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).
----- Original Message -----
From: "Abram Demski" <[EMAIL PROTECTED]>
To: <agi@v2.listbox.com>
Sent: Tuesday, October 28, 2008 3:47 PM
Subject: Re: [agi] constructivist issues
Mark,
Thank you, that clarifies somewhat.
But, *my* answer to *your* question would seem to depend on what you
mean when you say "fully defined". Under the classical interpretation,
yes: the question is fully defined, so it is a "pi question". Under
the constructivist interpretation, no: the question is not fully
defined, so it is a "cat question".
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)?
--Abram Demski
On Tue, Oct 28, 2008 at 3:28 PM, Mark Waser <[EMAIL PROTECTED]> wrote:
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
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agi
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