^{page 131 note 1} I use Professor Burnet's text. It will be convenient to use capital letters to designate the similes themselves, and small letters for the sun, the line and the cave, from which the similes are named.

^{page 133 note 1} Phaedo, 79a 1, 81a 5, 83b 4; Rep. 525d; Tim. 28b 7, 31b 4.

^{page 133 note 2} I say definition rather than terms because Plato's vocabulary is fluid. This has caused much of the difficulty in interpreting these similes.

^{page 133 note 3} Caird, , Evolution of Theology in the Greek Philosophers, I. 162Google Scholar.

^{page 133 note 4} Natorp, , Platos Ideenlehre, p. 192 sqqGoogle Scholar.

^{page 134 note 1} In this as in other points the Timaeus misleads if we seek to interpret our analogy by means of the metaphors which Plato uses there. It describes creation, and the application of the metaphor of offspring is determined accordingly; but our metaphor is simply the basis of a fertile analogy by which the relation of the forms to the Good may be grasped. The metaphor in the Timaeus explains a causal relation; this metaphor merely gives the link of likeness between type and antitype, without cosmological implications, Though I have not space to elaborate the point, the Timaeus is the source of the misinterpretametations noted above (see e.g. Caird and Natorp).

^{page 134 note 2} Cratylus, 409 a, is a useful commentary; ἤλιος is connected with αἰολεῖν ὅτι ποικ⋯λλει ἰὼν τ⋯γιγν⋯μενα ⋯κ τ⋯ς γ⋯ς. Cf. Clem. Alex., , Eel.Proph. 26, 3, andGoogle ScholarDion, , Or. III. 74Google Scholar.

^{page 135 note 1} It is surely a mistake to found upon this passage for Plato's theory of vision. Steinhart, followed by others, criticizes Plato for failing to see that hearing too needs a medium. But the word medium is imported by himself. Since man does not live now in vacuo, now in the ambientair, the physical medium of hearing may be disregarded as a constant. But sight differs from all other senses independing on a variable condition, the light. This variability is the point of the simile. When Adam (507c) saysthat the conditions peculiar to seeing—namely, light and darkness—do not affect the other senses, hemisses the meaning, which is that no other sense has similar peculiar conditions (ἰδ⋯ᾳ ⋯π' αὐτ⋯ το⋯γο πεϕκός).

^{page 135 note 2} 507C 19, προσδεῖ; dI, ⋯⋯ν μ⋯ παραγ⋯νηταιτρ⋯τον;d5, προσεῖ; d12, προσδεῖται.

^{page 135 note 3} 474d-475e. This must be interpreted in the light of the analysis of the soul in Book IV., where the three ways of life in the Pythagorean apologue of the Olympian games are the basis of the three tendencies of the soul which find their outlet in the ideal state. See Stocks, , Mind, 04, 1915Google Scholar.

^{page 135 note 4} Chalcidus, , Commentarius in Timaeum, CCXLVGoogle Scholar. After describing the three flames necessary to vision, he adds: ‘quorum si quid deerit, impediri uisum necesse est.’ Adam gives a list of eight terms in the parallelism between the Good and the sun (Rep., vol. II. p. 69): these translations of nuances in the text, however, merely obscure the fact that there is but a triple ratio, in which Sight: Colour need the third term in order to become operative.

^{page 136 note 1} I venture to give this name to the whole simile, which forms a connected and consistent picture, although a better name would be the simile of the Sun, if that name were not already adopted by usage for the first of its three parts.

^{page 137 note 1} I do not for the present attempt to define the objects in u.

^{page 137 note 2} See below (B) for Plato's purpose in using the singular of this word.

^{page 138 note 1} Adam's whole exposition is vitiated by the failure to distinguish between the class to which the originals and images belong, and the collection of visibles and opinables which would, in a complete classification, be included in the class (see e.g. Vol. II., p. 157).

