This is because inconsistent theories prove everything, including their consistency.

As a result, paraconsistent logics, unlike classical and other logics, can be used to formalize inconsistent but non-trivial theories.

In non-paraconsistent logics, there is only one inconsistent theory: the trivial theory that has every sentence as a theorem.

Paraconsistent logic makes it possible to distinguish between inconsistent theories and to reason with them.

Paraconsistent logic has been proposed as a means of reasoning with and revising inconsistent theories and belief systems.

The result, however, would likely be hundreds, if not thousands, of lawsuits around the country, many of them on inconsistent theories and providing inconsistent results.

Examples: theories with a finite model, and the inconsistent theory.

Since the world is full of many mutually inconsistent theories, the combination of disagreements between them is multidimensional.

We cannot say what blundering systems were broached, what inconsistent theories advanced by these bold spirits.

Thus both options lead us to a contradiction and we have an inconsistent theory.