This paper discusses the intellectual justification of scientometrics through the claim that it is part of the quest for a quantitative science of science. Initially, I will make a brief description of scientometrics' historical background. Next, I will explain that those disciplines that have been satisfactorily mathematized always contain two distinct basic components: an axiomatic, defining the operations that can be realized with the available data, and an interpretation of their meaning. Counting papers and citations is a way to collect (...) statistical data about scientific activities, and therefore the axiomatic basis of scientometrics comes from statistics. Regarding the interpretation of scientometrics, I will argue that the meanings attributed to their key concepts are usually borrowed from economics. Then I discuss how the promise of a science of science becomes a too well adjusted historical narrative that apparently justifies the economic concerns of governments and private corporations. (shrink)