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The Problem of Foundation in Early Nyāya and in Navya-Nyāya

The evaluation of arguments was not the sole concern of logicians in ancient India. Early Nyāya and the later Navya-Nyāya provide an interesting example of the interaction between logic and ontology. In their attempt to develop a kind of property-location logic (Navya-)Naiyāyikas had to consider what kind of restrictions they should impose on the residence relation between a property and its locus (which might again be a property). Can we admit circular residence relations or infinitely descending chains of properties, each depending on its successor as its locus? Early Naiyāyikas and to some extent also Navya-Naiyāyikas regard these phenomena as a kind of absurdity and they want to rule them out. Their intuitions about properties are close to well-founded systems of set theory, whereas the author of the Navya-Nyāya work Upādhidarpaṇa is a proponent of a non-well-founded property concept. Despite certain similarities with sets properties are still regarded as intensional objects in Navya-Nyāya. In the present article I demonstrate that a Quine/Morse-style extension of George Bealer's property calculus T1 (with or without a property adaptation of the axiom of regularity) may serve as a formal system which adequately mirrors the Navya-Nyāya property-location logic.