In that case, shouldn't
you agree with the classical perspective on Godelian incompleteness,
since Godel's incompleteness theorem is about mathematical systems?
It depends. Are you asking me a fully defined question within the current
axioms of what you call mathematical systems (i.e. a pi question) or a cat
question (which could *eventually* be defined by some massive extensions to
your mathematical systems but which isn't currently defined in what you're
calling mathematical systems)?
Saying that Gödel is about mathematical systems is not saying that it's not
about cat-including systems.
----- Original Message -----
From: "Abram Demski" <[EMAIL PROTECTED]>
To: <agi@v2.listbox.com>
Sent: Tuesday, October 28, 2008 12:06 PM
Subject: Re: [agi] constructivist issues
Mark,
Yes, I do keep dropping the context. This is because I am concerned
only with mathematical knowledge at the moment. I should have been
more specific.
So, if I understand you right, you are saying that you take the
classical view when it comes to mathematics. In that case, shouldn't
you agree with the classical perspective on Godelian incompleteness,
since Godel's incompleteness theorem is about mathematical systems?
--Abram
On Tue, Oct 28, 2008 at 10:20 AM, Mark Waser <[EMAIL PROTECTED]> wrote:
Hi,
We keep going around and around because you keep dropping my
distinction
between two different cases . . . .
The statement that "The cat is red" is undecidable by arithmetic
because
it can't even be defined in terms of the axioms of arithmetic (i.e. it
has
*meaning* outside of arithmetic). You need to construct
additions/extensions to arithmetic to even start to deal with it.
The statement that "Pi is a normal number" is decidable by arithmetic
because each of the terms has meaning in arithmetic (so it certainly can
be
disproved by counter-example). It may not be deducible from the axioms
but
the meaning of the statement is contained within the axioms.
The first example is what you call a constructivist view. The second
example is what you call a classical view. Which one I take is eminently
context-dependent and you keep dropping the context. If the meaning of
the
statement is contained within the system, it is decidable even if it is
not
deducible. If the meaning is beyond the system, then it is not decidable
because you can't even express what you're deciding.
Mark
----- Original Message ----- From: "Abram Demski" <[EMAIL PROTECTED]>
To: <agi@v2.listbox.com>
Sent: Tuesday, October 28, 2008 9:32 AM
Subject: Re: [agi] constructivist issues
-------------------------------------------
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
-------------------------------------------
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
