The paper analyses what is said and what is presupposed by the Principle of Compositionality for semantics, as it is commonly stated. The Principle of Compositionality is an axiom which some semantics satisfy and some don’t. It says essentially that if two expressions have the same meaning then they make the same contribution to the meanings of expressions containing them. This is a sensible axiom only if one combines it with (a) a converse, that if two expressions make the same contribution to the meanings of (say) sentences containing them, then they have the same meaning; and (b) some assumption that two expressions which can’t meaningfully be substituted for each other have different meanings. (The paper formalizes (a) as a full abstraction principle, and (b) as ‘Husserl’s principle’.) Moreover the Principle of Compositionality speaks only about when two expressions have the same meaning; it adds nothing whatever about what that meaning might be (the ‘representation problem’). Some recent discussions by writers in linguistics and logic are assessed. The paper finishes by reviewing the history of the notion of compositionality
