I don't get how under Total Utilitarianism you can have the Repugnant Conclusion in the real world. You simply can't add trillions of trillions of trillions ... etc of people to "beat" the original optimal solution. Even considering the future generations.
Definition 1. World is any pair (P, w) where P is a finite set which represents all people who have ever lived and will live; and w is a function from P to ℝ which represents total well being of people in the world.
Definition 2. Utility of a world (P, w) is defined as
\[ \sum_{h \in P} w(h). \]
Theorem. For any world (P, w) for any positive real number t there exists a world (Q, y) such that the range of the function y does not include numbers greater than t and utility of (Q, y) is greater than utility of (P, w).
Proof is obvious.
So, what do you not understand?
@p this is cool an mathy, but you can't birth a few trillion people on a same planet because physics (and economics)
@dpwiz Lol, same planet? Do you even far (and possibly not so far) future?
@p It is increasingly difficult to apply the decision "at the same time" due to relativity.
If the Repugnant Conclusion requires that we have to consider infinities, then I just don't care and T.U. is flawless for all practical purposes.
@dpwiz Repugnant conclusion does not need infinite sets of people. However for the theorem to be applicable as I stated it, finite sets of all sizes must be allowed.
IMO total utilitarianism does have a problem with infinite sets of moral patients.
>all practical purposes
I don't think I know many practical enough purposes where it can be applied. And as they become less practical (like thinking how the future of humanity should be shaped), its problems become more important.
Just to be clear, total utilitarianism is my favorite utility function (even though it is not well defined because of problem with infinite sets). However I prefer to count well being of person-moments and not of persons.
Can you explain what it is you're saying about special relativity? I don't know special relativity theory.
@p there is no a single moment of "now" between spatially distinct points. That means there can't physically be a single decision that impacts infinitely many agents at "once".
