It is often worthwhile to listen to intelligent people, even if they are fantastically wrong about basic facts of the very subject that they're discussing. One often hears someone reasoning within a context of radically wrong assumptions. A priori, one would expect such reasoning to be almost wholly worthless. How could false premises lead to reliable conclusions?

But somehow, in my experience, it often doesn't work that way. Of course, the propositional content of the claims will often be false. Nonetheless, within the system of inferences, substructures of inferences will often be isomorphic to deep structures of inferences following from premises that I do accept.

The moral reasoning of moral realists can serve as an example. A moral realist will base his moral conclusions on the assumption that moral properties (such as good and evil) exist independently of how people think. His arguments, read literally, are riddled with this assumption through-and-through. Nonetheless, if he is intelligent, the inferences that he makes often map to highly nontrivial, but valid, inferences within my own system of moral thought. It might be necessary to do some relabeling of terms. But once I learn the relabeling "dictionary", I find that I can learn highly nontrivial implications of my premises by translating the implications that the realist inferred from his premises.