Q: Does "besides me" mean "I don't know"?
A: It could, but when you look at the whole sentence you realize that the writer thinks the promise shouldn't have been made in the first place. It's like saying, "I don't think you should have made the promise in the first place, but it's good that you kept your word."
If you have a question about the English language and would like to ask one of our many English teachers and language experts, please click the button below to let us know: