Hi Ed! I said:
"And, in fact, one of the most powerful features of Mathematics is the
ability to change it around at will. Since axioms are so arbitrary, one can
make up as many mathematical systems as one likes."
And you, Ed, said:
"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."
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.
Ed, what is the assumption of the number 2?
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