I think I disagree with @David Schwartz. I'd read Aristotle's claim differently. I don't think he's offering a definition of ``good'' here per se (and despite what he says).* It's more that he's giving three different examples of the kind of thing that it is proper to attribute the property of goodness to.
In other words, I think he's saying there are three kinds of good things:
- First, those things which we "ought to choose for their own sake". Let's call these intrinsic goods.
- Second, things which are chosen "for the sake of something else." Let's call these instrumental goods.
- Finally, there if there is something that is the ultimate object of desire then that thing should be called good too.
An example of the first kind of thing is happiness.** Aristotle says in Nicomachean Ethics Book I that happiness is just desirable for its own sake. Now Aristotle knows of course that some people want bad things, so the mere fact that somebody wants something that does make that thing intrinsically good. But he does think that virtuous people who have been brought up properly, who have lots of experience of the world, and who have thought carefully about life will be able to know which things are worth wanting and which aren't. The intrinsically valuable things are the ones that such people would want, and since we want to be like those people, those are the ones we should want too.
An example of an instrumental good would be exercise. I don't like exercise itself, I find it painful. However, exercise is a means toward an end (good health) that I do want, therefore there is a sense in which exercise is good, even though it is not the thing I want per se. It's the thing that gets me the thing that is intrinsically good, so it exercise is instrumentally good as a means toward that end.
The final thing about the ultimate object of desire refers back to a little puzzle Aristotle takes up at the beginning of Nicomachean Ethics I. Is there just one thing that is intrinsically good that all other goods are instrumental goods for attaining, or are there many diverse goods? This is a famous interpretative problem in Aristotle, but I think Aristotle thinks that happiness is the one good or goal of all human activity, and other things that look like intrinsic goods are just part of "happiness" in some way. Obviously, if happiness is that for the sake of which all human activities are done, then happiness is good. Now the reference to other kinds of things, sensitive creatures (animals) and so forth is simply to indicate that for Aristotle humans are just one specific kind of animal with one specific kind of nature and one specific kind of end. Happiness is a very human thing and there might be other ultimate goals of the activities of other kinds of creatures. I don't know what more to say about this alternative though, b/c it looks very obscure to me what these might be and I'm not aware of anywhere else that Aristotle discusses it, although I don't know his biological works very well.
*The reason I say this is that Aristotle has a quite precise technical notion of what it is to give a definition of something that involves being able to express that thing's essence in terms of which kinds or types it belongs to. "Man is a rational animal" is an example of a definition in this technical sense. Words like "good," "being," and "one" are what Aristotle calls ``transcendental'' properties, because they aren't kinds or types, rather they are properties that things of every kind can have.
**"Happiness" for Aristotle is not just an emotional feeling or psychological state. It refers to a kind of holistic evaluation of one's life. "Blessedness"or "flourishing" might be a better translation.
