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.
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