Logos01 comments on A response to "Torture vs. Dustspeck": The Ones Who Walk Away From Omelas - Less Wrong
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Ending the dialogue may probably be the best option. I am only going to provide you one example of paradoxes you have demanded, since it was probably my fault that I haven't understood your request. (Next time I exhibit similar lack of understanding, please tell me plainly and directly what you are asking for. Beware illusion of transparency. I really have no dark motives to pretend misunderstanding when there is none.)
So, the most basic problem with choosing "specks" over "torture" is that which is already described in the original post: torturing 1 person for 50 years (let's call that scenario X(0)) is clearly better than torturing 10 people for 50 years minus 1 second (X(1)); to deny that means that one is willing to subject 9 people to 50 years of agony just to spare 1 person one second of agony. X(1) is then better than torturing 100 people for 50 years minus 2 seconds (X(2)) and so on. There are about 1,5 billion seconds in 50 years, so let's define X(n) recursively as torturing ten times more people than in scenario X(n-1) for time equal to 1,499,999,999/1,500,000,000 of time used in scenario X(n-1). Let's also decrease the pain slightly in each step: since pain is difficult to measure, let's precisely define the way torture is done: by simulating the pain one feels when the skin is burned by hot iron on p percent of body surface; at X(0) we start with burning the whole surface and p is decreased in each step by the same factor as the duration of torture. At approximately n = 3.8 * 10^10, X(n) means taking 10^(3.8*10^10) people and touching their skin with a hot needle for 1/100 of a second (the tip of the needle which comes into contact with the skin will have 0.0001 square milimeters). Now this is so negligible pain that a dust speck in the eye is clearly worse.
So, we have X(3.8*10^10) which is better than dust specks with just 10^(3.8*10^10) people (a number much lower than 3^^^3), and you say that dust specks are better than X(0). Therefore there must be at least one n such that X(n) is strictly worse than X(n+1). Now this seems paradoxical, since going from X(n) to X(n+1) means reducing the amount of suffering of those who already suffer by a tiny amount, roughly one billionth, for the price of adding nine new sufferers for each existing one.
(Please note that this reasoning doesn't assume anything about utility functions - it uses only preference ordering - nor it assumes anything about direct or indirect consequences of torture.)
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.