It seems good, for the record, to post the two texts which Lear thinks articulate with especial clarity the notion of approximation. The first is Aristotle, De Anima 2.4.415a25-b7:
The acts in which [the nutritive soul] manifests itself are reproduction and the use of food, because for any living think which has reached its normal development and which is unmutilated...the most natural act is the production of another like itself, an animal producing an animal, a plant a plant, in order that, as far as its nature allows, it may partake in [metechwsin] the eternal and divine. For all things desire this, and do whatever they do in accordance with their natures for the sake of [heneka] this. The phrase 'that for the sake of which' is ambiguous; it may mean either the end to achieve which or the being in whose interest the act is done. Since then no living thing is able to partake in what is eternal and divine by uninterrupted continuance (for nothing perishable can ever remain one and the same), it tries to achieve that end in the only way possible to it, and success is possible in varying degrees; so it remains not indeed as the self-same individual but continues its existence in something like itself--not numerically but specifically one.The second is Plato, Symposium 207c9-208b6, from which the Aristotle passage seems to borrow:
For among animals the principle is the same as with us, and mortal nature seeks so far as possible to live forever and be immortal. And this is possible in one way only: by reproduction, because it always leaves behind a new young one in place of the old...And in that way everything mortal is preserved, not, like the divine, by always being the same in every way, but because what is departing and aging leaves behind something new, something such as it had been. By this device, Socrates, what is mortal shares [metechei] in immortality, whether it is a body or anything else, while the immortal has another way. So don't be surprised if everything naturally values its own offspring, beause it is for the sake of immortality that everything shows this zeal, which is Love.(These passages are quoted by Lear on pp. 80-81, in a section entitled, "Imitation in Aristotle's Natural Philosophy".)
On the basis of these passages, Lear claims:
1. When X in the way described imitates or approximates Y, then we can say that X acts for the sake of Y, and this is a distinct and third way in which one thing can act for the sake of another, besides "instrumental and constitutive relations" (82).But, two difficulties:
2. "[T]he value of the approximation depends on the value of the object it approximates. In other words, the paradigm is the source of value for the things approximating it."
--What seems lacking in Lear's first claim (but which is important in Plato's passage) is talk of possessing a good. What Plato seems to have in mind is: we want to possess some good, which strictly we cannot have, and thus we contrive to possess the thing most like it, which we can have. But when we make this adjustment, it's not clear how approximation will apply to the relation between philosophical contemplation and actions of the virtues of character in NE, because we can possess philosophical contemplation.
--I don't quite see how 2. is implied by the passages (but perhaps readers of Dissoi Blogoi will disagree). In fact, 2. seems problematic, for a fairly obvious reason. To the extent that an imitation (or approximation) is successful, then the imitation has the very same attributes that make the thing imitated valuable. But then why would the value of the imitation be dependent on the value of the thing imitated, rather than freestanding?
Lear notes this last difficulty at n. 29, p. 83 (acknowledging Kieran Setiyabut for pointing it out). But, as far as I can see, she does not reply to it. The best she says is: "I am not sure that there are any arguments to show that we ought (or ought not) to see things as Aristotle does, at least not any I can rehearse in the scope of this book"(84). But that's beside the point, because what is at issue is, assuming for the moment that we do in fact 'see things as Aristotle does', then why, on this view, should we hold that the value of the imitation depends upon the value of the thing imitated?