 The proponent wants to answer that \(A\) is a set, which would trigger material considerations (is \(A\) a set or not?). See below for material dialogues  (Section 3.2.4).  In order to avoid (for whatever reason) these material considerations, initial concessions may be added to the thesis in square brackets, for instance \(A: \bset\). When accepting to play, the opponent also accepts these concessions for the sake of the argument.