Re: Equality and subclass axioms

From: Graham Klyne <gk-lists@dial.pipex.com>
Date: Tue, 28 Nov 2000 18:30:35 +0000
Message-Id: <4.3.2.7.2.20001128182039.00e403c0@pop.dial.pipex.com>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

```At 02:23 PM 11/26/00 -0500, Peter F. Patel-Schneider wrote:
>I don't understand how going from if definitions to iff definitions changes
>this worry.  If I believe that all triangles have three sides (an if
>definition), perhaps because Ian says so, and I also believe that all
>triangles have four sides (another if definition), perhaps because Jim says
>so, then there will be no objects that satisfy my beliefs about triangles
>and if I try to state that some object is a triangle, I will get an
>inconsistency.   The situation appears to be completely analogous with iff
>definitions---again there will be no objects that satisfy my beliefs about
>triangles and if I try to state that some object is a triangle, I will get
>an inconsistency.

I think this reasoning depends on the premise that "having three sides" and
"having four sides" are mutually exclusive possibilities (which, according
to conventional planar geometry, they are).  But if we divorce ourselves
from specific realities, why should we not be able to say:

[foo]---numberOfSides-->"3"
[   ]---numberOfSides-->"4"

of some resource?  I think this is where the second 'f' in 'iff' comes from.

Compare the _structure_ above with a statement like:

[bar]--author-->"first person"
[   ]--author-->"second person"

My point is that the mutual exclusivity (the 'iff') is a feature of the
domain knowledge associated with the property used, not of the framework
used to make such statements.

#g

------------------------------------------------------------
Graham Klyne                       Content Technologies Ltd.
Strategic Research              <http://www.mimesweeper.com>
<Graham.Klyne@mimesweeper.com>
------------------------------------------------------------
```
Received on Wednesday, 29 November 2000 16:08:08 UTC

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