Scientometrics, as a rule, is considered in details – the more accurate and expressive the detailing, the more effective is the accounting of scientific research: the measurement of quantitative parameters of the results of scientific activity is aimed at improving the quality of scientific communication and, ultimately, the progress of science. This led to the transition from usual bibliometrics to scientometrics, and later to other more sophisticated forms of accounting for scientific activity, which can be divided into infometrics and altmetrics. Infometrics and its modifications take into account everything that could be formalized, while altmetrics seeks to include qualitative parameters in the realm of quantitative measurements. In this article, attention is focused precisely on the analysis of the relationship between quantitative methods and quantitative indicators of scientific activity with the progress of science thanks to a comparative assessment of bibliometrics, scientific metrics and infometrics from philosophical positions. A way out of the problematic situations in which attempts to provide a quantitative description of the quality of scientific activity inevitably fall, should be sought beyond the quantitative methods themselves – in the identification of their ultimate goal. Such a goal is the development of humanity through the progress of science. The UN program “Transforming Our World: Agenda 2030 for Sustainable Development” offers a systematic vision of ways to accomplish this task, which, in particular, sets the goal of achieving equal development opportunities for every person. Bibliometrics, scientometrics and infometrics contribute to overcoming many types of social inequality – provided that people are actively involved in scientific activity: personal scientific achievements level out property, gender, religious, ethnic and many other types of social inequality and give every participant of scientific research access to a public career and personal development. The development of each person on a rational basis is the ultimate goal of science, which is the basis of the philosophy of the strategy of global sustainable development of Mankind.