Mark, Yes, I do keep dropping the context. This is because I am concerned only with mathematical knowledge at the moment. I should have been more specific.
So, if I understand you right, you are saying that you take the classical view when it comes to mathematics. In that case, shouldn't you agree with the classical perspective on Godelian incompleteness, since Godel's incompleteness theorem is about mathematical systems? --Abram On Tue, Oct 28, 2008 at 10:20 AM, Mark Waser <[EMAIL PROTECTED]> wrote: > Hi, > > We keep going around and around because you keep dropping my distinction > between two different cases . . . . > > The statement that "The cat is red" is undecidable by arithmetic because > it can't even be defined in terms of the axioms of arithmetic (i.e. it has > *meaning* outside of arithmetic). You need to construct > additions/extensions to arithmetic to even start to deal with it. > > The statement that "Pi is a normal number" is decidable by arithmetic > because each of the terms has meaning in arithmetic (so it certainly can be > disproved by counter-example). It may not be deducible from the axioms but > the meaning of the statement is contained within the axioms. > > The first example is what you call a constructivist view. The second > example is what you call a classical view. Which one I take is eminently > context-dependent and you keep dropping the context. If the meaning of the > statement is contained within the system, it is decidable even if it is not > deducible. If the meaning is beyond the system, then it is not decidable > because you can't even express what you're deciding. > > Mark > > > ----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]> > To: <agi@v2.listbox.com> > Sent: Tuesday, October 28, 2008 9:32 AM > Subject: Re: [agi] constructivist issues ------------------------------------------- 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
