Word for two or more feasible yet opposing explanations for the same observations?

Question

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.)

Answer 1

I think the expression competing explanations fits the bill here. It's a common-enough way of expressing the idea that there are multiple explanations for some phenomenon, each (at least as far as our state of knowledge at the time of expression goes) with some merit and some likelihood of being correct.

In OP's sentence we might replace the underscores thiswise:

My my, Dr. Geometrigonomestein, we have here a competition, for both explanations are quite complete and believable indeed.

Answer 2

If two hypotheses to a described phenomenon are both plausible but do exclude each other - i.e. only one is or can be true - the hypotheses contradict each other, or are contradictory.

Synonyms include: opposition, opposite, antithetical, contrary, contrasting, conflicting, at variance, at odds, opposing, clashing, divergent, discrepant, different; inconsistent, incompatible, irreconcilable

Answer 3

dualidox for two remarkably plausible yet contradictory beliefs or hypotheses; pluralidox for more than two.

...with the disclaimer that I'm taking the liberty to coin new words ;) . Otherwise phrases such as "competing explanations" or "two equally plausible but incompatible explanations", as suggested by High Performance Mark and JD2000.

Answer 4

Antithesis

a contrast or opposition between two things.
"the antithesis between occult and rational mentalities"

from Oxford Online Dictionary.

The competing frameworks are antithetical.