A supposition is a guess or a hypothesis. Your supposition that your kids will automatically wash their hands before dinner is probably false. You'd best remind them to do it or risk dirty hands at dinner.
What's the difference between an assumption and a supposition — both nouns that are often taken as synonyms for each other? An assumption is an idea or theory that is usually made without proof. A supposition, on the other hand, has the connotation that the idea or theory is testable and provable. If you are to meet someone named Hunter, you may make the assumption that you are meeting a man. But if you know that Hunter lives in an all-female dorm, you may have the supposition that Hunter is a woman.