On 21 Jan 2014, at 04:20, LizR wrote:
On 21 January 2014 14:25, meekerdb <[email protected]> wrote:
On 1/20/2014 5:00 PM, LizR wrote:
On 21 January 2014 06:42, meekerdb <[email protected]> wrote:
On 1/20/2014 1:11 AM, LizR wrote:
On 20 January 2014 18:51, meekerdb <[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.
So you are saying "there's a biggest number, but we don't know what
it is. But it's big. Really big. You may think it's a long way down
the road to the chemist, but that's peanuts copared to this number.
You just can't imagine how vastly, mind-boggling huge it is..."
Or words to that effect (with thanks to the late and occasionally
great Douglas Adams).
Why would you want to do that? It seems like an unnecessary extra
axiom that doesn't have any purpose or utility.
Only to make the UDA non valid. It works, if Brent meant a
mathematical ultrafinitism. But this change comp, like it changes
elementary arithmetic (which suppose at least that 0 ≠ s(x), and x
≠ y implies s(x) ≠ s(y), which can't be true in ultrafinitism).
Ultrafinitism makes all current physical theories meaningless. That is
asking a lot to escape the UDA.
Bruno
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
