[Top] [All Lists]

Re: [ontolog-forum] PROF Swartz ON DEFINITIONS

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Wed, 22 Sep 2010 11:47:23 -0500
Message-id: <4C9A331B.50801@xxxxxxxx>
On 9/22/2010 11:19 AM, John F. Sowa wrote:
> ...
> PS:  Whenever you read a math paper that starts off by saying
> "A whatchamacallit is an n-tuple (A, B, C, D, E)..." you have
> found somebody whose mind was warped by people like Dieudonné.    (01)

This is just not true, John.  In many branches of mathematics -- set
theory and computability theory especially spring to mind -- it is often
important to represent a complex mathematical notion as a class of
well-defined mathematical *objects* for which one can define properties
and on which one can define operations. Representing the separate
components of a complex notion by means of n-tuples is a very clear and
convenient way of doing so -- indeed, I can't think of any other way of
doing it that wouldn't amount to the same thing.  A particularly clear
example: In model theory, interpretations for first-order languages have
to be well-defined objects that can stand in, e.g., the "true-in"
relation.  An intepretation, however, is a complex entity, requiring at
the least a domain D and an interpretation function V mapping lexical
elements into appropriate semantic values constructed over the domain.
(Interpretations of Common Logic dialects are more complex still.)  The
obvious way to present such an entity as a well-defined object is to
define it as an ordered pair <D,V>.  The matter becomes especially
critical when one is doing formal model theory in the context of set
theory where one has to be careful that a given notion can be
represented as a legitimate set.    (02)

-chris    (03)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (04)

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