such knowledge, the opposite would seem abstractly possible. But it proves to be only verbally or apparently possible. Determinately viewed, only the “actual sum” is possible.
In general, when we judge in universal ways, we begin, before we attain an insight into the truth of our judgment, by stating, as abstractly possible, more ideal alternatives than in the end will prove to be determinately possible, or to be valid possibilities. In the exact sciences, or, again, in case of those practically important realms of Being which we view as subject to our choice, — whenever we win control over a system of ideas, and assert a truth, or decide upon a course of action, and whenever we do this upon the basis of general principles, — our insight is always destructive of merely abstract possibilities, and, where our knowledge takes the form of universal judgments, they are always primarily such destructive judgments, so far as they relate to external objects. They tell us, indirectly, what is, in the realm of external meanings, but only by first telling us what is not.
The consequence is that universal categorical judgments, being always primarily negative in force, enlighten us regarding that realm of the external meanings which is still for us, at this stage, the realm of Being, only by virtue of the junction, overt or implied, of the universal categorical judgments with disjunctive judgments, i.e. with judgments of the either, or type. One who inquires into a matter upon which he believes himself able to decide in universal terms, e.g. in mathematics, has present to his mind, at the outset, questions
