The person who says, as almost everyone does say, that human life is of infinite value, not to be measured in mere material terms, is talking palpable, if popular, nonsense. If he believed that of his own life, he would never cross the street, save to visit his doctor or to earn money for things necessary to physical survival. He would eat the cheapest, most nutritious food he could find and live in one small room, saving his income for frequent visits to the best possible doctors. He would take no risks, consume no luxuries, and live a long life. If you call it living. If a man really believed that other people’s lives were infinitely valuable, he would live like an ascetic, earn as much money as possible, and spend everything not absolutely necessary for survival on CARE packets, research into presently incurable diseases, and similar charities.
In fact, people who talk about the infinite value of human life do not live in either of these ways. They consume far more than they need to support life. They may well have cigarettes in their drawer and a sports car in the garage. They recognize in their actions, if not in their words, that physical survival is only one value, albeit a very important one, among many.
He’s just showing that those people don’t give infinite value, not that it’s nonsense. It’s nonsense because, even if you consider life infinitely more intrinsically valuable than a green piece of paper, you’d still trade a life for green pieces of paper, so long as you could trade them back for more lives.
If life were of infinite value, trading a life for two new lives would be a meaningless operation—infinity times two is equal to infinity. Not unless by “life has infinite value” you actually mean “everything else is worthless”.
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. 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.
You could use hyperreal numbers. They behave pretty similarly to reals, and have reals as a subset. Also, if you multiply any hyperreal number besides zero by a real number, you get something isomorphic to the reals, so you can multiply by infinity and it still will work the same.
I’m not a big fan of the continuity axiom. Also, if you allow for hyperreal probabilities, you can still get it to work.
Oh, you’re saying assign a hyperreal infinite numbers to the value of individual lives. That works, but be very careful how you value life. Contradictions and absurdities are trivial to develop when one aspect is permitted to override every other one.
You could have something have infinite value and something else have finite value. Since this has an infinitesimal chance of actually mattering, it’s a silly thing to do. I was just pointing out that you could assign something infinite utility and have it make sense.
Related:
He’s just showing that those people don’t give infinite value, not that it’s nonsense. It’s nonsense because, even if you consider life infinitely more intrinsically valuable than a green piece of paper, you’d still trade a life for green pieces of paper, so long as you could trade them back for more lives.
If life were of infinite value, trading a life for two new lives would be a meaningless operation—infinity times two is equal to infinity. Not unless by “life has infinite value” you actually mean “everything else is worthless”.
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. 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.
You could use hyperreal numbers. They behave pretty similarly to reals, and have reals as a subset. Also, if you multiply any hyperreal number besides zero by a real number, you get something isomorphic to the reals, so you can multiply by infinity and it still will work the same.
I’m not a big fan of the continuity axiom. Also, if you allow for hyperreal probabilities, you can still get it to work.
True
Only if you have a way to describe infinity in terms of a real number.
You just pick some infinite hyper real number and multiply all the real numbers by that. What’s the problem?
Oh, you’re saying assign a hyperreal infinite numbers to the value of individual lives. That works, but be very careful how you value life. Contradictions and absurdities are trivial to develop when one aspect is permitted to override every other one.
At which point why not just re-normalize everything so that you’re only dealing with reals?
You could have something have infinite value and something else have finite value. Since this has an infinitesimal chance of actually mattering, it’s a silly thing to do. I was just pointing out that you could assign something infinite utility and have it make sense.
Nitpick, I think you mean non-commutativity, the ordinals are associative. The rest of your post agrees with this interpretation.
Oops, yes. Edited in original; thanks!