Demonstration proves the inherence of essential
attributes in things. Now attributes may be essential for two reasons:
either because they are elements in the essential nature of their
subjects, or because their subjects are elements in their essential
nature. An example of the latter is odd as an attribute of
number-though it is number's attribute, yet number itself is an
element in the definition of odd; of the former, multiplicity or the
indivisible, which are elements in the definition of number. In
neither kind of attribution can the terms be infinite. They are not
infinite where each is related to the term below it as odd is to
number, for this would mean the inherence in odd of another
attribute of odd in whose nature odd was an essential element: but
then number will be an ultimate subject of the whole infinite chain of
attributes, and be an element in the definition of each of them.
Hence, since an infinity of attributes such as contain their subject
in their definition cannot inhere in a single thing, the ascending
series is equally finite. Note, moreover, that all such attributes
must so inhere in the ultimate subject-e.g.
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