When, at an unknown but manifestly early period, speculation regarding the duration and destiny of the world began, the thinkers of those days had two analogies to guide them, and consequently two divergent conclusions were reached. The first was the recurrent cycle of the seasons; the second, the growth, maturity, decay and death of the human and all other animal bodies. Reasoning from the one, some arrived at the conclusion that the world, at least the earth and mankind, had passed and would always continue to pass through a series of epochs, limited in number, which when they had ended would recommence, and so on indefinitely. From the other datum the result was reached that as a man dies and does not come to life again (for even the fairly wide-spread and early doctrine of reincarnation supposed only that the soul would be given a new earthly body of some kind, not that the whole individual would return), so the earth, or the universe generally, would grow old and die and that would be the end of it. It is the purpose of this paper to examine these two ideas and one or two offshoots of them as they are known to have appeared in the two classical civilizations of Europe, and especially in Greece, and if possible to draw some tentative conclusions as to which, if either, can be found more characteristic of native thought.