Any interdisciplinary programme faces the problems
whether the multiple disciplines brought together
really have any points of contact among them and
to what extent will they be benefited from the
pursuit of one another. The International Conference
on Logic, Navya-Nyaya and Applications: A Homage
to Bimal Krishna Matilal is likely to face such
questions too. The assembly of scholars will try
to seek answers to such issues in the context
of modern logic and the ancient Indian system
of Navya-Nyaya.
Logic originated as a branch of knowledge in ancient
cultures like the Indian or Greek within the ambit
of philosophy. In each culture investigations
into the principles of valid inference (or logic)
had been one of the main concerns of knowledge.
In Greece it was in the form of syllogism while
in India these were included within the Nyaya
system. With the development of the Navya-Nyaya
school in the fourteenth century, logic in India
became relatively formal. In the West, logic continued
to be a branch of philosophy until Leibniz and
later Boole initiated a mathematical way of 'doing'
logic. Since then mathematicians and philosophers
developed modern symbolic logic deriving motivations
and methods primarily from mathematics and foundational
questions of mathematics. Logic turned out to
be mathematical in which it adopted symbolic language,
formalistic method and objectivity in attitude.
Gradually it has been integrated with other branches
of mathematics e.g. model theory, descriptive
set theory and non-standard analysis. Since the
later half of the last century computer scientists
have taken a significant role in the development
of logic. Computer science has not only given
rise to new logical issues but has also suggested
new devices to answer them. It is primarily because
of these interventions that logic has become so
diversified in our times. Nowadays we do not talk
of Logic, but of 'logics'. Besides intuitionistic
logic, many-valued and modal logics which had
their beginnings earlier, there are now numerous
logic-systems such as non-monotonic logics, fuzzy
logics, linear logics, temporal logics, paraconsistent
logics, free logics, rough logics and the like.
Besides, there are areas of computer applications
of logic such as artificial intelligence, logic
programming, model checking etc. Classical techniques
(e.g. proof-theoretic ordinals) and new ones (e.g.
games) are used for the analysis of logics appearing
in computer science. Many of the new logics not
only have computer applications but also give
rise to important philosophical issues.
Navya-Nyaya cannot be considered as formal
logic in the sense of present times. It is an
offshoot of the Nyaya system which was originally
intended to be a comprehensive philosophy having
an ontology of its own. The logical apparatus
and the analysis of language developed by the
Nyaya system were originally devised to lend
support to this ontology. But the Nyaya techniques
of drawing conclusions from given premises and
the Nyaya way of analyzing language were borrowed
by the other systems of Indian philosophy. This
suggests that the Nyaya system has a formal
core which is relatively, if not absolutely,
independent of its ontological commitments and
can be applied to entirely different contexts.
The system of Navya-Nyaya includes elements
of both deductive and inductive logics, it was
seriously concerned with the issue of empirical
generalization and was concerned not only with
the end-products of reasoning but also with
the process of human reasoning.
There have been several attempts to understand
Navya-Nyaya in modern terms, for example in
terms of First-order Predicate Logic or Graph
Theory, and at the same time short-comings of
these approaches have also been pointed out.
In what sense, then, the term 'logic' may be
applied to such an Indian system of philosophy?
Bimal Krishna Matilal, to whose memory this
conference is dedicated, a pioneer in this field
of research, answered thus, " 'Logic' I
shall here understand to be the systematic study
of informal inference-patterns, the rules of
debate, the identification of sound inference
vis-à-vis sophistical arguments, and
similar topics" (Introducing Indian Logic,
in Indian Logic: A Reader ed. Jonardan Ganeri,
Curzon Press, 2001, p.183). The main objective
of his studying an ancient Indian system such
as Navya-Nyaya was to explain its significance
and relevance to modern discussions in the area
called "philosophical logic". Issues
in philosophical logic like those of ontological
commitments, existence and truth are also addressed
by Navya-Nyaya. This opens up the possibility
of an interface between the approaches and conclusions
of the different traditions.
This conference is homage to Bimal Krishna
Matilal who was one of the few thinkers who
devoted major part of his philosophical career
to initiating meaningful dialogues between the
philosophical traditions of the East and the
West.
One of the immediate occasions of holding this
conference is the fifteenth commemoration of
the untimely demise in 1991 of Bimal Krishna
Matilal. The other immediate occasion is to
hold a conference as a sequel of the First
Indian Conference On Logic And Its Relationship
With Other Disciplines from January 8 to 13,
2005 at the Indian Institute of Technology,
Bombay. The conference devoted itself
to modern as well as ancient Indian logics.
It was an extremely successful International
Conference in which it was proposed that the
next one be held in Kolkata in 2007 and a logic
school be held in between. Accordingly, an International
winter school in logic was organized in January,
2006, at the same venue. Holding this conference
in its conformity with the proposal taken at
Bombay perfectly fits in achieving both the
above mentioned objectives.
The present conference will address the following
topics and related issues in a balanced manner:
