By Richard von Mises (from ‘Positivism: A Study in Human Understanding,’ published in German in 1939 and translated and revised in English in 1956)

7. Summary. In conclusion we wish to summarize in brief and as concise sentences as possible some of the main results that the seven parts of this book have presented.

(I) It is the oldest experience and the primitive theories derived from them that are preserved in the traditional stock of language. Through word formulations as well as through various grammatical rules certain typifications of the most frequently occurring relations have been created, and everybody speaking the language must use them. An improvement of knowledge is possible only if one approaches linguistic usage critically and does not regard the existing words and standardized locutions as fixed and unchangeable elements in the construction of a world picture.

(II) The analysis of knowledge leads to the search for the simplest basic sentences upon which further development can rest. We find them in the so-called “protocol sentences,” i.e., short linguistic indications of the immediately observed present—without claiming that their range can be delineated sharply. That which, by means of a specific set of linguistic rules, can be reduced in principle to protocol sentences is understandable empiricist language. We consider scientific those statements which are connectible with the not explicitly discarded rules of everyday language and expression, the reducibility to protocol sentences appears as an analysis of the world into elements (receptions) in Mach’s sense.

(III) The goal of all scientific endeavor is to discover connections between observable phenomena, such that out of a partially given complex the remaining elements can be constructed in thought. Starting from single observations, general propositions are set up in a constructive manner as conjectures (the so-called inductive inference) and these are then, by a continual increase in conciseness of the concepts, built up to tautological (axiomatic) systems, which are disconnected from ordinary language. By means of the (nonrigorous) coordination between the language of the tautologies and that of the protocol sentences, one derives from the sentences deduced within the system statements about reality that can be verified by observation. No theory is uniquely determined by the phenomena; they all contain arbitrary elements. No theory is final; they are all subject to continual testing by new observations.

(IV) The observation of a uniform, stable connection that exists under certain circumstances among specific groups of phenomena leads to the concept of causality. This concept finds its mathematically precise expression in the differential equations of physics, which express the continuous temporal changes of a variable by other observational quantities. Correlations that do not occur without exception but with a stable value of relative frequency lead to the concept of probability, which is given a precise form by the theory of the mathematical “collective.” Physics in its present stage makes use of both kinds of description and it cannot be predicted whether one of them will sometime gain and keep the upper hand. None of the popular theories that speak of destruction and causality, of metasciences, of the supernatural, or of miracles can stand a critical linguistic examination.

(V) The whole of science can be resolved (in a vague way) into separate sciences, according to the realms of phenomena that each treats. The idea that there exists a fundamental unbridgeable difference in method or even in the kind of “understanding” between the natural sciences and the humanities is untenable. In history and the social sciences, too, one deals with observations, inductive generalizations, hence theories, and with the first approaches to tautological systems; every result is, in the last analysis, a proposition verifiable in experience. Physics and the branches of knowledge bordering on it are characterized by the fact that they deal with the simplest phenomena, i.e., with those which can be better isolated than all others, and this accounts for the fact that these sciences are more advanced with respect to the accumulation of experiences and to their epistemological elaboration.

(VI) The desire to arrive at practically useful answers (predictions) in the most difficult and most general questions of life leads to the construction of systems of metaphysical propositions, which are characterized by their strictly limited connectibility and allow of a verification by observation only in a very vague form. Progress of research leads in every sphere away from metaphysics, toward the realm of connectible, scientific theories. In the works of poetry, fine arts, music, etc., general contents of experience, condensed into moods and feelings, are communicated by means of special “languages,” whose conventions are assimilated in education and instruction. None of these contents can be translated without loss from one language into another one. We do not know of an objective definition of the “beautiful” independent of the apprehending subject. A scientific theory, as well as a work of art, is always only a one-sided hint to possible experiences, never their complete exhaustion.

(VII) From personal commands, which regulate the social life on a primitive stage, there develops the meaning of general, independent ought sentences or norms of conduct. The justification of a system of norms can consist only of sentences that express connections between observable phenomena (actions and their consequences), and which, therefore, belong to the positive sciences, particularly to sociology. The acceptance or rejection of a normative system by a group occurs through a collective act of resolution, in which every individual acts under the influence of the various impacts of society. The alleged existence of an objective scale of moral values, inborn in all men, is not supported by any observation. The religious systems are metaphysical attempts at an explanation of the world, undertaken for the purpose of setting up norms of behavior. We expect from the future that to an ever-increasing extent scientific knowledge, i.e., knowledge formulated in a connectible manner, will control life and the conduct of men.