Here's another slant . . . .
I really liked Pei's phrasing (which I consider to be the heart of
"Constructivism: The Epistemology" :-)
Generally speaking, I'm not
"building some system that learns about the world", in the sense that
there is a correct way to describe the world waiting to be discovered,
which can be captured by some algorithm. Instead, learning to me is a
non-algorithmic open-ended process by which the system summarizes its
own experience, and uses it to predict the future.
Classicists (to me) seem to frequently want one and only one truth that must
be accurate, complete, and not only provable but for proofs of all of it's
implications to exist (which is obviously thwarted by Tarski and Gödel).
So . . . . is true that light is a particle? is it true that light is a
wave?
That's why Ben and I are stuck answering many of your questions with
requests for clarification -- Which question -- pi or cat? Which subset of
what *might* be considered mathematics/arithmetic? Why are you asking the
question?
Certain statements appear obviously untrue (read inconsistent with the
empirical world or our assumed extensions of it) in the vast majority of
cases/contexts but many others are just/simply context-dependent.
----- Original Message -----
From: "Abram Demski" <[EMAIL PROTECTED]>
To: <agi@v2.listbox.com>
Sent: Wednesday, October 29, 2008 10:08 AM
Subject: Re: [agi] constructivist issues
Ben,
Thanks, that writeup did help me understand your viewpoint. However, I
don't completely unserstand/agree with the argument (one of the two,
not both!). My comments to that effect are posted on your blog.
About the earlier question...
(Mark) So Ben, how would you answer Abram's question "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)?"
(Ben) "well-defined" is not well-defined in my view...
To rephrase. Do you think there is a truth of the matter concerning
formally undecidable statements about numbers?
--Abram
On Tue, Oct 28, 2008 at 5:26 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
Hi guys,
I took a couple hours on a red-eye flight last night to write up in more
detail my
argument as to why uncomputable entities are useless for science:
http://multiverseaccordingtoben.blogspot.com/2008/10/are-uncomputable-entities-useless-for.html
Of course, I had to assume a specific formal model of science which may
be
controversial. But at any rate, I think I did succeed in writing down my
argument in a more
clear way than I'd been able to do in scattershot emails.
The only real AGI relevance here is some comments on Penrose's nasty AI
theories, e.g.
in the last paragraph and near the intro...
-- Ben G
On Tue, Oct 28, 2008 at 2:02 PM, Abram Demski <[EMAIL PROTECTED]>
wrote:
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).
>
>
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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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