It is, however, a frustrating pattern, and is causing me to lose interest in this dialogue.
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.)
That is counter-intuitive, but isn't the anti-torture answer something analogous to sets? That is:
R(0) is the set of all real numbers. We know that it is an uncountable infinity, and therefore larger than any countable infinity. Set R(n) is R(0) with n elements removed. As I understand it, so long as n is a countable infinity or smaller, R(n) is equal in size to R(0). [EDITED TO REMOVE INCORRECT MATH.]
To cash out the analogy, it might be that certain torture scenarios are preferable to other torture scenarios, but all non-torture scenarios are less ba...
For those not familiar with the topic, Torture vs. Dustspecks asks the question: "Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?"
Most of the discussion that I have noted on the topic takes one of two assumptions in deriving their answer to that question: I think of one as the 'linear additive' answer, which says that torture is the proper choice for the utilitarian consequentialist, because a single person can only suffer so much over a fifty year window, as compared to the incomprehensible number of individuals who suffer only minutely; the other I think of as the 'logarithmically additive' answer, which inverts the answer on the grounds that forms of suffering are not equal, and cannot be added as simple 'units'.
What I have never yet seen is something akin to the notion expressed in Ursula K LeGuin's The Ones Who Walk Away From Omelas.If you haven't read it, I won't spoil it for you.
I believe that any metric of consequence which takes into account only suffering when making the choice of "torture" vs. "dust specks" misses the point. There are consequences to such a choice that extend beyond the suffering inflicted; moral responsibility, standards of behavior that either choice makes acceptable, and so on. Any solution to the question which ignores these elements in making its decision might be useful in revealing one's views about the nature of cumulative suffering, but beyond that are of no value in making practical decisions -- they cannot be, as 'consequence' extends beyond the mere instantiation of a given choice -- the exact pain inflicted by either scenario -- into the kind of society that such a choice would result in.
While I myself tend towards the 'logarithmic' than the 'linear' additive view of suffering, even if I stipulate the linear additive view, I still cannot agree with the conclusion of torture over the dust speck, for the same reason why I do not condone torture even in the "ticking time bomb" scenario: I cannot accept the culture/society that would permit such a torture to exist. To arbitrarily select out one individual for maximal suffering in order to spare others a negligible amount would require a legal or moral framework that accepted such choices, and this violates the principle of individual self-determination -- a principle I have seen Less Wrong's community spend a great deal of time trying to consider how to incorporate into Friendliness solutions for AGI. We as a society already implement something similar to this, economically: we accept taxing everyone, even according to a graduated scheme. What we do not accept is enslaving 20% of the population to provide for the needs of the State.
If there is a flaw in my reasoning here, please enlighten me.