That semantics for natural languages must be compositional is one of the most widely accepted principles in the philosophy of language. Recently, however, the principle has been questioned by at least three writers: Stephen Schiffer in Remnants of Meaning, Eva Kittay in Metaphor: Its Cognitive Force and Linguistic Structure and L. J. Cohen in "A Problem about Ambiguity in Truth Theoretic Semantics". The compositionality hypothesis, unlike typical conjectures in mathematics, is not based on the fact that we have in hand compositional semantics for most natural languages and are making the bold extrapolation to those few not yet analyzed. No, in spite of the fact that we have no adequate semantics for any natural language we feel that there MUST be compositional semantics for ALL natural languages, because otherwise people could not learn them. In spite of this feeling and its supporting argument(s), Schiffer, Cohen and Kittay question whether we OUGHT to believe the compositional semantics hypothesis. But before responding to their skepticism I want to inquire more carefully what, more precisely, is a compositional semantics for a natural language? Since we believe the Compositionality Hypothesis on the basis of a non-constructive existence proof, a natural way to assess its content is to look at what the proof establishes. This requires more precision about the proof. Although it is at least implicit in many earlier writers, the compositionality claim for semantics was first explicitly made, to my knowledge, by Davidson in "Theories of Meaning and Learnable Languages" in 1965.