Ben, My discussion of "meaning" was supposed to clarify that. The final definition is the broadest I currently endorse, and it admits meaningful uncomputable facts about numbers. It does not appear to get into the realm of set theory, though.
--Abram On Tue, Oct 21, 2008 at 12:07 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > >> >> >> But, worse, there are mathematically well-defined entities that are >> not even enumerable or co-enumerable, and in no sense seem computable. >> Of course, any axiomatic theory of these objects *is* enumerable and >> therefore intuitively computable (but technically only computably >> enumerable). Schmidhuber's super-omegas are one example. > > My contention is that the first use of the word "are" in the first sentence > of > the above is deceptive. > > The whole problem with the question of whether there "are" uncomputable > entities is the ambiguity of the natural language term "is / are", IMO ... > > If by > > "A exists" > > you mean communicable-existence, i.e. > > "It is possible to communicate A using a language composed of discrete > symbols, in a finite time" > > then uncomputable numbers do not exist > > If by > > "A exists" > > you mean > > "I can take some other formal property F(X) that applies to > communicatively-existent things X, and apply it to A" > > then this will often be true ... depending on the property F ... > > My question to you is: how do you interpret "are" in your statement that > uncomputable entities "are"? > > ben > > ________________________________ > 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
