The following pages, which do not constitute either a treatise or a text-book, are addressed, primarily, to Indian audience in the departments of philosophy and mathematics in our univer-sities and colleges. Even if I refrain to be apologetic, it would be immodest not to admit that, being a self-instructed indivi-dual, I do not have either the requisite scholarship to write a treatise, or the necessary talent to work out a text-book. More-over, there are several treatises and text-books, which are easily available to Indian readers, and which I cannot replace. However, this monograph will be of some use to those who have taken to logical studies, by being, as I believe, a good supple-ment to many a text-book, and a preliminary to the most important treatises. In working it out, I kept in mind the requirements and the equipment of philosophers and mathe-maticians in this country. I had an opportunity to make my own assessment of these when I was lecturing to the teachers of philosophy in our colleges and universities, first at the Summer School in Logic organised by the University of Rajasthan, and later on at the Winter School in Philosophy organised by the University of Delhi. Subsequently I offered a fairly advanced course in logic to students whose primary interest was philosophy and had no training in mathematics, and also some students of similar interest but with sufficient training in mathematics though not in logic. Working with that batch of students, which, in terms of the prevailing standards, is a fair sample of the best students in the country, I found that none of the mono-graphs available to us could be used in that course. The excellent monographs of Church, Kleene, Novikov and others are too comprehensive and exhaustive to be suitable to class rooms in our universities. They contain more than what an Indian student can take in, in a single course. There are other works of moderate comprehensiveness which are popular in our academic circles, for instance Irving Copi's Symbolic Logic whone first edition has been adapted as compulsory reading material after it has been found to be defective and the second revised edition, which is not however free from blemishes, has been kept in the market. This, despite its merits, is prohibitive in cost, and also is rather inelegant in the treatment of the subject, especially in the later half. And the two works which are available in fair-price Indian editions, namely those of Hughes and Londey, and Stoll, are also not suitable to our needs. The former does present all the material that we would like to impart to our students at the post-graduate level, but does not present it with the sophistication that the present day logical writing has come to achieve. The latter does meet the needs of our mathematicians interested in foundational studies, but not the needs of our philosophers interested in logic, though it would be of great help to them in under-standing the basic concepts of pure mathematics. But it is possible to meet the needs of philosophers in this country, by supplementing it with some additional metatheoretic material relating to sentential calculus and first order functional calculus.
This is precisely what I had in my mind when I started scribing what is contained in the following pages. This modest venture of mine received a setback. I had to keep it in abeyance for some time, as (having realised that the conditions in our colleges and universities are not conducive to any creative and context-oriented teaching that is relevant to our academic situation and Our academic goals) I preferred to be an academic drop-out. A ubsequent vicissitude in my academic fortune induced me to ake it up again, and make another attempt to see whether I ould tag my work to the academic needs of the country. This farch when I joined the Indian Institute of Advanced Study a Fellow, I found that I have sufficient time and resources to give it a near-finishing touch, despite my preoccupation with my research project in philosophy of logic. And when the Director of the Institute Professor Niharranjan Ray came forward to take it up for publication, I was delighted at the prospect of a native academician like me of being some use to our academic circles in meeting their needs, even if the result were to be a mere drop in the bucket. I should add that the following pages would have been blank but for my students Madhu, Vatsala, Sulabha, and Harischandra. They ventured, for the first time in the logical wilderness that our country today is, to do some logic, and thereby tempted me to experiment. How patient they were with, and how much confidence they kept in, my experiment! They, indeed, are my teachers, for they made me learn myself so that I may teach them what I learnt. I am thankful to the helpful and accommodative printers for decoding my illegible manuscript to present it in legible print.
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