How To Solve Moral Conundrums with Computability Theory

I give nothing as duties; What others give as duties, I give as living impulses. Abstract Walt Whitman 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 ineluctably leads us to a Confucian moral principle. In 1931, Gödel introduced his Incompleteness Theorem. The results showed that, roughly, consistency and completeness cannot coexist in a formal system. In Gödel, Escher, Bach, the most seminal treatment on the topic thus far, Hofstadter puts it this way: "for any record player, there are records which it cannot play because they will cause its indirect self-destruction" There is an inkling of intuition here that may be grasped, but the precise mathematical idea is difficult to understand, and Hofstadter's explanation cannot be said to be precise or thorough. Rather than explain the theorem in detail, however, I want to explain how the theorem has been applied, or complained about, so that the reader can build a better intuition about it. The theorem has had a sizable impact in academic philosophy, most notably in the form of arguments against determinism, and as arguments against strong AI. However, as far as the author's knowledge goes, its implications have not been milked to their full potential in academic moral philosophy. The theorem has certainly been discussed in moral philosophy, however, such as in the following speech by the British philosopher J. R. Lucas [Luc98]: Moral and political philosophy will be different once reason is allowed to regain its ancient sway.... Although the way Gödel's theorem was proved follows a somewhat standard route, the upshot of the proof is that reasoning, even mathematical reasoning, By doing that it becomes free.