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paper-machine comments on A response to "Torture vs. Dustspeck": The Ones Who Walk Away From Omelas - Less Wrong
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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.
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.
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?
I don't understand what you mean by "practically infinitesimal". Are you saying the negative utility incurred by a dust speck is zero? Also, what do you mean by "nearly... infinite"? Either a quantity is infinite or finite.
You've completely lost me. If X is the negative utility of N dust specks, and Y the negative utility of fifty years of torture, then the first sentence implies that X > Y. Then the second sentence defines a second kind of negative utility, Z, due to other consequences. It goes on to imply that X + Z < Y. All quantities involved are positive (i.e., the units involved are antiutilons), so there's a contradiction somewhere, unless I've misread something.
Nearly zero. That's part of the hypothesis: that it be the smallest possible unit of suffering. If the logarithmic scale of quantification for forms of suffering holds true, then forms of suffering at the maximal end of the scale would be practically infinite comparably.
Correct, but a number that approaches infinity is not itself necessarily infinite; merely very large. 3^^^3 for example.
The negative utility yet considered. Also, keep in mind that we're at this point priveleging the hypothesis of torture being chosen: we are allowing the number of speckings to be adjusted but leaving the torture fixed. (While it doesn't really change anything in the discussion, it bears noting for considerations of the final conclusion.)
No, it implies that Z(X) + X < Z(Y) + Y.
My argument rests on the notion that the Z-function value of X is effectively zero, and my further assertion that the Z-function value of Y is such that it overwhelms, when added to Y, the value of X.
As long as it's nonzero, then as I stated before, there exists some N such that N dust specks have greater negative utility than fifty years of torture. 3^^^3 and 50 are just proxies for whatever the true numbers are.
This is a category error. 3^^^3 does not approach infinity. It's a fixed number, it's not going anywhere.
The rest of your comment clarifies the offending inequality.
Can you intelligibly grasp it? Or is it "unimaginably large"? For purposes of human consideration, I do not feel it necessary to differentiate between a truly infinite number and one that is "pseudo-infinite" (where by pseudo-infinite I mean 'beyond our comprehension'). I admit this is an imperfect hack.
That way lies the madness of pre-Weierstrass analysis.