 which he thinks of as an expression “of the Boolean algebra of classes—or better, of class concepts” (1946a [BE: 956]). According to this proposal, the concept of a brother is a kind of “product” of the concepts of a male and a sibling. (Of course, this ignores the relational nature of both sides of the equation. For example, the only siblings relevant to the definition are the brother’s siblings; other siblings are ignored, and so the analysis is incomplete. But we shall nonetheless stick to Church’s formulation.) The problem as Church sees it is this: