Gittin 51: Swearing to Prove One's Honesty

A case of a person who has 2 daughters and 1 son as heirs - the case has its own complications, but the crux of the matter is how much of a given was it that the daughters would inherit from the estate to provide for the daughters' dowries? Also, when one volunteers to return lost property, the finder doesn't have to swear that he's returning everything he found (or who would ever return anything). Why is swearing (or not) a matter of tikkun olam? Plus, how to handle a singular opinion.