I am a Peircean pragmatist ... I have no objection to using infinities in mathematics ... they can certainly be quite useful. I'd rather use differential calculus to do calculations, than do everything using finite differences.
It's just that, from a science perspective, these mathematical infinities have to be considered finite formal constructs ... they don't existP except in this way ... I'm not going to claim the pragmatist perspective is the only subjectively meaningful one. But so far as I can tell it's the only useful one for science and engineering... To take a totally different angle, consider the thought X = "This is a thought that is way too complex for me to ever have" Can I actually think X? Well, I can understand the *idea* of X. I can manipulate it symbolically and formally. I can reason about it and empathize with it by analogy to "A thought that is way too complex for my three-year-old past-self to have ever had" , and so forth. But it seems I can't ever really think X, except by being logically inconsistent within that same thought ... this is the Godel limitation applied to my own mind... I don't want to diss the personal value of logically inconsistent thoughts. But I doubt their scientific and engineering value. -- Ben G On Tue, Oct 21, 2008 at 10:43 PM, Abram Demski <[EMAIL PROTECTED]>wrote: > Ben, > > How accurate would it be to describe you as a finitist or > ultrafinitist? I ask because your view about restricting quantifiers > seems to reject even the infinities normally allowed by > constructivists. > > --Abram > > > ------------------------------------------- > 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/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "Nothing will ever be attempted if all possible objections must be first overcome " - Dr Samuel Johnson ------------------------------------------- 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
