The Linear Utility Hypothesis does imply that there is no extra penalty (on top of the usual linear relationship between population and utility) for the population being zero, and it seems to me that it is common for people to assume the Linear Utility Hypothesis unmodified by such a zero-population penalty. Furthermore, a zero-population penalty seems poorly motivated to me, and still does not change the answer that Linear Utility Hypothesis + zero-population penalty would suggest in the thought experiment that you quoted, since you can just talk about populations large enough to dwarf the zero-population penalty.
Refuting a weak argument for a hypothesis is not a good way to refute the hypothesis, but that’s not what I’m doing; I’m refuting weak consequences of the Linear Utility Hypothesis, and “X implies Y, but not Y” is a perfectly legitimate form of argument for “not X”.
The Linear Utility Hypothesis does imply that there is no extra penalty (on top of the usual linear relationship between population and utility) for the population being zero, and it seems to me that it is common for people to assume the Linear Utility Hypothesis unmodified by such a zero-population penalty. Furthermore, a zero-population penalty seems poorly motivated to me, and still does not change the answer that Linear Utility Hypothesis + zero-population penalty would suggest in the thought experiment that you quoted, since you can just talk about populations large enough to dwarf the zero-population penalty.
Refuting a weak argument for a hypothesis is not a good way to refute the hypothesis, but that’s not what I’m doing; I’m refuting weak consequences of the Linear Utility Hypothesis, and “X implies Y, but not Y” is a perfectly legitimate form of argument for “not X”.