I'm not sure that conceptual soundness has any meaning in fields which don't even in principle admit to predictive power or provably correct solutions. It might be possible to imagine a rigorous approach to, say, textual criticism, but in actual practice the work that gets done is approached along aesthetic lines, and the people running humanities departments seem aware of and happy with this.

Of course, this wouldn't apply to the related field of social science, and many of its subfields do seem to fail both of Vladimir's tests.