Regarded just as a small object, my heart has no apparent function. Only as a part of my living body is my heart's function evident. A formal definition might be: X has function F in context C with success condition S, just in case X's F-ing is causally necessary to C's S-ing.
From #1 and #2. Since #1 considers the parts of a living being collectively, it does not follow that each part taken singly has a function. But the 'I', the 'self' as construed in #2, makes the decisions, clearly needed to survive. So the 'I' does have the function of survival.
Recall from #1's Why that to have a function is to be necessary to achieve a success condition. So in a well-ordered, successful system, X does F. A particular system might be disordered, so we can only say 'X ought to F'. E.g. “Human body temperature ought to be less than 45°C”.
From #3 and #4. Note that the 'ought' of #4-5 is a only a prima facie ought; it might be over-ruled by other conflicting oughts. ('I ought not make myself and others suffer needlessly' comes to mind.) But #5 secures an initial presumption that a well-ordered 'I' seeks life.
If we understand 'happiness' as the psychological condition in which one is glad to be alive, then it is clear that at least chronic and intense unhappiness is a grave threat to life. Some measure of happiness is therefore essential if life is to be embraced.
To the person living it, a life just is what it contains. So to be glad for my life, I need to be glad for what it contains. And I will be glad for the contents of my life only if I value them.
To value something is not just to be affected by it, but to regard that response as justified, deserved. I might be subject to an appetite or addiction that I regard as bad. But to support a happy life, I need to feel that the objects of my devotion are worthy of it.
This actually follows from #8. To seek just my own happiness is to take it as the only worthy ultimate goal of action. It demotes the actual contents of my life to mere means and regards them as unworthy on their own. But that implies that contrary to #8, I do not find them good.
This follows from #5-8. We have not yet discovered what is good. But we have found that happiness, if it is an intrinsic good, is not one that can do the job of leading to happiness. Rather, happiness can only be a side effect of our dedication to independently worthwhile goods.