It is ambiguous, the meaning of whether Aragorn was saying "He will not let Minas Tirith to fall," or just saying "Minas Tirith will not fall" in general. It still remains an oath however, he is pledging to Boromir that his city will not fall. I don't think Aragorn is the type of person to to basically lie to Boromir just so he can sleep peacefully. He did declare Boromir "forgiven," and I just don't see Aragorn trying to let Boromir die peacefully. I see it as an oath he gave on a man's death bed, which holds extreme importance through the rest of books, and movies. He's now got a pledge to a dying man over his head.
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Fenris Penguin
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