On 21 Jan 2014, at 21:30, meekerdb wrote:
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 <meeke...@verizon.net> wrote:
On 1/20/2014 1:11 AM, LizR wrote:
On 20 January 2014 18:51, meekerdb <meeke...@verizon.net> 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.
Right.
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.
The fact that the ultrafinitist can't know what he is doing, does not
entail that the computationalist can know what he is doing. So you are
right, but I was not implying the contrary.
Bruno
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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