Aristotle, in a remarkable passage of the Metaphysica (Γ. p. 1005, a. 20 seqq.) takes pains to distinguish the Logic of Mathematics from Mathematics themselves — as a separate province and matter of study. He claims the former as belonging to Philosophia Prima or Ontology. Those principles which mathematicians called Axioms were not peculiar to Mathematics (he says), but were affirmations respecting Ens quatenus Ens: the mathematician was entitled to assume them so far as concerned his own department, and his students must take them for granted: but if he attempted to explain or appreciate them in their full bearing, he overstepped his proper limits, through want of proper schooling in Analytica (ὅσα δ’ ἐγχειροῦσι τῶν λεγόντων τινὲς περὶ τῆς ἀληθείας, ὃν τρόπον δεῖ ἀποδέχεσθαι, δι’ ἀπαιδευσίαν τῶν ἀναλυτικῶν τοῦτο δρῶσιν· δεῖ γὰρ περὶ τούτων ἥκειν προεπισταμένους, ἀλλὰ μὴ ἀκούοντας ζητεῖν — p. 1005, b. 2.) We see from the words of Aristotle that many mathematical enquirers of his time did not recognise (any more than Plato recognised) the distinction upon which he here insists: we see also that the term Axioms had become a technical one for the principia of mathematical demonstration (περὶ τῶν ἐν τοῖς μαθήμασι καλουμένων ἀξιωμάτων — p. 1005, a. 20); I do not concur in Sir William Hamilton’s doubts on this point. (Dissertations on Reid’s Works, note A. p. 764.)
The distinction which Aristotle thus brings to notice, seemingly for the first time, is one of considerable importance.
[43] This is forcibly put by Plato, Epistol. vii. 344 B. Compare Plato, Republic, vi. 499 A. Phædrus, 276 A-E. τὸν τοῦ εἰδότος λόγον ζῶντα καὶ ἔμψυχον, &c.
Though Plato, in the Phædrus, declares oral teaching to be the only effectual way of producing a permanent and deep-seated effect — as contrasted with the more superficial effect produced by reading a written exposition: yet even oral teaching, when addressed in the form of continuous lecture or sermon (ἄνευ ἀνακρίσεως καὶ διδαχῆς, Phædrus, 277 E; τὸ νουθετητικὸν εἶδος, Sophistês, p. 230), is represented elsewhere as of little effect. To produce any permanent result, you must diversify the point of view — you must test by circumlocutory interrogation — you must begin by dispelling established errors, &c. See the careful explanation of the passage in the Phædrus (277 E), given by Ueberweg, Aechtheit der Platon. Schrift. pp. 16-22. Direct teaching, in many of the Platonic dialogues, is not counted as capable of producing serious improvement.
When we come to the Menon and the Phædon, we shall hear more of the Platonic doctrine — that knowledge was to be evolved out of the mind, not poured into it from without.
Plato never published any of the lectures which he delivered at the Academy.
Since we thus find that Plato was unconquerably averse to publication in his own name and with his own responsibility attached to the writing, on grave matters of philosophy — we cannot be surprised that, among the numerous lectures which he must have delivered to his pupils and auditors in the Academy, none were ever published. Probably he may himself have destroyed them, as he exhorts Dionysius to destroy the Epistle which we now read as second, after reading it over frequently. And we may doubt whether he was not displeased with Aristotle and Hestiæus[44] for taking extracts from his lectures De Bono, and making them known to the public: just as he was displeased with Dionysius for having published a work purporting to be derived from conversations with Plato.
[44] Themistius mentions it as a fact recorded (I wish he had told us where or by whom) that Aristotle stoutly opposed the Platonic doctrine of Objective Ideas, even during the lifetime of Plato, ἱστορεῖται δὲ ὅτι καὶ ζῶντος τοῦ Πλάτωνος καρτερώτατα περὶ τούτου τοῦ δόγματος ἐνέστη ὁ Ἀριστοτέλης τῷ Πλάτωνι. (Scholia ad Aristotel. Analyt. Poster. p. 228 b. 16 Brandis.)
Plato would never publish his philosophical opinions in his own name; but he may have published them in the dialogues under the name of others.
That Plato would never consent to write for the public in his own name, must be taken as a fact in his character; probably arising from early caution produced by the fate of Sokrates, combined with preference for the Sokratic mode of handling. But to what extent he really kept back his opinions from the public, or whether he kept them back at all, by design — I do not undertake to say. The borrowed names under which he wrote, and the veil of dramatic fiction, gave him greater freedom as to the thoughts enunciated, and were adopted for the express purpose of acquiring greater freedom. How far the lectures which he delivered to his own special auditory differed from the opinions made known in his dialogues to the general reader, or how far his conversation with a few advanced pupils differed from both — are questions which we have no sufficient means of answering. There probably was a considerable difference. Aristotle alludes to various doctrines of Plato which we cannot find in the Platonic writings: but these doctrines are not such as could have given peculiar offence, if published; they are, rather abstruse and hard to understand. It may also be true (as Tennemann says) that Plato had two distinct modes of handling philosophy — a popular and a scientific: but it cannot be true (as the same learned author[45] asserts) that his published dialogues contained the popular and not the scientific. No one surely can regard the Timæus, Parmenidês, Philêbus, Theætêtus, Sophistês, Politikus, &c., as works in which dark or difficult questions are kept out of sight for the purpose of attracting the ordinary reader. Among the dialogues themselves (as I have before remarked) there exist the widest differences; some highly popular and attractive, others altogether the reverse, and many gradations between the two. Though I do not doubt therefore that Plato produced powerful effect both as lecturer to a special audience, and as talker with chosen students — yet in what respect such lectures and conversation differed from what we read in his dialogues, I do not feel that we have any means of knowing.