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:

Sameness:Substance::Equality:Quantity::Similarity:Quality.

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!