X-Message-Number: 20939
Date: Wed, 22 Jan 2003 08:38:31 -0500
From: Thomas Donaldson <>
Subject: CryoNet #20930 - #20938

Hi everyone!

About identity, a bit of mathematics might help with this 
controversy. Identity requires certain characteristics, which
are fairly obvious. If A == B then B== A. A == A. And if
A == B and B == C, then A == C.

Beyond these features there is no special characteristic of
ANY trait of objects which makes them identical or not. If
you have ever studied Lebesgue integration, for instance,
you will have one function declared "equal" to another if
they only differ on a set of measure 0. The integers, for
instance, form a set of measure 0. Therefore for Lebesgue
integration two functions which differ on the integers
remain identical. To apply such ideas to people (perhaps
with a bit of humor :) ) we can define two people as identical
if their heads, arms, and legs are all on the same position
on their body. This means (by this definition) that almost
everyone is identical to everyone else. As for Lebesgue
integration, the important fact about "identical" functions
is that their integrals are the same. Lebesgue integration
is a case in which it is REASONABLE to define identity 
as I did above. 

Implication: there is NO special set of characteristics
which makes two things of whatever kind identical. What is
important here is not just the physical world (which affects
just which characters follow the 3 requirements I listed at
the beginning) but just what we WANT to be identical, for
whatever reason. If we find it useful to say that functions
are identical if they are equal at every point, then we've
defined one sense of identity. If we find it useful to 
have them be identical if they are equal except on a set
of measure 0, then we define another sense of identity.

Rather than further arguments about what is the truest
sense of identity, it may be useful for the opponents to
think carefully about HOW THEY WANT to define identity.

          Best wishes and long long life to all,

                Thomas Donaldson

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