Here it is argued, with the help of Tsongkhapa's interpretation of Candrakīrti's theory of persons, and on the basis of the character of Vasubandhu's encounter with the Pudgalavādins in the "Refutation of the Theory of Self," that in his Madhyamakāvatārabhāṣya. Candrakīrti most likely identifies the theory of persons he attributes to the Sāṃmitīyas with the theory of persons Vasubandhu presents in the "Refutation," and the theory of persons he attributes to the Āryasāṃmitīyas with the Pudgalavādins' theory of persons, to which Vasubandhu objects in that same work. He interprets Vasubandhu's thesis, that persons exist as their aggregates, as the thesis of the Sāṃmitīyas, that persons possess the essence of the aggregates, and interprets the Pudgalavādins' thesis, that persons exist apart from their aggregates as their identity-free substratum, as the thesis of the Āryasāṃmitīyas, that persons possess an essence of something that is neither other than nor the same as the aggregates. It is explained that Candrakīrti's interpretations both rest on the assumption that existence is the possession of an essence and mirror the assumptions upon which Vasubandhu and the Pudgalavādins object to one another's thesis.