Some ancient authors attribute to Anaximander of Miletus the doctrine of infinite worlds. By this could be meant worlds which exist simultaneously, follow consecutively, or merely transformations in one world. Co-existing worlds, however, were attributed to Anaximander most probably as a result of his unique cosmology of circles of heavenly bodies proceeding under the Earth. Aristotle’s reference to the account of the alternating inception and demise of the world would then correspond to the remarks about the temporal cycles in Anaximander. In comparison with the continuous changes of the world, however, the emergence of a new world originally means the demise of the preceding one. On the basis of the incompatibility of the “unmoving” infinite and the biological background of cosmogony, it may be supposed that just as everything living emerges, so the emerged world is subject to demise. After its emergence, however, there comes the time for a further world, in a similar way to how everything living maintains a continuity in the succession of generations. Progressively, thus, the particular worlds follow on from one another.