^{page 138 note 2} See Mr. Stocks's criticism of such attempts.

^{page 138 note 3} One does not say that I: 2 is 3. The same consideration removes the difficulty felt about the equality of the two middle sections. In the equation ½=¼ it does not occur to one to say that the denominator of the first is equal to the numerator of the second fraction, because each is determined by the other term in the ratio, The ratios as a whole are equal. In the Line the equality is one of clearness; other considerations are irrelevant.

^{page 139 note 1} 517b; Lindsay's translation.

^{page 139 note 2} See postscript.

^{page 140 note 1} The ‘visible region’ in this passage is the symbolical ⋯ρατ⋯ς τ⋯πος of the Sun (508c 2), of the Line (509d 2)–yes, and of this simile too. On the page before this passage the philosopher is said to gaze at last directly at the sun, the lord of all things in the visible realm (516c 1), and it is mentioned again in this very paragraph (517c 2), where the link between the Good and its symbol is recalled from 506e 2–the link of goodness. Further, in the final summary (532c-d) the progress of the soul is likened to the rise of the clearest in the body to the sight of the highest in the bodily and visible region. This is an obvious echo of our passage; yet Adam can say (517c) that ‘Plato's guardians are not to rest satisfied with the εἰκών or ἕκγονος of the Good.’ This confuses an image meant for the enlightenment of Plato's readers with the intellectual training given to the guardians. It is, I submit, impossible to take this summary as a warning against the dangers of astronomy. Once for all: if we may adopt Mr. Doughty's name for the fair region where the poets of his country dwell apart(Clouds, p. 9), the ἔρατ⋯ς τ⋯πος is the Sunfield, where philosophers learn to look upon truth.

^{page 140 note 2} Cf. 509d, where the same type of definition is used in comparing symbol andantitype.

^{page 141 note 1} This denial is really a justifiable refusal to admit that the images, as such, have metaphysical import, or to add to them in order to make them a grade of reality.

^{page 141 note 2} On the Idea of the Good in Plato's Republic, Chicago Studies, I.

^{page 142 note 1} See the notes on 514b, 515b, Vol. II. p. 163, 517c, and 516a.

^{page 142 note 2} J. Phil. X. pp. 139–141.

^{page 142 note 3} Plato mentions this contrast again and again. See 516a, e9, 517 b, d6; 518a 2, a6, b3, c7, 520c 2, 521c 2, c6, 532c. This list may show the vital importance of the distinction between the darkness of the whole cave and the light outside.

^{page 142 note 4} The meaning of σκεναστ⋯ in 515c is limited by 515a 1. Note Plato's contemptuous παντοδαπ⋯ … παντοῖα in 514b–53.

^{page 143 note 1} αὐτ⋯ is the lower line. But theories which suppose that the dependence of Becoming upon Being is in question appear to reverse the proportion, thus: ‘as images are to originals, so is δοξαστ⋯ν to γνωστ⋯ν.’ But the latter is the ruling ratio, because it has already been fixed in Book V.

^{page 143 note 2} 478c 11, and 14, σαϕηνε⋯ᾳ)(⋯σαϕε⋯ᾳ; 479c 8, σκοτωδ⋯στερα)(ϕαν⋯τερα.

^{page 143 note 3} 478a 10, b2, b3, 479d 7.

^{page 144 note 1} See Wilamowitz-Moellendorff, Herakles, v. 55. τ⋯ σαϕ⋯ς is τ⋯ β⋯βαιον or τ⋯ πιατ⋯ν (see below on πἰστις); but in the hands of the Neo-Platonists this becomes: χει οὖν τ⋯ ⋯β⋯βαιον ⋯ τοια⋯τη π⋯στις an exact inversion of Plato's sense (Iamblichus, , De Comm. Math. Sc. VIII.)Google Scholar.

