For this mutual entailment yields four conclusions: the existence of one entails the existence of the other; its absence entails the absence of the other; the existence of the other entails the existence of the first; and its absence entails the absence of the first.

This is what logicians call a connected conditional syllogism. They say that affirming the antecedent yields the consequent, and denying the consequent yields the denial of the antecedent. When entailment operates in both directions, affirming either of the mutually entailing terms yields the affirmation of the other, and denying either yields the denial of the other.

The explanation in this case is as follows: if reason is the foundation by which the validity of revelation is known, as they themselves have stated, then, as explained above, calling it a foundation does not mean that revelation depends upon it for its actual existence or intrinsic truth. Rather, it is the foundation of our knowledge of revelation—that is, evidence for us of its validity.

If that is so, it is well known that the implication from the evidence must hold invariably in the forward direction: the evidence entails what it proves. Thus, the existence of the evidence entails the existence of what it proves. The converse, however, need not hold: the absence of the evidence does not entail the absence of what it proves.

Created beings illustrate this, for they are a sign of the Creator. Their existence entails the existence of the Creator, but the existence of the Creator does not entail their existence.