Choosing the best of all possible worlds
I've been thinking about yesterday's problem from Brian Weatherson's interactive philosophy blog. Instead of a solution I've found a name: "Forrest's Paradox" (see §2.5 in Lewis, On the Plurality of Worlds).
Knowing the name, it is now easy to create even stranger problems of the same kind. First a reformulation of the original problem.
Suppose there are infinitely many people living infinitely long lives. Those lives consist of temporal segments, which I'll call 'stages'. (It doesn't matter how long those segments are and whether the persons themselves are their life.) The problem is to decide between the following two possibilities, where green stages are happy and red stages unhappy.
Considering people (columns), the first looks better, because here every column is almost entirely green (the red parts are always finite). Considering times (rows), the second looks better, because there every row is almost entirey green.
Now look at these possibilities:
Intuitively, the first world seems to be much better, no matter if we consider times or people. Now let's do some Humean shuffling. First, we label the stages of the first world as shown in the left image below. Then consider a world where these stages are rearranged as shown in the right image.
Either those two worlds are really equally good or there is some principle that says that the total good changes when it is redistributed among the inhabitants of a world.