What promise does Elizabeth make to her Aunt Gardiner regarding Mr. Wickham in Austen's Pride and Prejudice?
[Aunt Gardiner]: "Seriously, I would have you be on your guard. Do not involve yourself or endeavour to involve him in an affection which the want of fortune would make so very imprudent. I have nothing to say against him; he is a most interesting young man; and if he had the fortune he ought to have, I should think you could not do better. But as it is, you must not let your fancy run away with you. You have sense, and we all expect you to use it."
[Elizabeth]: "In short, my dear aunt, I should be very sorry to be the means of making any of you unhappy; but since we see every day that where there is affection, young people are seldom withheld by immediate want of fortune from entering into engagements with each other, how can I promise to be wiser than so many of my fellow-creatures if I am tempted, or how am I even to know that it would be wisdom to resist? All that I can promise you, therefore, is not to be in a hurry. I will not be in a hurry to believe myself his first object. When I am in company with him, I will not be wishing. In short, I will do my best."
"Perhaps it will be as well if you discourage his coming here so very often. At least, you should not remind your mother of inviting him."
"As I did the other day," said Elizabeth with a conscious smile: "very true, it will be wise in me to refrain from that. But do not imagine that he is always here so often. It is on your account that he has been so frequently invited this week. You know my mother's ideas as to the necessity of constant company for her friends. But really, and upon my honour, I will try to do what I think to be the wisest; and now I hope you are satisfied."
In a sense, Elizabeth gives Aunt Gardiner a negative promise and a positive promise. The negative promise is what Elizabeth cannot say she will not do while the positive promise is what she says she can do, and it has two parts.
Aunt Gardiner speaks to Elizabeth to caution her against seeking or encouraging an attachment of love with Wickham. At this point, she is beguiled by Wickham as much as Elizabeth is and thinks that if Wickham had "the fortune he ought to have" Elizabeth would do well to look forward to a marriage with him (she learns, of course, to have a different opinion of Wickham). She stresses that her caution is based completely on the fact that neither of the two have an independent fortune: if they marry, they will be in want and have no one to turn to for help.
Elizabeth, once she is persuaded to take the conversation seriously ("Elizabeth, you are not serious now."), says that she is not able to promise to think more clearly and rationally than other young people who fall in love and marry without adequate income. This is the negative promise: she in effect promises to be unable to be wiser than others.
"... how can I promise to be wiser than so many of my fellow-creatures if I am tempted, or how am I even to know that it would be wisdom to resist?"
After this, Elizabeth gives her Aunt her two-part positive promise. She promises to do nothing to further an attachment. She promises not to be wishing for his affection. She promises "not to be in a hurry" and not to expect that she has secured his affection. Essentially, she is promising not to do anything to encourage an attachment. In response to her Aunt's further caution, she also promises to discourage contact and avoid invitations to Longbourne.
"All that I can promise you, therefore, is not to be in a hurry. I will not be in a hurry to believe myself his first object. When I am in company with him, I will not be wishing. ..."
"[It] will be as well if you discourage his coming here so very often. ..."
"[V]ery true, it will be wise in me to refrain from that."
Mrs. Gardiner cautions Lizzy against falling in love with Wickham because of his lack of money. While Lizzy explains that she is not in love with Mr. Wickham yet, she doesn't outright promise her aunt she will not fall in love with him. She notes that young people often fall in love imprudently, and she is not above doing so herself. She does, however, promise that she will not be in a hurry to capture or claim his affections and will be careful not to encourage his frequent visits at Longbourn (see Vol. II, Chpt. III).