The idiom "不可理喻" is formed through a logical, four-character construction common in Classical Chinese: "不可" means "cannot" or "unable to"; "理" is "to reason with" or "to argue logically"; and "喻" is "to make understand" or "to enlighten". Thus, it builds sequentially, first establishing impossibility ("不可"), then specifying the action of applying reason ("理"), and finally targeting the goal of making someone comprehend ("喻"), to create the complete figurative meaning of "impervious to reason" or "so unreasonable that no argument can get through to them".