What if in discussion the critic refuses to recognize an emotionally expressed (alleged) argument of her interlocutor as an argument, accusing him of having presented no argument at all. In this paper, we shall deal with this reproach, which taken literally amounts to a charge of having committed a fallacy of non-argumentation. As such it is a very strong, if not the ultimate, criticism, which even carries the risk of abandonment of the discussion and can, therefore, not be made without burdening oneself with correspondingly strong obligations. We want to specify the fallacies of non-argumentation and their dialectic, i.e., the proper way to criticize them, the appropriate ways for the arguer to react to such criticism, and the appropriate ways for the critic to follow up on these reactions. Among the types of fallacy of non-argumentation, the emphasis will be on the appeal to popular sentiments (argumentum ad populum). Our aim is to reach, for cases of (alleged) non-argumentation, a survey of dialectical possibilities. By making the disputants themselves responsible for the place of emotion in their dialogues, we hope to contribute to a further development of the theory of dialectical obligations.