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Negative Existentials and Non-denoting Terms
Paul Schweizer
Institute for Language, Cognition and Computation
School of Informatics, University of Edinburgh
paul@inf.ed.ac.uk
Abstract.
Logical and semantical issues surrounding non-denoting terms have
been investigated since ancient times, in both the Western and Indian philo-
sophical traditions. And in a more applied formal setting, such issues have also
gained importance in constructive mathematics, as well as computer science
and software engineering. The paper first presents a strategic exploration of log-
ical treatments of reference failure in Western thought, and then goes on to pro-
vide a comparative examination of the issue in the Indian tradition, particularly
with respect to the dispute between the Yogācāra-Sautrāntika school of Budd-
hism and the Nyāya school of Hinduism. The paper concludes by advancing a
formalization of the Buddhist
apoha
semantical theory in terms of a dual-
domain Free logic.
1
The Analysis of Non-existence in Western Logic
It is a distinctive feature of human language and thought that we can introduce terms
purporting to designate some object or entity in the world, but where no such object
or entity exists. And we can then go on to use such terms to make grammatically well
formed assertions which appear to be
meaningful
, and indeed many of these meaning-
ful assertions about non-existent objects seem to be either
true
or
false
. This pheno-
menon poses some deep challenges for philosophy and logical theory which have
been recognized and investigated since ancient times, in both the Western and Indian
traditions. And in a more applied formal setting, such issues have also gained impor-
tance in constructive mathematics, as well as computer science and software engi-
neering. In the context of ancient Greek philosophy, a well known version of the
problem is articulated in Plato's riddle of non-being, often referred to as the predica-
ment of 'Plato's beard'. Let us suppose that Plato was always a clean shaven individual
and never sported facial hair. In such a case, we would seem to be asserting a true
proposition with the negative existential statement 'Plato's beard did not exist'. But if
Plato's beard did not exist, then exactly what are we talking about when we say that he
didn't have one? And how can we make any coherent assertion involving the term
'Plato's beard' when, by hypothesis, it fails to denote? Even the cogency of the see-
mingly innocent 'Plato did not have a beard' seems threatened.
