Logos01 comments on A response to "Torture vs. Dustspeck": The Ones Who Walk Away From Omelas - Less Wrong
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X(0)) is a smaller value of anti-utility than X(1)), absolutely. I do not, however, know that the decrease of one second is non-negligible for that measurement of anti-utility, under the definitions I have provided.
That math gets ugly to try to conceptualize (fractional values of fractional values), but I can appreciate the intention.
This is a non-trivial alteration to the argument, but I will stipulate it for the time being.
"Clearly"? I suffer from opacity you apparently lack; I cannot distinguish between the two.
The paradox exists only if suffering is quantified linearly. If it is quantified logarithmically, a one-billionth shift on some position of the logarithmic scale is going to overwhelm the signal of the linearly-multiplicative increasing population of individuals. (Please note that this quantification is on a per-individual basis, which can once quantified be simply added.)
This is far from being a paradox: it is a natural and expected consequence.
Then substitute "worse or equal" for "worse", the argument remains.
Same thing, doesn't matter whether it is or it isn't. The only things which matters is that X(n) is preferable or equal to X(n+1), and that "specks" is worse or equal to X(3.8 * 10^10). If "specks" is also preferable to X(0), we have circular preferences.
So, you are saying that there indeed is n such that X(n) is worse than X(n+1); it means that there are t and p such that burning p percent of one person's skin for t seconds is worse than 0.999999999 t seconds of burning 0.999999999 p percent of skins of ten people. Do I interpret it correctly?
Edited: "worse" substituted for "preferable" in the 2nd answer.
Yes.