> Its not circular since it's not a synonym. Repeated addition and scaling are properties of the operations respectively on some or all subsets of the reals, and that these properties are not what these operations *are*. They are models of properties of some or all of the operations, not the operations themselves.
Sorry -- I'm not taking your explanations at face value -- you are far too inventive to be credible in these matters. Nobody talks like this but you, "models of properties" and whatnot.