BESSARIO | ARGYROPYLUS

...by participation in the One itself: the species original: "species"; here meaning the Platonic Forms are numbers. He held that the One itself is a substance, and not merely a property of something else, just as the Pythagoreans did. He also said that numbers were the causes of existence for other substances, just as they did. But to create a duality The "Indefinite Dyad," a principle of multiplicity in Platonic thought instead of the infinite as a single thing, and to make the infinite out of the "great and the small": this was his own unique contribution. Furthermore, he placed numbers beyond sensible things, whereas they [the Pythagoreans] say numbers are the things themselves; also, they did not place mathematical objects between the two.
65 ¶ Therefore, making the One and numbers distinct from actual things—unlike the Pythagoreans—and the introduction of the Species occurred because of the investigation into definitions original: "perscrutationem"; literally "scrutiny," referring to the dialectic method of Socrates. For those who came before were not skilled in dialectic. He made duality a "second nature" because numbers, except for the first ones, are most aptly generated from it as if from a certain mold. Yet the reality is the opposite. For it is not likely to happen this way. For now, they make many things from matter, but the species generates only once. It appears that from one piece of matter, one table is made. But he who introduces the species, which is one, makes many tables. Similarly, the male relates to the female. For she is filled from a single union, but the male can fill many. And yet, these are but imitations of those first principles. Thus did Plato determine the questions proposed to him.
66 ¶ It is clear from what has been said that he uses only two causes: the "what it is" the formal cause and the "material cause." For the species are the causes of the "what it is" for other things, and the One is the cause for the species. And he identifies what the underlying matter is, of which the species are predicated: in the case of sensible things, these are the species; in the species, it is the One. This underlying matter is the duality: the Great and the Small. Furthermore, he attributed the cause of good and evil to these elements, one to each. This is what we say certain earlier philosophers—Empedocles and Anaxagoras—sought to a greater degree.
Empedocles. Anaxagoras.

67 ¶ Briefly and summarily, therefore, we have run through who has spoken concerning principles and truth, and how they did so. We have gathered this much from them: that of those who spoke of principle and cause, no one has said anything beyond what we have determined in our works on nature referring to Aristotle's Physics. Rather, all of them—though obscurely—seem to have touched upon those causes to some extent.

...for by participation in the One, they assert that the forms themselves are the numbers. Yet he [Plato] held that the One itself is a substance, just as the Pythagoreans did, and that there is nothing else called "One." And likewise, he said numbers were the causes of substance for the rest (as they did). But to have made a duality 8 instead of the infinite as one, and to have made the infinite out of the "great and the small": this is his own specialty. And besides, he said numbers exist apart from sensible things, while they said numbers were the things themselves; and they do not place mathematicals in the middle between them.
¶ Therefore, making the One and number apart from things themselves—not as the Pythagoreans did—and also the introduction of forms, was surely due to his consideration of logical differentiation original: "differendo"; referring to dialectic. For the earlier ones did not share in the faculty of differentiation. He made duality another nature for this reason: because numbers (except the first) are aptly made and generated from it as if from a certain seal. Yet this happens the opposite way. For it is not consistent with reason that it should happen so. For they [the Platonists] make many things from matter, while the form generates for them only once. From one piece of matter, one table is seen to be made. But he who 9 brings the form of one makes many, as is evident. The male relates to the female in the same way. For the female becomes pregnant from one coitus, but the male makes many females pregnant. And yet these things are imitations of those principles. Plato, therefore, determined these sought-after matters in this way.
¶ It is clear from what has been said that he uses only two causes: the "what it is" and the "matter." For the forms are the causes of the "what it is" for the rest, but the One is the cause for the forms. And what is the underlying matter, by which they are derived? In sensible things, it is the forms; in forms, it is the One. For the duality is this: the "Great" and the "Small." Furthermore, he assigned the cause of good and evil to both elements respectively. This indeed is what we say some of the earlier philosophers, namely Empedocles and Anaxagoras, sought.
¶ In brief and summary fashion, we have narrated who spoke of principles and truth, and in what manner. Nevertheless, we have this much from them: I say that no one of those speaking of principle and cause said anything beyond those things which were determined by us in those books concerning nature. But all, albeit obscurely, seem to have touched upon them.