The problem is that the utility isn’t constant. If you, today are indifferent to what happens on future Tuesdays, then you will also think it’s a bad thing that your future self cares what happens on that Tuesday. You will therefore replace your current self with a different self that is indifferent to all future Tuesdays, including the ones that it’s in, thus preserving the goal that you have today.
The problem is that the utility isn’t constant. If you, today are indifferent to what happens on future Tuesdays, then you will also think it’s a bad thing that your future self cares what happens on that Tuesday. You will therefore replace your current self with a different self that is indifferent to all future Tuesdays, including the ones that it’s in, thus preserving the goal that you have today.
Good point. I have to remember not to confuse expected utility with future utility.