Ben, What, then, do you make of my definition? Do you think deductive consequence is insufficient for meaningfulness?
I am not sure exactly where you draw the line as to what is really meaningful (as in finite collections of finite statements about finite-precision measurements) and what is only indirectly meaningful by its usefulness (as in differential calculus). Perhaps any universal statements are only meaningful by usefulness? Also, it seems like when you say Godel's Incompleteness, you mean Tarski's Undefinability? (Can't let the theorems be misused!) About the theorem prover; yes, absolutely, so long as the mathematical entity is understandable by the definition I gave. Unfortunately, I still have some work to do, because as far as I can tell that definition does not explain how uncountable sets are meaningful... (maybe it does and I am just missing something...) --Abram On Wed, Oct 22, 2008 at 12:30 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > >> >> So, a statement is meaningful if it has procedural deductive meaning. >> We *understand* a statement if we are capable of carrying out the >> corresponding deductive procedure. A statement is *true* if carrying >> out that deductive procedure only produces more true statements. We >> *believe* a statement if we not only understand it, but proceed to >> apply its deductive procedure. > > OK, then according to your definition, Godel's Theorem says that if humans > are computable there are some things that we cannot understand ... just > as, for any computer program, there are some things it can't understand. > > It just happens that according to your definition, a computer system can > understand some fabulously uncomputable entities. But there's no > contradiction > there. > > Just like a human can, a digital theorem prover can "understand" some > uncomputable entities in the sense you specify... > > ben g > > ________________________________ > agi | Archives | Modify Your Subscription ------------------------------------------- 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
