12.Enough upon that side of the question.But how does the perfection [goodness] of numbers, lifeless things, depend upon their particular unity? Just as all other inanimates find their perfection in their unity.
If it should be objected that numbers are simply non-existent, we should point out that our discussion is concerned [not with units as such, but] with beings considered from the aspect of their unity.
We may again be asked how the point- supposing its independent existence granted- participates in perfection.If the point is chosen as an inanimate object, the question applies to all such objects: but perfection does exist in such things, for example in a circle: the perfection of the circle will be perfection for the point;it will aspire to this perfection and strive to attain it, as far as it can, through the circle.
But how are the five genera to be regarded? Do they form particulars by being broken up into parts? No; the genus exists as a whole in each of the things whose genus it is.
But how, at that, can it remain a unity? The unity of a genus must be considered as a whole-in-many.
Does it exist then only in the things participating in it? No;it has an independent existence of its own as well.But this will, no doubt, become clearer as we proceed.
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.
14.Why is Quality, again, not included among the Primaries?
Because like Quantity it is a posterior, subsequent to Substance.
Primary Substance must necessarily contain Quantity and Quality as its consequents; it cannot owe its subsistence to them, or require them for its completion: that would make it posterior to Quality and Quantity.
Now in the case of composite substances- those constituted from diverse elements- number and qualities provide a means of differentiation: the qualities may be detached from the common core around which they are found to group themselves.But in the primary genera there is no distinction to be drawn between simples and composites; the difference is between simples and those entities which complete not a particular substance but Substance as such.Aparticular substance may very well receive completion from Quality, for though it already has Substance before the accession of Quality, its particular character is external to Substance.But in Substance itself all the elements are substantial.
Nevertheless, we ventured to assert elsewhere that while the complements of Substance are only by analogy called qualities, yet accessions of external origin and subsequent to Substance are really qualities; that, further, the properties which inhere in substances are their activities [Acts], while those which are subsequent are merely modifications [or Passions]: we now affirm that the attributes of the particular substance are never complementary to Substance [as such]; an accession of Substance does not come to the substance of man qua man; he is, on the contrary, Substance in a higher degree before he arrives at differentiation, just as he is already "living being" before he passes into the rational species.
15.How then do the four genera complete Substance without qualifying it or even particularizing it?
It has been observed that Being is primary, and it is clear that none of the four- Motion, Stability, Difference, Identity- is distinct from it.That this Motion does not produce Quality is doubtless also clear, but a word or two will make it clearer still.
