I've been thinking about this a bit more. I think I've changed my position on the stone paradox.
As I think I mentioned earlier in the thread, my first instinct was to see the stone paradox as an earlier version of Hilbert's Hotel, only with a being with infinite capabilities instead of a hotel with an infinite number of rooms and an infinite number of guests.
If we interpret omnipotence in terms of limitlessness (which isn't how it's interpreted universally, but it's common enough, I think), then the paradox resolves itself. It only seems like a paradox because of the unstated assumption that a being that can be beaten by omnipotence can't be omnipotent itself, but now I don't think this is necessarily true.
Whichever ability wins out - whether making the rock unliftable or lifting the rock - it doesn't imply that the losing ability isn't limitless. One infinity can be less than another infinity and still be infinite: for instance, a line of tiles one tile wide stretching off into infinity is going to have fewer tiles than another line two tiles wide and stretching off to infinity, but both have an infinite number of tiles.
Short version: at least one common and accepted understanding of omnipotence resolves the paradox without any funny business. This makes me wonder whether the stone paradox, to the extent that it's a paradox at all, is just rooted in either semantics or in a misunderstanding of how infinities work.
As I think I mentioned earlier in the thread, my first instinct was to see the stone paradox as an earlier version of Hilbert's Hotel, only with a being with infinite capabilities instead of a hotel with an infinite number of rooms and an infinite number of guests.
If we interpret omnipotence in terms of limitlessness (which isn't how it's interpreted universally, but it's common enough, I think), then the paradox resolves itself. It only seems like a paradox because of the unstated assumption that a being that can be beaten by omnipotence can't be omnipotent itself, but now I don't think this is necessarily true.
Whichever ability wins out - whether making the rock unliftable or lifting the rock - it doesn't imply that the losing ability isn't limitless. One infinity can be less than another infinity and still be infinite: for instance, a line of tiles one tile wide stretching off into infinity is going to have fewer tiles than another line two tiles wide and stretching off to infinity, but both have an infinite number of tiles.
Short version: at least one common and accepted understanding of omnipotence resolves the paradox without any funny business. This makes me wonder whether the stone paradox, to the extent that it's a paradox at all, is just rooted in either semantics or in a misunderstanding of how infinities work.