How Would Approximation Work Here?

I think many of us regard ourselves as floundering in trying to grasp this notion of 'approximation'. I don't take that itself to cast suspicion on the notion. Rather, I think it's extremely difficult to understand what it means to say that ethical action is reasonable (as I do believe).

Here's the sort of thing about which Aristotle says something fairly definite. Can we say with some confidence whether or not approximation works here?

I go to the store and make a purchase. Say, I buy a box of candies for $6. I give the cashier a $10 bill. The cashier mistakenly believes I've used a $20 bill and gives me $14 in change. I don't count my change until later, when I'm in another store and take out money to pay for something else. Then I discover the extra money and realize that the cashier had made a mistake.

There's no issue of getting caught or being found out. It was an 'honest mistake' and the sum is relatively small. Nonetheless I decide that I'll go back and return the extra $10. Let's suppose that I don't think that "I should" go back, or that "it would be wrong" if I didn't. Let's just say that this strikes me as a good thing to do. Maybe I remember the story of Honest Abe Lincoln from my youth, and I remember, too, that I've often thought that I'd like to do something similarly admirable.

So I return the money. Now, in doing so, I part with $10 that I didn't need to part with. But Aristotle would regard this as a quasi-exchange (see NE 9.8). I part with the $10, and in that respect lose something, but the action which I did was 'noble' (kalon), and I somehow gain this kalon aspect of the action in doing it. Since what is kalon is better than what is useful or chresimon (always or for the most part--it doesn't matter which, because it doesn't matter here) I'm actually better off (Aristotle thinks) having gone back to the store to return the money than if I had pocketed the extra money and returned home, or bought something with it.

I'm fairly confident this way of looking at this 'just' action is Aristotelian in spirit. Now the question is: Does it make sense (does it help, does it seem correct) to say that my returning the money is an 'approximation' to philosophical contemplation?

Another question (which is like one I raised in one of my first posts on the book): Is it that (i) my returning the money is similar to philosophical contemplation, or that (ii) my returning the money is similar to objects of philosophical contemplation (in being kalon)? If the latter, then perhaps we'd want to say: the object of philosophical contemplation and virtuous action is the same, the kalon, but one obtains the kalon in action by doing a kalon action, whereas one obtains the kalon in thinking by thinking about something kalon.

This would make virtuous actions similar to philosophical contemplation, yet I don't see that we should say that the former 'approximates' the latter, unless we held that the kalon of virtuous action approximated the kalon which we contemplate in philosophical contemplation. And yet it would seem bizarre to hold that the sort of kalon produced by the just action described above, which involves (as Aristotle thinks) simple equalities, such as that 6 = (10 - 14) +10 , approximate the kalon of those objects that a philosopher would want to contemplate. (It hardly seems, too, that the great worth of virtuous actions is captured in the reflection: "True enough, 5=5 is a fairly boring truth, but, given that you're in no position to contemplate now, and you need to buy food, that's the best you can achieve for now.")

Btw, Lear deals with courage, moderation, and magnanimity in Happy Lives, but not justice (for space limitations, she explains). But isn't this unfortunate?--because it would seem that justice (as Aristotle understands it, as involving equalities) would likely provide the most promising examples for a theory of 'approximation'.