On Thu, Jan 22, 2015 at 12:48 AM, Bruce Kellett <[email protected]> wrote:
> 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. So one of them is true, but can you (or anyone in this universe) prove: 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 ? If you answer no to all 10 of those questions, then none of those statements is provable by any entity operating within this universe, yet we know one of the statements is true. So Pi is a mathematical object with properties that don't depend on the physical existence of conceptions/proofs realized by entities or processes operating physically. It follows then that if these properties don't depend on physical processes of this universe, that even if this universe did not exist at all, those properties would not be affected. And from that it follows that mathematical properties and truth statements concerning them have an existence independent of physics, hence mathematical realism. Jason -- 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/d/optout.
