On the puzzle of the self-torturer
The crux of the puzzle of the self-torturer is how one takes reasonable advantage of collecting $10,000 without ending up the worse for it, i.e. hurting oneself. Two important issues of the puzzle include vagueness and intransitivity.
First, the difference between setting 1 and setting 2 are minimal as well as between setting 500 and setting 501 or setting 499, but the difference between setting 501 and setting 1 is enormous. Even though there is no noticeable difference between individual settings, there is a large difference between settings quite a distance apart from one another, i.e. setting 1 and setting 950. So, it would seem that the difference between local settings is vague, but the difference between global settings is distinct. A second issue of concern in this puzzle is that of intransitivity. One cannot infer from the fact that there is little difference between setting 1 and setting 2 and between setting 2 and setting 3 that setting 3 is just as preferable as setting 1. The intransitivity between these settings creates confusion in the puzzle.
Questions: how can one determine the difference between settings if the difference is so vague? Why is vagueness a problem? Is it that vagueness cannot be projectibly determined? In other words, is the problem with vagueness merely the idea that one cannot adequately pinpoint when the setting “is comfortable” as opposed to when the setting “is not comfortable?” On the issue of intransitivity, could one conceive of a principle of intransitivity that corresponds to one’s rationality? Are all issues of intransitivity irrational?