The Necessity of Contingency.

Suppose (for reductio) that there are no contingent facts. Then, it would be true that “no contingent facts obtain.” Since it isn’t a necessary truth that no contingent facts obtain, this would be a contingent fact. Therefore, it is logically necessary that there be contingent facts, or else it is logically impossible that any fact be contingent.

So, either all facts are necessary (i.e., modal collapse), or it is a necessary fact that there is at least one contingent fact. There is a necessary fact N which is just the infinitely long disjunction of all logically possible contingent propositions {C1 v C2 v C3 v… Cn,}, including the contingent proposition that no other contingent facts obtain.