Aggregation of Harms and the Sorites Paradox

Today in Malory Seminar (don't ask), for some reason, discussion turned to aggregation of harms, something I discussed quite a lot in the early days of this blog. I presented the argument from Alastair Norcross's paper, which I fully agree with. Briefly, here is the argument:

It is possible to construct a list of slightly-increasing harms, from 'having a mild headache' to 'being tortured to death'. For any two consecutive items on that list, H1 and H2, where H2 is slightly worse than H1, there is some finite number of instances of H1 such that that number would outweigh one instance of H2. So, for instance, a billion bad headaches is worse than one REALLY bad headache. But, given the transitivity of 'worse than', this means that there is some (astronomical) finite number of headaches that is worse than one instance of being tortured to death.

Many people find this conclusion counterintuitive. I do too, but I'm convinced by the argument. My professor (like many of my readers last time around) was not. I found her response very puzzling, though. She said roughly the following. "The argument you're giving is just an instance of the Sorites paradox. Therefore, it is unconvincing, because either: (1) the Sorites paradox has a solution, in which case that solution will also apply to your argument, or (2) the Sorites paradox has no solution, in which case we shouldn't worry about instances of it." I was blown away at the psychological ease with which she discussed especially the second possibility. "If the sorites paradox has no solution"! Surely she's not asking us to accept that some contradictions might be true! All paradoxes must have solutions! If not, the world is seriously gone to hell. I also have doubts about the plausibility with which we can describe this as an instance of the Sorites Paradox, but my thoughts there aren't yet developed enough even for web publishing. They have something to do with what might be the impossibility of vagueness about 'better than'.