26 April 2005

Differential Diagnosis of 'Approximation'

A mistake interpreters of a text often make is to fail to make a comparative argument. It is necessary to argue, not simply that one's favored interpretation is supported by the text, but also that it is better supported than plausible alternatives.

This is an analogue of what physicians call 'differential diagnosis.' Suppose there is an array of symptoms which might indicate the presence of exotic disease E. But those symptoms are also commonly associated with a much less exotic, and much more common, disease C. Then it's important to rule out that C is the cause of the symptoms before treating for E, typically by finding some symptom or sign which only E causes, not C. This is the 'differential diagnosis'.

So we might ask, as regards Lear's notion of 'approximation', whether, for texts which might be taken to support Aristotle's reliance on this relatively uncommon notion, there is not some more common Aristotelian idea, which those texts would similarly support, and, if so, how this more common idea would be ruled out.

In fact there is a more common idea of this sort: analogy. Analogy is the genus of which 'approximation' is the species. Whenever X approximates Y, then X and Y are analogous; but (I take it) it's not always the case that, when X and Y are analogous, one approximates the other. (If it is always the case, then 'approximation' is a fancy, and misleading, name for 'analogy'.) For instance, reproduction in mortal animals is an analogue of uninterrupted divine life. But presumably that mortal life approximates divine life goes beyond their merely being analogous.

(Digression: But how does it go beyond this, except that mortal animals strive to be immortal, that is, that they reproduce in order to be immortal (as Plato says)? But note that, if this is the difference, it's not clear that one could ever argue in the following way: "X is for the sake of Y, because X approximates Y." Why? Because you'd have to establish first that X is for the sake of Y, in order to establish that X and Y were a case of approximation rather than simple analogy. That is, you'd have to reason, "X approximates (and isn't merely an analogue of) Y, because X is for the sake of Y." And yet it seems that Lear needs to argue in the problematic way.)

Suppose we grant all of the following: practical reasoning is a sort of contemplation (theoria tis); there's some sort of likeness (homoioma ti) between practical reasoning and contemplation; (even) practical reasoning shares in (metechei) contemplation. How do we rule out that Aristotle isn't asserting the weaker, and more common, idea that practical reasoning and contemplation are analogous?

Lear recognizes the problem. At various points in her argument, she says that what she has established so far is merely that the one is analogous to the other. She correctly takes this to be a preliminary result, and she acknowledges that she needs to say more to establish, rather, that the one is an approximation of the other.

This leads to two questions: What more does she need to show (the differential diagnosis)? And does Lear succeed in showing it?

Lear apparently thinks that she needs to show either of two things. (i) That there is an ordering between the two analogates, so that it's proper to hold that the one has 'more' or is 'especially' (malista) what the other is. Thus: if philosophical contemplation is contemplation to a greater degree than practical reasoning, or if it is malista contemplation, then practical reasoning is an approximation of philosophical contemplation. (ii) That the one analogate is for the sake of the other.

This is clear from her remarks on p. 89:

We should notice, however, that if contemplation and the exercise of practical wisdom are good merely by analogy, there is no reason to think that one is worth choosing for the sake of the other or is indeed inferior to it in any way at all. In an ordinary analogy, where A:B::C:D, there need be no priority of one relation over the other. Since Aristotle believes that contemplation is superior to the exercise of practical wisdom (NE VI.7) and is indeed its end (as I hope eventually to show), mere analogy does not sufficiently describe the connection between contemplation and morally virtuous action.
Two observations:

1. Although an analogy, as Lear says, need not have an ordering, it's not true that it cannot have an ordering. Thus, for instance, Aristotle thinks that:
And yet sameness is prior to similarity (it is 'more a unity') because substance is prior to quality. Presumably we don't want to say that similarity approximates sameness. (Or do we?) In which case that there is ordering cannot serve to make the differential diagnosis between approximation and analogy.

