


     D1 relatives must be opaque on Aristotle’s view otherwise the way Aristotle characterizes them does not make sense. Following D1, Aristotle explains various formal properties of relatives, according to his view. For example, relatives have contraries: virtue is contrary to vice (6b15-b18). Relatives admit of degree: more similar and less similar are degrees of being similar (6b19-27). Relatives reciprocate (6b28-7b9). For example: if parent and offspring is a relative-correlative pair, then parent is parent of offspring and offspring is parent of child. In the course of his discussion of reciprocity, Aristotle relies on the following further assumption (7a31-b9):

(Exclusivity) If X and Y is a relative and correlative pair, then X relates only to Y.

But for the Exclusivity schema to hold, Aristotle must understand relatives opaquely here. Suppose that ‘parent’ and ‘offspring’ are a relative-correlative pair and replace X and Y:

(Ex) Parent relates only to offspring

(Ex) may not be true if it is read transparently, since some particular parent may not be the parent of some given offspring. Thetis is a parent of Achilles, but not a parent of Ajax. But (Ex) is true if read transparently: any parent is parent of some offspring or other. Thus, the only way for all instances of the exclusivity schema to hold is if relative terms are read opaquely here. Since exclusivity applies to all D1 relatives, Aristotle must understand all D1 relatives opaquely. So D1 tells us that we need to view relatives opaquely.

D2, on the other hand, captures what I have called the transparent way of reading relative statements. At 8a35-b14, Aristotle connects D2 with an epistemic criterion, the so-called ‘principal of cognitive symmetry’ which he suggests will tell us whether some relative is a D2 relative or not:

PCS: If someone knows any relative definitely he will also know definitely that in relation to which it is spoken of

The test distinguishes between D1 relatives and D2 relatives on the grounds that we know the correlatives of D1 relatives only in one way, while we know the correlatives of D2 relatives only in another way. 8b4-13 tells us that the two ways of knowing the correlative are knowing definitely with knowing indefinitely. For example, take the relative term ‘double’. Can I know that 4 is double without knowing that it is double of 2? Yes, if I know that 4 is an even number. Knowing that 4 is an even number means that I know that it is double of something. But knowing that 4 is double of something is a case of knowing indefinitely: I know 4 is double of something or other, but I don’t know what precisely it is double of. That is, I know indefinitely, that 4 is double if ‘4 is double of the half’ is read opaquely. The PCS is supposed to apply to all D2 relatives and no D1 relatives. The PCS applies to all and only relatives, transparently construed. So D2 relatives are relatives viewed transparently.

What about knowing definitely? To know definitely that 4 is double, according to Aristotle, I need to know what it is double of, namely, 2. This is the result we would expect when we view ‘double’ transparently. ‘4 is double of something’, when ‘double’ is viewed transparently, would tell us what 4 is double, namely, 2. If I know definitely that 4 is double, then I can know the correlative, in this case, 2. Hence PCS applies to relatives understood transparently. PCS is supposed to apply to D2 relatives. So PCS applies to D2 relatives. In short: D1 relatives are opaque, while D2 are transparent.

    • djr
    • February 15th, 2014

    I’m confused by your discussion of the (Ex) example. You say that “parent relates only to offspring” may not be true on a transparent reading (you then go on to say that it is true if read transparently, but I take it that you meant to type “opaquely”). It’s of course true that some particular parent may not be the parent of some particular offspring, and even that each particular parent is not the parent of most offspring. But I don’t see how that fact makes (Ex) false on a transparent reading. First, for (Ex) to be false, parent would need to be related to something other than offspring; but Thetis and Ajax show only that every parent is not related to every offspring, not that parent is related to something other than offspring. Second, even on a transparent reading (Ex) does not claim that every parent is related to every offspring, but simply that for any parent there is some particular offspring that the parent is the parent of. So I don’t see how exclusivity fails to hold of relative – correlative pairs read transparently (or, of course, opaquely).

    I suspect I’m misunderstanding the transparent/opaque distinction. No?

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