Mark, The question that is puzzling, though, is: how can it be that these uncomputable, inexpressible entities are so bloody useful ;-) ... for instance in differential calculus ...
Also, to say that uncomputable entities don't exist because they can't be finitely described, is basically just to *define* existence as "finite describability." So this is more a philosophical position on what "exists" means than an argument that could convince anyone. I have some more detailed thoughts on these issues that I'll write down sometime soon when I get the time. My position is fairly close to yours but I think that with these sorts of issues, the devil is in the details. ben On Tue, Oct 28, 2008 at 6:53 AM, Mark Waser <[EMAIL PROTECTED]> wrote: > Abram, > > I could agree with the statement that there are uncountably many > *potential* numbers but I'm going to argue that any number that actually > exists is eminently describable. > > Take the set of all numbers that are defined far enough after the decimal > point that they never accurately describe anything manifest in the physical > universe and are never described or invoked by any entity in the physical > universe (specifically including a method for the generation of that > number). > > Pi is clearly not in the set since a) it describes all sorts of ratios in > the physical universe and b) there is a clear formula for generating > successive approximations of it. > > My question is -- do these numbers really exist? And, if so, by what > definition of exist since my definition is meant to rule out any form of > manifestation whether physical or as a concept. > > Clearly these numbers have the potential to exist -- but it should be > equally clear that they do not actually "exist" (i.e. they are never > individuated out of the class). > > Any number which truly exists has at least one description either of the > type of a) the number which is manifest as or b) the number which is > generated by. > > Classicists seem to want to insist that all of these potential numbers > actually do exist -- so they can make statements like "There are uncountably > many real numbers that no one can ever describe in any manner." > > I ask of them (and you) -- Show me just one. :-) > > > ------------------------------ > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <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
