This study comments on six notabilia found in the general observations with which Brinkley begins his treatise on supposition in his Summa logicae: i) the logico-metaphysical explanation of the distinction between significatio and suppositio, ii) the ontic division principle of supposition, iii) the relationship between supposita and truth-makers, iv) what seems to be a late resurgence of natural supposition, v) a pragmatic suspension of the regula appellationum and vi) Brinkley’s apparently incompatible claims that there are communicable things and that there (...) are only singular things, a position that is a medieval form of immanent realism. Based on the two manuscripts that contain the treatise on supposition, an appendix offers a provisional edition of part of Brinkley’s Summa, a collaboration between the author and Joël Lonfat. (shrink)