^{page 144 note 2} In 509d 9 σαϕηνε⋯ᾳ κα⋯ ⋯σαϕε⋯ᾳ is a case of polar expression. Εἰκασ⋯α and its images must be clear as δι⋯νοια and is clear.

^{page 144 note 3} Parua Naturalia, 461a 15, 464b 9; and compare Keats's figure: ‘mingles … with a billowy main | A sun, a shadow of a magnitude.’ Plato's figure is the more ordinary one, so common in poets, of a mirror-like surface. Contrast with λεῖα κα⋯ ϕαν⋯ (510a) Plutarch's ⋯μνδραv ⋯μϕ⋯σεις τ⋯ς ⋯ληθε⋯ας (De Iside, c. 9).

^{page 144 note 4} Electra, 774, 1109, 885.

^{page 145 note 1} Thucydides, III. 20. Cf, ⋯κ τ⋯ν εἰκ⋯των κρ⋯νειν, and note the series εἰκ⋯ς, εἰκ⋯ζω, εἰκασ⋯α εἰκ⋯ζω ⋯κ or ⋯π⋯ τινος means ‘I infer from evidence.’ If we neglect the reference to the future, we may compare the saying, μ⋯ντις δ' ἄριστος ὅστις εἰκ⋯ζει καλ⋯ς with Plutarch's comment: μ⋯λλον δ' ⋯ μ⋯ν ‘εἰκ⋯ζων καλ⋯ς’ … ἰχνοσκοπύ⋯ντι κα⋯ στιβε⋯οντι δι⋯ τ⋯ν εὐλ⋯γων τ⋯ μ⋯λλον ŏμοι⋯ς ⋯στι (De Pyth. Orac. 10); when his inference is confirmed he becomes a μ⋯ντις σαϕ⋯ς or πιστ⋯ς.

^{page 145 note 2} Alcibiades I. 132d; cf. Phaedrus, 250b.

^{page 145 note 3} See also Mr. Stocks's account, though I cannot follow his view of εἰκασ⋯α or agree that the two states are real levels of apprehension.

^{page 145 note 4} That δι⋯νοια is under some ⋯ν⋯γκη is clear from 510b 5, 511a 4, C7.

^{page 145 note 5} Perhaps the best example of the scope of the metaphor of natural images come from Cratylus. According to him names as naturally correspond to things as sensations to the objects of sense. ‘For names are like the natural and not the artificial images of visible things, such as shadows and the reflections found in water or in mirrors; and those men name in the true sense who say such a word, while those who do not, pronounce no word, but utter a mere sound: and this is the expert's business, to hunt down that name proper to each thing which nature has provided, just as it is the part of the keen-sighted to discern accurately the reflections proper to each thing’ (Ammonius, On Aristotle's, De Interpretation, 34, 24, Busse)Google Scholar. I owe the reference to a remark in my friend Mr. W. D. Woodhead's unpublished paper on ‘Greek Etymology.’ Cf. Proclus, , In Cratylum XVIIGoogle Scholar.: “Οτι τ⋯ ϕ⋯σει τετραχῷς … ἢ ὡς αἱ σκια⋯ κα⋯ αἱ ⋯μϕ⋯σεις ⋯ν τοῖς κατ⋯πτροις. For a modern example of the indirect seeing of object under a limitation, see Mr. Warde Fowler's charming book on Aeneas at the Site of Rome (ed. 1): ‘Twice it has happened to me to find tree shadows reflected with such marvellous clearness that I was ableto examine with my glass the shadow of a bird which was actually in the top of a tall tree.’ This is εἰκασἰα. Remembering the distinction made by the schools between ‘aenigmatical or specular vision’ and ‘immediate or direct vision,’ we might render Plato's play on εἰκασ⋯α by ‘speculation,’ and say that δι⋯νοια is ‘specular,’ νο⋯ς ‘direct.’ For a reminiscence of the Platonic and Pauline figures see Clem. Alex., , Strom. I. xix. 94, 1Google Scholar.

