Isthmian 8.25-48

Here at I.8.25–48, the myth about the conception of Achilles by Thetis shows that this hero is the son that Zeus never had: it is foretold that if either Zeus or Poseidon mates with Thetis, the son to be born would be greater than his father. That is why it is ordained by the gods that Thetis must be married off to Peleus. And the bitter fact is, Peleus is a mortal. So, since Peleus as one of the two parents of Achilles is mortal, Achilles must be mortal as well, even though his other parent is Thetis, who is not only immortal but even endowed with limitless cosmic powers. Mortality is the dominant gene, as it were. So Achilles, despite the limitless potential he inherits from Thetis, is subject to death.