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 Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=20939