> > > 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: 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
