On 1/21/2014 2:26 AM, Bruno Marchal wrote:
On 21 Jan 2014, at 02:25, meekerdb wrote:
On 1/20/2014 5:00 PM, LizR wrote:
On 21 January 2014 06:42, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 1/20/2014 1:11 AM, LizR wrote:
On 20 January 2014 18:51, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
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.
Surely the real test is whether it works better than any other theory. (The
phrase "unreasonable effectiveness" appears to indicate that it does.)
Would it work any less well if there were a biggest number?
I don't know. I would imagine so, because that would be a theory with an ad hoc extra
clause with no obvious justification, so every calculation would have to carry extra
baggage around. If I raise a number to the power of 100, say, I have to check first
that the result isn't going to exceed the biggest number, and take appropriate action
- whatever that is - if it will... what would be the point of that?
Just make it an axiom that the biggest number is bigger than any number you calculate.
In other words just prohibit using those "..." and "so forth" in your theorems.
Just to be sure, step 8 shows that a physicalist form of ultrafinitism (there is a
primitively ontological universe, and it is small) is a red herring.
If you assume a mathematical ultrafinitism, then yes, UDA does no more go through. But
mathematical ultrafinitism makes it impossible to even define comp, so that is really a
stopping at step zero.
So, yes, an ultrafinitist *mathematician* can say yes to the doctor (without knowing
what it does), and survive, and this is one little universe.
But he can't know what it does in an infinitist universe either. I thought that's why
you've always emphasized that saying "yes" to the doctor was a bet, not something one
could be certain of.
Brent
If UDA leads to mathematical ultrafinitism, that is enough a reductio ad
absurdo to me.
God created 0, 1, ... and when getting 10^100, he felt tired and stop. Then he *has* to
create a primitive physical universe, if he want see Adam and Eve indeed.
Bruno
Brent
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