯πα⋯δευτοι κα⋯ ⋯ληθε⋯ας ⋯πειροι, who should not be allowed to rule (519b8). They are stunted ψυχ⋯ρια (a3) that have missed the ⋯ρετ⋯ ψυχ⋯ς. Compare this contrast: τ⋯ς ψυχ⋯ς τ⋯ς εὐϕυεστ⋯τας κακ⋯ς παιδαγωγ⋯ας τυχοὑσας and ⋯ν…μαθ⋯σεως προσηκοὑσησ τὑχῃ in 491e1–92a2; the early part of Book VI is the best commentary on the cave.

It would follow from usage and from Plato's description that ⋯παιδενσ⋯α cannot simply be identified with δ⋯ζα. A lad who profits from the ‘first education’ values the right things, though he cannot give an account of them yet; the ⋯πα⋯δευτος is blind to them and has learned to value the wrong things—that is why he must be rescued. His quality is positive, as vulgarity and Philistinism are positive.

^{page 206 note 2} 514a5. The sense of ⋯κ πα⋯δων is given by such phrases as δ⋯γματα ⋯κ πα⋯δων περ⋯ δικα⋯ων κα⋯ καλ⋯ν (538C6), and ⋯ς π⋯λαι εῖχεν δ⋯ζας ⋯κ παιδ⋯ς περ⋯ καλ⋯ν τε κα⋯ α⋯σχρ⋯ν (574d5). The burden of these books is that the young must be rescued before they are indurated in wrong opinions; cf. 519a9. When it is proposed to segregate the ten-year-olds, this is not the routine of the ideal city. They are taken out of the cave because the cave society will be too much for them.

^{page 207 note 1} κα⋯ οὖπαρ ⋯μῖν κα⋯ ⋯μῖν ⋯ π⋯λις ο⋯κ⋯σεται ⋯λλ' οὐκ ⋯ναρ (c6); ἔστι σοι δυνατ⋯ γεν⋯σθαι πόλις εὗ ο⋯κουμ⋯νη(521a1). Similarly in 540d2 the city is not an empty hope if only the philosophers remain steadfast.

^{page 209 note 1} There is no ground in the context for supposing that προσαπτ⋯ον means the detailed application of the Cave to the Line in a quasi-geometrical sense. My own former rendering (‘attach’) also assumed that Plato meant to furnish a detailed key to the symbolism. He did not equate symbols already sufficiently intelligible; he likened the experience of the prisoner to the experience of philosophers in politics, and I now see that τ⋯ν ε⋯κ⋯να προσαπτ⋯ον means ‘apply the parable’ (παραβολ⋯!). The application intended is given in the following pages. This use is sanctioned by Aristotle: τα⋯τα δ⋯ προσ⋯ψε δι⋯ τ⋯ς κατ' ⋯ναλογ⋯αν μεταϕορ⋯ς (Rhet. 141234; cf. de somn. 455b21). Clauses A2 and 3 form a chiasmus recalling for immediate application the prison and the visible field contrasted in the allegory; clause B begins the long application.

^{page 209 note 2} 516c. Compare with ⋯ϕομοιο⋯ντα the phrase in 532C2: δι' ⋯τ⋯ρου τοιοὑτου ϕωτ⋯ς ὡς πρ⋯ς ἥλιον κρ⋯νειν. I suggest that Plato means, ‘compare and then interpret,’ not ‘the comparison is the interpretation.’

^{page 209 note 3} 'Eλπ⋯ς is the working hypothesis that points to the solution. See Heidel, , The Heroic Age of Science, p. 85, n. 14Google Scholar.

^{page 210 note 1} Or by stars in the allegory.

^{page 210 note 2} They do, however, relegate the ‘sciences’ excluded from the propaedeutic to the level of opinion.