Authors: Eberhard Guhe
Keywords: Indian logic, Navya-Nyāya, intensionality, property
theories, negation.
Abstract
The present paper deals with an aspect of the Navya-Nyāya "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-Nyāya 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-Naiyāyikas'
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".
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