Research on reciprocals has uncovered a variety of semantic contributions that the reciprocal can make, creating problems for proposals that the reciprocal unambiguously means something weak (e.g., Langendoen 1978). However, there is no real evidence that reciprocals are ambiguous, despite previous claims to the contrary (e.g., Fiengo and Lasnik 1973). First, we classify the apparently heterogeneous list of meanings proposed in previous research into a natural taxonomy, showing how they arise from a small stock of logical operations and predicates. Second, we exhibit a partial ordering of the various reciprocal meanings according to logical strength, which we make crucial use of in determining what reciprocals mean in each specific context where they appear. Third, we hypothesize that a reciprocal statement expresses the strongest candidate meaning that is consistent with known properties of the relation expressed by the scope of the reciprocal. This hypothesis is supported by analysis of a large collection of examples we have gathered from various corpora.
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