On 20 Jan 2014, at 06:51, meekerdb wrote:
On 1/19/2014 3:41 PM, Jason Resch wrote:
On Jan 19, 2014, at 3:31 PM, meekerdb <meeke...@verizon.net> 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.
You seem not to appreciate that this dissipates the one essential
advantage of mathematical monism: we understand mathematics
(because, I say, we invent it). But if it's a mere human invention
trying to model the Platonic ding and sich then PA may not be the
real arithmetic. And there will have to be some magic math stuff
that makes the real arithmetic really real.
That is right. But there will still be much less magic than the one
you would need to make the human real, without using arithmetic or
math (or physics based on math).
With your move here, we get closer to the fairy tale religion and God-
of-the-gap.
It is not a coincidence that the belief in "naive fairy tale"
religions grows together with "naive material universe".
Fairy tales creator loves fairy tale creation.
Bruno
Brent
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