Whether the increase is linear or logarithmic does not change anything - in both cases there could be a number N large enough that the disutility of N dust specks is larger than that of one torture.
This does not follow. One torture could possess effectively infinite disutility, potentially. But that's irrelevant, as I was simply expressing the notion of logarithmic scaling of pain. Especially since we're dealing with a nearly-negligible kind of pain on the lower end. A "mind-fucking large number" of nearly-0-value instances of pain would not necessarily find its way back up the scale to the "mind-fucking large number" of anti-utilons induced by the torture-for-fifty-years.
An infinitessimal amount of pain, multiplied by a non-infinite "mind-fuckingly-large number", would not be guaranteed to exceed "1", let alone achieve its own "mind-fuckingly large number" all over again.
That is the entire point of noting the logarithmic nature of pain -- I was pointing out that the disutility experienced by the torture victim itself, according to that metric, was also a "mind-fuckingly large number". I should have expected this to be obvious from the fact that logarithmic functions are unbounded.
That is why Eliezer picked a mindfuckingly large number like 3^^^3 - to sidestep nitpicking over the exact shape of the utility function.
And if disutility added linearly that would be a successful achievement on his part.
What would make a difference was if the disutility was a bounded function, hence Zack's suggestion of the logistic function.
Zack's suggestion was not appropriate to describing my position even slightly. I strongly disagree with the logistic function. My assertion is not that there is an upper bound to how much suffering can be received by dust-specking, but rather that there is no upper bound on the suffering of torture.
But that still only considers the primary consequences.
(Many people have been trying to tell you this in this thread, including TimS who seems to agree with your conclusions. You may want to update.)
Many people have been trying to tell me many things. Mostly that my premise is invalid in its face -- but not a single one of them has provided anything resembling a non-illogical reason for their dismissal of my position.
I only update my beliefs when provided with legitimate arguments or with evidence. Nothing to this point has passed the muster of being non-contradictory.
There is further reason for my maintaining this position, however: even when I specifically stipulated the linear-additive -- that is, when I stated that the direct suffering of the torture victim was less than that of the dust-speckings -- by introducing the secondary consequences and their impact I STILL was left choosing the dust-speckings as the 'lesser of two evils'.
And that, in fact, was the real "core" of my argument: that we must not, if we are to consider all the consequences, limit ourselves solely to the immediate consequences when deciding which of the two sets of outcomes has the greater disutility. I further object to the notion that "suffering" vs. "pleasure" is the sole relevant metric for utility. And based on that standard, the additional forms of disutility comparing between the dust-speckings as opposed to the torture strongly weigh against the torture being conducted; the dust-speckings, while nuisancesome, simply do not register at all as a result on those other metrics.
An infinitessimal amount of pain, multiplied by a non-infinite "mind-fuckingly-large number", would not be guaranteed to exceed "1", let alone achieve its own "mind-fuckingly large number" all over again.
That is the entire point of noting the logarithmic nature of pain
The term "logarithmic" does not capture that meaning. Your concept of "infinitesimal" such that you can never get to 1 by multiplying it by a number no matter how large is not a part of "standard" mathematics; you can get somethi...
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.