Posterior Analytics   

of its own species. Nor (the other alternative) can a quale be
reciprocally predicated of a quale, nor any term belonging to an
adjectival category of another such term, except by accidental
predication; for all such predicates are coincidents and are
predicated of substances. On the other hand-in proof of the
impossibility of an infinite ascending series-every predication
displays the subject as somehow qualified or quantified or as
characterized under one of the other adjectival categories, or else is
an element in its substantial nature: these latter are limited in
number, and the number of the widest kinds under which predications
fall is also limited, for every predication must exhibit its subject
as somehow qualified, quantified, essentially related, acting or
suffering, or in some place or at some time.
I assume first that predication implies a single subject and a
single attribute, and secondly that predicates which are not
substantial are not predicated of one another. We assume this
because such predicates are all coincidents, and though some are
essential coincidents, others of a different type, yet we maintain
that all of them alike are predicated of some substratum and that a
coincident is never a substratum-since we do not class as a coincident
anything which does not owe its designation to its being something
other than itself, but always hold that any coincident is predicated
of some substratum other than itself, and that another group of
coincidents may have a different substratum. Subject to these
assumptions then, neither the ascending nor the descending series of
predication in which a single attribute is predicated of a single
subject is infinite. For the subjects of which coincidents are
predicated are as many as the constitutive elements of each individual
substance, and these we have seen are not infinite in number, while in
the ascending series are contained those constitutive elements with
their coincidents-both of which are finite. We conclude that there
is a given subject (D) of which some attribute (C) is primarily
predicable; that there must be an attribute (B) primarily predicable
of the first attribute, and that the series must end with a term (A)
not predicable of any term prior to the last subject of which it was
predicated (B), and of which no term prior to it is predicable.
The argument we have given is one of the so-called proofs; an
alternative proof follows. Predicates so related to their subjects
that there are other predicates prior to them predicable of those
subjects are demonstrable; but of demonstrable propositions one cannot
have something better than knowledge, nor can one know them without
demonstration. Secondly, if a consequent is only known through an
antecedent (viz. premisses prior to it) and we neither know this
antecedent nor have something better than knowledge of it, then we
shall not have scientific knowledge of the consequent. Therefore, if
it is possible through demonstration to know anything without
qualification and not merely as dependent on the acceptance of certain
premisses-i.e. hypothetically-the series of intermediate
predications must terminate. If it does not terminate, and beyond
any predicate taken as higher than another there remains another still
higher, then every predicate is demonstrable. Consequently, since
these demonstrable predicates are infinite in number and therefore
cannot be traversed, we shall not know them by demonstration. If,
therefore, we have not something better than knowledge of them, we
cannot through demonstration have unqualified but only hypothetical
science of anything.
As dialectical proofs of our contention these may carry
conviction, but an analytic process will show more briefly that
neither the ascent nor the descent of predication can be infinite in
the demonstrative sciences which are the object of our
investigation. 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