Mark, Yes.
I wouldn't normally be so picky, but Godel's theorem *really* gets misused. Using Godel's theorem to say made it sound (to me) as if you have a very fundamental confusion. You were using a theorem about the incompleteness of proof to talk about the incompleteness of truth, so it sounded like you thought "logically true" and "logically provable" were equivalent, which is of course the *opposite* of what Godel proved. Intuitively, Godel's theorem says "If a logic can talk about number theory, it can't have a complete system of proof." Tarski's says, "If a logic can talk about number theory, it can't talk about its own notion of truth." Both theorems rely on the Diagonal Lemma, which states "If a logic can talk about number theory, it can talk about its own proof method." So, Tarski's theorem immediately implies Godel's theorem: if a logic can talk about its own notion of proof, but not its own notion of truth, then the two can't be equivalent! So, since Godel's theorem follows so closely from Tarski's (even though Tarski's came later), it is better to invoke Tarski's by default if you aren't sure which one applies. --Abram On Sat, Oct 25, 2008 at 4:22 PM, Mark Waser <[EMAIL PROTECTED]> wrote: > So you're saying that if I switch to using Tarski's theory (which I believe > is fundamentally just a very slightly different aspect of the same critical > concept -- but unfortunately much less well-known and therefore less > powerful as an explanation) that you'll agree with me? > > That seems akin to picayune arguments over phrasing when trying to simply > reach general broad agreement . . . . (or am I misinterpreting?) > > ----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Friday, October 24, 2008 5:29 PM > 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