2. It's hazardous to argue, as Lear apparently wishes to do: "X and Y are analogous; Aristotle thinks that Y is better than X, and X is for the sake of Y; therefore Aristotle thinks that X approximates Y" because precisely at issue is whether 'approximation' captures the notion of 'for the sake of' that is at play!


Anonymous said...

There's a good line from Be Cool, which isn't the best movie: don't be hatin', be participatin'.

Anonymous said...

One of my problems in assessing Lear's Approximation Thesis is that NE. X. 7-8 says so little about what theoria actually is. We must chase and try to put together discussions scattered throughout the Corpus.
For example, does Aristotle allow that theoria can be creative work, as in discovering & constructing novel math proofs of important conjectures? If so, then theoria is in part a matter of planning good strategy & tactics in our proof-seeking. A kind of Euboulia will be vital to it , just as practical reasoning requires excellence in deliberation. Perhaps practical euboulia will try to imitate & follow a more rigorous theoretic euboulia.
In any case, until we have a much better picture of what theoria comprises, I don't see how we can speculate very fruitfully on its connections with practical reasoning.

Anonymous said...

Excellent point. (And I need to look more carefully at what Lear takes theoria  to be.) I suppose that if the 'approximation' thesis were very helpful, then, given Aristotle's sketchiness, we might take theoria be whatever it needs to be (within reasonable bounds) for 'approximation' to work out correctly. 

Posted by Michael Pakaluk

sean kelsey said...

Disclaimer: I haven't read Lear's book yet. But the notion of approximation intrigues me so I thought I'd try feeling my way along. I will proceed abstractly but to fix ideas we might (below) let "X" be "acting justly" and let "Y" be "contemplating" and let "F" be "living well."

Suppose that X is the sort of thing that's done for its own sake and that X and Y are analogues. I guess that, in Aristotle, the second supposition means something like this, that in a way X and Y are the same (they are the same in that there is some single thing (call it "F") which they both are, except that what "being F" is (for X) is the same as what "being F" is (for Y) only by analogy. This is by contrast with the case where there is a single account of what it is to be F which tells us equally and straightforwardly both what being F is for X and what being F is for Y, as would be the case if e.g. "X" was "human being" and "Y" was "giraffe" and "F" was "animal.")

OK. Suppose we now ask: what would it be to say that, in addition to being analogous to Y, X approximates Y? Here's a suggestion: it would be to say that Y is more (*malista*, *kurioteros*) the thing X and Y both are than X is. (And let's follow for now Michael's remark that "approximating" is a special case of "being analogous to.")

Question: on this account of approximation, would it follow from the fact that X is for its own sake and that X approximates Y that X is for Y? Here I'm tempted to say: if X is done for its own sake, i.e. for the sake of X, and if Y *just is* what X is, namely F, except only more so, then it seems that it should follow that X is done for the sake of Y. More concretely: if acting justly is done for its own sake, i.e. for the sake of acting justly, and if contemplating *just is* what acting justly is, namely living well, except only more so, then it seems that it should follow that acting justly is done for the sake of contemplating.

Here it is natural to protest: but this couldn't possibly follow, because X and Y are different!!! But in protesting in this way aren't we failing to take seriously--failing to let our reasoning be controlled by--the point that X approximates Y, i.e. that "what X is" and "what Y is" are one and the same thing, F, except that Y is even more the thing that X is, namely F, than X itself is?

Probably we must assume in addition: not only is X the sort of thing that's done for its own sake, but the reason X is the sort of thing that's done for its own sake is that X is F (sc. the very thing that Y also is). (This is by contrast with the case where the reason X is done for its own sake is not that X is F, but that X is some other more specific thing G, which Y is not.) Put another way: we must assume in addition that the single thing F which X and Y both are is not so to speak a generic thing, so that the reason X is F and Y is F would have to do with the fact that X is G and Y is H and G, where H are so to speak distinct and coordinate species of F.

I suspect this "additional" assumption is in fact implicit in the supposition that X approximates Y.