Do we have Vague Projects?

Tenenbaum and Raffman (2012) claim that "most of our projects and ends are vague." (p.99)  But I'm not convinced that any plausibly are.  I've already discussed the self-torturer case, and how our interest in avoiding pain is not vague but merely graded.  I think similar things can be said of other putative "vague" projects.

Self-Torturers without Diminishing Marginal Value

My last post mentioned in passing that the puzzle of the self-torturer may be complicated by the fact that money has diminishing marginal value.  This can mean that a few increments (of pain for $$) may be worth taking even if a larger number of such increments, on average, are not.  So to make the underlying issues clearer, let us consider a case that does not involve money.

Irrational Increments for the Self-Torturer

Recall that the Self-Torturer (ST) gets $10 000 for each turn of a dial that permanently increases the pain he feels for the rest of his life by a negligible amount.  Each individual increment seems worth making, the thought goes, but 1000 increments would leave ST in intense agony, which no amount of money can compensate for.

It seems intuitively clear to me that ST would soon reach a point at which additional increments -- even considered in isolation -- are not worth it.