Do we need two fundamental teleological concepts?

There are two teleological concepts: that of a telos and that of proper function. Each of them helps us make certain teleological judgments. Do we need them both? Could we, for instance, define the telos of a system as what is achieved when the system is properly functioning? Or define proper function as the achievement of the telos in a system and all its (relevant?) subsystems?

I don't know for sure that we need them both, but neither of the two specific proposals is correct. Consider the case of an excellent mathematician is striving to solve an extremely difficult mathematical problem, her mathematical faculties are all working properly, but she fails. It is not a necessary condition for the proper function of mathematical faculties that they be able to solve every mathematical problem there is. Both of the attempted reductions neglect the phenomenon that our teleologies can push us above our proper functioning. An excellent mathematician or athlete may already be functioning above our proper level of functioning, but nonetheless there will be telê that she doesn't have fulfilled. (Though, perhaps, we may want to say that all humans are mathematically and athletically defective, due to the Fall, in which case we could maintain that the mathematician is not functioning properly if there are any soluble problems she can't solve. But even if this view of humans is true, we could imagine that mathematicians of some other species are functioning properly and yet failing to solve problems.)

It seems that we need the concept of proper function to tell us what is good enough, what is normal. But we need the concept of a telos to supply us with comparisons between instances of proper function. The mathematician who solves and who fails to solve are both functioning properly, are both functioning sufficiently well, but the one who solves is functioning better--precisely because she achieves her telos in respect of that process. Or, alternately, we may say that both are functioning properly, but one is functioning merely normally and the other supernormally--again, a distinction that mere proper function does not seem capable of making.

Maybe there is a more clever way of relating the two concepts.

More on the meaning of life

Both of the following claims are plausible to me but appear to be in tension:

1. A full finite "Aristotelian" life of seriously attempting to practice the intellectual and ethical virtues could be satisfactory.
2. I rightly find a finite purely natural life unsatisfactory (our hearts are rightly restless until they find rest in God).

When thinking about this, one can put the focus on the finite length of life or on the lack of a supernatural component in the Aristotelian life.

But now observe that (1) and (2) are not logically contradictory. To see that, notice that there are several logically possible stories to be told on which both (1) and (2) are true. The first story is that of grace and fallenness: I am fallen, and without the supernatural component of grace in my life, I couldn't actually lead a life of seriously attempting to practice the virtues—I would, instead, slide into vice unless I happened to die early (in which case the life wouldn't be "full"), and eventually I would abandon the serious attempts to practice the virtues. If that story is true, then (2) is true, because any finite purely natural life would be a life without grace (by definition of "natural") and hence could not be a full "Aristotelian" life.

A second, complementary way to reconcile (1) and (2) is this. I have received the grace of longing for the joy of supernatural union with God. The grace of Christ both makes me long for that joy and directs me to it. As a result of that grace, my heart is restless unless it rests in God. (I don't know if Augustine would allow that the truth of his dictum is dependent on grace.) Given the grace to have the intensively infinite beatitude of union with God, any purely natural life would indeed be objectively unsatisfactory. But, nonetheless, an Aristotelian life could be fully satisfactory—not to me as I am, but to a hypothetical human being who is both unfallen (and hence can live the Aristotelian life) and has not received the grace of that longing.

A generalization of the second way to reconcile (1) and (2) is this. We read (1) in this way: There are possible beings in many ways like us who would be rightly satisfied by a finite Aristotelian life. But these possible beings are not us. Here, "are not us" can be read in two ways. First, as we did in the second way: they are not us who are graced with a longing for God. Second, we could have a completely different reading: they are not human. On this reading, the finite Aristotelian life is not a life for human beings, but for perhaps hypothetical non-humans who do not have the infinite beatitude of union with God as their telos. This gives us a third way to reconcile (1) and (2).

However, a natural human life is indeed sufficient to fulfill the human being's natural needs. It takes grace to long for more than the natural needs. So human beings should, in fact, be able to be satisfied with a natural life, absent grace, at least if they are unfallen. This makes the third way to reconcile (1) and (2) problematic. However we can focus not on the naturalness of the Aristotelian life in (1), but on its finitude. It may be that living forever is actually natural to us. (That we needed the fruit of the tree of life is compatible with this, because there is nothing absurd about needing external goods to live out our nature.) If so, then the beings that would rightly be satisfied with a finite Aristotelian life (note that Aristotle himself was open to the possibility of an afterlife) are not humans.

These three answers appear compatible with one another, and all appear plausible, so the full story is that an infinite Aristotelian life would be satisfactory to us, if we were unfallen and ungraced, but fallen as we all are, and by and large graced as we are (I think grace is offered to all at some point, but for some that point may not yet have come), we rightly find the thought of such a life insufficient. And a finite Aristotelian life would be satisfactory only to humanoids who are not human. The story also explains why some people might find an infinite Aristotelian life satisfactory—for they have not received grace—and why some might feel satisfied by the thought of a finite Aristotelian life—for their aspirations are lowered by the fall.