>> 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 ...
Differential calculus doesn't use those individual entities . . . .
>> 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."
I never said any such thing. I referenced a class of numbers that I defined as
never physically manifesting and never being conceptually distinct and then
asked if they existed. Clearly some portion of your liver that I can't define
finitely still exists because it is physically manifest.
>> So this is more a philosophical position on what "exists" means than an
>> argument that could convince anyone.
Yes, in that I basically defined my version of exists as physically manifest
and/or described or invoked and then asked if that matched Abram's definition.
No, in that you're now coming in with half (or less) of my definition and
arguing that I'm unconvincing. :-)
----- Original Message -----
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 11:44 AM
Subject: Re: [agi] constructivist issues
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. :-)
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--
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
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