g. in line must be either straightness or curvature,
in number either oddness or evenness. For within a single identical
genus the contrary of a given attribute is either its privative or its
contradictory; e.g. within number what is not odd is even, inasmuch as
within this sphere even is a necessary consequent of not-odd. So,
since any given predicate must be either affirmed or denied of any
subject, essential attributes must inhere in their subjects of
necessity.
Thus, then, we have established the distinction between the
attribute which is 'true in every instance' and the 'essential'
attribute.
I term 'commensurately universal' an attribute which belongs to
every instance of its subject, and to every instance essentially and
as such; from which it clearly follows that all commensurate
universals inhere necessarily in their subjects. The essential
attribute, and the attribute that belongs to its subject as such,
are identical. E.g. point and straight belong to line essentially, for
they belong to line as such; and triangle as such has two right
angles, for it is essentially equal to two right angles.
An attribute belongs commensurately and universally to a subject
when it can be shown to belong to any random instance of that
subject and when the subject is the first thing to which it can be
shown to belong.
Pages:
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28