CDIProvider.isInitialized() javadoc should be clarified. I believe the spec should be more specific and define what it means for a CDIProvider to be initialized. E.g. "a CDIProvider is initialized if at least one CDI container was started and is still running".

CDI.shutdown() currently must throw an IllegalStateException if the container is already stopped (actually, the javadoc is missing this piece of information). However, there is no way how to find out whether a CDI container is running or not. CDIProvider.isInitialized() would be usable if multiple running containers were forbidden (which I hope will not be). Also it wouldn't make sense to ask an instance of CDIProvider whether a concrete CDI instance is running...