Ed
Yet the choice of the new set of axioms does not appear to be arbitrary, and
hence you can't quite make mathematics do whatever you wish.
David
To which I would like to reply: There are two places where a choice is made:
1. At concept time...when the Mathemetician/Philosopher brings forth a new
axiom
2. At publication time...when the new system derived from these axioms is
shown to the world
Ed, if we limit the number of different axioms at concept time, we limit the
universe's ability to choose. Let's encourage creativity. I know what you
are saying, that Quality will choose and the choice isn't arbitrary. But I
am not talking about that at all. I am talking about the phenomenon that
Pirsig was trying to teach to his student by making her write about the
brick.
I am saying that axioms are statements accepted without proof. Since you
need no proof, you are free to make up whatever you like. You are
unconstrained. Constraint will come later when your system is judged by its
usefulness.
David, I get what you mean now, and agree. Any attempt to "pre-screen" what
might or might not be "useful" can stifle creative insights. It's often good
to play with ideas and then see if something of value surfaces.
Ed, what is the assumption of the number 2?
1
Ed
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