I was doing logic problems on the board in class and thinking about rock climbing, and I was struck by the joy of knowing one's made progress on a finite task. You can be pretty confident that if you've got an existential premise and you've set up an existential elimination subproof then you've made progress. You can be pretty confident that if you've got to a certain position on the wall and there is no other way to be at that height then you've made progress. And there is a delight in being really confident that one has made progress.
Moreover, the value of the progress doesn't seem here to be merely instrumental. Even if in the end you fail, still having made progress feels valuable in and of itself. One can try to say that what's valuable is the practice one gets, or what the progress indicates about one's skills, but that doesn't seem right. It seems that the progress itself is valuable. Of course, it has to be genuine progress, not mere going down a blind alley (though recognizing a blind alley, in a scenario where there are only finitely many options, is itself progress).
The value of progress (as such) at a task derives from the value of fulfilling the task, much as the value of striving at a task derives from the value of fulfilling it. But in both cases this is not a case of end-to-means value transfer. Maybe this has something to do with the idea developed by Robert M. Adams of standing for a good. Striving and a fortiori progress are ways of standing and moving in favor of a task. And that's worthwhile even if one does not accomplish the task.
