Utpaladeva’s detailed commentary (the Vivṛti or Ṭīkā) on his own Īśvarapratyabhijñā treatise was certainly the most innovative text of the Pratyabhijñā corpus; unfortunately, however, to date we only have access to fragments of this work. We owe to Raffaele Torella the discovery, edition and translation of an important passage of Utpaladeva’s lost commentary (covering 13 of the 190 verses of the treatise) on the basis of a unique, very incomplete Vivṛti manuscript; but many more Vivṛti fragments have recently come to light. They were found in annotations written in the margins of manuscripts containing other Pratyabhijñā texts. The lengthiest of these newly discovered fragments covers three thus far entirely unknown chapters of Utpaladeva’s magnum opus, the first of which has been edited and translated by Isabelle Ratié in a monograph about to be published. The present article is part of a series of papers devoted to the edition, translation and explanation of shorter fragments found in the margins of manuscripts containing Abhinavagupta’s commentaries on Utpaladeva’s treatise. The first of these studies (“Some hitherto unknown fragments of Utpaladeva’s Vivṛti (I): on the Buddhist controversy over the existence of other conscious streams”, in R. Torella & B. Bäumer (eds.), Utpaladeva, Philosopher of Recognition, Delhi: DK Printworld, 2016, pp. 224-256) dealt with a fragment explaining verses 1.5.4-5; it focused on the Buddhist controversy between Vijñānavādins and Sautrāntikas over the existence of other conscious streams (santānāntara) and on the possibility of intersubjectivity if, as the Vijñānavādins claim, nothing exists outside consciousness. The paper included in the present volume deals with fragments of the Vivṛti on the following verses (1.5.6-9), which argue against the Sautrāntikas’ thesis that we must infer the existence of a reality external to consciousness in order to account for phenomenal variety. In these fragments Utpaladeva shows not only that, as already emphasized by the Vijñānavādins, postulating the existence of an external world is of no use in the realm of everyday practice, and that an external object must have contradictory properties whether it is understood as having parts or not, but also that the very act of mentally producing the concept (and therefore the inference) of an external object is in fact impossible to perform, because an object by nature alien to consciousness is simply unthinkable. Text available here: https://paris3.academia.edu/IsabelleRati%C3%A9.