Aristotle determines eristic argument as argument which either operates upon the basis of acceptable premisses (ἔνδοξα) and merely give the impression of being deductive, or argument which truly is deductive but operates upon the basis of premisses which seem to be acceptable, but are not (or, again, argument which uses both of these mechanisms). I attempt to understand what Aristotle has in mind when he says that someone is deceived into accepting premisses which seem to be acceptable but which are really not, and how this disqualifies such arguments from being dialectical. In the first section of the paper I interpret Aristotle’s notion of ἔνδοξα in terms of a relational concept of acceptability. Real ἔνδοα are propositions which are accepted by a qualified group or individual. False ἔνδοα may also be accepted by someone or some group, and may even be true, but they are used to serve the purposes of eristical argumentation, which departs from certain standards of dialectical argumentation articulated in the notion of ἔνδοξα as a norm for premiss-acceptance. In particular, eristic arguments may even be valid in the sense of a συλλογισμός while still failing to be proper dialectical arguments. In the second part of the paper I consider how this can be, in examining certain types of fallacies in the Sophistical Refutations and the relationship between fallacious argumentation and false ἔνδοξα.