Members and Gunk
Suppose there are at least proper-class many possibilia. Does it follow that some fusions of possibilia are not members of any set? For the last two years or so I thought it does. My reasoning was that if some of the possibilia correspond one-one with all the sets, then some atoms of possibilia also correspond one-one with all the sets (for there cannot be proper-class many fusions of set-many atoms); but since there are always more fusions of atoms than atoms, it follows that there must be more fusions of atoms of possibilia than sets, and hence that some (in fact, most) of these fusions lack a singleton. This does not take into account atomless possibilia, but I always thought the reasoning would easily carry over, by something like the fact that even with gunk
if there are k things, then there are j distinct things, with k <= 2^j.
But now it seems that this is not a fact at all. So could all fusions of possibilia be members if only most of the possibilia were gunk?
(Not that it would really make a difference: I can't imagine how one could believe that there are proper-class many possibilia, but only set-many atoms of possibilia.)