Just as in the hypothetical syllogism we cannot say that where a certain condition does not hold, the conditioned also does not hold. Thus the argument fails. But this definition yields no insight into the conditions which make it necessary. These conditions are needed in order to determine whether, in resorting to this concept, we are thinking anything at all. All alleged examples are take from judgments, not things and their existence.
Every geometrical proposition is absolutely necessary.
The absolute necessity of the judgment is only a conditioned necessity of the thing, or of the predicate in the judgment. In an identical proposition, if I reject the predicate while retaining the subject, contradiction results, and I therefore say that the former belongs necessarily to the latter. God is omnipotent' is a necessary judgment. We cannot reject omnipotence if we posit a deity. But if we reject the deity there is no omnipotence or any other predicates given so there is no contradiction.