Here's the new thread for posting quotes, with the usual rules:
- Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself
- Do not quote comments/posts on LW/OB
- No more than 5 quotes per person per monthly thread, please.
Not quite so! We could presume that value isn't restricted to the reals + infinity, but say that something's value is a value among the ordinals. Then, you could totally say that life has infinite value, but two lives have twice that value.
But this gives non-commutativity of value. Saving a life and then getting $100 is better than getting $100 and saving a life, which I admit seems really screwy. This also violates the Von Neumann-Morgenstern axioms.
In fact, if we claim that a slice of bread is of finite value, and, say, a human life is of infinite value in any definition, then we violate the continuity axiom... which is probably a stronger counterargument, and tightly related to the point DanielLC makes above.
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... (read more)