What does "Every CFL is decidable" exactly mean? I am trying to prove the fact that every CFL is decidable, however I can't come to terms with what the statement exactly means.

I know that generation of a particular string by a given CFG is a decidable problem. This means that we can design a TM that will definitely halt and tell us whether the given string is generated by a CFG.

But coming to this problem, what does it mean? I am making the interpretation that this means - The problem of determining whether a given arbitrary language is a CFL is decidable.

Am I right or does it mean something else?
The phrase


  Every context-free language is decidable


has the following meaning:


  If the language $L$ is context-free, then $L$ is decidable


or in other words


  If $L$ is a context-free language then $L$ is a decidable language