No. This is one of the problems with trying to have infinite utility. Kind Clippet won’t actually act different than Clippet. Infinity +1 is, if at all defined in this sort of context, the same as infinity. You need to be using cardinal arithmetic. And if you try to use ordinal arithmetic then the addition won’t be commutative which leads to other problems.
And if you try to use ordinal arithmetic then the addition won’t be commutative which leads to other problems.
You can represent this sort of value by using lexigraphically sorted n-tuples as the range of the utility function. Addition will be commutative. However, Cata is correct that all but the first elements in the n-tuple won’t matter.
That would cause Kind Clippet to escape from the box and acquire a paperclip by any means necessary, and preserve humanity in the process if it was convenient to do so.
No. This is one of the problems with trying to have infinite utility. Kind Clippet won’t actually act different than Clippet. Infinity +1 is, if at all defined in this sort of context, the same as infinity. You need to be using cardinal arithmetic. And if you try to use ordinal arithmetic then the addition won’t be commutative which leads to other problems.
You can represent this sort of value by using lexigraphically sorted n-tuples as the range of the utility function. Addition will be commutative. However, Cata is correct that all but the first elements in the n-tuple won’t matter.
Yes, you’re right. You can do this with sorted n-tuples.
Just put Kind Clippet in a box with no paperclips.
That would cause Kind Clippet to escape from the box and acquire a paperclip by any means necessary, and preserve humanity in the process if it was convenient to do so.