Is there a noun for when there are two or more feasible yet opposing explanations or interpretations of the same observations/evidence? For example, two people look at the arrangement of the balls on a billiard table. They each come up with separate scenarios of what occurred in the game to create the current arrangement. Both explanations are valid possibilities, however they oppose each other; they cannot both be true. One or both of them are incorrect.
So we might say, "My my, Dr. Geometrigonomestein, we have here a ___, for both explanations, while contradictory, are each quite complete and believable indeed."
Similar to the word "paradox", except that paradox refers to a seeming contradiction that turns out to be true, such as a beginner bicyclist finding it easier to ride fast rather than very slowly.
Really I'm thinking more about ideological frameworks where multiple frameworks can feasibly and thoroughly "make sense of the world", even though they can hardly both be true. (I find this phenomena fascinating.) (Though I recognize that there are also many cases where two seemingly opposed explanations can actually be reconciled as both true in different senses.)