In this article, I explore the encounter of the Mādhva philosopher Vyāsatīrtha with the works of the Navya-Naiyāyika Gaṅgeśa Upādhyāya. The article is based on original translations of passages from Vyāsatīrtha’s Nyāyāmr̥ta and Tarkatāṇḍava. Philosophically, the article focuses on the issue of empty-terms/nonexistent entities, particularly in the context of the theory of inference. I begin by outlining the origin of the Mādhva and Nyāya positions about these issues in their respective analyses of perceptual illusion. I then contrast the role of (...) Gaṅgeśa’s thought in the Nyāyāmr̥ta and Tarkatāṇḍava and show how Vyāsatīrtha responds to Gaṅgeśa’s ideas in different ways in those texts. I conclude with a discussion of how Vyāsatīrtha defends the Mādhva theory of “substrate-free” qualities against Gaṅgeśa in order to show that we can think and make valid inferences about nonexistent things. (shrink)