The main idea animating the present paper is that the general aim of debates, such as the one involving the notorious case of the Master Argument, is the ponderation of logical principles by confronting them with some set of assertions and other endorsed principles on the meaning explanation of connectives, quantifiers and modality. As suggested by Seel (2017), the point of the specific case of the MA is about examining Aristotle’s notion of possibility – as implemented by the Possibility Principle (i.e., If it is necessary that if A then B, then B is possible if A is) and the Possibility Rule (i.e., If A is possible, and if B follows from the assumption of A, then B is is possible) in the context of a dialectical debate where it has been asserted that a given proposition is possible, even it is neither true now nor it will ever be, and where at the same time the irrevocability of the past has been endorsed. This suggests to study the MA debate in a setting based on Marion’s (2020) reconstruction of Aristotle’s Dialectical Bouts, adapted to propositions affected by modalities. The setting of Dialectical Bouts for the MA proposed includes •Propositions affected by Reichenbach’s (1948, § 5) three-folded temporal reference, namely: the point of speech S, the point of reference R and the point of the event E. This constitutes our take on Vuillemin’s (1977, 1979, 1984, 1996) suggestion of a “double indexation”. •The dialogical meaning explanation for modalities understood as involving hypotheticals. •The dialogical rules that settle the commitments undertaken when endorsing Aristotle’s Possibility Principle. In fact, in relation to the notion of possibility at work in Vuillemin’s (1996) reconstruction we explored different formulations of the Possibility Rule. Still, there remains a dearth of researches confronting the different formulations of the Possibility Rule with the texts studied by Crubellier (2010) and Rosen and Malink (2012). More generally and coming back to my remarks above, one of the most fruitful insights that can be gained from Vuillemin’s writings on the MA, is that such kind of debates provide an instance of a general pattern for reasoning that I shall call Dialectical Bouts of Material Admissibility (BMA). The rationale behind such kind of argumentation-pattern is to examine the incorporation of new (epistemological, ontological or logical) principles against the background of the commitments undertaken by endorsing a specific set of assertions and meaning explanations. They display the kind of abductive procedure stressed by Crubellier’s (2014) study of syllogism. Under this perspective Ebbinghaus’s (1964) casting of the inferential moves that reduce imperfect syllogisms to perfect ones as implementing an admissibility procedure, represents a logical generalization of the material procedures at stake in the Dialectical Bouts of Material Admissibility. Furthermore if, as stressed by Duthil-Novaes (2005) Medieval Obligations represent a development of Aristotelian Bouts aimed at the ludic exercise of consistency maintenance, DMA should be rather linked to the Islamic tradition of dialectical theory [jadal, munāẓara, ādāb al-baḥth], aimed at the epistemological task of what Young (2017) calls the forging of principles, including legal and deontic ones. In a more contemporary setting, DMA can be related to Brandom’s (2000, pp. 66-77) considerations on Non-Conservative Extensions, where the point of dialectical procedures is put under public Socratic scrutiny the discovery and elucidation of concepts. This general point on Dialectical Bouts of Material Admissibility can be seen as underlying Vuillemin’s project of linking the study of the MA with the classification of philosophical systems. The present paper does not contain a fully developed study on such Dialectical Bouts, but it is rather is an invitation to pick up the gauntlet that Jules Vuillemin threw into the ring.