In the crime novels by Sir Arthur Conan-Doyle, central character, detective, Sherlock Holmes described his approach to evidence-analysis as the discarding of the impossible; then, whatever remains, however unlikely, must be the truth.
How to express this in Latin?
an ablative absolute: "impossibilibus missis" = "with the impossible (things having been) discarded";
"quodcumque manet (originally, quodcumque relinquit)" = "whatever remains"; (An interesting debate [Comments] on the passive/ active forms of "relinquo" unfolded. A case can be made for either.)
"quantalibet incredulitas" = "no matter how great the disbelief";
a neuter, impersonal gerundive: "deinde est credendum" = "then it-ought-to-be-believed"/ "then it must be believed"/ (using English impersonal pronoun "one") "then one must believe (it).
Alternatively, result clause: "ut id crederetur" = "so it is to be believed" --this does not provide the element of obligation.
"impossibilibus missis, quodcumque manet, quantalibet incredulitas, deinde est credendum" =
"With the impossible discarded, whatever remains, no matter how great the disbelief, then it must be believed."
Is this correct?