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.

there's still a yet larger number such that this number of dust specks is worse than torture.

He (and I) deny this statement is true. There is no sum of sufferings that add up to torture. It is analogous to the fact that the sum of a countably infinite number of countably infinite sets is not as large as the set of real numbers.

I don't know why Logos insists that logarithmic captures this idea.

Are you saying that 3^^^3 is not sufficiently large? Then consider 3^^^^3.

I'm saying that dust-specks are practically infinitessimal comparatively, and that's in direct comparison. Ergo; a nearly or potentially truly infinite number of dust-speckings would be required to equal one torturing for fifty years, just in terms of direct suffering.

If we were to include the fact that such a torturing would result in the total personality destruction of several reconstructed psyches over the period of that 50 years, I don't necessarily know that such a torture couldn't rightly be called effectively infinite suffering for a single individual.

there's still a yet larger number such that this number of dust specks is worse than torture.

In terms solely of the immediate and direct suffering, certainly. In terms of that suffering and the other consequences -- individual self-determination, for example; or social productivity costs, etc., even an infinite number of dust-speckings begins to become insufficient to the task of equalling a single fifty-year torture. How much those additional elements 'count' as compared to the suffering alone is a question which is not immediately available to simple calculation; we have no means of converting the various forms of utility into a single comparable unit.

Everything else is just accounting that we can't feasibly calculate anyway.

We're already comparing two unimaginably large numbers against one another. For example; the adjustment of 3^^^3 to 3^^^^3 -- how would you decide on the torture vs. dust-speckings if we did the same to torture? What number of years of torture would need to "exceed" 3^^^3 dust-speckings? 51? 500? 50^50?