Mark, You assert that the extensions are judged on how well they reflect the world.
The extension currently under discussion is one that allows us to prove the consistency of Arithmetic. So, it seems, you count that as something observable in the world-- no mathematician has ever proved a contradiction from the axioms of arithmetic, so they seem consistent. If this is indeed what you are saying, then you are in line with the classical view in this respect (and with my opinion). But, if this is your view, I don't see how you can maintain the constructivist assertion that Godelian statements are undecidable because they are undefined by the axioms. It seems that, instead, you are agreeing with the classical notion that there is in fact a truth of the matter concerning Godelian statements, we're just unable to deduce that truth from the axioms. --Abram On Tue, Oct 28, 2008 at 7:21 AM, Mark Waser <[EMAIL PROTECTED]> wrote: >>> *That* is what I was asking about when I asked which side you fell on. > > Do you think such extensions are arbitrary, or do you think there is a > fact of the matter? > > The extensions are clearly judged on whether or not they accurately reflect > the empirical world *as currently known* -- so they aren't arbitrary in that > sense. > > On the other hand, there may not be just a single set of extensions that > accurately reflect the world so I guess that you could say that choosing > among sets of extensions that both accurately reflect the world is > (necessarily) an arbitrary process since there is no additional information > to go on (though there are certainly heuristics like Occam's razor -- but > they are more about getting a usable or "more likely" to hold up under > future observations or more likely to be easily modified to match future > observations theory . . . .). > > The world is real. Our explanations and theories are constructed. For any > complete system, you can take the classical approach but incompleteness (of > current information which then causes undecidability) ever forces you into > constructivism to create an ever-expanding series of shells of stronger > systems to explain those systems contained by them. ------------------------------------------- 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
