``The absence of the difference from a pot is potness'' -- Axiomatic Proofs of Theorems Concerning Negative Properties in Navya-Ny\=aya

Abstract

The present paper deals with an aspect of the Navya-Ny\=aya ``logic of property and location'' (Matilal) in classical Indian philosophy, namely the so-called ``absences'' (\textit{abh\=ava}). Following George Bealer (\textit{Quality and Concept}, Oxford 1982) we may regard these negative properties as the result of applying certain algebraic operations to property terms, which Bealer names after their corresponding propositional or first-order operations (``negation of a property'', ``conjunction of properties'', ``existential generalization of a property'' etc.). Bealer introduces these operations in his property theories in order to explain how the denotation of a complex property term can be determined from the denotation(s) of the relevant syntactically simpler term(s). An interesting case in Navya-Ny\=aya is the ``conjoint absence'' (\textit{ubha\-y\=a\-bh\=a\-va}), which can be regarded as the Sheffer stroke applied to property terms. We will show that an extension of Bealer's axiomatic system T1 may serve to prove some of the Navya-Naiy\=ayikas' intuitions concerning iterated absences, such as ``the relational absence of the difference from a pot'', ``the relational absence of the relational absence of a pot'' or ``the relational absence of the relational absence of the relational absence of a pot''. The former, e.g., was claimed to be identical to the universal ``potness''.

Keywords

• Indian logic
• Navya-Ny\=aya
• intensionality
• property theories
• negation.