I feel confused. “a space I can measure distances in” is a strong property of a value, and it does not follow from your initial 5 axioms, and seems contrary to the 5th axiom.
In fact, your own examples given further seem to provide a counterexample—i.e., if someone prefers being a whale to 400 actual orgasms, but prefers 1⁄400 of being a whale to 1 orgasm, then both “being a whale” and “orgasm” have some utility value, but they cannot be used as units to measure distance.
If you’re in a reality where a>b and 2a<2b, then you’re not allowed to use classic arithmetic simply because some of your items look like numbers, since they don’t behave like numbers.
“Hawaii” can’t be used as a unit to measure distance, nor can “the equator”, but “the distance from Hawaii to the equator” can. Similarly, “the difference between 0 orgasms and 1 orgasm” can be used as a unit to measure utilities (you could call this unit “1 orgasm”, but that would be confusing and silly if you had nonlinear utility in orgasms: 501 orgasms could be less than or more than “1 orgasm” better than 500).
Also, did you mean to have these the other way around?:
I feel confused. “a space I can measure distances in” is a strong property of a value, and it does not follow from your initial 5 axioms, and seems contrary to the 5th axiom.
In fact, your own examples given further seem to provide a counterexample—i.e., if someone prefers being a whale to 400 actual orgasms, but prefers 1⁄400 of being a whale to 1 orgasm, then both “being a whale” and “orgasm” have some utility value, but they cannot be used as units to measure distance.
If you’re in a reality where a>b and 2a<2b, then you’re not allowed to use classic arithmetic simply because some of your items look like numbers, since they don’t behave like numbers.
“Hawaii” can’t be used as a unit to measure distance, nor can “the equator”, but “the distance from Hawaii to the equator” can. Similarly, “the difference between 0 orgasms and 1 orgasm” can be used as a unit to measure utilities (you could call this unit “1 orgasm”, but that would be confusing and silly if you had nonlinear utility in orgasms: 501 orgasms could be less than or more than “1 orgasm” better than 500).
Also, did you mean to have these the other way around?: