On 17 Jan 2015, at 23:29, Jason Resch wrote:
On Sat, Jan 17, 2015 at 3:47 PM, meekerdb <meeke...@verizon.net>
wrote:
On 1/17/2015 12:38 PM, Jason Resch wrote:
On Saturday, January 17, 2015, meekerdb <meeke...@verizon.net> wrote:
> On 1/17/2015 2:29 AM, Jason Resch wrote:
>
> Do you believe the 10^(10^(10^100))th decimal digit of Pi has a
certain definite value, which is either 0, 1, 2, 3, 4, 5, 6, 7, 8,
or 9?
> If so, would you still believe this if you knew that this number
is too difficult to ever compute by anyone in this universe?
> Does this not point to a discontinuity between mathematical truth
and conceivably of that truth by us limited creatures with limited
minds in a limited universe? Perhaps it does take faith to believe
that digit takes a certain value between 0 and 9, but it's easier
for me to accept that on faith than the converse (that it is not
any one of those digits).
>
> That supports my contention that mystics insist on making up
answers even about things that are defined as unknowable. How do
you feel about, "That's a meaningless question."
>
I don't like it because it's theoretically answerable, just not
accessible to us. Was the question what are stars meaningless to
the cave men who had no hope of solving it in their time? No, it at
least provided an impetus to keep searching.
The trillionth digit of pi didn't miraculously only come into
existence when computers capable of determining it were invented.
Does it exists even when calculated?
I think the digit has a definite value (whether calculated or not).
Does pi exist - even though it cannot be calculated?
I don't know if Pi exists, but a program exists that computes
successive digits of Pi.
Yes, Pi is a computable real number. It can be represented by some
total computable function in arithmetic, so PA can prove the existence
of Pi, through some Gödel number of a program generating Pi. Of
course, this existence can already be considered epistemological: it
is an abstract property of natural numbers. It is not a natural
number, which in the TOEs that I proposed, are the only basically, or
primary, ontological object.
Does the number two exist?
I think so. In so far as it has objective properties which can be
studied (as any other object in science).
OK. And everybody believes in RA axioms, and in RA theorems, and of
course Ex(x= s(s(0))) is a simple theorem of RA.
It *might* make sense to say that 2 does not exist like a chair can
exist, but it is easier to explain how a chair work by using numbers,
than explaining the existence of 2 (even in just the mind) from
complex object like chair or other bosons and fermions, which assumes
the existence of the numbers.
Bruno
Jason
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