Book 1
19
Again, one number can be composed of several numbers, but how can one Form be composed of several Forms? And if the one number is not composed of the other numbers themselves, but of their constituents (e.g. those of the number 10,000), what is the relation of the units? If they are specifically alike, many absurdities will result, and also if they are not (whether (a) the units in a given number are unlike, or (b) the units in each number are unlike those in every other number).That the words in brackets give the approximate sense seems clear from Aristot. Met. 13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it out of the Greek. For in what can they differ, seeing that they have no qualities? Such a view is neither reasonable nor compatible with our conception of units.
20
Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called intermediate by some thinkers.Cf. vi. 4. But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things here and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible.i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.
