This paper argues that a language can exist and flourish in a community even if none of of the members of the community has any communication Intentions; and that reference to the notion of communication Intention can therefore be dispensed with in the core account of the nature of linguistic meaning. Certainly one cannot elucidate the notion of linguistic meaning without reference to psychological notions; the communication-Intention theorists are right about this. They are, however, wrong about which psychological notions are needed. It is not possession of the ability to (Intentionally) mean something that is crucial— the possession and exercise of communication Intentions. What is crucial is rather the possession of certain semantic psychological attitudes. To possess such semantic psychological attitudes (semantic attitudes for short) is to be disposed to take certain publicly observable phenomena— such as sights and sounds— as (non-naturally) meaning something. The paper argues that it is possible to describe circumstances in which one can in so doing be said to understand their meaning.