On 1/20/2014 1:21 AM, Bruno Marchal wrote:
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 <[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.
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.
The love is not very apparent. Religionists here have opposed teaching evolution, the
big-bang, and the neural basis of mind. So far as I know they have not objected to
arithmetic.
Brent
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