  It is doubtful that this understanding of Independence is sufficient, however. For Independence is meant to substantiate an analogy between mathematical objects and ordinary physical objects. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. In short, mathematical objects are just as “real” as ordinary physical objects (if not even more so, as Plato thought). 