organisms, although this does not mean that the ontology of vague objects is
uncontested. Vague objects can be conceived as persisting through time and
being identical with themselves only in the non-Leibnizian sense that they have
temporal parts. They are comparable to social entities such as cities, political
parties, nations, and tribes, which lack sharp boundaries as the relations of
membership in these entities is indeterminate. Fuzzy logic attempts to make up
for the shortcomings of classical logic, while holding on to a concept of identity
which, while admitting vagueness, is still based on the individual.
Non-Western approaches
As the discussion so far has shown, the question of identity in logic cannot easily
be separated from the question of a coherent worldview. It is not surprising,
therefore, that outside classical logic we find different conceptions of ‘identity’.
In Buddhist philosophy as developed by Dignāga (480 CE–540 CE) and
Dharmakīrti (died 660 CE), for example, identity plays a role as identity of
essence and identity of extension, much as in Frege’s logic of sense and
reference. However, the thinking on which these concepts rest is distinctive.
In the Aristotelian tradition, the individual is the basis of all classification and
hence of all thought. The problem of vagueness leads to the somewhat artificial
construction of the self-sameness of individuals that persist through time by
virtue of having temporal parts. In Buddhist logic, by contrast, the
impermanence of all being is the point of departure. Like Western thinkers,
Buddhist philosophers grappled with the problem of how cognition, language,
and the world are related; however, unlike the former, the latter do not take as
given the ‘world out there’, and they do not proceed from the assumption that its
secrets are for us to uncover. Ultimate knowledge of the material world is not
possible. A consequence for the notion of ‘individual’ acknowledged by many
Buddhist philosophers is that, rather than being characterized by positive
properties, the individual is characterized negatively. The doctrine of non-self
(Sanskrit anātman) is at the heart of identity (Sanskrit tādātmya).
Identity is established by exclusion:
(7) ,
x is not not-x.