> If we define 'processed' as fully committed, then messages ca be processed exactly once. If it can be processed once, it can be delivered exactly once if you accept the simplest definition of that word.

I don't see how. Let's take a simple example of a the receiving end of a messaging system, where the messaging system can do whatever it wants to enforce idempotency or whatever semantics it wants, and calls, in-process, some `handler()` method of the application.

The useful processing happens somewhere in `handler()`. No matter what point you identify as the point where processing happens inside handler() it won't have delivered/processed-once semantics: it will potentially be called multiple times. The fact that the messaging system will internally have a commit step after handler() completes which is idempotent is irrelevant: as a user of the system you care how many times handler() is called.