escatology is actually a misspelling of eschatology, The branch of theology that is concerned with the end of the world or of humankind.

A belief or a doctrine concerning the ultimate or final things, such as death, the destiny of humanity, the Second Coming, or the Last Judgment.

The other parent of this bastard is scatology, where the dog's other end is concerned. Maybe the fact that both words refer to extremes has led to the mixup.