Any proposition can be a postulate.

Let p be a proposition. It is logically necessary that p is permitted to be a postulate. It is logically necessary that the proposition "p is true in the actual world" is permitted to be a postulate.

If p is a postulate, then: p is true and no contradiction exists.

Proof. It is given that p is a postulate. Then by definition of postulate, p is true.

Assume some contradiction exists. Then there is a contradiction. Discharge the assumption. It is thus proved by contradiction that it is not true that some contradiction exists. So, no contradiction exists.

By conjunction introduction, p is true and no contradiction exists. This concludes the proof.

Since the proposition "p is true and no contradiction exists" is true at all times that p is a postulate, there is never a problem with p being a postulate.

In the proposed debate "The Absolute Russell Set Exists," which I recently cited on social media and is located at http://www.debate.org/debates/The-Absol ... -Exists/1/, I, Paul E. Mokrzecki, postulated the existence of the absolute Russell set. The proposition "the absolute Russell set exists" can be postulated without contradiction and thus without trouble.