John Clark wrote:
On 18 January 2015 at 18:27, Jason Resch <[email protected]
<mailto:[email protected]>> wrote:
> Do you believe that *one and only one* of the following
statements is true?
the 10^(10^(10^100))th decimal digit of pi is 0
the 10^(10^(10^100))th decimal digit of pi is 1
the 10^(10^(10^100))th decimal digit of pi is 2
the 10^(10^(10^100))th decimal digit of pi is 3
the 10^(10^(10^100))th decimal digit of pi is 4
the 10^(10^(10^100))th decimal digit of pi is 5
the 10^(10^(10^100))th decimal digit of pi is 6
the 10^(10^(10^100))th decimal digit of pi is 7
the 10^(10^(10^100))th decimal digit of pi is 8
the 10^(10^(10^100))th decimal digit of pi is 9
Either you answer yes, or no to that question. If you answer
yes, I don't see how you can escape mathematical realism.
Seth Lloyd has estimated that the maximum number of computations that
could be performed in the visible universe is about 10^121 operations on
10^90 bits, if this is insufficient to find your number is it
meaningful to say pi has a 10^(10^(10^100))th decimal digit? I don't
know, it depend on if mathematics gave rise to physics or physics gave
rise to mathematics.
Realist and constructivist approaches to mathematics do not cover all
the possibilities. You can believe that one of the above statements is
true without knowing which is true. It is logically necessary that one
of the statements is true, given the meanings of the terms involved.
This does not entail mathematical realism.
Bruce
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