On Wed, Oct 29, 2008 at 11:19 AM, Abram Demski <[EMAIL PROTECTED]>wrote:
> Ben, > > So, for example, if I describe a Turing machine whose halting I prove > formally undecidable by the axioms of peano arithmetic (translating > the Turing machine's operation into numerical terms, of course), and > then I ask you, "is this Turing machine non-halting", then would you > answer, "That depends on what the meaning of is, is"? Or does the > context provide enough additional information to provide a more full > answer? > > --Abram hmmm... you're saying the halting is provable in some more powerful axiom system but not in Peano arithmetic? The thing is, a Turing machine is not a real machine: it's a mathematical abstraction. A mathematical abstraction only has meaning inside a certain formal system. So, the "Turing machine inside the Peano arithmetic system" would neither provably halt nor not-halt ... the "Turing machine inside some other formal system" might potentially provably halt... But the question is what does this mean about any actual computer, or any actual physical object -- which we can only communicate about clearly insofar as it can be boiled down to a finite dataset. The use of the same term "machine" for an observable object and a mathematical abstraction seems to confuse the issue. -- Ben ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
