Mark, That is thanks to Godel's incompleteness theorem. Any formal system that describes numbers is doomed to be incomplete, meaning there will be statements that can be constructed purely by reference to numbers (no red cats!) that the system will fail to prove either true or false.
So my question is, do you interpret this as meaning "Numbers are not well-defined and can never be" (constructivist), or do you interpret this as "It is impossible to pack all true information about numbers into an axiom system" (classical)? Hmm.... By the way, I might not be using the term "constructivist" in a way that all constructivists would agree with. I think "intuitionist" (a specific type of constructivist) would be a better term for the view I'm referring to. --Abram Demski On Tue, Oct 28, 2008 at 4:13 PM, Mark Waser <[EMAIL PROTECTED]> wrote: >>> Numbers can be fully defined in the classical sense, but not in the > > constructivist sense. So, when you say "fully defined question", do > you mean a question for which all answers are stipulated by logical > necessity (classical), or logical deduction (constructivist)? > > How (or why) are numbers not fully defined in a constructionist sense? > > (I was about to ask you whether or not you had answered your own question > until that caught my eye on the second or third read-through). > > ------------------------------------------- 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
