Truth is identity.  It is, in principle, possible to reduce all truths to identities. Derived truths divide into two classes:  necessary and contingent; truths of reasoning and truths of fact, truths of essence and truths of existence.  The unity of all three classes of truths takes its bearing form the scientia Dei.

The assimilation of truths from facts to truths of reasoning is the ideal of a knowledge of actual beings, a knowledge from the sheer concepts of reason of what can be empirically experienced, a knowledge of beings from pure reason (a la Kant's Kritik der Reinen Vernunft).

The essence of truth as such resides in the identity of subject with predicate.  Knowledge of truths is accordingly a grasp of identities.   There are then different signs and criteria for the truth of cognition, depending on whether the identities are either manifest or must first be proved, and proved in the double sense of necessary  and contingent truths.

Identities, primary truths, wear their identity character for all to see.  What indicates their truth is just this manifest identity itself (A is A).  If we make this criterion for  the truth of primary truths into a principle, the principle would itself be: A is A, the principle of identity.  The principle of knowledge of primary truths is nothing other than the most elementary of primary truths.  that is essential.  The criterion, identity, is itself the first truth and the source of truth (the cogito of Descartes).  Accordingly, we should note that this principle does not remain extrinsic to those cognitive statements for which it is the guiding principle.  Rather, it itself belongs to the statements as their first statement.

Leibniz:

"An absolutely necessary proposition is one which can be reduced to identities or onw whose opposite implies a contradiction...For whatever implies a contradiction, or whatever has an opposite that is necessary, is called impossibility"

Monadology

Criterion of necessary truths is, in accord with their essence, reducibility to identities.  reducibility to identities, however, denotes an accordance with identities.  What is not in accord but in discord with identities "speaks against" (contra-dicts) identities and contains a contradiction.  Reducibility  to identities denotes non-contradiction.  Whatever contains a contradiction is what cannot at all be, since essence denotes unessential and this denotes ideal essence--what basically cannot be is impossible.

On the other hand, since the principle of non-contradiction is at bottom the principle of identity, it cannot be restricted to a class of identities, but must be related to all identities, and therefore also to contingent truths.  In proving contingent truths we make no real use of the principle because it is impossible for us to carry out the reduction to identities.

Since truth is an essential characteristic of knowledge--false knowledge is not knowledge--the essence of truth, hitherto defined as identity, must become clear with the clarification of the idea of knowledge.