Various moral conundrums plague population ethics: the Non-Identity Problem, the Procreation Asymmetry, the Repugnant Conclusion, and more. I argue that the aforementioned moral conundrums have a structure neatly accounted for, and solved by, some ideas in computability theory. I introduce a mathematical model based on computability theory and show how previous arguments pertaining to these conundrums fit into the model. This paper proceeds as follows. First, I do a very brief survey of the history of computability theory in moral philosophy. Second, I follow various papers, and show how their arguments fit into, or don't fit into, our model. Third, I discuss the implications of our model to the question why the human race should or should not continue to exist. Finally, I show that our model may be interpreted according to a Confucian-Taoist moral principle.