送交者: eng 于 2005-6-21, 00:33:43:
回答: Quick frankly, don't know what you're talking about. 由 steven 于 2005-6-20, 17:17:48:
You don't know what I'm talking about doesn't mean that I don't.
Like what you said: "The description is a human invention, but not the properties themselve." What I'm talking about is that people knew about these properties before they knew how to describe it in a "formal" way. For Arabians in ancient times, addition is so self-evident and effective that they don't bother to describe it formally. For them, axioms are not really necessary.
IMHO, axioms like Peano's, are "human inventions" that would help us to understand those properties better, or even to understand math itself better, but they are not necessary in all maths under all circumstances.