On Sun, Jan 18, 2015 at 8:55 AM, Stathis Papaioannou <[email protected]> wrote:
> On 18 January 2015 at 18:43, Jason Resch <[email protected]> wrote: > > > > > > On Sun, Jan 18, 2015 at 1:12 AM, meekerdb <[email protected]> wrote: > >> > >> On 1/17/2015 9:27 PM, Jason Resch 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. > >> > >> > >> By observing that "real" and "true" are different attributes. > > > > > > True is enough to yield reality, under computationalism. > > Isn't that circular? > If you assume it is true (independent of our ability or anything in the universe's ability to conceive it), then it is true independently of the universe, and hence you get arithmetical realism. Number relations and numbers exist independently of the physical universe. If number relations exist then program's and their executions exist, and by computationalism some of those programs will have beliefs like that they're living on a planet called Earth and reading a post on the Everything list. If on the other hand you assume it is false (that not one and only one of the above 10 statements is true) then you can avoid mathematical realism, but that seems to assume some kind of ultrafinitism. 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.