^{page 146 note 1} If the Line is assimilated to the Cave, one is obliged to take refuge in the assumption of a good and a bad ε⋯κασ⋯α, of a true and a false π⋯στις, or else merge both states together in the cave, where all cats are grey in the dark. But this is a tacit admission that the words must be given two meanings or no specific meaning if they apply to both cave and lower line. And has π⋯στις, true or false, any meaning at all if applied to the utter incredulity of the prisoner when faced round to the puppets?

^{page 146 note 2} For the insistence on method compare ζπτεῖν(510b 5), πορευμ⋯νη (b6), μ⋯θοδον (b8, C5), ζ⋯τησιν (511a 4), ⋯ο⋯σαν ⋯κβ⋯νειν (as, 6), etc. The primitive meaning of way (⋯δό⋯ς) is very near the surface in Plato's whole discussion. Cf. Diels, , Parmenides, p. 47Google Scholar: ‘Wenn Plato sagt ⋯ διαλεκτικ⋯ μ⋯θοδος μ⋯νη τα⋯τη πορε⋯εται (Rep. VII. 533c), so findet eine eigentliche Personification statt, indem die gleichsam zu ᾰνθρωπος μεθοδε⋯ων wird.’ In the Cave we shall find even clearer indications that Plato has in mind the figure of a way.

^{page 147 note 1} Nettleship, , Lectures, p.254Google Scholar. See also ProfessorWilson's, Cook valuable article in Class. Rev. 1904, pp. 258–9Google Scholar. The latter suggests that Plato forgot the ethical forms, and instances the Cave to prove that ethical notions have the same kind of gradations in respect of truth and reality as scientific notions. All one can answer is thatthe structure of the Line exactly anticipates the division of the intellectual education, and that all difficulty disappears if we abandon the unjustified assumption that the Line shows a continuous classification in progress. As for the Cave, that argument implies that it can be paralleled with the Line in all its extent, and that the several states in it contemplate all notions and forms at successive levels of truth and reality. ButI hope to show that the second supposition is untenable too.

^{page 148 note 1} 533C, ⋯κιν⋯τονς. This is opposed to the procedure of dialectic—τ⋯ς ὺποθ⋯σεις ⋯ναιρο⋯σα (533C). It is useful to recall the contrast between ⋯κ⋯νητα ν⋯μιμα (Thuc. I. 11) and ν⋯μον ⋯ναιρεῖν. Cf. Laws, 846c.

^{page 148 note 2} See Part II., end.

^{page 148 note 3} 510b 4, d5, 511a.

^{page 148 note 4} Theaet. 147e.

^{page 148 note 5} See e.g. Theon, of Smyrna, , Comm. de Rebus Mathematicis, p. 32Google Scholar (Hiller). Plato has been criticized for confusion in his treatment of this section, but the criticism rests on aconfusion λογιστικ⋯ and ⋯ριθμητικ⋯.

^{page 148 note 6} 510d, π ρ ο σ χρ⋯νται 511c, προσχρώμενος.

^{page 148 note 7} The ‘visible images,’ which the mathematician ‘moulds and draws,’ are of course among the σκενατ⋯ν τ⋯νος in b'.

^{page 149 note 1} Euthydemus, 290c.

^{page 150 note 1} Poetics, 1457b 16. Compare the excellent example in Gorgias, 465b; and see Olympiodorus, , Prolegomena XXVIIGoogle Scholar. for Plato's use of the method of ⋯ναλογ⋯α.

^{page 150 note 2} 532a.

^{page 150 note 3} This consideration seems to weigh against the attempt to extract from Plato's language here or in Book VII. an implied admission that the objects of mathematics are ‘many.’

^{page 151 note 1} The contention that the third section is not νοητ⋯ν really seems to rest upon the idea that forms in their relation to the Good alone are νοητ⋯ in the proper sense; but we have seen that the last section cannot be so limited.