The significance of mathematical logic: words of Alfred Tarski

Reference: Introduction to Logic, and to the Methodology of Deductive Sciences by Alfred Tarski, Oxford University Press, New York; available in Amazon India.

Just my two cents worth: Of course, Euclid introduced the deductive method about 2500 years back. Prof Tarski says there is more to it 🙂

(below I just present his motivational explanation in the preface, 1937 A.D)

In the opinion of many laymen mathematics is today already a dead science; after having reached an unusually high degree of development/sophistication, it has become petrified in rigid perfection. This is an entirely erroneous view of the situation; there are but few domains of scientific research which are passing through a phase of such intensive development at present as mathematics. Moreover, this development is extraordinarily manifold: mathematics is expanding in all possible directions, it is growing in height, in width, and in depth. It is growing in height, since, on the soil of its old theories which look back upon hundreds if not thousands of years of development, new problems appear again and again, and ever more perfect results are being achieved. It is growing in width, since its methhods permeate other branches of sciences, while its domain of investigation embraces increasingly more comprehensive ranges of phenomena and ever new theories are being included in the large circle of mathematical disciplines. And finally it is growing in depth, since its foundations become more and more firmly established, its methods perfected, and its principles stabilized.

It has been my intention in this book to give those readers who are interested in contemporary mathematics, without being actively concerned with it, at least a very general idea of that third line mathematical development, that is, its growth in depth. My aim has been to acquaint the reader with the most important concepts of a discipline which is known as mathematical logic, and which has been created for the purpose of a firmer and more profound establishment of the foundations of mathematics; this discipline, in spite of its brief existence of barely a century, has already attained a high degree of perfection and plays today a role in the totality of our knowledge that far transcends its originally intended boundaries. It has been my intention to show that the concepts of logic permeate the whole of mathematics, that they comprehend all specifically mathematical concepts as special cases, and that logical laws are constantly applied — be it consciously or unconsciously — in mathematical reasonings.

Cheers,

Nalin Pithwa.

The book is quite accessible with some moderate concentration 🙂

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