Monday, November 23, 2015

Values cannot be accurately modeled by real numbers

Consider a day in a human life that is just barely worth living. Now consider the life of Beethoven. For no finite n would having n of the barely-worth-living days be better than having all of the life of Beethoven. This suggests that values in human life cannot be modeled by real numbers. For if a and b are positive numbers, then there is always a positive integer n such that nb>a. (I am assuming additiveness between the barely-liveable days. Perhaps memory wiping is needed to ensure additiveness, to avoid tedium?)


Anonymous said...

It is not obvious to me that you are right in the example, since in general I see nothing repugnant about the supposedly repugnant conclusion. But in any case you are assuming something false by assuming that the days should be additive in that way, at least if you want to measure utility in the von Neumann–Morgenstern way, which may be the only reasonable way to model utility with real numbers. If you do it their way, you must set a bound to utility in order to get a reasonable model of the utility of real people, because e.g. a real person will not pay $10 for a probability of one in a googolplex of some reward, no matter what that reward is (e.g. even if that reward is living for a googolplex days).

In other words, the days decrease in marginal utility, and consequently your argument does not follow even assuming that you are right in regard to the example.

Erenan said...

I recall someone once remarking on a blog somewhere that if you ascribed value to human fetuses and human children (say, five years old or whatever) such that for any number of fetuses you'd always prefer the death of the fetuses over the death of a single child, then this implies that you in fact ascribe no moral value at all to fetuses. I think the intuition behind this remark was the same thought as the intuitive mathematical "nb > a" concept here.

My problem with the thought was that if it were true, then we wouldn't be able to hold chains of this value relation. That is, if for instance I would rather sacrifice any number of starfish than kill a single human fetus and simultaneously would rather sacrifice any number of fetuses than kill a single five year old child, the "zero moral value" assumption above implies that I ascribe zero moral value to fetuses and simultaneously that I ascribe more moral value to fetuses than I do to starfish, which seems plainly to be a contradiction (since if fetuses are more valuable than starfish, then they are of nonzero moral value). Yet we seem to be perfectly capable of holding such value relations.