If we want to assign infinite value to lives compared to slices of bread, we don’t need exotic ideas like transfinite ordinals. We can just define value as an ordered pair (# of lives, # of slices of bread). When comparing values we first compare # of lives, and only use # of slices of bread as a tiebreaker. This conforms to the intuition of “life has infinite value” and still lets you care about bread without any weird order-dependence.
This still violates the continuity axiom, but that, of itself, is not an argument against a set of preferences. As I read it, claiming “life has infinite value” is an explicit rejection of the continuity axiom.
Of course, Kaj Sotala’s point in the original comment was that in practice people demonstrate by their actions that they do accept the continuity axiom; that is, they are willing to trade a small risk of death in exchange for mundane benefits.
If we want to assign infinite value to lives compared to slices of bread, we don’t need exotic ideas like transfinite ordinals. We can just define value as an ordered pair (# of lives, # of slices of bread). When comparing values we first compare # of lives, and only use # of slices of bread as a tiebreaker. This conforms to the intuition of “life has infinite value” and still lets you care about bread without any weird order-dependence.
This still violates the continuity axiom, but that, of itself, is not an argument against a set of preferences. As I read it, claiming “life has infinite value” is an explicit rejection of the continuity axiom.
Of course, Kaj Sotala’s point in the original comment was that in practice people demonstrate by their actions that they do accept the continuity axiom; that is, they are willing to trade a small risk of death in exchange for mundane benefits.