So let’s suppose that the pain of solitary confinement without anything interesting to do can never add up to the pain of 50 years torture. According to this, would you honestly choose to suffer the solitary confinement for 3^^^3 years, rather than the 50 years torture?
You’ve already defined the answer; “the pain of solitary confinement without anything interesting to do can never add up to the pain of 50 years torture.” If that’s so, then shouldn’t I say yes?
To some extent, my preferences do tell me to work on a “minimize the worst pain I will ever experience,” so it doesn’t seem that ridiculous to say that there is SOME amount of torture that even a Nearly Infinite duration of “something slightly less bad than torture” doesn’t add up to.
Going back to the math, it seems as though at least one of the following must be true for a “reasonable”, non-sadistic preference function:
1) For all I1 > 0, lim (NT->+â) U(NT,I1) = lim (NT->+â) U(NT, I2) for all I2 such that 0 < I2 < I1
2) There exists an I1 > 0 such that lim (NT->+â) U(NT,I1) > lim (NT->+â) U(NT, I1 - ε) for all ε such that 0 < ε < I1
3) There exists an I1 > 0 such that lim (NT->+â) U(NT,I1) < lim (NT->+â) U(NT, I1 + ε) for all ε > 0
In the first case, we have the case that, for any NT1, I1, and I2 such that I1 > I2 > 0, there exists a NT2 such that U(NT1,I1) < U(NT2,I2), no matter how small I2 is and how large NT1 and I1 are.
In the second and third cases, we have a situation in which there is an I1 and I2 such that I1 > I2 and are arbitrarily close together, and there is an NT1 such that U(NT1, I1) > lim (NT->+â) U(NT, I2).
I have to bite the bullet on one of these problematic conclusions, so I’ll bite the bullet on #2.
“An Impossibility Theorem for Welfarist Axiologies” is an interesting paper on a similar subject; given the choice of which of the criteria I have to reject, I choose to reject “The Minimal Non-Extreme Priority Principle”.
You’ve already defined the answer; “the pain of solitary confinement without anything interesting to do can never add up to the pain of 50 years torture.” If that’s so, then shouldn’t I say yes?
To some extent, my preferences do tell me to work on a “minimize the worst pain I will ever experience,” so it doesn’t seem that ridiculous to say that there is SOME amount of torture that even a Nearly Infinite duration of “something slightly less bad than torture” doesn’t add up to.
Going back to the math, it seems as though at least one of the following must be true for a “reasonable”, non-sadistic preference function:
1) For all I1 > 0, lim (NT->+â) U(NT,I1) = lim (NT->+â) U(NT, I2) for all I2 such that 0 < I2 < I1
2) There exists an I1 > 0 such that lim (NT->+â) U(NT,I1) > lim (NT->+â) U(NT, I1 - ε) for all ε such that 0 < ε < I1
3) There exists an I1 > 0 such that lim (NT->+â) U(NT,I1) < lim (NT->+â) U(NT, I1 + ε) for all ε > 0
In the first case, we have the case that, for any NT1, I1, and I2 such that I1 > I2 > 0, there exists a NT2 such that U(NT1,I1) < U(NT2,I2), no matter how small I2 is and how large NT1 and I1 are.
In the second and third cases, we have a situation in which there is an I1 and I2 such that I1 > I2 and are arbitrarily close together, and there is an NT1 such that U(NT1, I1) > lim (NT->+â) U(NT, I2).
I have to bite the bullet on one of these problematic conclusions, so I’ll bite the bullet on #2.
“An Impossibility Theorem for Welfarist Axiologies” is an interesting paper on a similar subject; given the choice of which of the criteria I have to reject, I choose to reject “The Minimal Non-Extreme Priority Principle”.