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From: Henry Story <henry.story@bblfish.net>
Date: Wed, 9 Feb 2005 10:42:03 +0100
Message-Id: <935b90e7912efda84cb837ccbc35c508@bblfish.net>
Cc: Roy T. Fielding <fielding@gbiv.com>, Atom Syntax <atom-syntax@imc.org>, bloged <users@bloged.dev.java.net>
To: semantic-web@w3.org

Just a point of clarification about identity. (I thought the example
is fun enough that it may be of interest)

As we all know Madonna is a material girl, and she lives in a material
world [1].

Madonna is a US citizen also. Let us imagine the day she received her
social security card through the post. That day Madonna, the material
girl, had a very specific material constitution. Let us call the set
of cells, organic and inorganic material that composed Madonna that
moment M1.

Now let us stipulate that two material things are equal if they are
made of exactly the same matter.

That afternoon Madonna goes to the beauty salon where she gets her hair
cut and fingernails and toe nails clipped. The resulting material girl
call her M2 is no longer the same as M1, as M2 is M1 less some hair
and nail material. M2 may also contain a little more water (she was
drinking some beauty drink during the process). So M1 is not the same
material thing as M2.

Both M1 and M2 are also girls, and have a functional relation to a
social security number. Ie M1 and M2 each only have 1 social security
number. There are in fact a very large number of such material Madonnas
Mx that have a functional relation to that same social security number.
So clearly the inverse relation (from social security to temporal 
Material Madonnas) is not functional.

Now let us think of the mereological fusion [2] of all of these
Material Madonnas, and let us call that MM. MM also has a functional
relation to the social security number. But it is also clear that
there is an inverse functional relation from social security number
to MM.

So the social security number identifies madonna in two ways.

1. via a functional relation
     temporalId:  temporal material madonnas --> social security number
2. via an inverse functional relation
     fusionId: MM --> social security number

Given a social security number we can via the fusionId relation
get a hold of the mereological fusion of that person, and from
the mereological fusion we can find the individual temporal parts,
each of which of course have a temporalId relation to the same social
security number.

The above can probably be also put in terms of set theory, and
so in terms of rdf graphs. In which case it clearly shows how
rdf can speak about temporal and non temporal identity.

Henry Story

[1] http://www.lyricsfreak.com/m/madonna/86925.html
     audio clip: http://tinyurl.com/5k9et
[2] http://plato.stanford.edu/entries/mereology/
Received on Wednesday, 9 February 2005 09:42:06 UTC

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