This article seeks to introduce a greater degree of precision into our understanding of Madhyamaka Buddhist ontological non-foundationalism, focussing specifically on the Madhyamaka founder Nāgārjuna (c. 150–250 CE). It distinguishes four senses of what the ‘foundation’ whose existence Mādhyamikas deny means; that is, (1) as ‘something that stands under or grounds things’ (a position known as generic substantialism); (2) as ‘a particular kind of basic entity’ (specific substantialism); (3) as ‘an individual essence (a haecceity or thisness of that object) by means of which it is identical to that very object, to itself’ (modal essentialism); and (4) as ‘an essence in the absence of which an object could be of a radically different kind or sort of object than it in fact is’ (sortal essentialism). It then proceeds to delineate the Madhyamaka refutation of the specific substantialist position in terms of its argued denial of dharma as basic entity; of generic substantialism and modal essentialism in terms of its argued denial of svabhāva as both foundation for and essence of putative entities; and of sortal essentialism in terms of its argued denial of essentialist conceptions of conceptual thought (vikalpa), mental construction (prapañca), and in short the entire domain of ratiocination (kalpanā), by means of its notion of conceptual imputation (prajñaptir upādāya)—a denial strictly speaking ontological, but of what are putative epistemic entities. The final portion of the article explains the relationship of ontological to other forms of non-foundationalism according to Madhyamaka.