The Analytical (Quantitative) Theory of Science and its Implications for the Nature of Scientific Discovery

Abstract

Within the last few years a new level has been reached in a germinating field of study that has developed from quantitative sociology of science, research on science indicators statistics, general bibliometrics, and citation analysis. From these advances I feel it is now possible to put forward, albeit tentatively and with many reservations and much uncertainty at several places in the technical detail, a comprehensive analytical theory of science. By this I mean a conceptual framework that is consistent and extensive and can be related both quantitatively and qualitatively to several places in the historical and philosophical examination of science. It is the function of this paper to explore the apparently far-reaching implications of this theory for the nature of the concepts implied. This will be done in developing one topic and discussing briefly two other separate researches in the field that display this new approach to the explicand of ‘Science of Science’ or ‘Science Studies’, viz:

• (1) A study of the Ups and Downs in the History of Science and Technology ¹ shows how quantification of almost anything in a time series can throw light on what otherwise might be apparent only to a very competent Toynbee-like historian. It also gives an objective method for commenting on the periodization of science and suggests that the Scientific Revolution has a precursor-like role and that the Industrial Revolution may be merely an artifact of historiographical convenience.

• (2) A study of Cumulative Advantage Processes by statistical mathematics² gives results that go from a very simple probabilistic model to yield quantitative laws in agreement with empirical evidence, and thereby explain the peculiarities of all well-known regularities in scientometrics and bibliometrics. This gives a conceptual basis for the sociological hierarchies prevailing in the scientific community.

• (3) Recent discoveries by Griffith and Small show that science can be mapped by using the technique of co-citation analysis. The resultant map is surprisingly two-dimensional, and this indicates that irrespective of the mapping procedure, the structure of science can be ascertained in a very graphic and provocative fashion. One important result is that the paper atoms cluster into sub-discipline molecules each corresponding to an invisible college; there is no other level of aggregation. This result enables one to conjecture that science can be modelled after a cooperatively solved jigsaw puzzle. It can be shown that this model has important features that seem to provide rather more exactly the sort of features often spoken of as Kuhnian paradigms, which it thereby explains and extends. Another important feature of this evidence is that it strongly suggests that scientific instruments and methods procedures have a much more important role than usually allowed for by historians and philosophers of science. It may well be that the true importance of instruments lies not in their testing of theories but in the provision of new sense data not expected nor indeed desired by the paradigmatists.