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[ontac-forum] A farewell to classes

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Mon, 23 Jan 2006 12:28:22 -0600
Message-id: <20060123182822.GA699@xxxxxxxx>
On Mon, Jan 23, 2006 at 02:08:31AM -0500, John Sowa wrote:
> JS>> Why not just use the word 'type', whose common meaning
> >> implies the axioms we want to use?
> CM> I found your arguments that type is somehow more natural
> > than class entirely unpersuasive.  I think it is fraught with very
> > similar ambiguities.
> There is a very big difference between ambiguity and inconsistency.
> The general definition I suggested for 'type' in my previous note
> (copy below) is ambiguous in the sense that it allows many different
> special cases, but it does not create any inconsistency with any of
> them.
> The problem with 'class' is that many, if not most of the special
> cases are defined extensionally, and they would be inconsistent with
> an intensional definition along the lines we require for ontology.    (01)

Pretty much exactly the same is true of "type".  The red-herring of
methods in OO programming aside, both classes and types are mostly
intensional in computer science.  And as for logical contexts, like
classes in set theory, types are extensional in almost every
well-developed account of type theory in both its simple and ramified
guises (the occasionally intensional (and often confused) character of
types in Russell's own writings notwithstanding).  In ordinary usage,
classes, no less than types, are highly intensional -- the class of
politicians, the Virginia class of submarines, the class of people born
before 1940, the upper class, etc.  There frankly is no ordinary use of
the term that is extensional.  And people who are familiar with its
extensional meanings are quite well aware of this -- as are those
familiar with the extensional meanings of "type".  The two terms have
almost identical virtues and liabilities in regard to the spectrum of
uses.    (02)

But this tempest in a teapot has gone on long enough.  The matter is
officially closed, so we should take any further discussion off list
(especially now that I've had the last word :-) .    (03)

-chris    (04)

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