The Limits of Science

Outline of Logic and of the Methodology of the Exact Sciences

Leon Chwistek

• Publisher: Routledge
• Year: 2014
• Print ISBN:
  9780415225441
• eBook ISBN:
  9781317829843
• Topic: Filosofía
• Subtopic: Historia y teoría filosóficas

This is Volume III of eight in a series on the Philosophy of Logic and Mathematics. Originally published in 1948, this book portrays an outline of logic and of the methodology of the exact sciences.

CHAPTER I

INTRODUCTION

I. We are living in a period of unparalleled growth of anti-rationalism. Exact thinking based upon the principle of consistency is the sacrificial goat to which all the disasters of our times have been imputed. The World War and all the orgies of domineering capitalism have been attributed to rationalism developed in accordance with the requirements of exact thinking. Exact thinking is blamed for drying up the sources of the sacred enthusiasm and for causing the emotional exhaustion of our epoch. Exact thinking, it is alleged, has become the source of the excessive growth of materialistic culture, as well as the shrinkage and sterilization of spiritual life. The demand for a new logic, for new laws of thought more suitable to the needs of spiritual life, has become the hobbyhorse for a whole galaxy of obscure and false doctrines, from the revived dialectic of Hegel to pragmatism, universalism, and the phenomenology of Husserl.

These doctrines have arisen in many cases owing to widespread ignorance, while at other times they have been dictated by completely dishonest tendencies. Their source is the tragic disintegration of science over a period of years and the despair born out of a perception of the weakness of scientific procedure.

The history of the spiritual culture of mankind may be reduced to the struggle between faith in the creative power of exact thinking on the one hand, and doubt and powerless self- humiliation in the face of the irresponsible aberrations of fanatics who never attempt to solve any concrete problem and relinquish the pleasure of overcoming real difficulties on the other hand. This struggle has been carried on for centuries with varying fortune. But at present we have entered into a period of incredible abasement of science, a period of the noisy superiority of groups of puffed-up eulogists of irrational nonsense, who are leading mankind toward open crime and violence—as a rule unknowingly but often quite consciously.

2. Reflecting on this sad state of affairs, Professor Wladyslaw Natanson writes:

“Ought we not to regard it as evil for comprehensive science to give instruments of incalculable power to nations who have not grown up to them morally ? We have conquered the forces of nature but we have not conquered ourselves. As a consequence myopic egoism arises, and as usual disasters ensue; we are retarded, we are turned back. In silence with apparent equanimity science betrays its high mission. Science has much to say to the nations. When will it say it ? When will it find inspiration and power enough to warn, to restrain, to convince ?”¹

I think that one cannot leave these disturbing questions without attempting to answer them. One must at any cost ferret out the source of the evil, reveal it in all its nakedness, and completely root it out.

It will be seen that the matter is much clearer than would appear on the surface for basically nothing but fear and general inertia prevent the solution of these problems.

3. Despite all efforts, inherited prejudices concerning the metaphysical foundations of science have not as yet been overcome.

The critical attitude, with which laymen credit great scholars is not sufficiently far-reaching. When Bruno Winawer, the author of many comedies, derided the philosophers, he contrasted them with the representatives of the exact sciences and called the latter creators of new forms of life on earth.² He did not, however, observe that these same scholars humble themselves before philosophers and desire at any cost to set themselves up as specialists who discover the bases of philosophy.

Winawer could maintain this view so long as he did not read the popular lectures of Schrödinger, the creator of the wave theory.³ On reading them, he was startled by the mass of irresponsible phrases and crude analogies contained therein, which compared contemporary physics with the so-called new reality in art, and the electrons with separate human individuals. He became even more disturbed when I assured him that this is a common fact and similar cases can be cited by the dozen.

4. It is a fact that naturalists of the extremely critical type restrict themselves too often to detailed investigations in their own field and disregard the endeavour for a rationalistic view of the world. Naturalists have a peculiar foible: they indulge in metaphysical prejudices and seek popularity in the name of doctrines which go far beyond the bounds of sound reason and exact thought. Unfortunately they have great influence.

Things have come to such a pass, that to talk to-day about the distinction between the representatives of pure science and the metaphysician is indeed difficult; for in the writings of famous mathematicians, physicists, astronomers, and biologists, abject surrender to the authority of deplorable and fruitless metaphysical endeavours is found. I shall give the following examples:

The famous German mathematician, Hermann Weyl, prefaced his book entitled Raum, Zeit, Materie (a work in which he endeavoured to include Einstein’s theory in his system) with a philosophical introduction typical of a professional metaphysician of inferior quality. In his opinion it is a sad necessity that philosophy oscillates from system to system—a sad state of affairs which “we cannot dispense with unless we are to convert knowledge into a meaningless chaos”.¹ In other words, bearing in mind the tragic maxim, “All beginnings are obscure,”¹ we are forced to build on uncertain foundations.

In the entire conception of the foundations of science offered by Weyl, one finds no trace of that modesty and unpretentiousness in the presentation of a theory which is worthy of a representative of the exact sciences. There is no recognition of that fundamental principle, that the point of departure in constructing a world view should not be a confused metaphysics, but simple and clear truths based upon experience and exact reasoning. Weyl entirely neglects the fact that physical theories are pure abstractions, which one cannot even regard as images of reality and that their rule reduces to this, that they make possible the systematic classification of phenomena as well as investigations directed toward the discovery of unknown phenomena. He ignores the fact that if philosophy is to be taken seriously it must restrict itself to a critical analysis of the relation of scientific theories to experience and cannot be the basis of these theories. He does not limit his ill-timed ambitions and seek the founda...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• AUTHOR’S PREFACE TO THE ENGLISH EDITION
• TRANSLATORS’ PREFACE
• PREFACE TO INTRODUCTION AND APPENDIX
• BIBLIOGRAPHY
• INTRODUCTION
• CHAP.
• APPENDIX : THE FUNDAMENTAL SYSTEM OF SEMANTICS
• INDEX OF NAMES
• SUBJECT INDEX
• INDEX OF SYMBOLS
• DIAGRAMS: