On several occasions I have pointed out that the lesson taught us by recent developments in physics regarding the necessity of a constant extension of the frame of concepts appropriate for the classification of new experiences leads us to a general epistemological attitude which might help us to avoid apparent conceptual difficulties in other fields of science as well. Since, however, the opinion has been expressed from various sides that this attitude would appear to involve a mysticism incompatible with the true spirit of science, I am very glad to use the present opportunity of addressing this assembly of scientists working in quite different fields but united in their striving to find a common ground for our knowledge, to come back to this question, and above all to try to clear up the misunderstandings which have arisen.

The rapid development of physics, the result of observations made and ideas introduced within the last few decades, has brought about a change in the whole system of physical concepts. This fact is common knowledge, and has already attracted the attention of philosophers. It is less well known that geometry too has had its crises, and undergone a reconstruction. For centuries, so-called “geometrical intuition” was used as a method of proof. In geometrical demonstrations, certain steps were allowed because they were “self-evident,” because the correctness of the conclusion was “shown by the adjoined diagram,” etc. A crisis occurred in geometry because such intuition proved to be untrustworthy. Many of the propositions regarded as self-evident or based upon the consideration of diagrams turned out to be false. And so Euclidean geometry was reconstructed by methods free from all intuitive elements and strictly logical in nature. Moreover, for more than a century, various other geometries have been devised purely as logical constructions. Since they start with assumptions different from those of Euclid, and lead to conclusions partly in contradiction with his theorems, they are called “non-Euclidean.” Nevertheless, each one of these geometries is a closed system of propositions exempt from contradiction. Recently, some of them have even found application in physics.

Recent discussions in the physical literature, designed to clarify the logical position of modern physical theory, have brought to light an amazing divergence of fundamental attitudes which may well bewilder the careful student of physics as well as philosophy. Quantum mechanics, representing an abstract formalism, should be capable of having its logical structure analyzed with great precision like any other mathematical discipline. Its consequences in all problems to which its method can be applied are so unambiguous, consistent, and successful in predicting physical experience as to disperse immediately all thoughts of possible discrepancies in its fundamental texture. Yet it must be said that even the founders of quantum theory are not in harmony in their various expositions of the bases of that theory. However, while this situation seems disquieting on the face of it, there is no cause for serious brow raising, for it is a fact that there exists agreement with regard to the central axioms of the theory, and that the ambiguities affect only their philosophical interpretation, a field in which differences of opinion may at present be honestly entertained.

To be scientific is to be objective. This is a sine qua non in the social scientists’ efforts to keep their researches on a par with those of the natural scientists. The extreme differences of subject matter in the two fields, however, make it difficult to maintain an even standard of objectivity. Whether objectivity is defined in the strict Cartesian sense or in a broader sense also makes a difference. The Cartesian meaning threatens to enslave the social sciences to Physics as the Lord of All Sciences, and this possibility is so familiar that it needs but brief comment. A broader interpretation of objectivity meets with complications which are only inadequately recognized as yet, and which may call for reinterpretation of the scope of science or else may open up new and independent avenues of opportunity beyond the limitations of science.