Also, I don't prefer to define "meaning" the way you do ... so clarifying issues with your definition is your problem, not mine!!
On Wed, Oct 22, 2008 at 1:03 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > 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/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." -- Robert Heinlein ------------------------------------------- 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
