 As to the second question concerning the extent to which Plato believed that ethics was amenable to quantification, stated earlier, Plato’s confidence in a mathematically structured order of the universe that also includes human nature was greatly enhanced by the progress made by the scientists of his day. This seems to be the rationale for his depiction in the Timaeus of the world’s creation as a construction by a divine craftsman who makes use of proportion, and who also takes care to give a geometrical construction to the four elements (a factor left out of consideration here). This conviction is echoed in the Philebus’ emphasis on measure and proportion as the ultimate criteria of goodness. It should be noted, however, that Plato carefully refrains from going into any specifics about concrete mathematical relations. Even in the Timaeus, he does not apply his complicated system of proportions when it comes to specifying the actual size, distance, and speed of the heavenly bodies. Nor does he indicate in the Philebus how the art of establishing the limits of good mixtures should be attained. It therefore remains an open question to what extent Plato regarded mathematical physics and metaphysics as viable projects. That Plato went some way in that direction seems to be indicated by claims in later reports on his theory of the Forms, that he either treated the Forms as numbers or associated numbers with them. Because Aristotle is quite vociferous in his criticism of this theory in Book A of the Metaphysics (A 6; A 9) and further expands his criticism of ideas as numbers or idea-numbers in books M and N, there must be some substance to that claim. As the obscurities in Aristotle’s various reports indicate, the doctrine cannot ever have reached a definitive stage, for at one point he complains that Plato’s theory relied on too few numbers (Met. 1084a10–27), while elsewhere he objects that, (1073a20): “they speak of numbers now as unlimited, now as limited by the number 10.” That Plato never presented this theory in a magisterial form is confirmed by the reports on his public ‘lecture on the good’. It scandalized the general audience because Plato, instead of speaking about the good in the ordinary sense, as expected by the uninformed public, spoke about mathematics and “finally, that the Good is one” (cf. Aristoxenos, Harmonica, II, 30). But it was not just the general public who found the message hard to comprehend. As Simplicius reports, even Plato’s mature students – such as Aristotle, Heraclides Ponticus, and Hestiaeus – took notes on the lecture, “because it was stated enigmatically”. Simplicius also reports that Porphyry, his source, used the Philebus to unravel the enigma (In Aristotelis physica 453,29). Given the disagreements in our sources, it may forever remain a matter of debate how far Plato went in his mathematization of his ethics and metaphysics. It seems clear, however, that he must at least have entertained the hope that all that is good rests on ‘due measure’ in a more than metaphorical sense. We may well ask why he shouldered his philosophy with such heavy baggage that made it inaccessible to the mathematically untrained, an inaccessibility that largely persists to this day and age. Clearly, there is one conviction that Plato never gave up: The nature of all things requires knowledge, and that condition applies most of all to the Good. And if it takes mathematical knowledge to comprehend what is good, then that is the way to go.