It seems to me that "The Doomsday Hypothesis" (and similar arguments) only become valid when the set is complete. For instance, if we assume civilisation started in earnest circa 10,000 BCE, then what would someone conclude if they were born in the year 8,000 BCE? They would conclude that civilisation only has 2,000 years of life left and would end circa 6000 BCE. So much for "The Doomsday Hypothesis".