Right, I think "metaphysical" sounds too mystical for most people. A better word is "abstract". Numbers are abstract things. You don't have to believe in them

Right, I think "metaphysical" sounds too mystical for most people. A better word is "abstract". Numbers are abstract things. You don't have to believe in them because in a sense they don't exist, they exist only as a definition. Anybody can come up with a definition but the usefulness of doing so is based on whether the definition is self-contradictory or not and whether there are useful rules of deriving more abstract things out of them. 1 + 2 = 3. Fortunately abstract things like numbers can be made semi-concrete by representing them in a physical medium such as pen and paper or computer-memory. Then we can observe how they behave and verify event by observation the soundness of our rules for manipulating them. 1 + 2 seems to always be 3.