unanswerable

adj

1. Not answerable; impossible to answer.
2. Impossible to dispute or rebut; irrefutable; conclusive.

   “If I have not said much about it before, it was, of course, that the Professor's earnest desire was that no possible rumor of the unanswerable argument which we carried should be allowed to leak out until the moment came when his enemies were to be confuted.”

   “The map is never an unanswerable argument in transportation.”

noun

1. Something that cannot be answered.

   “These unanswerables are left open to the viewer's own construction by the sculptor.”