Book 13
1
Now that we have dealt with the problems concerning the Ideas, we had better re-investigate the problems connected with numbers that follow from the theory that numbers are separate substances and primary causes of existing things. Now if number is a kind of entity, and has nothing else as its substance, but only number itself, as some maintain; then either (a) there must be some one part of number which is primary, and some other part next in succession, and so on, each part being specifically differentThis statement bears two meanings, which Aristotle confuses: (i) There must be more than one number-series, each series being different in kind from every other series; (2) All numbers are different in kind, and inaddible. Confusion (or textual inaccuracy) is further suggested by the fact that Aristotle offers no alternative statement of the nature of number in general, such as we should expect from his language. In any case the classification is arbitrary and incomplete.—
2
and this applies directly to units, and any given unit is inaddible to any other given unit; or (b) theyThe units. are all directly successive, and any units can be added to any other units, as is held of mathematical number; for in mathematical number no one unit differs in any way from another.
