Are you saying that 3^^^3 is not sufficiently large? Then consider 3^^^^3.
Whatever epsilon you assign to dust specks, there’s still a yet larger number such that this number of dust specks is worse than torture. Everything else is just accounting that we can’t feasibly calculate anyway.
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?
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.
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.
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.
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.
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.
Why do you concede this? All the suffering you list after this is just as direct.
None of the things I listed afterwards were “suffering” at all. “Suffering” is not “the absence of pleasure”—it is “the antithesis of pleasure”. “Utility” is not synonymous with “enjoyment” or “pleasure”. (Also, please do recall that hedonistic utilitarianism is far from the only form of utilitarianism in existence.)
Saying that torture-without-most-of-the-things-that-make-it-wrong is not so bad might be true,
What.. ? Just… who are you reading in these threads? I am finding myself more and more convinced that you are responding to the writings of someone other than me. You seem to have a persistent habit of introducing notions to our discussions—in a manner as though you were responding to something I had written—that just bear in no way whatsoever to anything I have written or implied by my writings.
I’ll concede that suffering might not be the right word. But everything later in that sentence are essential parts of why torture is wrong. If torture didn’t imply those things (i.e. wasn’t torture), then it would be the right choice compared to dust-specks.
But everything later in that sentence are essential parts of why torture is wrong.
Of course those things are essential parts of why torture is wrong. They would have to be, for my argument to be valid.
If torture didn’t imply those things (i.e. wasn’t torture), then it would be the right choice compared to dust-specks.
Are you simply unaware that the conventional wisdom here on Less Wrong is that the proper answer is to choose to torture one person for fifty years rather than dust-speck 3^^^3 people?
Are you simply unaware that the conventional wisdom here on Less Wrong is that the proper answer is to choose to torture one person for fifty years rather than dust-speck 3^^^3 people?
Yes, that is the conventional wisdom. I agree with you that it is wrong, because the features of torture you describe are why the badness quality of torture cannot be achieved in the sum of huge amounts of a lesser badness.
You seem to think that someone could think dust-specks was the right answer without taking into account those essential parts of torture. Otherwise, why do you think that the secondary effects of allowing torture were not considered in the original debate?
As you noted in your post, people in the original thread objected to choosing torture for reasons that basically reduce to the “non-additive badness” position. For me, that position is motivated by the badness of torture you described in your post. So I read the other commenters charitably to include consideration of the sheer wrongness of torture. I simply can’t see why one would pick dust-specks without that consideration.
Now you say I’m reading them too charitably. I’ve been told before that I do that too much. I’m not sure I agree.
Are you saying that 3^^^3 is not sufficiently large? Then consider 3^^^^3.
Whatever epsilon you assign to dust specks, there’s still a yet larger number such that this number of dust specks is worse than torture. Everything else is just accounting that we can’t feasibly calculate anyway.
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.
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.
Why do you concede this? All the suffering you list after this is just as direct.
Saying that torture-without-most-of-the-things-that-make-it-wrong is not so bad might be true, but it isn’t useful.
None of the things I listed afterwards were “suffering” at all. “Suffering” is not “the absence of pleasure”—it is “the antithesis of pleasure”. “Utility” is not synonymous with “enjoyment” or “pleasure”. (Also, please do recall that hedonistic utilitarianism is far from the only form of utilitarianism in existence.)
What.. ? Just… who are you reading in these threads? I am finding myself more and more convinced that you are responding to the writings of someone other than me. You seem to have a persistent habit of introducing notions to our discussions—in a manner as though you were responding to something I had written—that just bear in no way whatsoever to anything I have written or implied by my writings.
Why is this?
I’ll concede that suffering might not be the right word. But everything later in that sentence are essential parts of why torture is wrong. If torture didn’t imply those things (i.e. wasn’t torture), then it would be the right choice compared to dust-specks.
Of course those things are essential parts of why torture is wrong. They would have to be, for my argument to be valid.
Are you simply unaware that the conventional wisdom here on Less Wrong is that the proper answer is to choose to torture one person for fifty years rather than dust-speck 3^^^3 people?
Yes, that is the conventional wisdom. I agree with you that it is wrong, because the features of torture you describe are why the badness quality of torture cannot be achieved in the sum of huge amounts of a lesser badness.
You seem to think that someone could think dust-specks was the right answer without taking into account those essential parts of torture. Otherwise, why do you think that the secondary effects of allowing torture were not considered in the original debate?
Because I read the original submission and its conversation thread.
This is a bit of Meta-Comment about commenting:
As you noted in your post, people in the original thread objected to choosing torture for reasons that basically reduce to the “non-additive badness” position. For me, that position is motivated by the badness of torture you described in your post. So I read the other commenters charitably to include consideration of the sheer wrongness of torture. I simply can’t see why one would pick dust-specks without that consideration.
Now you say I’m reading them too charitably. I’ve been told before that I do that too much. I’m not sure I agree.