Negation in Intuitionistic Logic and Navya Nyaya

Very often western scholars on Philosophy express a prejudiced view that the Indians are never really interested in Philosophy, they are interested in religion. They bear this misconception because their knowledge of Indian philosophy is limited only to translation of some religious texts. But Indian Philosophy has its rationalistic literature, a literature that deals with mathematics, astronomy, grammar, semantics and logic. Even the multi facet Vedanta has a strong resemblance with non theological rationalists. Of special importance in this respect however, is the literature of the Navya Nyaya for that school is specialized in epistemology, logic and semantics. That is why the author has taken pains to systematize intuitionistic logic, negation and Navya Nyaya. The book opens with the critical examination of classical two-valued logic, goes through matrix method, logic and finally examines critically the concept of negation in general and intuitionistic negation and negation of Navya Nyaya in particular.

Ms. (Dr.) Bani Sengupta is a reader in Philosophy in S.K. University (Bihar) where she has been teaching logic in higher classes for the last 25 years. She is deeply engrossed in the study and research in symbolic logic, which is her choice subject. She has contributed a number of research papers in various national and international conferences and seminars. The present book is the outcome of her research work in the field of symbolic logic and Navya Nyaya. She proposes to publish a series of her work in symbolic logic in the near future and some of them are already in the pipeline.

The book Negation in Intuitionistic Logic and Navya-Nyaya by Dr. (Ms.) Bani Sengupta is a laudable attempt to organize the various aspects of the complex problem of negation. Her attempt has already been appraised and vindicated by the evaluators of her thesis on which she got her Ph.D. degree of which this work is the modified version. The study of the problem of negation is one of the most important problems of Philosophy because it involves many logical, epistemological and metaphysical aspects. The problem has been treated differently in various systems of Indian and Western Philosophy. The problem is so typical and deep-rooted that the solution provided by different systems to it, even determines the shape and nature of the systems itself. When this issue is taken up, many question crop up. What is the meaning and nature of negation? On what is it based? What is the status of negation? What is the way of knowing it and what can be negated, what cannot? Answer to each of these questions form integral part of the different systems of philosophy. There is a controversy on each of these issues which is not only between the two different systems but there is intra-system controversies among them too.

The problem of negation includes various issues such as assertions about the knowledge of negation, the status of the negated and the question of the possibility of universal negation etc. On the basis of in depth analysis undertaken so far it can be averred that negation is primary and simple. It can neither be derived nor defined; every attempt to do so can be shown to pre suppose it. Controversies on each of the questions related to it can very well be debated, asserted and controverter but affirmation-negation framework is always there as 'operation of denial', although the scope for its exaltation as 'negation matrix' (B.K. Motilal, Logic, Language and Reality, pp. 126-27) for its logical explanation is always wide open.

Logic is the systematic study of the structure of propositions and of the general condition of valid inference by a method which abstracts from the content or the matter of the propositions and deals only with their logical form. This distinction is made when we distinguish between the logical soundness and a validity of a piece of reasoning and the truth of the premises, from which it proceeds and in this sense is familiar in everyday usages.

A precise statement of the distinction made with reference to a particular language or system of notation, a formalized language which shall avoid the exactness and systematically misleading irregularities a structure and expression that are found in ordinary languages and shall follow or reproduce the logical form at the expense, where necessary. To adopt a particular formalized language is to adopt a particular system of logical analysis.

The formal method may be defined by saying that it deals with the objective form of sentences which express proposition and provides criteria of meaningfulness and of other notions associated with these notions of logical compatibility, analytic of logical truth Logic has been described as modal logic too. Historically logic has been divided into four school of thought namely:

(a) Traditional school of logic as represented by Aristotle.

(b) Idealistic or metaphysical school of logic as represented by F.H. Bradley or others.

(c) Pragmatic school of logic as represented by Schiller, and

(d) Modern school of logic as represented by Russell, Whitehead, Stabbing and other. This school of logic is also known as realistic school of logic or mathematical school of logic or modern school of logic.

Traditional school of logic is that part of the ancient and medieval logic which survived the decline of scholasticism and long remained with little change as the traditionally important part of philosophy. It is exhibited as a part of modern logic. In traditional school of logic all the propositions are expressed in the subject predicate form because it deals with the proposition only The traditional school is the oldest school where assertion is made about the ideas through the language.

In Idealistic school of logic we do not find a clear cut line of demarcation between form and matter. This school maintains that our units are ideas, are not thinkings, but they are judgements. Ideas constitute the material of our judgement but from metaphysical point of view, it is the judgement which is the unit of thought. This school differs from the traditional school of logic because idealistic school accepts single idea in a judgement, on the contrary, traditionally there are two ideas in a judgement Single idea of idealistic school is a logical idea and it is the content of a judgement. The distinction between the two schools is regarding the method of analysis.

**Contents and Sample Pages**