Capítulo 19. Chapter XIX.—Concerning Whole And Part
[2.19.215] Whole and part we shall discuss in what we call our physical treatise,[292] but at present we have to deal with the so-called division of the whole into its parts. When a man says that the decad is being divided into one and two and three and four, the decad is not being divided into these. For as soon as its first part, say one, is subtracted—granting for the moment that this can be done—there no longer subsists the decad but the number nine, something quite different from the decad.
[2.19.216] Hence the division and the subtraction of the other parts is not made from the decad but from some other numbers, and these vary with each subtraction.
Probably then it is impracticable to divide the whole into what are called its parts. For, in fact, if the whole is divided into parts, the parts ought to be comprised in the whole before the act of division, but probably they are not so comprised. Thus for example—to base our argument once more on the decad—they say that nine is certainly a part of the decad, since it is divided into one plus nine. But so likewise is the number eight, since it is divided into eight plus two; and so also are the numbers seven, six, five, four, three, two and one.
[2.19.217] If then all these numbers are included in the decad, and when added together with it make up fifty-five, then fifty-five is included in the number ten, which is absurd. Therefore neither are its so-called parts included in the decad nor can the decad be divided into them, as a whole into parts, since they are not even seen in it at all.
[2.19.218] And the same objections will confront us in the case of magnitudes[293] also, supposing one should wish, for example, to divide the magnitude of ten cubits. Probably, then, it is not practicable to divide a whole into parts.