the tradition of normative English grammar is that "shall" expresses a determination or volition, whereas "will" expresses a fact statement.
Actually, believe it or not, the tradition of "normative English grammar" (i.e. high-status language) is that what you what you wrote is correct for persons other than the first. For the first person (I/we), it's the reverse.
I honestly don't know what the origin of this distinction is, unless it's the fact that British people seem to say "I shall" a lot.
Neither "shall" nor "will" originated as any sort of future marker. Originally "will" denoted intention, and "shall" denoted obligation. "He will do that" |-> "He intends to do that", "He shall do that" |-> "He is obligated to do that". The first-person/others asymmetry comes from what you can know about what you intend vs. what you can know about what others intend.
Update: This post has also been superseded - new comments belong in the latest thread.
The second thread has now also exceeded 500 comments, so after 42 chapters of MoR it's time for a new thread.
From the first thread: