The phrase "settle once and for all" means to conclude a matter definitely and permanently. There are several other synonyms that convey the same meaning, including "resolve conclusively," "decide once and for all," "determine without dispute," "settle beyond doubt," and "put an end to uncertainty." These phrases all emphasize the importance of reaching a final, irrevocable decision, without any further debate or controversy. Whether it is a legal dispute, a family argument, or a scientific controversy, settling something "once and for all" is often seen as the best way to bring closure and ensure that everyone involved can move on.