The place of an anthropic argument in the discrimination between various cosmological models is to be reconsidered following the classic criticisms of Paul C. W. Davies and Frank J. Tipler. Different versions of the anthropic argument against cosmologies involving an infinite series of past events are analysed and applied to several instructive instances. This not only is of historical significance but also presents an important topic for the future of cosmological research if some of the contemporary inflationary models, particularly Linde's chaotic inflation, turn out to be correct. Cognitive importance of the anthropic principle(s) to the issue of extraterrestrial intelligent observers is reconsidered in this light and several related problems facing cosmologies with past temporal infinities are also clearly defined. This issue not only is a clear example of the epistemological significance of the anthropic principle but also has consequences for such diverse topics as the search for extraterrestrial intelligence, epistemological status of cosmological concepts, theory of observation selection effects, and history of modern astronomy.