Alice, Bob and Chuck each come into existence at 1 o'clock.
- Alice lives for one hour. She feels continuous and unchanging morally innocent pleasure during that hour with no pain.
- Bob lives for two hours. During the first hour his experiences are exactly like Alice's; during the second hour, these experiences re-run.
- Chuck has the same internal stream of subjective experiences as Bob, but is accelerated by a factor of two relative to external time, so he lives only for one hour.
Now, let's add some axioms about hedonic value:
- If x and y have the same internal stream of subjective experiences, though perhaps at different external rates, their lives are hedonically equally.
- If x and y live during the same period of external time, and at each moment experience the same pleasure or pain, their lives are hedonically equal.
- If x and y live hedonically equal lives, and y and z live hedonically equal lives, then x and z live hedonically equal lives (hedonic equality is transitive).
- The same pleasant experience lived twice is hedonically better than when lived once.
Now, we have a contradiction. For by (1), Chuck and Bob's lives are hedonically equal. But by (2), Alice's and Chuck's lives are hedonically equal. Here's why. Take any time t between 1 and 2 o'clock, i.e., any time during the lives of Alice and Chuck. Because the pleasure is constant during that hour-long period, Alice's pleasure at t is the same as her pleasure at (say) 1:30. And for the same reason, Chuck's pleasure at t is the same as his pleasure at (say) 1:15. But Chuck's state at 1:15 is the same as Bob's state at 1:30, since Chuck lives the same life that Bob does, but twice as fast. And Bob's state at 1:30 is the same as Alice's state at 1:30. So, Chuck's pleasure at t is equal to Alice's pleasure at t, and hence by (2) Alice's and Chuck's lives are hedonically equal. Hence, by transitivity, Alice's and Bob's lives are hedonically equal. And this contradicts (4).
Assuming our hedonic axioms (1)-(4) are correct, the story about Alice, Bob and Chuck leads to a contradiction. So what's wrong with the story? I think it's the assumption that it's possible for pleasure to be continuous. Instead, I submit, temporally extended pleasure has to be discrete, made up of a finite number of pieces of pleasure. These pieces might be instantaneous or temporally undivided but extended. And of course the argument can be run with pain in place of pleasure as well.