Book 13
13
Again, the ways in which the objects of mathematics are generated prove our point;
14
for they are generated first in the dimension of length, then in that of breadth, and finally in that of depth, whereupon the process is complete. Thus if that which is posterior in generationi.e., in the natural order of development. Thus generation (γένεσις) is used in two different senses in this argument, which therefore becomes invalid (Bonitz). is prior in substantiality, body will be prior to plane and line, and in this sense it will also be more truly complete and whole, because it can become animate; whereas how could a line or plane be animate? The supposition is beyond our powers of apprehension.
15
Further, body is a kind of substance, since it already in some sense possesses completeness; but in what sense are lines substances? Neither as being a kind of form or shape, as perhaps the soul is, nor as being matter, like the body; for it does not appear that anything can be composed either of lines or of planes or of points,
16
whereas if they were a kind of material substance it would be apparent that things can be so composed. Let it be granted that they are prior in formula; yet not everything which is prior in formula is also prior in substantiality. Things are prior in substantiality which when separated have a superior power of existence; things are prior in formula from whose formulae the formulae of other things are compounded. And these characteristics are not indissociable.
17
For if attributes, such as moving or white, do not exist apart from their substances, white will be prior in formula to white man, but not in substantiality; for it cannot exist in separation, but always exists conjointly with the concrete whole—by which I mean white man.
18
Thus it is obvious that neither is the result of abstraction prior, nor the result of adding a determinant posterior—for the expression white man is the result of adding a determinant to white.
