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

摘要

The evaluation of arguments was not the sole concern of logicians in ancient India. Early Nyya and the later Navya-Nyya provide an interesting example of the interaction between logic and ontology. In their attempt to develop a kind of property-location logic (Navya-)Naiyyikas 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 Naiyyikas and to some extent also Navya-Naiyyikas 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-Nyya work Updhidarpana is a proponent of a non-well-founded property concept. Despite certain similarities with sets properties are still regarded as intensional objects in Navya-Nyya. 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-Nyya property-location logic.