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Section 13

13. We turn to ask why Quantity is not included among the primary genera, and Quality also.

Quantity is not among the primaries, because these are permanently associated with Being. Motion is bound up with Actual Being [Being-in-Act], since it is its life; with Motion, Stability too gained its foothold in Reality; with these are associated Difference and Identity, so that they also are seen in conjunction with Being. But number [the basis of Quantity] is a posterior. It is posterior not only with regard to these genera but also within itself; in number the posterior is divided from the prior; this is a sequence in which the posteriors are latent in the priors [and do not appear simultaneously]. Number therefore cannot be included among the primary genera; whether it constitutes a genus at all remains to be examined.

Magnitude [extended quantity] is in a still higher degree posterior and composite, for it contains within itself number, line and surface. Now if continuous magnitude derives its quantity from number, and number is not a genus, how can magnitude hold that status? Besides, magnitudes, like numbers, admit of priority and posteriority.

If, then, Quantity be constituted by a common element in both number and magnitude, we must ascertain the nature of this common element, and consider it, once discovered, as a posterior genus, not as one of the Primaries: thus failing of primary status, it must be related, directly or indirectly, to one of the Primaries.

We may take it as clear that it is the nature of Quantity to indicate a certain quantum, and to measure the quantum of the particular; Quantity is moreover, in a sense, itself a quantum. But if the quantum is the common element in number and magnitude, either we have number as a primary with magnitude derived from it, or else number must consist of a blending of Motion and Stability, while magnitude will be a form of Motion or will originate in Motion, Motion going forth to infinity and Stability creating the unit by checking that advance.

But the problem of the origin of number and magnitude, or rather of how they subsist and are conceived, must be held over. It may, thus, be found that number is among the primary genera, while magnitude is posterior and composite; or that number belongs to the genus Stability, while magnitude must be consigned to Motion. But we propose to discuss all this at a later stage.

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