We see farther from this remark:—First, that Plato’s lectures were often above what his auditors could appreciate — a fact which we learn from other allusions also: Next, that they were not confined to a select body of advanced pupils, who had been worked up by special training into a state fit for comprehending them.[10] Had such been the case, the surprise which Aristotle mentions could never have been felt. And we see farther, that the transcendental doctrine delivered in the lectures De Bono (though we find partial analogies to it in Philêbus, Epinomis, and parts of Republic) coincides more with what Aristotle states and comments upon as Platonic doctrine, than with any reasonings which we find in the Platonic dialogues. It represents the latest phase of Platonism: when the Ideas originally conceived by him as Entities in themselves, had become merged or identified in his mind with the Pythagorean numbers or symbols.
[10] Respecting Plato’s lectures, see Brandis (Gesch. der Griech.-Röm. Phil. vol. ii. p. 180 seq., 306-319); also Trendelenburg, Platonis De Ideis et Numeris Doctrina, pp. 3, 4, seq.
Brandis, though he admits that Plato’s lectures were continuous discourses, thinks that they were intermingled with discussion and debate: which may have been the case, though there is no proof of it. But Schleiermacher goes further, and says (Einleitung. p. 18), “Any one who can think that Plato in these oral Vorträgen employed the Sophistical method of long speeches, shows such an ignorance as to forfeit all right of speaking about Plato”. Now the passage from Aristoxenus, given in the preceding note, is our only testimony; and it distinctly indicates a continuous lecture to an unprepared auditory, just as Protagoras or Prodikus might have given. K. F. Hermann protests, with good reason, against Schleiermacher’s opinion. (Ueber Plato’s schriftstellerische Motive, p. 289.)
The confident declaration just produced from Schleiermacher illustrates the unsound basis on which he and various other Platonic critics proceed. They find, in some dialogues of Plato, a strong opinion proclaimed, that continuous discourse is useless for the purpose of instruction. This was a point of view which, at the time when he composed these dialogues, he considered to be of importance, and desired to enforce. But we are not warranted in concluding that he must always have held the same conviction throughout his long philosophical life, and in rejecting as un-platonic all statements and all compositions which imply an opposite belief. We cannot with reason bind down Plato to a persistence in one and the same type of compositions.
The lectures De Bono may perhaps have been more transcendental than Plato’s other lectures.
This statement of Aristotle, alike interesting and unquestionable, attests the mysticism and obscurity which pervaded Plato’s doctrine in his later years. But whether this lecture on The Good is to be taken as a fair specimen of Plato’s lecturing generally, and from the time when he first began to lecture, we may perhaps doubt:[11] since we know that as a lecturer and converser he acquired extraordinary ascendency over ardent youth. We see this by the remarkable instance of Dion.[12]
[11] Themistius says (Orat. xxi. p. 245 D) that Plato sometimes lectured in the Peiræus, and that a crowd then collected to hear him, not merely from the city, but also from the country around: if he lectured De Bono, however, the ordinary hearers became tired and dispersed, leaving only τοὺς συνήθεις ὁμιλητάς.
It appears that Plato in his lectures delivered theories on the principles of geometry. He denied the reality of geometrical points — or at least admitted them only as hypotheses for geometrical reasoning. He maintained that what others called a point ought to be called “an indivisible line”. Xenokrates maintained the same doctrine after him. Aristotle controverts it (see Metaphys. A., 992, b. 20). Aristotle’s words citing Plato’s opinion (τούτῳ μὲν οὖν τῷ γένει καὶ διεμάχετο Πλάτων ὡς ὄντι γεωμετρικῷ δόγματι, ἀλλ’ ἐκάλει ἀρχὴν γραμμῆς· τοῦτο δὲ πολλάκις ἐτίθει τὰς ἀτόμους γραμμάς) must be referred to Plato’s oral lectures; no such opinion occurs in the dialogues. This is the opinion both of Bonitz and Schwegler in their comments on the passage: also of Trendelenburg, De Ideis et Numeris Platonis, p. 66. That geometry and arithmetic were matters of study and reflection both to Plato himself and to many of his pupils in the Academy, appears certain; and perhaps Plato may have had an interior circle of pupils, to which he applied the well-known exclusion — μηδεὶς ἀγεωμέτρητος εἰσίτω. But we cannot make out clearly what was Plato’s own proficiency, or what improvements he may have introduced, in geometry, nor what there is to justify the comparison made by Montucla between Plato and Descartes. In the narrative respecting the Delian problem — the duplication of the cube — Archytas, Menæchmus, and Eudoxus, appear as the inventors of solutions, Plato as the superior who prescribes and criticises (see the letter and epigram of Eratosthenes: Bernhardy, Eratosthenica, pp. 176-184). The three are said to have been blamed by Plato for substituting instrumental measurement in place of geometrical proof (Plutarch, Problem. Sympos. viii. 2, pp. 718, 719; Plutarch, Vit. Marcelli, c. 14). The geometrical construction of the Κόσμος, which Plato gives us in the Timæus, seems borrowed from the Pythagoreans, though applied probably in a way peculiar to himself (see Finger, De Primordiis Geometriæ ap. Græcos, p. 38, Heidelb. 1831).
[12] See Epist. vii. pp. 327, 328.