Full Idea
A problem with compositionality is negative existential propositions. If some of the terms of the proposition are empty, and don't refer, then compositionality implies that the whole will lack meaning too.
Gist of Idea
Negative existentials with compositionality make the whole sentence meaningless
Source
Stephen Read (Thinking About Logic [1995], Ch.5)
Book Reference
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.123
A Reaction
I don't agree. I don't see why compositionality implies holism about sentence-meaning. If I say 'that circular square is a psychopath', you understand the predication, despite being puzzled by the singular term.