Ancient origins of a modern anthropic argument against cosmologies involving infinite series of past events are considered. It is shown that this argument--which in modern times has been put forward by distinguished cosmologists such as Paul C. W. Davies and Frank J. Tipler--originates in pre-Socratic times and is implicitly present in the cyclical cosmology of Empedocles. There are traces of the same line of reasoning throughout the ancient history of ideas, and the case of a provocative statement of Thucydides is briefly analysed. Moreover, the anthropic argument has been fully formulated in the epic of Lucretius, confirming it as the summit of ancient cosmology. This not only is of historical significance but also presents an important topic for the philosophy of cosmology provided that some of the contemporary inflationary models, particularly Linde's chaotic inflation, turn out to be correct.