[Top] [All Lists]

Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 13 Feb 2007 14:37:10 -0600
Message-id: <C5FC0697-B213-4A3B-BE9A-3F34808626D2@xxxxxxxx>
On Feb 13, 2007, at 2:18 PM, Pat Hayes wrote:
> ...For example, adding the power to make
> definitions to IKL would make the entire logic paradoxical, and
> re-create the Russell paradox in CL.    (01)

Pat, I agree strongly with your general point, but I think what you  
say here is not true about CL and moreover reflects an incorrect  
concept of definitions (which puzzles me because I know you know what  
a good definition of "definition" is!).  What you say above seems to  
identify "the power to make definitions" with the ability to call  
things into existence ex nihilo.  But that is *exactly* what one  
cannot do in giving a definition.  A critical condition on a genuine  
definition is that it be *non-creative*: A definition (within a  
theory) cannot entail the existence of anything that was not already  
entailed by the theory.  Hence, any purported definition in IKL of a  
Russell set (property, class, type, whatever), or any other  
paradoxical entity, would be illegitimate, for the same reason that  
the Russell set {x | x not in x} is illegitimate in ZF set theory.   
You can't prove the existence of a set of all non-self-membered sets  
in ZF, hence, you can't legitimately introduce the name "{x | x not  
in x}", as it violates the non-creative condition on definitions.   
Same for CL.    (02)

-chris    (03)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (04)

<Prev in Thread] Current Thread [Next in Thread>