We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when one requires compositional semantics to be "systematic" (that is the meaning function cannot be arbitrary, but must belong to some class), one can easily distinguish between compositional and non-compositional semantics. We also present an example of a simple grammar for which there is no "systematic" compositional semantics. This implies that it is possible to distinguish "good" and "bad" grammars on the basis of whether they can have compositional semantics. As a result, we believe that the paper clarifies the concept of compositionality and opens a possibility of making systematic comparisons of different systems of grammars and NLU programs.