paper-machine comments on A response to "Torture vs. Dustspeck": The Ones Who Walk Away From Omelas - Less Wrong

-4 Post author: Logos01 30 November 2011 03:34AM

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Comment author: [deleted] 30 November 2011 04:40:26PM *  1 point [-]

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.

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.

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.

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.

Comment author: Logos01 30 November 2011 04:50:35PM -2 points [-]

Are you saying the negative utility incurred by a dust speck is zero?

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.

Either a quantity is infinite or finite.

Correct, but a number that approaches infinity is not itself necessarily infinite; merely very large. 3^^^3 for example.

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.

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.)

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.

No, it implies that Z(X) + X < Z(Y) + Y.

so there's a contradiction somewhere, unless I've misread something.

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.

Comment author: [deleted] 30 November 2011 05:02:38PM 1 point [-]

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.

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.

Correct, but a number that approaches infinity is not itself necessarily infinite; merely very large. 3^^^3 for example.

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.

Comment author: Logos01 30 November 2011 05:20:06PM *  0 points [-]

This is a category error. 3^^^3 does not approach infinity. It's a fixed number, it's not going anywhere.

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.

Comment author: [deleted] 30 November 2011 05:23:15PM 3 points [-]

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').

That way lies the madness of pre-Weierstrass analysis.

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