The point I was trying to make is mathematical: for sensible definitions of “finitely greater” the statement “if we have a sequence of objects, each of which is only finitely greater than its predecessor, then every object on the list is only finitely greater than eany earlier object” is true, but not relevant to the question of whether or not there exist infinitely large objects.
But extremely relevant to the question whether or not there exist infinitely large objects on the list.
Not at all. People who treat some things as infinitely worse than others don’t do so because they believe that a list that includes both somehow stops being a list, and the threat starter never implied anything in that direction. They just have inconsistent preferences (at least in the sense of being money-pumpable). Either that or they bite the bullet and admit that there is at least one particular item infinitely worse than the preceding for any such list. Denying that a list is a list is just nonsense.
We are in violent agreement (but I’m coming off worse!).
rstarkov suggested that people may have “utility functions” that don’t take real values.
Endoself’s comment “showed” that this cannot be, starting from the assumption that everybody has a preference system that can be encoded as a real-valued utility function. This is nonsense.
My non-disagreement with you seems to have stemmed from me not wanting to be the first person to say “order-type”, and us making different assumptions about how various poster’s positions projected onto our own internal models of “lists” (whatever they were).
You shouldn’t have used the worlds “not relevant”, that implied the statement had no important implications for the problem at all, rather than proving the (very relevant since the topic is ulilitarism) hidden assumption wrong for that set of people (unless they bit the bullet).
But extremely relevant to the question whether or not there exist infinitely large objects on the list.
Whether or not everybody has a list is precisely the question asked in the top post of this thread.
Not at all. People who treat some things as infinitely worse than others don’t do so because they believe that a list that includes both somehow stops being a list, and the threat starter never implied anything in that direction. They just have inconsistent preferences (at least in the sense of being money-pumpable). Either that or they bite the bullet and admit that there is at least one particular item infinitely worse than the preceding for any such list. Denying that a list is a list is just nonsense.
We are in violent agreement (but I’m coming off worse!).
rstarkov suggested that people may have “utility functions” that don’t take real values.
Endoself’s comment “showed” that this cannot be, starting from the assumption that everybody has a preference system that can be encoded as a real-valued utility function. This is nonsense.
My non-disagreement with you seems to have stemmed from me not wanting to be the first person to say “order-type”, and us making different assumptions about how various poster’s positions projected onto our own internal models of “lists” (whatever they were).
You shouldn’t have used the worlds “not relevant”, that implied the statement had no important implications for the problem at all, rather than proving the (very relevant since the topic is ulilitarism) hidden assumption wrong for that set of people (unless they bit the bullet).