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Studies in Indian Philosophy
arise in the case of the naming relation itself. The first step presents no difficulty : we can fix the relation as an object of thought. Nor is there any obstacle to selecting a name; on the contrary, various languages incorporate several syntactic devices capable of forming names of relations. In the first place one can specify the characteristic domain and counterdomain of the relation, as in forming the name 'the parent-child relation. Secondly one can nominalize one of the verb-forms which express the relation, as in forming the name 'the dominance relation' from the transitive verb 'domi. nates'. Thirdly one can find a uniquely descriptive phrase, as in forming the name 'the natural ordering relation among the positive integers' for the relation.
Having fixed the relation as an object of thought, and having selected one or another suitable expression to name it, the only thing left would be tying the two together within the naming relation. And the last stop is the hardest, for in the special case at hand, one is called upon to make a relation one of its own relata; and this almost invariably binds one in a conceptual knot. The parent-child relation is neither a parent nor a child; no elephant dominates the dominance relation; no number is greater than or less than the natural ordering relation among the positive integers. Nor does this seem to be an historical accident of classification or usage, How could it be otherwise ? How could any relation be one of its own relata ?
To sharpen this question a bit, let us consider a parallel question that has received much attention in the theory of sets : could any set be a member of itself? As Bertrand Russell observed at the beginning of this century, sets are not ordinarily members of hemselves; but there might be thought to be some extraordinary sets which are members of themselves, 15 Let us consider this possibility. The set of all man. goes is certainly not itself a mango. But its complement, the set of all non-mangoes isn't a mango either, and so we have a set that "should” belong to itself. This line of thought leads
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