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.
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.