1 An example of incoherent is an essay that changes positions halfway through. 2  An example of incoherent is a person who talks nonsense and makes no sense. 3  An example of incoherent is something written or said by a person who has only a very limited grasp of the language in which he is speaking. An example of incoherent is an essay that changes positions halfway through. 2  An example of incoherent is a person who talks nonsense and makes no sense. 3  An example of incoherent is something written or said by a person who has only a very limited grasp of the language in which he is speaking.