Kitap 13
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But if the units are inaddible in the sense that any one unit is inaddible to any other, the number so composed can be neither mathematical number (since mathematical number consists of units which do not differ, and the facts demonstrated of it fit in with this character) nor Ideal number. For on this view 2 will not be the first number generated from Unity and the indeterminate dyad, and then the other numbers in succession, as theyThe Platonists. say 2, 3, because the units in the primary 2 are generated at the same time,This was the orthodox Platonist view of the generation of ideal numbers; or at least Aristotle is intending to describe the orthodox view. Plato should not have regarded the Ideal numbers as composed of units at all, and there is no real reason to suppose that he did (see Introduction). But Aristotle infers from the fact that the Ideal 2 is the first number generated (and then the other Ideal numbers in the natural order) that the units of the Ideal 2 are generated simultaneously, and then goes on to show that this is incompatible with the theory of inaddible units. whether, as the originator of the theory held, from unequalsi.e., the Great-and-Small, which Aristotle wrongly understands as two unequal things. It is practically certain that Plato used the term (as he did that of Indeterminate Dyad) to describe indeterminate quantity. See Introduction.(coming into being when these were equalized), or otherwise—
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since if we regard the one unit as prior to the other,This is a necessary implication of the theory of inaddible units (cf. Aristot. Met. 13.6.1, 2). it will be prior also to the 2 which is composed of them; because whenever one thing is prior and another posterior, their compound will be prior to the latter and posterior to the former.So the order of generation will be: (i) Unity (ungenerated); (2) first unit in 2; (3) second unit in 2; and the Ideal 2 will come between (2) and (3).
