Rescher's Principle of Decreasing Marginal Returns of Scientific Research

In his book "Scientific Progress", Rescher (1978, German ed. 1982, French ed. 1993)developed a principle of decreasing marginal returns of scientific research, which is based, interalia, on a law of logarithmic returns and on Lotka's law in a certain interpretation. In the presentpaper, the historical precursors and the meaning of the principle are sketched out. It is reported onsome empirical case studies concerning the principle spread over the literature. New bibliometricdata are used about 19th-century mathematics and physics. They confirm Rescher's principleapart from the early phases of the disciplines, where a square root law seems to be moreapplicable. The implication of the principle that the returns of different quality levels grow theslower, the higher the level, is valid. However, the time-derivative ratio between (logarithmized)investment in terms of manpower and returns in terms of first-rate contributors seems not to belinear, but rather to fluctuate vividly, pointing to the cyclical nature of scientific progress. Withregard to Rescher's principle, in the light of bibliometric indicators no difference occurs betweena natural science like physics and a formal science like mathematics. From mathematical progressof the 19th century, constant or increasing returns in the form of new formulas, theorems andaxioms are observed, which leads to a complementary interpretation of the principle of decreasingmarginal returns as a principle of scientific "mass production".