[72] That Plato intended, by this elaborate geometrical construction, to arrive at a continuous geometrical proportion between the four elements, he tells us (p. 32 A-B), adding the qualifying words καθ’ ὅσον ἦν δυνατόν. M. Boeckh, however (De Platonicâ Corporis Mundani Fabricâ, pp. viii.-xxvi.), has shown that the geometrical proportion cannot be properly concluded from the premisses assumed by Plato:— “Platonis elementorum doctrinam et parum sibi constare, neque omnibus numeris absolutam esse, immo multis incommodis laborare, et divini ingenii lusui magis quam disciplinæ severitati originem debere fatebimur; nec profundiorem et abstrusiorem naturæ cognitionem in eâ sitam esse suspicabimur — in quem errorem etiam Joh. Keplerus, summi ingenii homo, incidit”.
Respecting the Dodekahedron, see Zeller, Gesch. der Philos. ii. p. 513, ed. 2nd. There is some obscurity about it. In the Epinomis (p. 981 C) Plato gives the Æther as a fifth element, besides the four commonly known and recited in the Timæus. It appears that Philolaus, as well as Xenokrates, conceived the Dodekahedron as the structural form of Æther (Schol. ad Aristot. Physic. p. 427, a. 16, Brandis): and Xenokrates expressly says, that Plato himself recognised it as such. Zeller dissents from this view, and thinks that nothing more is meant than the implication, that the Dodekahedron can have a sphere described round it more readily than any of the other figures named.
Opponents of Plato remarked that he κατεμαθηματικεύσατο τὴν φύσιν, Schol. ad Aristot. Metaph. A. 985, b. 23, p. 539, Brandis. Aristotle devotes himself in many places to the refutation of the Platonic doctrine on this point; see De Cœlo, iii. 8, 306-307, and elsewhere.
[73] Plato, Timæus, p. 56 C. ὅπηπερ ἡ τῆς Ἀνάγκης ἑκοῦσα πεισθεῖσα τε φύσις ὑπεῖκε.
[74] Plato, Timæus, pp. 55-56.
Such was the mode of formation of the four so-called elemental bodies.[75] Of each of the four, there are diverse species or varieties: and that which distinguishes one variety of the same element from another variety is, that the constituent triangles, though all similar, are of different magnitudes. The diversity of these combinations, though the primary triangles are similar, is infinite: the student of Nature must follow it out, to obtain any probable result.[76]
[75] Plato, Timæus, p. 57 C. ὅσα ἄκρατα καὶ πρῶτα σώματα.
The Platonist Attikus (ap. Eusebium, Præp. Ev. xv. 7) blames Aristotle for dissenting from Plato on this point, and for recognising the celestial matter as a fifth essence distinct from the four elements. Plato (he says) followed both anterior traditions and self-evident sense (τῇ περὶ αὐτὰ ἐναργείᾳ) in admitting only the four elements, and in regarding all things as either compounds or varieties of these. But Aristotle, thinking to make parade of superior philosophical sagacity, προσκατηρίθμησε τοῖς φαινομένοις τέτταρσι σώμασι τὴν πέμπτην οὐσίαν, πάνυ μὲν λαμπρῶς καὶ φιλοδώρως τῇ φύσει χρησάμενος, μὴ συνιδὼν δὲ ὅτι οὐ νομοθετεῖν δεῖ φυσιολογοῦντα, τὰ δὲ τῆς φύσεως αὐτῆς ἐξιστορεῖν. This last precept is what we are surprised to read in a Platonist of the third century B.C. “When you are philosophising upon Nature, do not lay down the law, but search out the real facts of Nature.” It is truly Baconian: it is justly applicable as a caution to Aristotle, against whom Attikus directs it; but it is still more eminently applicable to Plato, against whom he does not direct it.
[76] Plato, Timæus, p. 57 D.