Leibniz was the chief representative of his school. Hume does not fit into this classification because he denied the possibility of human knowledge, and hence was a skeptic . Kant credited his recollection of Hume as having awakened him from his dogmatic slumber. Before he absorbed Hume's lesson, Kant had been trained in the Leibnizian school, hence as a noologist. Thus the principle of contradiction was the priniciple of possibility.
Actuality is known through the principle of sufficient reason.
The principle of sufficient reason states that whatever is actual ,whatever exists, does so by virtue of a reason why it exists rather than not. In Leibniz's system, we know that God has a sufficient to create the best possible world, so we know that the best possible world exists. Hume recognized that the principle of sufficient reason, if true at all, is a necessary truth. He then inquired as to the justification of such a principle. If it is necessarily true, then its opposite is impossible, and therefore its falsehood is unthinkable.