The Problem of Foundation in Early Nyāya and in Navya-Nyāya
History and Philosophy of Logic, 2014
The evaluation of arguments was not the sole concern of logicians in ancient India. Early Nyāya a... more 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 Upādhidarpan. a 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.
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