Wow, great questions!
Practicality. First off, what feelings help us with is practical (in the sense in which philosophers use “practical reason”). Feelings drive us towards better values in situations we actually face in our lives. Which better values are found, then, depends on which situations we’ve actually faced. And those values can be tested in those situations.
Epistemic Gain. To know by reason that our new values are better than our old values (and thus that our feelings led us true) does not require an ultimate justification of the new values, but just a way to evaluate the transition as one of epistemic gain. The key idea is from Charles Taylor:
Feelings and Reason. I would tend to label everything that goes on in the feeling → appreciating → grappling → reconciling process as “reason.” But if you prefer to separate feelings and reason, most philosophers would at least consider the latter three stages as kinds of reasoning. They are not, however, examples of reasoning from first principles. I don’t believe reasoning from first principles is even theoretically sufficient for any agent’s knowing how to live. Taylor and Velleman each make this point well in different ways.
Final aims. There’s a recurrent question in philosophy of an ultimate value that all other values reduce to. I am open to the idea that there is, and even that it might be mathematical (some variety of negentropy or something). Hippies might say it’s love or peace. But one thing is clear about all these proposals: even if there’s a final aim, it’s not practical. One needs to have a working set of thousands of intermediate values in order to face the world with cleverness and craft. And it seems the problem of evaluating these intermediate values in their relation to some highest value is—even if theoretically possible—computationally intractable for us, given the richness of the world.
Do Feelings Mislead? As mentioned above, we can use reason to check the work feelings do in us—by checking the value transitions for epistemic gain. I’ve never known feelings to lead me wrong, in the sense that either (a) they drove me to assign conflict between values which weren’t in conflict, or (b) a new reconciliation was not available on reflection to transform the situation. That said, I don’t have much besides this 100% personal success rate with which to argue for the reliability of feelings.
My highest aim. No, integrity or internal coherence is not my highest aim. As above, I’m not sold on the relevance of having a highest aim. But integrity—or as Velleman calls it self-awareness and self-understanding—is vitally important in the lives of planning and cooperating and identity-having agents. Michael Bratman (in his “Intentions, Plans, and Practical Reason”) elegantly shows we could not function as we do without rough predictions of what will be important to us in the future, and Velleman (in “Practical Reflection”) shows that a drive towards integrity is fundamental even to the distinction we make between conscious and unconscious acts. In my Is Anything Worth Maximizing I argue that it’s integrity which solves the prisoner’s dilemma and makes sense of the particular kind of cooperation we see among humans.
Thanks for asking. It’s a nice opportunity to show the background thinking behind the essay and give credit to my favorite 20th century philosophers.