On Jan 19, 2014, at 3:31 PM, meekerdb <[email protected]> wrote:
On 1/19/2014 9:45 AM, Bruno Marchal wrote:
But why should that imply *existence*.
It does not. Unless we believe in the axioms, which is the case for
elementary arithmetic.
But what does "believe in the axioms" mean. Do we really believe we
can *always* add one more? I find it doubtful. It's just a good
model for most countable things. So I can believe the axioms imply
the theorems and that "17 is prime" is a theorem, but I don't think
that commits me to any existence in the normal sense of "THAT exists".
Axioms are a human invention which only approach the truth that was
already there. Our picking some axioms to believe in changes nothing.
Jason
Brent
But then we believe in the existence of prime numbers, and in the
many relative computational states.
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