Appearing to Contradict?

In a previous post, I have made use of the idea that some propositions appear to contradict one another. In another post I implied that any appearance of contradiction is identical to an actual contradiction. These two ideas can be explained by explaining what an apparent contradiction is and how it is different from an actual contradiction.

An actual contradiction is simple. A and not-A is a contradiction. Any set of propositions that generate that are also contradictory. So is any set of propositions conjoined with a logically necessary truth, or a conceptually necessary truth. For example, the propositions this square is red all over and this square is green all over form a contradictory set because it is a conceptually necessary truth that no square can be red all and green all over at the same time.

An apparent contradiction cannot be any set of first-order propositions. Any such set would either be contradictory, or it would be consistent. The appearance of contradiction in such a set would be the same as the reality.

Because of this, an apparent contradiction must contain second-order propositions. Not only this, but at least some of them must be about which proposition a certain sentence expresses. Let's consider the example of the doctrine of the Trinity. Any such doctrine states the sentence that "God is one". It also states that "God is three". Any first analysis of these sentences takes them to be stating the propositions God is one unit and God is three units. These propositions form a contradictory set along with the logically necessary truth if something is one unit then it is not three units. So if the doctrine of the Trinity is not a contradiction, then those sentences cannot express the propositions that they appear at first to express. Yet this is a second-order proposition about what propositions are actually expressed by a sentence! In fact, any Trinitarian believer believes that the "is" of the first sentence, and the "is" of the second are not the same relation. This does not tell us what the Trinitarian doctrine is, but what it is not. It is also the second-order proposition used in order to avoid having two sentences express contradictory propositions.

An apparent contradiction is not a contradiction at all. It is a set of sentences that appear to express a set of contradictory propositions, but are believed to express a different set of propositions instead. Without the second-order belief, one would be believing in a contradiction.