I’m claiming that we should only ever reason about infinity by induction-type proofs. Due to the structure of the thought experiment, the only thing that is possible to use for to count in this way is galaxies, so (I claim) counting galaxies is the only thing that you’re allowed to use for moral reasoning. Since all of the galaxies in each universe are moral equivalents (either all happy but one or all miserable but one), how you rearrange galaxies doesn’t affect the outcome.
(To be clear, I agree that if you rearrange people under the concepts of infinity that mathematicians like to use, you can turn HEAVEN into HELL, but I’m claiming that we’re simply not allowed to use that type of infinity logic for ethics.)
Obviously this is taking a stance about the ways in which infinity can be used in ethics, but I think this is a reasonable way to do so without giving up the concept of infinity entirely.
Why is the only thing that we can use galaxies? We can compare people in any ways.
If you rearrange people, standard mathematics says that you can turn HEAVEN into HELL. Infinity/1 billion = infinity. You have to change the math of infinity, not just the math of ethics where you add up infinity.
I don’t think that it does? There are infinitely many arrangements, but the same proof by induction applies to any possible arrangement.
Wait, do you agree that rearranged heaven gets hell? If so, you either have to deny that HEAVEN>HELL or that arrangement matters.
You’re assuming we’re comparing them by galaxies. But there’s no natural way to individuate that explains why we should do that.
I’m claiming that we should only ever reason about infinity by induction-type proofs. Due to the structure of the thought experiment, the only thing that is possible to use for to count in this way is galaxies, so (I claim) counting galaxies is the only thing that you’re allowed to use for moral reasoning. Since all of the galaxies in each universe are moral equivalents (either all happy but one or all miserable but one), how you rearrange galaxies doesn’t affect the outcome.
(To be clear, I agree that if you rearrange people under the concepts of infinity that mathematicians like to use, you can turn HEAVEN into HELL, but I’m claiming that we’re simply not allowed to use that type of infinity logic for ethics.)
Obviously this is taking a stance about the ways in which infinity can be used in ethics, but I think this is a reasonable way to do so without giving up the concept of infinity entirely.
Why is the only thing that we can use galaxies? We can compare people in any ways.
If you rearrange people, standard mathematics says that you can turn HEAVEN into HELL. Infinity/1 billion = infinity. You have to change the math of infinity, not just the math of ethics where you add up infinity.